*Edited by Heidi Kloos, Bradley J. Morris and Joseph L. Amaral*

As a whole, the essays in this book address theoretical and empirical issues related to children's learning and cognition. The first essay, titled Learning in Cognitive Niches, treats the process of sense making on a theoretical level, discussing the complexity of factors that give rise to children's learning. It is followed by an essay, titled Using the Dynamics of a Person-Context System to Describe Children's Understanding of Air Pressure, that applies ideas from complexity science and dynamics-systems theory to children's learning about science. The next four essays summarize and synthesize already published findings, in an effort to go beyond individual viewpoints and present a more nuanced picture of children's sense making. In particular, two of these summaries, Preschoolers Learning Science: Myth or Reality? and The Emergence of Scientific Reasoning, focus on children's ability to make sense of their physical environment. The essay Cognition and the Child Witness: Understanding the Impact of Cognitive Development in Forensic Contexts seeks to shed light on children's sense making relevant to forensic issues. And the essay Beyond the Black-and-White of Autism: How Cognitive Performance Varies with Context ventures in the area of autism, a disorder that demonstrates atypical processes of combining pieces of information. The final two essays provide original data to add to the discussion of what factors affect cognitive functioning. In particular, the essay Cognitive Fitness in Young Adult Video Game Players seeks to re-assess the often-assumed relation between video gaming and various aspects of thinking, memory, intelligence, and visual-spatial abilities. And the essay Impact of Moving Away from Home on Undergraduate Metacognitive Development explicitly connects life circumstances to the ability to monitor and control one's thinking. Together, the collection of essays are a further step towards understanding the process of sense making as children and young adults interact with their environment.

> ISBN 978-953-51-0855-9 ISBN 978-953-51-5103-6

Current Topics in Children's Learning and Cognition

Current Topics in Children's

Learning and Cognition

*Edited by Heidi Kloos,*

*Bradley J. Morris and Joseph L. Amaral*

Photo by Vladimirs / iStock


*3.2. Behavior of Spinel Crystal in CaO-SiO2-MgO-Al2O3-Cr2O3-FeO System*

The chemical compositions of spinel are shown in Table 2. When the heating time was prolonged from 0 min to 120 min, the calcium content decreased gradually from 1.38 at% to 0.68 at% and the chromium content increased from 16.55 at% to 22.78 at%. The content of calcium and iron showed a downward trend in spinel crystals. Nevertheless, the magnesium content showed an upward trend. As shown in Figure 4, the size of the spinel crystals increased from 9.42 μm to 10.73 μm when increasing the heating time from 0 min to 120 min, and the increase in the spinel size reached 13.91%.

**Table 2.** Chemical composition of the spinel crystals in Figure 4. Unit = atom%.

Cao et al. [12] showed that the size of the spinel crystals increased from 10.8 μm to 24.8 μm during the cooling process from 1350 ◦C to 1250 ◦C and the increase reached 129% with respect to the initial size of the spinel crystals. The increase reached 108% (4.25 μm to 8.88 μm), with the silicon content increasing from 5 wt% to 15 wt% [13]. Moreover, with the addition of FeO increasing from 2 wt% to 20 wt%, the increase in size reached 46% [8]. Compared with the literature data, the increase in the spinel size was moderate in the case studied here.

**Figure 4.** Effect of heat treatment time on the size of the spinel crystals at 1450 ◦C.


**A Hybrid Parallel Genetic Algorithm for Reliability Optimization**

Ki Tae Kim and Geonwook Jeon *Korea National Defense University, Republic of Korea*

### **1. Introduction**

126 Real-World Applications of Genetic Algorithms

Giffler, B. & Thomson, G. L. (1960). Algorithms for Solving Production Scheduling

Goldberg, D. (1989). Genetic Algorithms in Search, Optimization, and Machine Learning,

Heinonen, J. & Pettersson, F. (2007). Hybrid ant colony optimization and visibility studies

Jackson J. R. (1956). An Extension of Johnson's Results on Job Lot Scheduling, *Naval Research*

Johnson, S. M. (1954). Optimal two- and three-stage production schedules with setup times

Kacem, I.; Hammadi, S. & Borne, P. (2002). Approach by Localization and Multi-Objective

Merkle, D. & Middendorf, M. (2001). A new approach to solve permutation scheduling

Olivera, A. C.; Frutos, M. & Casal, R. (2006). Métodos para determinar secuencias de

Panwalker, S. & Iskander, W. (1977). A survey of scheduling rules, *Operations Research*, Vol.

