Fireworks algorithm ( FWA ) is a newly proposed swarm intelligence algorithm , which is used to solve optimization problems . However , the interaction of fireworks in FWA is not sufficient . In several situations , we are interested in computing the range not only of a specific function , but also its derivative(s ) . This is the case for virtually all problems considered in this book : for optimization problems , nonlinear equations , seeking Pareto-sets of multicriteria problems , etc . ; shortly : whenever we need to apply the interval Newton operator or enforce box-consistency ( or use other similar tools ) . This chapter reviews main manners to bound the derivatives ; the focus is on algorithmic differentiation , which turned out to be a very useful tool and ( unlike , e.g. , using finite-differences ) it is compatible with the interval analysis . Traditionally , future development strategies have been included as optimization decision variables . However , in practice , due to unpredictable factors , future plans tend to deviate from the solutions obtained in optimization problems . In a recent publication , we showed that a more prudent and realistic approach toward oilfield optimization is to consider future development plans as uncertain parameters to ensure that the obtained solutions remain robust when future plans change . In recent years , reinforcement learning , which enables robots to learn previously missing abilities , plays an increasingly important role in robotics , such as learning hard-to-code behaviors or optimizing problems without an accepted closed solution . The main problem of RL in robotics is that it is expensive and takes a long time to learn and operate . Surrogate model assisted evolutionary algorithms ( SAEAs ) are metamodel-based strategies usually employed on the optimization of problems that demand a high computational cost to be evaluated . SAEAs employ metamodels , like Kriging and radial basis function ( RBF ) , to speed up convergence towards good quality solutions and to reduce the number of function evaluations . This paper presents different models of hybrid algorithms that can be run on parallel architectures being used in optimization problems solving . In these models we used several techniques : genetic algorithms , ant colony and tabu search . Gradient-type Hopfield networks have been widely used in optimization problems solving . This paper presents a novel application by developing a matrix oriented gradient approach to solve a class of linear matrix inequalities ( LMIs ) , which are commonly encountered in the robust control system analysis and design . The group focusses both in research and teaching on following topics:• randomized algorithms• approximation and online algorithms• algorithms for interconnection networks• probabilistic analysis of algorithms• algorithmic game theoryApproachesforthedesignofalgorithmicsolutionstohardproblemsaremanifold . Foroptimization problems , a very suitable concept is that of approximation algorithms , whereonetriestoobtainprovablygoodsolutionsfortheproblem , inthesensethatthecost of the computed solution is at most a fraction apart from the cost of the optimalone . Another approach is to apply randomized algorithms , which are designed to givean optimal ( or good approximative ) solution with high probability . Ifa learning problem iscomplicated , itmay take amuchcomputation timetoobtain theoptimal pol- icy . Meanwhile , foroptimization problems , multi-agent search methods suchasgenetic algorithms andparticle swarm optimization (PSO)(2)havebeenrecognized that they areable tofindrapidly aglobal optimal solution for multi-modal functions withwidesolution space . Thus , inthereinforcement learning , an optimal policy could beobtained rapidly byusing multi-agent algorithms in whichmultiple agents learn through referring learning re- sults ofother agents . INTRODUCTION Introduction General Introduction History of Optimization Optimization Problems Mathematical Model Concept of Optimization Classification of Optimization Problems Organization of the Book References Exercises The Process of Optimization Introduction Decision Process Problem Identification and Clarification Problem Definition Development of a Mathematical Model Deriving a Solution Sensitivity Analysis Testing the Solution Implementation Chapter Summary Exercises Introduction to Modelling Introduction Components of a Mathematical Model Simple Examples Analysing a Problem Modelling a Simple Problem Linear Programming Model More Mathematical Models Integer Programming Multi-Objective Problem Goal Programming Nonlinear Programming Chapter Summary Exercises MODELLING More than 50 code descriptions were submitted by the authors to describe characteristic features of their programs . In all cases , the codes are well tested and documented , are currently used for solving practical optimization optimization problems , and are available on request either in form of a listing or on a magnetic tape . In most cases , the programming language is FORTRAN . Mathematical formulae for several statistical measures of decision scores are derived for multiple choice decision items . The modelling is extended to formulate optimization programming problems with the objectives of maximising the expected decision score and also to minimise the volatility in decision score . The decision parameters namely , number of optimal decision assignments can be derived through the developed Non-Linear Programming Problem ( NLPP ) . subsubsection : Optimization of SpecTN Ideally , SpecTN should be learned automatically along with the minimization of the prediction loss , as the case in STN ; however , in practice we find that such optimization is extremely challenging . This is because the parameters of in SpecTN is quadratic w.r.t the number of spectral bases , hundreds of times more than in the affine transformation matrix of STN . We hypothesize that separately training the models forces each submodel ( word and character ) to be strong enough to make high accuracy predictions and in some sense serves as a regularizer in the same way that dropout does for individual neurons . optimization . section : Impact of the Sentence - based Character Model where φ : S 1 → S 2 is a bijection . The EMD distance solves an optimization problem , namely , the assignment problem . For all but a zeromeasure subset of point set pairs , the optimal bijection φ is unique and invariant under infinitesimal movement of the points . Various methods have also been proposed to learn an image - to - image translation in the absence of training pairs . Recently , Chen and Koltun suggest that it might be hard for conditional GANs to generate high - resolution images due to the training instability and optimization issues . To avoid this difficulty , they use a direct regression objective based on a perceptual loss and produce the first model that can synthesize images . shows that the Optimized MMD distance is not continuous in the weak or Wasserstein topologies . This also causes optimization issues . Figure 1 ( a ) shows gradient vector fields in parameter space , In fact , the shortcut - only gating and 1 1 convolution cover the solution space of identity shortcuts ( i.e. , they could be optimized as identity shortcuts ) . However , their training error is higher than that of identity shortcuts , indicating that the degradation of these models is caused by optimization issues , instead of representational abilities . section : On the Usage of Activation Functions Therefore , we needs to learn a kernel matrix . However , directly optimizing is difficult because is contained in two inverse matrices . Recall that and have zero mean , then given a basis , the projected samples of the two classes will still center at zero , but may have different variances , as shown in Fig . distribution distance between the prediction distribution and a more accurate estimate of the true data distribution . To understand the effect of optimizing in this setting , let 's focus on an ideal case in which we are given the true data distribution so thatỹ As suggested in the original GAN paper , rather than training to minimize , we instead train to maximize . In addition , we divide the objective by while optimizing , which slows down the rate at which learns relative to . We use minibatch SGD and apply the Adam solver , with a learning rate of , and momentum parameters , . The process is repeated iteratively until convergence , augmenting the n - best list with the updated parameters at each iteration so as to obtain a better approximation of the full search space . Given that our optimization objective combines two translation systems , this would require generating an n - best list for first and , for each entry on it , generating a new n - best list with , yielding a combined n - best list with entries . So as to make it more efficient , we propose an alternating optimization approach where we fix the parameters of one model and optimize the other with standard MERT . The gating function ( see Section [ reference ] ) can be easily adopted into the gradient by discounting the contribution from convolution units that have been turned off by the gating function . In other words , We use stochastic gradient descent for the optimization of models . All the proposed models perform better with mini - batch ( in sizes ) which can be easily parallelized on single machine with multi - cores . These data , generated from sensing different physical events with diverse traffic types , have to reach their destinations with a specific Quality of Service ( QoS ) requirement . With the increasing usage of sensors in the various Internet of Things applications , there is a need to address the resource allocation for handling these critical data while satisfying their respective QoS requirements . In this work , we implemented a Value-based Utility traffic management mechanism using Software Defined Networking ( SDN ) to cope with QoS requirement in constrained sensor devices . Although orginally developed to allocate budget increases , the model may be used in allocating budget cuts as well ; this form of the model is also presented . The model can be extended hierarchically to incorporate resource allocation at the federal level . This modeling approach should be useful in all public sector programs characterized by multiple objective and hierarchical decisionmaking . There is provided a system and method for searching for resource allocation of a base station modem . The control system includes a search means for searching for resources allocated and receiving search radio channels to produce a multipath search results ; measuring means for measuring the mobility of terminal according to the search results ; and dispensing means according to the terminal measuring mobility suitably allocate resources to the common search search control means . In addition , the quality of multimedia services supported by these networks can not be represented by a concave function of the amount of allocated bandwidth . These factors unfortunately make the resource allocation problem for the wireless networks become a non-convex optimization problem . New distributed solution techniques will be presented to solve these problems and numerical examples will also be provided . However , the evolution of OTNs will simultaneously present challenges related to resource allocation in networking . For instance , with the evolution from WDM-OTNs to EONs , the resource allocation problem was transformed from the routing and wavelength assignment ( RWA ) problem to the routing and spectrum assignment ( RSA ) problem due to the additionally introduced constraint of spectrum contiguity . Similarly , specially designed algorithms are also expected to be essential for addressing the resource allocation problem in SCNs . In this paper an ontology driven multi-agent based framework for such RAL systems is proposed . The main emphasis of this framework is to describe a dynamic coordination model for Mobile Workforce Brokerage System , a multi-agent system which is utilized to automate the resource allocation process in presence of the abovementioned risks and challenges . The discussion about these concepts can be expanded to serve as a basis for linking managerial actions to market reactions . By establishing this linkage in a way that is both theoretically supportable and meaningful to managers , preplanning from the PARE perspective is a powerful tool for launching the resource allocation process in the right direction . An elicitation scheme for the CAP must therefore carefully choose the language in which it will model agent preferences to ensure succinct representations . The approach I propose is to embed learning algorithms for certain preference representations into the resource-allocation process . Preferences are elicited incrementally , and at well-defined breakpoints a tentative allocation is computed . First of all , based on the Visibility analysis , the rationality of the inspecting establishments was analyzed , the result can provide the basis to the layout of the monitoring implementation of the campus . The optimized path analysis and the resource allocation analysis were also done in the paper . They belong to issues of the network analysis , and these two results can provide evidence for the selection of patrol route and the response to the emergency in the campus . Software components are allocated to hardware components . Resource budget analysis , resource allocation analysis and end to end flow latency analysis are performed on Air Data system . Part of system model is redesigned depends on the analysis results . In this paper , a model which provides fault tolerance named â€œReplication and resubmission based adaptive decision for fault tolerance in real-time cloud computing (RRADFTRC)â€ for real time cloud computing is projected with result . In the projected model , the system endure the faults and makes the adaptive decision on the basis of proper resource allocation of tasks with a new style of approach in real time cloud vicinity . Selecting the right processor for a task is a complex problem in computational grids . The goal of resource allocation of tasks is the successful scheduling of tasks that reduces execution time . Usually , heuristic approaches are used for solving complex optimisation problems . All agents are peers and autonomous . Each is motivated to conserve its own resources while cooperating with other agents to achieve a global task or resource allocation goal . The ( initiating ) agent-that detects a problem-hastily forms an initial coalition by selecting neighboring agents that it considers to have high potential utilities , based on the capability of each neighbor and its respective inter-agent relationships . A promising approach to model such hierarchical and temporal representation is the multiscale RNNs [ reference ][ reference ][ reference ] . Based on the observation that high - level abstraction changes slowly with temporal coherency while low - level abstraction has quickly changing features sensitive to the precise local timing [ reference ] , the multiscale RNNs group hidden units into multiple modules of different timescales . In addition to the fact that the architecture fits naturally to the latent hierarchical structures in many temporal data , the multiscale approach provides the following advantages that resolve some inherent problems of standard RNNs : ( a ) computational efficiency obtained by updating the high - level layers less frequently , ( b ) efficiently delivering long - term dependencies with fewer updates at the high - level layers , which mitigates the vanishing gradient problem , ( c ) flexible resource allocation ( e.g. , more hidden units to the higher layers that focus on modelling long - term dependencies and less hidden units to the lower layers which are in charge of learning short - term dependencies ) . In addition , the learned latent hierarchical structures can provide useful information to other downstream tasks such Published as a conference paper at ICLR 2017 as module structures in computer program learning , sub - task structures in hierarchical reinforcement learning , and story segments in video understanding . The purpose of this paper is to analyze several algorithm design paradigms applied to a single problem – the 0/1 Knapsack Problem . The Knapsack problem is a combinatorial optimization problem where one has to maximize the benefit of objects in a knapsack without exceeding its capacity . It is an NP-complete problem and as such an exact solution for a large input is practically impossible to obtain . We seek to answer the question of how the resource should be allocated efficiently to minimise the long-term number of infections . We show that the optimal allocation strategy can be approximated by a solution to a knapsack-type problem , that is the problem of how to select items of varying values and weights to maximise combined value without going over certain combined weight . The weights and values are given as functions of the population sizes , initial conditions , and the disease parameters . Many complex real-world optimization problems are dynamic . In order to approach them is necessary to have tools that are able to adapt to the changes that take place in the time . Practical experiences showed that typically the algorithms need an essential adaptation to the specific problem for a successful application . Considering these requirements , we discuss various issues of the design and application of multiobjective evolutionary algorithms to real-life optimization problems . In particular , questions on problem-specific data structures and evolutionary operators and the determination of method parameters are treated . Due to the good performance of current SAT ( satisfiability ) and Max-SAT ( maximum ssatisfiability ) solvers , many real-life optimization problems such as scheduling can be solved by encoding them into Max-SAT . In this paper we tackle the course timetabling problem of the department of mathematics , Cairo University by encoding it into Max-SAT . This motivates us to start our analysis with evolutionary algorithms that are as simple as possible and consider fitness functions that are as simple as possible . We do not claim that such evolutionary algorithms are actually applied in practice or that example problems bear much resemblance to real optimization problems . It is then applied to optimal reactive power dispatch ( ORPD ) problem to verify the reliability and efficiency of BMO . Extensive comparative studies with other algorithms are conducted and from the simulation results , it is observed that BMO generally provides better results and exhibits huge potential of BMO in solving real optimization problems . Particle Swarm Optimization , a nature-inspired evolutionary algorithm , has been successful in solving a wide range of real-value optimization problems . However , little attempts have been made to extend it to discrete problems . Particle swarm optimization , a nature-inspired evolutionary algorithm , has been successful in solving a wide range of real value optimization problems . However , little attempts have been made to extend it to discrete problems . Differential evolution , a heuristic optimization algorithm , has been successful in solving a wide range of real-value optimization problems . However , it is of low efficiency in dealing with the discrete problems . For publishing a paper , these test problems have become almost a standard for demonstrating the advantage of newly proposed algorithms over the state-of-the-art . However , little thought has been given to whether these popular suits of test problems are of significance in the real-world , i.e. how much the test problems are relevant to real optimization cases . Third , it is no longer straightforward to come up with one single well-defined performance indicator to compare the performance of the developed algorithms . Here , the experiments were conducted on well-known six benchmark functions . Consequently , this implementation can be widely used in real optimizing problems . Gradient methods and their value in single-objective , real-valued optimization are well-established . As such , they play a key role in tackling real-world , hard optimization problems such as deformable image registration ( DIR ) . A key question is to which extent gradient techniques can also play a role in a multi-objective approach to DIR . Solution of NP-hard optimization problems by Hopfield neural network requires the determination of coefficients linked to the surrounding conditions of the optimization problem itself . Actually , this is a time-consuming task . Trees.- Lax Logical Relations.- Reasoning about Idealized ALGOL Using Regular Languages.- The Measurement Process in Domain Theory.- Invited Talk.- Graph Transformation as a Conceptual and Formal Framework for System Modeling and Model Evolution.- Monotone Proofs of the Pigeon Hole Principle.- Fully-Abstract Statecharts Semantics via Intuitionistic Kripke Models.- Algebraic Models for Contextual Nets.- Asymptotically Optimal Bounds for OBDDs and the Solution of Some Basic OBDD Problems.- Measures of Nondeterminism in Finite Automata.- LTL Is Expressively Complete for Mazurkiewicz Traces.- An Automata-Theoretic Completeness Proof for Interval Temporal Logic.- Invited Talk.- Which NP-Hard Optimization Problems Admit Non-trivial Efficient Approximation Algorithms?.- Deterministic Algorithms for k-SAT Based on Covering Codes and Local Search.- Closest Vectors , Successive Minima , and Dual HKZ-Bases of Lattices.- Variable Independence , Quantifier Elimination , and Constraint Representations.- Constraint Satisfaction Problems and Finite Algebras.- An Optimal Online Algorithm for Bounded Space Variable-Sized Bin Packing.- Resource Augmentation for Online Bounded Space Bin Packing.- Optimal Projective Algorithms for the List Update Problem.- Efficient Verification Algorithms for One-Counter Processes.- NP-Complete optimization problems are a well-known and widely used set of problems which surveyed and researched in the field of soft computing . Nowa days , because of the acceptable rate of achieving optimal or near-optimal solutions of the mentioned issues , using of nature-inspired algorithms are increasingly considered . The class of doubly chordal graphs , which is a subclass of chordal graphs and a superclass of strongly chordal graphs , arises in many application areas . Many NP-complete optimization problems on chordal graphs like domination and Steiner tree can be solved in polynomial time on doubly chordal graphs using doubly perfect elimination ordering of vertices . In this paper , we show that the computation of a doubly perfect elimination ordering in a doubly chordal graph with n vertices and m edges can be done in O(log2 n ) time using O(n + m ) processors on the CRCW PRAM model . Abstract A basic variable neighbourhood search ( VNS ) heuristic is applied for the first time to continuous min – max global optimization problems . The method is tested on a class of NP-hard global optimization problems arising from the synthesis of radar polyphase codes that has already been successfully treated by tabu search . The computational results show that VNS in average outperforms tabu search . A general VNS algorithm is implemented within the software package GLOB . The tests are performed on some standard test functions and on a class of NP-hard global optimization problems arising in practice . The computational results show the potential of the new software . One of the numerous NP-hard global optimization problems in theoretical chemistry is that of finding the global minimum energy structure of an atomic or molecular cluster . This paper describes our method of solving this problem with specialized genetic algorithms , both on the level of empirical model potentials and in combination with extremely expensive calculations from first principles . Maximum clique and independent set problems are classical NP-full optimization problems , the solutions of which are difficult to obtain from conventional methods . Hopfield network in neural network , which simulates the partial functions of a human brain through the ultra-large scale parallel computation , has been proven to have potentials in solving these problems in a reasonable period of time . The art gallery and watchman route problems ( AGP and WRP ) are NP-hard constrained optimization problems concerned with providing static and dynamic sensing , respectively , to environments such that the maximum amount of information is sensed at a minimal cost . What being an NP-hard problem means , practically , is that when an AGP or WRP solution is calculated for a particular time step t , any small change in the environment requires that an entirely new solution must be computed . In addition , a roulette wheel mechanism is used for scenario-generation process so that the forecast errors of coefficients are considered as random variables with known probability distribution functions . Then , each GENCO solves the bilevel optimization problem and maximizes its expected profit function . These bilevel problems are nonconvex , and the mathematical-based optimization technique is unable to handle the problem and obtain the nearly global optima . The learning process enforces that the sparse representation of a low-resolution image patch in terms of the low-resolution dictionary can well reconstruct its underlying high-resolution image patch with the dictionary in the high-resolution image patch space . The learning problem is modeled as a bilevel optimization problem , where the optimization includes an l1 norm minimization problem in its constraints . Implicit differentiation is employed to calculate the desired gradient for stochastic gradient descent . This nested nature introduces many difficulties such as nonconvexity and disconnectedness , and poses great challenges to traditional optimization methods . Using evolutionary algorithms in bilevel optimization has been demonstrated to be very promising in recent years . However , these algorithms suffer from low efficiency since they usually require a huge number of function evaluations . Abstract Bilevel optimization problems have received a growing attention in the recent past due to their relevance in practice . A number of studies on bilevel applications and solution methodologies are available for deterministic setup , but studies on uncertainties in bilevel optimization are rare . Abstract Bilevel optimization problems involve a hierarchical model where an upper level optimization problem is solved with a constraint on the optimality of a nested lower level problem . The use of evolutionary algorithms ( EAs ) and other metaheuristics has been gaining attention to solve bilevel problems , especially when they contain non-linear/black-box objective(s ) and/or constraint(s ) . The global solution of bilevel dynamic optimization problems is discussed . An overview of a deterministic algorithm for bilevel programs with nonconvex functions participating is given , followed by a summary of deterministic algorithms for the global solution of optimization problems with nonlinear ordinary differential equations embedded . Improved formulations for scenario-integrated optimization are proposed as bilevel dynamic optimization problems . Solution procedures for some of the problems are given , while for others open challenges are discussed . Roughly speaking , a specific feature of these problems is that their nonconvex nucleus can be transformed into a complementary convex structure which can then be shifted to a subspace of much lower dimension than the original underlying space . This approach leads to quite efficient algorithms for many problems of practical interest , including linear and convex multiplicative programming problems , concave minimization problems with few nonlinear variables , bilevel linear optimization problems , etc ... Bilevel linear optimization problems are the linear optimization problems with two sequential decision steps of the leader and the follower . In this paper , we focus on the ambiguity of coefficients of the follower in his objective function that hinder the leader from exactly calculating the rational response of the follower . Bilevel optimization studies problems where the optimal response to a second mathematical optimization problem is integrated in the constraints . Such structure arises in a variety of decision-making problems in areas such as market equilibria , policy design or product pricing . Abstract A number of studies can be found in the context of bilevel single objective optimization problems , but not many exist , which tackle the bilevel multi-objective problems . Deb and Sinha ( October , 2008 ) proposed a bilevel multi-objective optimization algorithm based on evolutionary multi-objective optimization ( EMO ) principles and discussed the issues involved in solving such a problem . We prove convergence of the method under mild conditions and show that it computes the exact hypergradient asymptotically . Small space and time complexity of our method allows us to solve large-scale bilevel optimization problems involving deep neural networks with up to 3.8 M upper-level and 1.4 M lower-level variables . We present results of our method for data denoising on MNIST/CIFAR10/SVHN datasets , for few-shot learning on Omniglot/Mini-Imagenet datasets and for training-data poisoning on MNIST/Imagenet datasets . For the energy-constrained cognitive networks , it is particularly important to improve their energy efficiency ( EE ) . We focus on the EE optimization of the continuous spectrum sensing ( CSS ) . The EE of the secondary user ( SU ) networks is derived . In this paper , we propose an optimal EE-based resource allocation method for the scalar broadcast channel ( BC-S ) . We introduce our EE framework , which includes an EE metric as well as a realistic power consumption model for the base station , and utilize this framework for formulating our EE-based optimization problem subject to a power as well as fairness constraints . We then prove the convexity of this problem and compare our EE-based resource allocation method against two other methods , i.e. one based on sum-rate and one based on fairness optimization . This paper proposes an EE based resource allocation method for the broadcast channel ( BC ) , where a linear power model is used to characterize the power consumed at the base station ( BS ) . Having formulated our EE based optimization problem and objective function , we utilize standard convex optimization techniques to show the concavity of the latter , and thus , the existence of a unique globally optimal energy-efficient rate and power allocation . Our EE based resource allocation framework is also extended to incorporate fairness , and provide a minimum user satisfaction in terms of spectral efficiency ( SE ) . In this paper , some notions of pointwise well-posedness for set optimization problems are introduced . Some relationships among these notions are established . This paper aims at studying the generalized well-posedness in the sense of Bednarczuk for set optimization problems with set-valued maps . Three kinds of B-well-posedness for set optimization problems are introduced . This paper introduces the essential stability for set optimization problems . Some kinds of essential stable sets of weakly minimal and minimal solutions are shown . Abstract : A previous analysis of second-order behavior of pattern search algorithms for unconstrained and linearly constrained minimization is extended to the more general class of mesh adaptive direct search ( MADS ) algorithms for general constrained optimization . Because of the ability of MADS to generate an asymptotically dense set of search directions , we are able to establish reasonable conditions under which a subsequence of MADS iterates converges to a limit point satisfying second-order necessary or sufficient optimality conditions for general set-constrained optimization problems . A previous analysis of second-order behavior of generalized pattern search algorithms for unconstrained and linearly constrained minimization is extended to the more general class of mesh adaptive direct search ( MADS ) algorithms for general constrained optimization . Because of the ability of MADS to generate an asymptotically dense set of search directions , we are able to establish reasonable conditions under which a subsequence of MADS iterates converges to a limit point satisfying second-order necessary or sufficient optimality conditions for general set-constrained optimization problems . We derive first- and second-order necessary optimality conditions for set-constrained optimization problems under the constraint qualification-type conditions significantly weaker than Robinson ’s constraint qualification . Our development relies on the so-called 2-regularity concept , and unifies and extends the previous studies based on this concept . 