Roy, B. & Sussman, B. (1964). Les problèmes d'ordonnancement avec contraintes

Sadeh, N. M. & Fox, M. S. (1995). Variable and value ordering heuristics for the Job Shop

Tsai, C. F. & Lin, F. C. (2003). A new hybrid heuristic technique for solving job-shop

Ullman, J. D. (1975). NP-complete scheduling problems. *Journal of Computer System sciences*,

Wu, C. G.; Xing, X. L.; Lee, H. P.; Zhou, C. G. & Liang, Y. C. (2004). Genetic Algorithm

Zalzala, A. M. S. & Flemming, P. J. (1997). Genetic Algorithms in engineering systems,

included, *Naval Research Logistics Quarterly*, Vol. 1, pp 61-68.

*Computing*, EvoWorkshops 2001, Vol. 2037, pp 484-494. Muth, J. F. & Thompson, G. L. (1964). Industrial Scheduling, Prentice-Hall Inc.

*Latino-Iberoamericano de Investigación Operativa*, Uruguay.

applied to a job-shop scheduling problem, *Applied Mathematics and Computation*, pp

Evolutionary Optimization for Flexible Job-Shop Scheduling Problems, *IEEE Trans.*

problems with ant colony optimization, *Proceedings of Applications of Evolutionary*

producción en un ambiente productivo complejo, *Proceedings of XIII Congreso*

scheduling constraint satisfaction problem, Tecnical report CMU-RI-TR-95-39,

scheduling problem, *Intelligent Data Acquisition and Advanced Computing Systems,*

Application on the Job Shop Scheduling Problem, *Machine Learning and Cybernetics,*

Problems, *Operations Reseach*, Vol. 8, pp 487-503.

*Logistics Quarterly*, Vol. 2, pp 201-203.

*Syst. Man Cybernetics*, Vol. 32.

Addison Wesley.

25 (1), pp 45-61.

disjonctives, *SEMA*.

Vol. 10, pp 384-393.

*Artificial Intelligence Journal*.

*Second IEEE International Workshop*.

*International Conference*, Vol. 4, pp 2102- 2106.

*London Institution of Electrical Engineers*.

989-998.

Reliability engineering is known to have been first applied to communication and transportation systems in the late 1940's and early 1950's. Reliability is the probability that an item will perform a required function without failure under stated conditions for a stated period of time. Therefore a system with high reliability can be likened to a system which has a superior quality. Reliability is one of the most important design factors in the successful and effective operation of complex technological systems. As explained by Tzafestas (1980), one of the essential steps in the design of multiple component systems is the problem of using the available resources in the most effective way so as to maximize the system reliability, or so as to minimize the consumption of resources while achieving specific reliability goals. The improvement of system reliability can be accomplished using the following methods: reduction of the system complexity, the allocation highly reliable components, and the allocation of component redundancy alone or combined with high component reliability, and the practice of a planned maintenance and repair schedule. This study deals with reliability optimization that maximizes the system reliability subject to resource constraints.

This study suggests mathematical programming models and a hybrid parallel genetic algorithm (HPGA). The suggested algorithm includes different heuristics such as swap, 2 opt, and interchange (except for reliability allocation problem with component choices (RAPCC)) for an improvement solution. The component structure, reliability, cost, and weight were computed by using HPGA and the experimental results of HPGA were compared with the results of existing meta-heuristics and CPLEX.

### **2. Literature review**

The goal of reliability optimization is to maximize the reliability of a system considering some constraints such as cost, weight, and so on. In general, reliability optimization divides into two categories: the reliability-redundancy allocation problem (RRAP) and the reliability allocation problem with component choices (RAPCC).