3D shape recovery in motion stereo is formulated as a matching optimization problem of multiple stereo images . The proposed method is a heuristic modification of dynamic programming applied to two-dimensional optimization problem . 3D shape recovery using real motion stereo images demonstrates a good performance of the algorithm in terms of reconstruction accuracy . We start with a simplified system of selling two complementary products without an assembly stage and find that the firm 's best choices can only be : ( a ) producing no products or producing only the product of less stock such that its target amount is not higher than the other product 's initial stock level , or ( b ) producing both products such that their target amounts are equal . Leveraging on these findings , the two-dimensional optimization problem is reduced to two single-dimensional sub-problems and the optimal solution is characterized . For a general assembly system with n components , we show that if initially the firm has more end-products than a certain level , she will neither produce any component nor assemble end-product ; if she does not have that many end-products but does have enough mated components , she will produce nothing and assemble up to that level ; otherwise she will try to assemble all mated components and plan production of components accordingly . A derivation schema might increase or decrease the accuracy of a forecast query . Thus , a two-dimensional optimization problem of minimizing the model cost and model usage error is introduced in this paper . Our solution consists of a greedy enumeration approach that empirically evaluates different configurations of forecast models . The practical finding of this compromise can be greatly facilitated if there are possibilities to formally assess the level of software quality and the cost of testing it using appropriate indicators . The paper attempts to describe a method of determining a program testing strategy as a result of solving a two-criteria optimization problem , with the program reliability coefficient and the cost of testing as component criteria . The paper consists of description of the program testing process and mathematical model of this process , formulation of the problem of two-criteria optimization of the program testing strategy , remarks on method of solving the problem that has been formulated . The construction of fault-tolerant graphs is a trade-off between costs and degree of fault-tolerance . Thus the construction of such graphs can be viewed as a two-criteria optimization problem . Any algorithm therefore should be able to generate a Pareto-front of graphs so that the right graph can be chosen to match the application and the user ’s need . The 3-D shape recovery in motion stereo is formulated as a matching optimization problem of multiple stereo images . The proposed method is a heuristic modification of dynamic programming applied to a 2-D optimization problem . The 3-D shape recovery using real motion stereo images demonstrates a good performance of the algorithm in terms of reconstruction accuracy . The optimal resource allocation for the proposed scheme is formalized as a 3-D mixed integer programming problem , which is a function of digital bandwidth , orthogonal power , and nonorthogonal power of analog signal . With divide and conquer strategy , we first search the space of digital bandwidth , which is constructed by the possible number of subcarriers in orthogonal frequency division multiplex system , then the optimization problem is reduced to a 2-D continuous optimization problem . We further decompose it into two 1-D continuous optimization problems , and prove they are convex 1-D functions unconditionally or conditionally , respectively . A large class of clustering problems can be formulated as an optimizational problem in which the best clustering is searched among all feasible clustering according to a selected criterion function . This clustering approach can be applied to a variety of very interesting clustering problems , as it is possible to adapt it to a concrete clustering problem by an appropriate specification of the criterion function and/or by the definition of the set of feasible clusterings . An analysis of the possible directiopns for further research is made . Methods are suggersted for optimizational analysis with reading the coupling gears ' efficiency as well as methods for multi-object optimization . We consider three optimization problems : system inversion , model matching with probably unstable plant , and full information control . A common theme in numerical solution of these problems is that the infimal performance among solutions has to be approximated before a suboptimal solution can be found . In this paper we consider the following robust two-block problem that arises in estimation and in full-information control : minimize the worst-case H/sup /spl infin// norm of a two-block transfer matrix whose elements contain H/sup /spl infin//-norm-bounded modeling errors . We show that , when the underlying systems are single-input/single-output , and if the modeling errors are " small enough " , then the robust , two-block problem can be solved by solving a one-dimensional family of appropriately-weighted " modeling-error-free " two-block problems . Furthermore , the stimulation level of each antibody based on mathematic model of the immune network was devised and used as the condition for antibody population regulation to maintain the population adversity . Finally , CHIA was applied to solve function optimizationn problems . The simulation results show CHIA not only has better performance than clonal selection algorithm ( CLONALG ) , but can efficiently avoid premature convergence .
Fireworks algorithm ( FWA ) is a newly proposed swarm intelligence algorithm , which is used to solve optimization problems . However , the interaction of fireworks in FWA is not sufficient .
In several situations , we are interested in computing the range not only of a specific function , but also its derivative(s ) . This is the case for virtually all problems considered in this book : for optimization problems , nonlinear equations , seeking Pareto-sets of multicriteria problems , etc . ; shortly : whenever we need to apply the interval Newton operator or enforce box-consistency ( or use other similar tools ) . This chapter reviews main manners to bound the derivatives ; the focus is on algorithmic differentiation , which turned out to be a very useful tool and ( unlike , e.g. , using finite-differences ) it is compatible with the interval analysis .
Traditionally , future development strategies have been included as optimization decision variables . However , in practice , due to unpredictable factors , future plans tend to deviate from the solutions obtained in optimization problems . In a recent publication , we showed that a more prudent and realistic approach toward oilfield optimization is to consider future development plans as uncertain parameters to ensure that the obtained solutions remain robust when future plans change .
In recent years , reinforcement learning , which enables robots to learn previously missing abilities , plays an increasingly important role in robotics , such as learning hard-to-code behaviors or optimizing problems without an accepted closed solution . The main problem of RL in robotics is that it is expensive and takes a long time to learn and operate .
Surrogate model assisted evolutionary algorithms ( SAEAs ) are metamodel-based strategies usually employed on the optimization of problems that demand a high computational cost to be evaluated . SAEAs employ metamodels , like Kriging and radial basis function ( RBF ) , to speed up convergence towards good quality solutions and to reduce the number of function evaluations .
This paper presents different models of hybrid algorithms that can be run on parallel architectures being used in optimization problems solving . In these models we used several techniques : genetic algorithms , ant colony and tabu search .
Gradient-type Hopfield networks have been widely used in optimization problems solving . This paper presents a novel application by developing a matrix oriented gradient approach to solve a class of linear matrix inequalities ( LMIs ) , which are commonly encountered in the robust control system analysis and design .
The group focusses both in research and teaching on following topics:• randomized algorithms• approximation and online algorithms• algorithms for interconnection networks• probabilistic analysis of algorithms• algorithmic game theoryApproachesforthedesignofalgorithmicsolutionstohardproblemsaremanifold . Foroptimization problems , a very suitable concept is that of approximation algorithms , whereonetriestoobtainprovablygoodsolutionsfortheproblem , inthesensethatthecost of the computed solution is at most a fraction apart from the cost of the optimalone . Another approach is to apply randomized algorithms , which are designed to givean optimal ( or good approximative ) solution with high probability .
Ifa learning problem iscomplicated , itmay take amuchcomputation timetoobtain theoptimal pol- icy . Meanwhile , foroptimization problems , multi-agent search methods suchasgenetic algorithms andparticle swarm optimization (PSO)(2)havebeenrecognized that they areable tofindrapidly aglobal optimal solution for multi-modal functions withwidesolution space . Thus , inthereinforcement learning , an optimal policy could beobtained rapidly byusing multi-agent algorithms in whichmultiple agents learn through referring learning re- sults ofother agents .