### **2.1 The reliability-redundancy allocation problem (RRAP)**

The RRAP is the determination of both optimal component reliability and the number of component redundancy allowing mixed components to maximize the system reliability

A Hybrid Parallel Genetic Algorithm for Reliability Optimization 129

This study deals with the reliability-redundancy allocation problem in a series-parallel

The relationship between the system reliability ( *RS* ) and the reliability of subsystem *i* ( *Ri* ),

1

The relationship between the reliability of subsystem *i* ( *Ri* ) and the reliability of

1 1 1 *ij m x*

*i ij j R r* =

component *j* available for subsystem *i* ( *ij r* ), in a parallel system, is shown in Eq. (2).

= ∏ (1)

=− − ∏ (2)

*n S i i R R* =

*RS* : system reliability

0, otherwise

system as shown in Fig. 1.

Fig. 1. Series-parallel system

in a series system, is shown in Eq. (1).

 = *ij*

*Ri* : reliability of subsystem *i*

*CS* : system-level constraint limits for cost *WS* : system-level constraint limits for weight

*j i x*

*ij r* : reliability of component *j* available for subsystem *i*

( ) 1, if component usedinsubsystem for RAPCC

**3.1 Reliability-redundancy allocation problem (RRAP)**

*ij c* : cost of component *j* available for subsystem *i wij* : weight of component *j* available for subsystem *i ui* : maximum number of components used in subsystem *i ij x* : quantity of component *j* used in subsystem *i* (for RRAP)

under cost and weight constraints. It is known as the NP-hard problem suggested by Chern (1992).

A variety of algorithms, as summarized in Tillman et al. (1977), and more recently by Kuo & Prasad (2000), Kuo & Wan (2007), including exact methods, heuristics and meta-heuristics have already been proposed for the RRAP. An exact optimal solution is obtained by exact methods such as cutting plane method (Tillman, 1969), branch-and-bound algorithm (Chern & Jan, 1986; Ghare & Taylor, 1969), dynamic programming (Bellman & Dreyfus, 1958; Fyffe et al., 1968; Nakagawa & Miyazaki, 1981; Yalaoui et al., 2005), and goal programming (Gen et al., 1989). However, as the size of problem gets larger, such methods are difficult to apply to get a solution and require more computational effort. Therefore, heuristics and metaheuristics are used to find a near-optimal solution in recent research.

The research using heuristics is as follows. Kuo et al. (1987) present a heuristic method based on a branch-and-bound strategy and lagrangian multipliers. Jianping (1996) has developed a method called a bounded heuristic method. You & Chen (2005) proposed an efficient heuristic method. Meta-heuristics such as genetic algorithm (Coit & Smith, 1996; Ida et al., 1994; Painton & Campbell, 1995), tabu search (Kulturel-Konak et al., 2003), ant colony optimization (Liang & Smith, 2004), and immune algorithm (Chen & You, 2005) have been introduced to solve the RRAP.

### **2.2 The reliability allocation problem with component choices (RAPCC)**

The RAPCC is the determination of optimal component reliability to maximize the system reliability under cost constraint. A problem is formulated as a binary integer programming model with a nonlinear objective function (Ait-Kadi & Nourelfath, 2001), which is equivalent to a knapsack problem with multiple-choice constraint, so that it is the NP-hard problem (Garey & Johnson, 1979). Some algorithms for such knapsack problems with multiple-choice constraint have been suggested in the literature (Nauss, 1978; Sinha & Zoltners, 1979; Sung & Lee, 1994).

A variety of algorithms including exact methods, heuristics, and meta-heuristics have already been proposed for the RAPCC. An exact optimal solution is obtained by branchand-bound algorithm (Djerdjour & Rekab, 2001; Sung & Cho, 1999). Meta-heuristics such as neural network (Nourelfath & Nahas, 2003), simulated annealing (Kim et al., 2004; Kim et al., 2008), tabu search (Kim et al., 2008), and ant colony optimization (Nahas & Nourelfath, 2005) have been introduced to solve the RAPCC. Also, Kim et al. (2008) solved the largescale examples by using a reoptimization procedure with tabu search and simulated annealing.

### **3. Mathematical programming models**

Notations and decision variables in the mathematical programming model are as follows.