INTRODUCTION Introduction General Introduction History of Optimization Optimization Problems Mathematical Model Concept of Optimization Classification of Optimization Problems Organization of the Book References Exercises The Process of Optimization Introduction Decision Process Problem Identification and Clarification Problem Definition Development of a Mathematical Model Deriving a Solution Sensitivity Analysis Testing the Solution Implementation Chapter Summary Exercises Introduction to Modelling Introduction Components of a Mathematical Model Simple Examples Analysing a Problem Modelling a Simple Problem Linear Programming Model More Mathematical Models Integer Programming Multi-Objective Problem Goal Programming Nonlinear Programming Chapter Summary Exercises MODELLING
More than 50 code descriptions were submitted by the authors to describe characteristic features of their programs . In all cases , the codes are well tested and documented , are currently used for solving practical optimization optimization problems , and are available on request either in form of a listing or on a magnetic tape . In most cases , the programming language is FORTRAN .
Mathematical formulae for several statistical measures of decision scores are derived for multiple choice decision items . The modelling is extended to formulate optimization programming problems with the objectives of maximising the expected decision score and also to minimise the volatility in decision score . The decision parameters namely , number of optimal decision assignments can be derived through the developed Non-Linear Programming Problem ( NLPP ) .
subsubsection : Optimization of SpecTN Ideally , SpecTN should be learned automatically along with the minimization of the prediction loss , as the case in STN ; however , in practice we find that such optimization is extremely challenging . This is because the parameters of in SpecTN is quadratic w.r.t the number of spectral bases , hundreds of times more than in the affine transformation matrix of STN .
We hypothesize that separately training the models forces each submodel ( word and character ) to be strong enough to make high accuracy predictions and in some sense serves as a regularizer in the same way that dropout does for individual neurons . optimization . section : Impact of the Sentence - based Character Model
where φ : S 1 → S 2 is a bijection . The EMD distance solves an optimization problem , namely , the assignment problem . For all but a zeromeasure subset of point set pairs , the optimal bijection φ is unique and invariant under infinitesimal movement of the points .
Various methods have also been proposed to learn an image - to - image translation in the absence of training pairs . Recently , Chen and Koltun suggest that it might be hard for conditional GANs to generate high - resolution images due to the training instability and optimization issues . To avoid this difficulty , they use a direct regression objective based on a perceptual loss and produce the first model that can synthesize images .
shows that the Optimized MMD distance is not continuous in the weak or Wasserstein topologies . This also causes optimization issues . Figure 1 ( a ) shows gradient vector fields in parameter space ,
In fact , the shortcut - only gating and 1 1 convolution cover the solution space of identity shortcuts ( i.e. , they could be optimized as identity shortcuts ) . However , their training error is higher than that of identity shortcuts , indicating that the degradation of these models is caused by optimization issues , instead of representational abilities . section : On the Usage of Activation Functions
Therefore , we needs to learn a kernel matrix . However , directly optimizing is difficult because is contained in two inverse matrices . Recall that and have zero mean , then given a basis , the projected samples of the two classes will still center at zero , but may have different variances , as shown in Fig .
distribution distance between the prediction distribution and a more accurate estimate of the true data distribution . To understand the effect of optimizing in this setting , let 's focus on an ideal case in which we are given the true data distribution so thatỹ
As suggested in the original GAN paper , rather than training to minimize , we instead train to maximize . In addition , we divide the objective by while optimizing , which slows down the rate at which learns relative to . We use minibatch SGD and apply the Adam solver , with a learning rate of , and momentum parameters , .
The process is repeated iteratively until convergence , augmenting the n - best list with the updated parameters at each iteration so as to obtain a better approximation of the full search space . Given that our optimization objective combines two translation systems , this would require generating an n - best list for first and , for each entry on it , generating a new n - best list with , yielding a combined n - best list with entries . So as to make it more efficient , we propose an alternating optimization approach where we fix the parameters of one model and optimize the other with standard MERT .
The gating function ( see Section [ reference ] ) can be easily adopted into the gradient by discounting the contribution from convolution units that have been turned off by the gating function . In other words , We use stochastic gradient descent for the optimization of models . All the proposed models perform better with mini - batch ( in sizes ) which can be easily parallelized on single machine with multi - cores .
These data , generated from sensing different physical events with diverse traffic types , have to reach their destinations with a specific Quality of Service ( QoS ) requirement . With the increasing usage of sensors in the various Internet of Things applications , there is a need to address the resource allocation for handling these critical data while satisfying their respective QoS requirements . In this work , we implemented a Value-based Utility traffic management mechanism using Software Defined Networking ( SDN ) to cope with QoS requirement in constrained sensor devices .
Although orginally developed to allocate budget increases , the model may be used in allocating budget cuts as well ; this form of the model is also presented . The model can be extended hierarchically to incorporate resource allocation at the federal level . This modeling approach should be useful in all public sector programs characterized by multiple objective and hierarchical decisionmaking .
There is provided a system and method for searching for resource allocation of a base station modem . The control system includes a search means for searching for resources allocated and receiving search radio channels to produce a multipath search results ; measuring means for measuring the mobility of terminal according to the search results ; and dispensing means according to the terminal measuring mobility suitably allocate resources to the common search search control means .
In addition , the quality of multimedia services supported by these networks can not be represented by a concave function of the amount of allocated bandwidth . These factors unfortunately make the resource allocation problem for the wireless networks become a non-convex optimization problem . New distributed solution techniques will be presented to solve these problems and numerical examples will also be provided .
However , the evolution of OTNs will simultaneously present challenges related to resource allocation in networking . For instance , with the evolution from WDM-OTNs to EONs , the resource allocation problem was transformed from the routing and wavelength assignment ( RWA ) problem to the routing and spectrum assignment ( RSA ) problem due to the additionally introduced constraint of spectrum contiguity . Similarly , specially designed algorithms are also expected to be essential for addressing the resource allocation problem in SCNs .
In this paper an ontology driven multi-agent based framework for such RAL systems is proposed . The main emphasis of this framework is to describe a dynamic coordination model for Mobile Workforce Brokerage System , a multi-agent system which is utilized to automate the resource allocation process in presence of the abovementioned risks and challenges .
The discussion about these concepts can be expanded to serve as a basis for linking managerial actions to market reactions . By establishing this linkage in a way that is both theoretically supportable and meaningful to managers , preplanning from the PARE perspective is a powerful tool for launching the resource allocation process in the right direction .
An elicitation scheme for the CAP must therefore carefully choose the language in which it will model agent preferences to ensure succinct representations . The approach I propose is to embed learning algorithms for certain preference representations into the resource-allocation process . Preferences are elicited incrementally , and at well-defined breakpoints a tentative allocation is computed .
First of all , based on the Visibility analysis , the rationality of the inspecting establishments was analyzed , the result can provide the basis to the layout of the monitoring implementation of the campus . The optimized path analysis and the resource allocation analysis were also done in the paper . They belong to issues of the network analysis , and these two results can provide evidence for the selection of patrol route and the response to the emergency in the campus .
Software components are allocated to hardware components . Resource budget analysis , resource allocation analysis and end to end flow latency analysis are performed on Air Data system . Part of system model is redesigned depends on the analysis results .
In this paper , a model which provides fault tolerance named â€œReplication and resubmission based adaptive decision for fault tolerance in real-time cloud computing (RRADFTRC)â€ for real time cloud computing is projected with result . In the projected model , the system endure the faults and makes the adaptive decision on the basis of proper resource allocation of tasks with a new style of approach in real time cloud vicinity .
Selecting the right processor for a task is a complex problem in computational grids . The goal of resource allocation of tasks is the successful scheduling of tasks that reduces execution time . Usually , heuristic approaches are used for solving complex optimisation problems .
All agents are peers and autonomous . Each is motivated to conserve its own resources while cooperating with other agents to achieve a global task or resource allocation goal . The ( initiating ) agent-that detects a problem-hastily forms an initial coalition by selecting neighboring agents that it considers to have high potential utilities , based on the capability of each neighbor and its respective inter-agent relationships .
A promising approach to model such hierarchical and temporal representation is the multiscale RNNs [ reference ][ reference ][ reference ] . Based on the observation that high - level abstraction changes slowly with temporal coherency while low - level abstraction has quickly changing features sensitive to the precise local timing [ reference ] , the multiscale RNNs group hidden units into multiple modules of different timescales . In addition to the fact that the architecture fits naturally to the latent hierarchical structures in many temporal data , the multiscale approach provides the following advantages that resolve some inherent problems of standard RNNs : ( a ) computational efficiency obtained by updating the high - level layers less frequently , ( b ) efficiently delivering long - term dependencies with fewer updates at the high - level layers , which mitigates the vanishing gradient problem , ( c ) flexible resource allocation ( e.g. , more hidden units to the higher layers that focus on modelling long - term dependencies and less hidden units to the lower layers which are in charge of learning short - term dependencies ) . In addition , the learned latent hierarchical structures can provide useful information to other downstream tasks such Published as a conference paper at ICLR 2017 as module structures in computer program learning , sub - task structures in hierarchical reinforcement learning , and story segments in video understanding .
The purpose of this paper is to analyze several algorithm design paradigms applied to a single problem – the 0/1 Knapsack Problem . The Knapsack problem is a combinatorial optimization problem where one has to maximize the benefit of objects in a knapsack without exceeding its capacity . It is an NP-complete problem and as such an exact solution for a large input is practically impossible to obtain .
We seek to answer the question of how the resource should be allocated efficiently to minimise the long-term number of infections . We show that the optimal allocation strategy can be approximated by a solution to a knapsack-type problem , that is the problem of how to select items of varying values and weights to maximise combined value without going over certain combined weight . The weights and values are given as functions of the population sizes , initial conditions , and the disease parameters .
Many complex real-world optimization problems are dynamic . In order to approach them is necessary to have tools that are able to adapt to the changes that take place in the time .
Practical experiences showed that typically the algorithms need an essential adaptation to the specific problem for a successful application . Considering these requirements , we discuss various issues of the design and application of multiobjective evolutionary algorithms to real-life optimization problems . In particular , questions on problem-specific data structures and evolutionary operators and the determination of method parameters are treated .
Due to the good performance of current SAT ( satisfiability ) and Max-SAT ( maximum ssatisfiability ) solvers , many real-life optimization problems such as scheduling can be solved by encoding them into Max-SAT . In this paper we tackle the course timetabling problem of the department of mathematics , Cairo University by encoding it into Max-SAT .
This motivates us to start our analysis with evolutionary algorithms that are as simple as possible and consider fitness functions that are as simple as possible . We do not claim that such evolutionary algorithms are actually applied in practice or that example problems bear much resemblance to real optimization problems .
It is then applied to optimal reactive power dispatch ( ORPD ) problem to verify the reliability and efficiency of BMO . Extensive comparative studies with other algorithms are conducted and from the simulation results , it is observed that BMO generally provides better results and exhibits huge potential of BMO in solving real optimization problems .
Particle Swarm Optimization , a nature-inspired evolutionary algorithm , has been successful in solving a wide range of real-value optimization problems . However , little attempts have been made to extend it to discrete problems .
Particle swarm optimization , a nature-inspired evolutionary algorithm , has been successful in solving a wide range of real value optimization problems . However , little attempts have been made to extend it to discrete problems .
Differential evolution , a heuristic optimization algorithm , has been successful in solving a wide range of real-value optimization problems . However , it is of low efficiency in dealing with the discrete problems .
For publishing a paper , these test problems have become almost a standard for demonstrating the advantage of newly proposed algorithms over the state-of-the-art . However , little thought has been given to whether these popular suits of test problems are of significance in the real-world , i.e. how much the test problems are relevant to real optimization cases . Third , it is no longer straightforward to come up with one single well-defined performance indicator to compare the performance of the developed algorithms .
Here , the experiments were conducted on well-known six benchmark functions . Consequently , this implementation can be widely used in real optimizing problems .
Gradient methods and their value in single-objective , real-valued optimization are well-established . As such , they play a key role in tackling real-world , hard optimization problems such as deformable image registration ( DIR ) . A key question is to which extent gradient techniques can also play a role in a multi-objective approach to DIR .
Solution of NP-hard optimization problems by Hopfield neural network requires the determination of coefficients linked to the surrounding conditions of the optimization problem itself . Actually , this is a time-consuming task .
Trees.- Lax Logical Relations.- Reasoning about Idealized ALGOL Using Regular Languages.- The Measurement Process in Domain Theory.- Invited Talk.- Graph Transformation as a Conceptual and Formal Framework for System Modeling and Model Evolution.- Monotone Proofs of the Pigeon Hole Principle.- Fully-Abstract Statecharts Semantics via Intuitionistic Kripke Models.- Algebraic Models for Contextual Nets.- Asymptotically Optimal Bounds for OBDDs and the Solution of Some Basic OBDD Problems.- Measures of Nondeterminism in Finite Automata.- LTL Is Expressively Complete for Mazurkiewicz Traces.- An Automata-Theoretic Completeness Proof for Interval Temporal Logic.- Invited Talk.- Which NP-Hard Optimization Problems Admit Non-trivial Efficient Approximation Algorithms?.- Deterministic Algorithms for k-SAT Based on Covering Codes and Local Search.- Closest Vectors , Successive Minima , and Dual HKZ-Bases of Lattices.- Variable Independence , Quantifier Elimination , and Constraint Representations.- Constraint Satisfaction Problems and Finite Algebras.- An Optimal Online Algorithm for Bounded Space Variable-Sized Bin Packing.- Resource Augmentation for Online Bounded Space Bin Packing.- Optimal Projective Algorithms for the List Update Problem.- Efficient Verification Algorithms for One-Counter Processes.-
NP-Complete optimization problems are a well-known and widely used set of problems which surveyed and researched in the field of soft computing . Nowa days , because of the acceptable rate of achieving optimal or near-optimal solutions of the mentioned issues , using of nature-inspired algorithms are increasingly considered .
The class of doubly chordal graphs , which is a subclass of chordal graphs and a superclass of strongly chordal graphs , arises in many application areas . Many NP-complete optimization problems on chordal graphs like domination and Steiner tree can be solved in polynomial time on doubly chordal graphs using doubly perfect elimination ordering of vertices . In this paper , we show that the computation of a doubly perfect elimination ordering in a doubly chordal graph with n vertices and m edges can be done in O(log2 n ) time using O(n + m ) processors on the CRCW PRAM model .
Abstract A basic variable neighbourhood search ( VNS ) heuristic is applied for the first time to continuous min – max global optimization problems . The method is tested on a class of NP-hard global optimization problems arising from the synthesis of radar polyphase codes that has already been successfully treated by tabu search . The computational results show that VNS in average outperforms tabu search .
A general VNS algorithm is implemented within the software package GLOB . The tests are performed on some standard test functions and on a class of NP-hard global optimization problems arising in practice . The computational results show the potential of the new software .
One of the numerous NP-hard global optimization problems in theoretical chemistry is that of finding the global minimum energy structure of an atomic or molecular cluster . This paper describes our method of solving this problem with specialized genetic algorithms , both on the level of empirical model potentials and in combination with extremely expensive calculations from first principles .
Maximum clique and independent set problems are classical NP-full optimization problems , the solutions of which are difficult to obtain from conventional methods . Hopfield network in neural network , which simulates the partial functions of a human brain through the ultra-large scale parallel computation , has been proven to have potentials in solving these problems in a reasonable period of time .
The art gallery and watchman route problems ( AGP and WRP ) are NP-hard constrained optimization problems concerned with providing static and dynamic sensing , respectively , to environments such that the maximum amount of information is sensed at a minimal cost . What being an NP-hard problem means , practically , is that when an AGP or WRP solution is calculated for a particular time step t , any small change in the environment requires that an entirely new solution must be computed .
In addition , a roulette wheel mechanism is used for scenario-generation process so that the forecast errors of coefficients are considered as random variables with known probability distribution functions . Then , each GENCO solves the bilevel optimization problem and maximizes its expected profit function . These bilevel problems are nonconvex , and the mathematical-based optimization technique is unable to handle the problem and obtain the nearly global optima .
The learning process enforces that the sparse representation of a low-resolution image patch in terms of the low-resolution dictionary can well reconstruct its underlying high-resolution image patch with the dictionary in the high-resolution image patch space . The learning problem is modeled as a bilevel optimization problem , where the optimization includes an l1 norm minimization problem in its constraints . Implicit differentiation is employed to calculate the desired gradient for stochastic gradient descent .