*n* : the number of subsystems *m* : the number of components

under cost and weight constraints. It is known as the NP-hard problem suggested by Chern

A variety of algorithms, as summarized in Tillman et al. (1977), and more recently by Kuo & Prasad (2000), Kuo & Wan (2007), including exact methods, heuristics and meta-heuristics have already been proposed for the RRAP. An exact optimal solution is obtained by exact methods such as cutting plane method (Tillman, 1969), branch-and-bound algorithm (Chern & Jan, 1986; Ghare & Taylor, 1969), dynamic programming (Bellman & Dreyfus, 1958; Fyffe et al., 1968; Nakagawa & Miyazaki, 1981; Yalaoui et al., 2005), and goal programming (Gen et al., 1989). However, as the size of problem gets larger, such methods are difficult to apply to get a solution and require more computational effort. Therefore, heuristics and meta-

The research using heuristics is as follows. Kuo et al. (1987) present a heuristic method based on a branch-and-bound strategy and lagrangian multipliers. Jianping (1996) has developed a method called a bounded heuristic method. You & Chen (2005) proposed an efficient heuristic method. Meta-heuristics such as genetic algorithm (Coit & Smith, 1996; Ida et al., 1994; Painton & Campbell, 1995), tabu search (Kulturel-Konak et al., 2003), ant colony optimization (Liang & Smith, 2004), and immune algorithm (Chen & You, 2005) have

The RAPCC is the determination of optimal component reliability to maximize the system reliability under cost constraint. A problem is formulated as a binary integer programming model with a nonlinear objective function (Ait-Kadi & Nourelfath, 2001), which is equivalent to a knapsack problem with multiple-choice constraint, so that it is the NP-hard problem (Garey & Johnson, 1979). Some algorithms for such knapsack problems with multiple-choice constraint have been suggested in the literature (Nauss, 1978; Sinha &

A variety of algorithms including exact methods, heuristics, and meta-heuristics have already been proposed for the RAPCC. An exact optimal solution is obtained by branchand-bound algorithm (Djerdjour & Rekab, 2001; Sung & Cho, 1999). Meta-heuristics such as neural network (Nourelfath & Nahas, 2003), simulated annealing (Kim et al., 2004; Kim et al., 2008), tabu search (Kim et al., 2008), and ant colony optimization (Nahas & Nourelfath, 2005) have been introduced to solve the RAPCC. Also, Kim et al. (2008) solved the largescale examples by using a reoptimization procedure with tabu search and simulated

Notations and decision variables in the mathematical programming model are as follows.

heuristics are used to find a near-optimal solution in recent research.

**2.2 The reliability allocation problem with component choices (RAPCC)**

been introduced to solve the RRAP.

Zoltners, 1979; Sung & Lee, 1994).

**3. Mathematical programming models**

*n* : the number of subsystems *m* : the number of components

*i* : index for subsystems ( *i n* = 1,2, , ) *j* : index for components ( *j m* = 1,2, , )

annealing.

(1992).

*RS* : system reliability *Ri* : reliability of subsystem *i CS* : system-level constraint limits for cost *WS* : system-level constraint limits for weight *ij r* : reliability of component *j* available for subsystem *i ij c* : cost of component *j* available for subsystem *i wij* : weight of component *j* available for subsystem *i ui* : maximum number of components used in subsystem *i ij x* : quantity of component *j* used in subsystem *i* (for RRAP) ( ) 1, if component usedinsubsystem for RAPCC 0, otherwise = *ij j i x*

### **3.1 Reliability-redundancy allocation problem (RRAP)**

This study deals with the reliability-redundancy allocation problem in a series-parallel system as shown in Fig. 1.

Fig. 1. Series-parallel system

The relationship between the system reliability ( *RS* ) and the reliability of subsystem *i* ( *Ri* ), in a series system, is shown in Eq. (1).

$$R\_S = \prod\_{i=1}^{n} R\_i \tag{1}$$

The relationship between the reliability of subsystem *i* ( *Ri* ) and the reliability of component *j* available for subsystem *i* ( *ij r* ), in a parallel system, is shown in Eq. (2).

$$R\_i = 1 - \prod\_{j=1}^{m} \left[1 - r\_{ij}\right]^{\chi\_{\bar{y}}} \tag{2}$$

A Hybrid Parallel Genetic Algorithm for Reliability Optimization 131

The objective function is to maximize the system reliability in a series system. Eq. (9) shows the cost constraint, Eq. (10) represents the multiple-choice constraint which is that the problem prohibits component redundancy, and Eq. (11) defines the decision variables.

The genetic algorithm is a stochastic search method based on the natural selection, reproduction, and evolution theory proposed by Holland (1975). The parallel genetic algorithm paratactically evolves by operating several sub-populations. This study suggests a hybrid parallel genetic algorithm for reliability optimization with resource constraints. The suggested algorithm includes different heuristics such as swap, 2-opt, and interchange (except for RAPCC) for an improvement solution. The suggested process of a hybrid parallel

The gene representation has to reflect the properties of the system structure. The suggested

The subsystem in Table 1 indicate the nominal number of subsystem. However, it is not necessary for this number to be one for the composition of a substantial objective function. The "Redundancy & Component" row represents the number of components available for each subsystem. For example, as shown Table 1, subsystem 1 consists of two components of C1, one component of C2, one component of C3. Table 1 can be expressed as shown in Fig. 4. The suggested algorithm for the RAPCC represents a gene by one string as shown in Table 2. The subsystem in Table 2 indicates the nominal number of subsystems. However, it is not necessary for the composition of a substantial objective function. The "Component" row represents the available component number for each subsystem. For example, as shown Table 2, a series system uses component No.3 in subsystem 1, component No.2 in subsystem

The population of a parallel genetic algorithm consists of an initial population and several sub-populations. The initial population is usually generated by the random and the heuristic generation method. The heuristic generation method tends to interrupt global search.

Redundancy & Component 2 1 1 0 1 0 2 0 1 3 0

Subsystem(Component Alternatives) 1(4) 2(3) 3(4)

algorithm for the RRAP represents a gene by one string as shown in Table 1.

= , 1,2, , *i n* = (10)

*xij* = {0,1} , 1,2, , *i n* = , *j m* = 1,2, , (11)

1

 1

**4. Hybrid parallel genetic algorithm**

genetic algorithm is shown in Fig. 3.

Table 1. Gene representation (RRAP)

2, …, and component No.5 in subsystem 6.

**4.2 Population**

**4.1 Gene representation**

*m ij j x* =

Using Eqs. (1) and (2), the mathematical programming model of the RRAP in a seriesparallel system is as follows.

$$\text{Maximize}\quad R\_S = \prod\_{i=1}^{n} R\_i = \prod\_{i=1}^{n} \left\{ 1 - \prod\_{j=1}^{m} \left[ 1 - r\_{ij} \right]^{x\_{\bar{\eta}}} \right\} \tag{3}$$

$$\text{Subject to } \sum\_{i=1}^{n} \sum\_{j=1}^{m} c\_{ij} \cdot x\_{ij} \le C\_S \tag{4}$$

$$\sum\_{i=1}^{n} \sum\_{j=1}^{m} w\_{ij} \cdot x\_{ij} \le \mathcal{W}\_S \tag{5}$$

$$1 \le \sum\_{j=1}^{m} \mathbf{x}\_{ij} \le u\_i \quad i = 1, 2, \cdots, n \tag{6}$$

$$\infty\_{ij} \ge 0 \text{ , } i = 1, 2, \cdots, n \text{ , } \ j = 1, 2, \cdots, m \text{ , integer} \tag{7}$$

The objective function is to maximize the system reliability in a series-parallel system. Eqs. (4) and (5) show the resource constraints with cost and weight. Eq. (6) shows the maximum and minimum number of components that can be used for each subsystem. Eq. (7) shows the integer decision variables.

#### **3.2 Reliability allocation problem with component choices (RAPCC)**

As shown in Fig. 2, a series system consisting of n subsystems where each subsystem has several component alternatives which can perform same functions with different characteristics is considered in this study. The problem is proposed to select the optimal combination of component alternatives to maximize the system reliability given the cost. Only one component will be adopted for each subsystem.