This nested nature introduces many difficulties such as nonconvexity and disconnectedness , and poses great challenges to traditional optimization methods . Using evolutionary algorithms in bilevel optimization has been demonstrated to be very promising in recent years . However , these algorithms suffer from low efficiency since they usually require a huge number of function evaluations .
Abstract Bilevel optimization problems have received a growing attention in the recent past due to their relevance in practice . A number of studies on bilevel applications and solution methodologies are available for deterministic setup , but studies on uncertainties in bilevel optimization are rare .
Abstract Bilevel optimization problems involve a hierarchical model where an upper level optimization problem is solved with a constraint on the optimality of a nested lower level problem . The use of evolutionary algorithms ( EAs ) and other metaheuristics has been gaining attention to solve bilevel problems , especially when they contain non-linear/black-box objective(s ) and/or constraint(s ) .
The global solution of bilevel dynamic optimization problems is discussed . An overview of a deterministic algorithm for bilevel programs with nonconvex functions participating is given , followed by a summary of deterministic algorithms for the global solution of optimization problems with nonlinear ordinary differential equations embedded . Improved formulations for scenario-integrated optimization are proposed as bilevel dynamic optimization problems . Solution procedures for some of the problems are given , while for others open challenges are discussed .
Roughly speaking , a specific feature of these problems is that their nonconvex nucleus can be transformed into a complementary convex structure which can then be shifted to a subspace of much lower dimension than the original underlying space . This approach leads to quite efficient algorithms for many problems of practical interest , including linear and convex multiplicative programming problems , concave minimization problems with few nonlinear variables , bilevel linear optimization problems , etc ...
Bilevel linear optimization problems are the linear optimization problems with two sequential decision steps of the leader and the follower . In this paper , we focus on the ambiguity of coefficients of the follower in his objective function that hinder the leader from exactly calculating the rational response of the follower .
Bilevel optimization studies problems where the optimal response to a second mathematical optimization problem is integrated in the constraints . Such structure arises in a variety of decision-making problems in areas such as market equilibria , policy design or product pricing .
Abstract A number of studies can be found in the context of bilevel single objective optimization problems , but not many exist , which tackle the bilevel multi-objective problems . Deb and Sinha ( October , 2008 ) proposed a bilevel multi-objective optimization algorithm based on evolutionary multi-objective optimization ( EMO ) principles and discussed the issues involved in solving such a problem .
We prove convergence of the method under mild conditions and show that it computes the exact hypergradient asymptotically . Small space and time complexity of our method allows us to solve large-scale bilevel optimization problems involving deep neural networks with up to 3.8 M upper-level and 1.4 M lower-level variables . We present results of our method for data denoising on MNIST/CIFAR10/SVHN datasets , for few-shot learning on Omniglot/Mini-Imagenet datasets and for training-data poisoning on MNIST/Imagenet datasets .
For the energy-constrained cognitive networks , it is particularly important to improve their energy efficiency ( EE ) . We focus on the EE optimization of the continuous spectrum sensing ( CSS ) . The EE of the secondary user ( SU ) networks is derived .
In this paper , we propose an optimal EE-based resource allocation method for the scalar broadcast channel ( BC-S ) . We introduce our EE framework , which includes an EE metric as well as a realistic power consumption model for the base station , and utilize this framework for formulating our EE-based optimization problem subject to a power as well as fairness constraints . We then prove the convexity of this problem and compare our EE-based resource allocation method against two other methods , i.e. one based on sum-rate and one based on fairness optimization .
This paper proposes an EE based resource allocation method for the broadcast channel ( BC ) , where a linear power model is used to characterize the power consumed at the base station ( BS ) . Having formulated our EE based optimization problem and objective function , we utilize standard convex optimization techniques to show the concavity of the latter , and thus , the existence of a unique globally optimal energy-efficient rate and power allocation . Our EE based resource allocation framework is also extended to incorporate fairness , and provide a minimum user satisfaction in terms of spectral efficiency ( SE ) .
In this paper , some notions of pointwise well-posedness for set optimization problems are introduced . Some relationships among these notions are established .
This paper aims at studying the generalized well-posedness in the sense of Bednarczuk for set optimization problems with set-valued maps . Three kinds of B-well-posedness for set optimization problems are introduced .
This paper introduces the essential stability for set optimization problems . Some kinds of essential stable sets of weakly minimal and minimal solutions are shown .
Abstract : A previous analysis of second-order behavior of pattern search algorithms for unconstrained and linearly constrained minimization is extended to the more general class of mesh adaptive direct search ( MADS ) algorithms for general constrained optimization . Because of the ability of MADS to generate an asymptotically dense set of search directions , we are able to establish reasonable conditions under which a subsequence of MADS iterates converges to a limit point satisfying second-order necessary or sufficient optimality conditions for general set-constrained optimization problems .
A previous analysis of second-order behavior of generalized pattern search algorithms for unconstrained and linearly constrained minimization is extended to the more general class of mesh adaptive direct search ( MADS ) algorithms for general constrained optimization . Because of the ability of MADS to generate an asymptotically dense set of search directions , we are able to establish reasonable conditions under which a subsequence of MADS iterates converges to a limit point satisfying second-order necessary or sufficient optimality conditions for general set-constrained optimization problems .
We derive first- and second-order necessary optimality conditions for set-constrained optimization problems under the constraint qualification-type conditions significantly weaker than Robinson ’s constraint qualification . Our development relies on the so-called 2-regularity concept , and unifies and extends the previous studies based on this concept .
3D shape recovery in motion stereo is formulated as a matching optimization problem of multiple stereo images . The proposed method is a heuristic modification of dynamic programming applied to two-dimensional optimization problem . 3D shape recovery using real motion stereo images demonstrates a good performance of the algorithm in terms of reconstruction accuracy .
We start with a simplified system of selling two complementary products without an assembly stage and find that the firm 's best choices can only be : ( a ) producing no products or producing only the product of less stock such that its target amount is not higher than the other product 's initial stock level , or ( b ) producing both products such that their target amounts are equal . Leveraging on these findings , the two-dimensional optimization problem is reduced to two single-dimensional sub-problems and the optimal solution is characterized . For a general assembly system with n components , we show that if initially the firm has more end-products than a certain level , she will neither produce any component nor assemble end-product ; if she does not have that many end-products but does have enough mated components , she will produce nothing and assemble up to that level ; otherwise she will try to assemble all mated components and plan production of components accordingly .
A derivation schema might increase or decrease the accuracy of a forecast query . Thus , a two-dimensional optimization problem of minimizing the model cost and model usage error is introduced in this paper . Our solution consists of a greedy enumeration approach that empirically evaluates different configurations of forecast models .
The practical finding of this compromise can be greatly facilitated if there are possibilities to formally assess the level of software quality and the cost of testing it using appropriate indicators . The paper attempts to describe a method of determining a program testing strategy as a result of solving a two-criteria optimization problem , with the program reliability coefficient and the cost of testing as component criteria . The paper consists of description of the program testing process and mathematical model of this process , formulation of the problem of two-criteria optimization of the program testing strategy , remarks on method of solving the problem that has been formulated .
The construction of fault-tolerant graphs is a trade-off between costs and degree of fault-tolerance . Thus the construction of such graphs can be viewed as a two-criteria optimization problem . Any algorithm therefore should be able to generate a Pareto-front of graphs so that the right graph can be chosen to match the application and the user ’s need .
The 3-D shape recovery in motion stereo is formulated as a matching optimization problem of multiple stereo images . The proposed method is a heuristic modification of dynamic programming applied to a 2-D optimization problem . The 3-D shape recovery using real motion stereo images demonstrates a good performance of the algorithm in terms of reconstruction accuracy .
The optimal resource allocation for the proposed scheme is formalized as a 3-D mixed integer programming problem , which is a function of digital bandwidth , orthogonal power , and nonorthogonal power of analog signal . With divide and conquer strategy , we first search the space of digital bandwidth , which is constructed by the possible number of subcarriers in orthogonal frequency division multiplex system , then the optimization problem is reduced to a 2-D continuous optimization problem . We further decompose it into two 1-D continuous optimization problems , and prove they are convex 1-D functions unconditionally or conditionally , respectively .