Fig. 2. Series system

Using Eq. (1), the mathematical programming model of the RAPCC in a series system is as follows.

$$\text{Maximize}\quad R\_S = \prod\_{i=1}^{n} \left( \sum\_{j=1}^{m} r\_{ij} \cdot \mathbf{x}\_{ij} \right) \tag{8}$$

$$\text{Subject to } \sum\_{i=1}^{n} \sum\_{j=1}^{m} c\_{ij} \cdot \mathbf{x}\_{ij} \le \mathbf{C}\_{\mathbf{S}} \tag{9}$$

$$\sum\_{j=1}^{m} \mathbf{x}\_{ij} = \mathbf{1}, \; i = \mathbf{1}, \; 2, \; \cdots, m \tag{10}$$

$$\mathbf{x}\_{ij} = \{0, 1\} \text{ , } \ i = 1, 2, \cdots, m \text{ , } \ j = 1, 2, \cdots, m \tag{11}$$

The objective function is to maximize the system reliability in a series system. Eq. (9) shows the cost constraint, Eq. (10) represents the multiple-choice constraint which is that the problem prohibits component redundancy, and Eq. (11) defines the decision variables.

### **4. Hybrid parallel genetic algorithm**

The genetic algorithm is a stochastic search method based on the natural selection, reproduction, and evolution theory proposed by Holland (1975). The parallel genetic algorithm paratactically evolves by operating several sub-populations. This study suggests a hybrid parallel genetic algorithm for reliability optimization with resource constraints. The suggested algorithm includes different heuristics such as swap, 2-opt, and interchange (except for RAPCC) for an improvement solution. The suggested process of a hybrid parallel genetic algorithm is shown in Fig. 3.

### **4.1 Gene representation**

130 Real-World Applications of Genetic Algorithms

Using Eqs. (1) and (2), the mathematical programming model of the RRAP in a series-

*Subject to*

1 1

*ij i*

The objective function is to maximize the system reliability in a series-parallel system. Eqs. (4) and (5) show the resource constraints with cost and weight. Eq. (6) shows the maximum and minimum number of components that can be used for each subsystem. Eq. (7) shows

As shown in Fig. 2, a series system consisting of n subsystems where each subsystem has several component alternatives which can perform same functions with different characteristics is considered in this study. The problem is proposed to select the optimal combination of component alternatives to maximize the system reliability given the cost.

Using Eq. (1), the mathematical programming model of the RAPCC in a series system is as

1 1

*i j*

= =

*n m*

1 1

*n m S ij ij i j R rx* = =

 = ⋅

*ij ij S*

*cx C*

∏ (8)

⋅ ≤ (9)

*x u*

*i j*

1

*j*

**3.2 Reliability allocation problem with component choices (RAPCC)**

*Subject to*

Only one component will be adopted for each subsystem.

 *Maximize*

=

1 *m*

= =

*n m*

111

*ij ij S*

*wx W*

1 1

*i j*

= =

*n m*

*S i ij iij RR r* ===

1 1 *ij x n nm*

*ij ij S*

*cx C*

∏∏∏ (3)

⋅ ≤ (4)

⋅ ≤ (5)

≤ ≤ , 1,2, , *i n* = (6)

0 *ij x* ≥ , 1,2, , *i n* = , *j m* = 1,2, , , Integer (7)

= = −−

parallel system is as follows.

the integer decision variables.

Fig. 2. Series system

follows.

 *Maximize*

The gene representation has to reflect the properties of the system structure. The suggested algorithm for the RRAP represents a gene by one string as shown in Table 1.

Table 1. Gene representation (RRAP)

The subsystem in Table 1 indicate the nominal number of subsystem. However, it is not necessary for this number to be one for the composition of a substantial objective function. The "Redundancy & Component" row represents the number of components available for each subsystem. For example, as shown Table 1, subsystem 1 consists of two components of C1, one component of C2, one component of C3. Table 1 can be expressed as shown in Fig. 4.

The suggested algorithm for the RAPCC represents a gene by one string as shown in Table 2.

The subsystem in Table 2 indicates the nominal number of subsystems. However, it is not necessary for the composition of a substantial objective function. The "Component" row represents the available component number for each subsystem. For example, as shown Table 2, a series system uses component No.3 in subsystem 1, component No.2 in subsystem 2, …, and component No.5 in subsystem 6.

### **4.2 Population**

The population of a parallel genetic algorithm consists of an initial population and several sub-populations. The initial population is usually generated by the random and the heuristic generation method. The heuristic generation method tends to interrupt global search.