A large class of clustering problems can be formulated as an optimizational problem in which the best clustering is searched among all feasible clustering according to a selected criterion function . This clustering approach can be applied to a variety of very interesting clustering problems , as it is possible to adapt it to a concrete clustering problem by an appropriate specification of the criterion function and/or by the definition of the set of feasible clusterings .
An analysis of the possible directiopns for further research is made . Methods are suggersted for optimizational analysis with reading the coupling gears ' efficiency as well as methods for multi-object optimization .
We consider three optimization problems : system inversion , model matching with probably unstable plant , and full information control . A common theme in numerical solution of these problems is that the infimal performance among solutions has to be approximated before a suboptimal solution can be found .
In this paper we consider the following robust two-block problem that arises in estimation and in full-information control : minimize the worst-case H/sup /spl infin// norm of a two-block transfer matrix whose elements contain H/sup /spl infin//-norm-bounded modeling errors . We show that , when the underlying systems are single-input/single-output , and if the modeling errors are " small enough " , then the robust , two-block problem can be solved by solving a one-dimensional family of appropriately-weighted " modeling-error-free " two-block problems .
Furthermore , the stimulation level of each antibody based on mathematic model of the immune network was devised and used as the condition for antibody population regulation to maintain the population adversity . Finally , CHIA was applied to solve function optimizationn problems . The simulation results show CHIA not only has better performance than clonal selection algorithm ( CLONALG ) , but can efficiently avoid premature convergence .
Improve enhanced fireworks algorithm with differential mutation Bounding Derivatives by Algorithmic Differentiation Closed-loop stochastic oilfield optimization for hedging against geologic, development, and operation uncertainty Robot Simulation and Reinforcement Learning Training Platform Based on Distributed Architecture A comparative study on surrogate models for SAEAs PARALLEL HYBRID METHODS USED IN OPTIMIZATION PROBLEMS SOLVING A neural network for linear matrix inequality problems Algorithms and Complexity Reinforcement Learning through Interaction amongMultiple Agents Optimization Modelling: A Practical Approach Software for Mathematical Programming Managerial Decision scoring with Stochastic Programming on Selected Scaling Measures of Likert's Format SyncSpecCNN: Synchronized Spectral CNN for 3D Shape Segmentation Morphosyntactic Tagging with a Meta-BiLSTM Model over Context Sensitive Token Encodings A Point Set Generation Network for 3D Object Reconstruction from a Single Image High-Resolution Image Synthesis and Semantic Manipulation with Conditional GANs On gradient regularizers for MMD GANs Identity Mappings in Deep Residual Networks Person re-identification by Local Maximal Occurrence representation and metric learning Tying Word Vectors and Word Classifiers: A Loss Framework for Language Modeling Image-to-Image Translation with Conditional Adversarial Networks An Effective Approach to Unsupervised Machine Translation Convolutional Neural Network Architectures for Matching Natural Language Sentences SDN-Enabled Value-Based Traffic Management Mechanism in Resource-Constrained Sensor Devices A Goal Programming Example in Public Health Resource Allocation Apparatus and method used for distributing searching resource of base station modem Use of Optimization Models for Resource Allocation in Wireless Ad-Hoc and Sensor Networks Multilayer Routing and Resource Assignment in Spatial Channel Networks (SCNs): Oriented Toward the Massive SDM Era An ontology driven, multi-agent based framework for automated resource allocation in Mobile Workforce Management systems The Basis for Adequate Preplanning A modular framework for multi-agent preference elicitation Safety Analysis Modeling of Campus Based on ArcGIS Embedded real-time system modeling and analysis using AADL Replication and Resubmission Based Adaptive Decision for Fault Tolerance in Real Time Cloud Computing: A New Approach Hybrid enhanced ant colony algorithm and enhanced bee colony algorithm for grid scheduling Satisficing coalition formation among agents Hierarchical Multiscale Recurrent Neural Networks Different Approaches to Solve the 0 / 1 Knapsack Problem Analysis of epidemiological models for disease control in single and multiple populations under resource constraints A fuzzy-set based strategy in dynamic environments Applying multiobjective evolutionary algorithms in industrial projects Solving the Course-timetabling Problem of Cairo University Using Max-SAT Methods for the Analysis of Evolutionary Algorithms Barnacles Mating Optimizer: A new bio-inspired algorithm for solving engineering optimization problems A Novel Particle Swarm Optimization Method Using Clonal Selection Algorithm A Novel Binary Particle Swarm Optimization Method Using Artificial Immune System A novel binary differential evolution algorithm based on artificial immune system Evolutionary Complex Engineering Optimization: Opportunities and Challenges Effect of the Pseudorandom Number Generators on the Standard Particle Swarm Optimization on a GPU Diversifying Multi-Objective Gradient Techniques and their Role in Hybrid Multi-Objective Evolutionary Algorithms for Deformable Medical Image Registration Tuning Hopfield neural network by a fuzzy approach Automata, languages and programming : 27th International Colloquium, ICALP 2000, Geneva, Switzerland, July 9-15, 2000 : proceedings Solving Maximal Covering Problem using Partitioned Intelligent Fish Algorithm Efficient parallel algorithm to compute a doubly perfect elimination ordering of a doubly chordal graph Solving spread spectrum radar polyphase code design problem by tabu search and variable neighbourhood search GLOB — A new VNS-based Software for Global Optimization Global geometry optimization of atomic and molecular clusters by genetic algorithms Solving Maximum Clique and Independent Set of Graphs Based on Hopfield Network Parallel photon mapping computations to enable fast approximate solutions to the art gallery and watchman route problems Scenario-Based Optimal Bidding Strategies of GENCOs in the Incomplete Information Electricity Market Using a New Improved Prey—Predator Optimization Algorithm Image super resolution based on couple dictionary learning Evolutionary Bilevel Optimization Based on Covariance Matrix Adaptation Robust and Reliable Solutions in Bilevel Optimization Problems Under Uncertainties Nested evolutionary algorithms for computationally expensive bilevel optimization problems: Variants and their systematic analysis Towards global bilevel dynamic optimization The complementary convex structure in global optimization Bilevel linear programming with ambiguous objective function of the follower Near-optimal Robust Bilevel Optimization Towards Understanding Evolutionary Bilevel Multi-Objective Optimization Algorithm Penalty Method for Inversion-Free Deep Bilevel Optimization Energy efficiency optimization of cognitive radio networks with continuous spectrum sensing Energy-efficiency based resource allocation for the scalar broadcast channel Energy Efficiency Contours for Broadcast Channels Using Realistic Power Models Pointwise well-posedness and scalarization in set optimization Generalized B-Well-Posedness for Set Optimization Problems On Essential Stable Sets of Solutions in Set Optimization Problems Second-Order Convergence of Mesh-Adaptive Direct Search Convergence of Mesh Adaptive Direct Search to Second-Order Stationary Points Necessary optimality conditions for constrained optimization problems under relaxed constraint qualifications Improved motion stereo matching based on a modified dynamic programming Optimal production planning for assembly systems with uncertain capacities and random demand Offline Design Tuning for Hierarchies of Forecast Models Method for determining the reliability parameters of software for complex decision support systems Evaluating Heuristic Optimization, Bio-Inspired and Graph-Theoretic Algorithms for the Generation of Fault-Tolerant Graphs with Minimal Costs Improved motion stereo matching based on a modified dynamic programming An Optimal Resource Allocation for Hybrid Digital–Analog With Combined Multiplexing Clustering relational data On the Structural Analysis of Coupled Planetary Gears Lower Bounds on the Infima in Some ${\cal H}_{\infty}$ Optimization Problems On robust two-block problems Chaotic Hypermutation Immune Algorithms Based on Immune Network Regulatory Mechanism
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SMC ICCSIP (1) 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) ACL 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition NeurIPS ECCV 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) ICLR 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) ACL NIPS ICOIN MSWiM AAMAS ICLR IEEE Congress on Evolutionary Computation GECCO ICNN HPCN Europe AIPR WCSP WCNC CVPR BTW ITI
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