A Hybrid Parallel Genetic Algorithm for Reliability Optimization 133

The fitness function to evaluate the solutions is commonly obtained from the objective function. Penalty functions were used for infeasible solutions by the random generation method in this study. Eqs. (12) and (13) show cost and weight penalty functions, respectively.

1, total cost

≤ =

1, total weight 1 , otherwise ≤ =

The multiplication of system reliability and penalty functions related to its cost and weight (except for RAPCC) were used to calculate the fitness of the solutions in the suggested

The selection method to choose the pairs of parents is applied by the roulette wheel method in the suggested algorithm. The roulette wheel method is one of the most common proportionate selection schemes. In this scheme, the probability to select an individual is proportional to its fitness. It is also stochastically possible for infeasible solutions to survive. The suggested algorithm applies the elitism strategy for the survival of an optimum solution

The crossover is the main genetic operator. It operates on two individuals at a time and generates offspring by combining both individuals' features. The crossover operator applies a uniform crossover in the suggested algorithm as shown in Fig. 5. The steps of the uniform

**Step 1.** Random numbers were generated for individuals and the individual for crossover

**Step 3.** For each bit of the mated individuals was generated a random number of either 0 or 1. **Step 4.** The two offspring bits were generated through a crossover of the two parents' bits

was selected by comparing the crossover rate for each individual.

when the random number associated with those bits was 1.

**Step 2.** The selected individuals were mated between themselves.

cos

*total t*

*total weight*

by generation in order to avoid the disappearance of an excellent solution.

*C*

*W*

*P*

*P*

1 , otherwise

*s*

*s*

*fitness R P P* = ⋅⋅ *SCW* (14)

*W*

(12)

(13)

*C*

Table 2. Gene representation (RAPCC)

algorithm as shown in Eq. (14).

**4.4 Selection**

**4.5 Crossover**

crossover are as follows.

**4.3 Fitness**

Subsystem 1 2 3 4 5 6 Component 3 2 4 1 3 5

Therefore, the initial population is generated by the random generation method in this study. The initial population is composed 500 individuals with 100 individuals allocated for each sub-population.

Fig. 4. System structure of Table 1

Table 2. Gene representation (RAPCC)

#### **4.3 Fitness**

132 Real-World Applications of Genetic Algorithms

Therefore, the initial population is generated by the random generation method in this study. The initial population is composed 500 individuals with 100 individuals allocated for

each sub-population.

Fig. 3. Hybrid parallel genetic algorithm

Fig. 4. System structure of Table 1

The fitness function to evaluate the solutions is commonly obtained from the objective function. Penalty functions were used for infeasible solutions by the random generation method in this study. Eqs. (12) and (13) show cost and weight penalty functions, respectively.

$$P\_c = \begin{cases} 1, & \text{total cost} \le C\_s\\ \frac{1}{total\\_cost}, & \text{otherwise} \end{cases} \tag{12}$$

$$P\_w = \begin{cases} 1, & \text{total weight} \le W\_s\\ \frac{1}{\text{total weight}}, & \text{otherwise} \end{cases} \tag{13}$$

The multiplication of system reliability and penalty functions related to its cost and weight (except for RAPCC) were used to calculate the fitness of the solutions in the suggested algorithm as shown in Eq. (14).

$$\text{fitness} = \mathbf{R}\_S \cdot \mathbf{P}\_C \cdot \mathbf{P}\_W \tag{14}$$

#### **4.4 Selection**

The selection method to choose the pairs of parents is applied by the roulette wheel method in the suggested algorithm. The roulette wheel method is one of the most common proportionate selection schemes. In this scheme, the probability to select an individual is proportional to its fitness. It is also stochastically possible for infeasible solutions to survive. The suggested algorithm applies the elitism strategy for the survival of an optimum solution by generation in order to avoid the disappearance of an excellent solution.

#### **4.5 Crossover**

The crossover is the main genetic operator. It operates on two individuals at a time and generates offspring by combining both individuals' features. The crossover operator applies a uniform crossover in the suggested algorithm as shown in Fig. 5. The steps of the uniform crossover are as follows.

A Hybrid Parallel Genetic Algorithm for Reliability Optimization 135

Migration parameter Sub-population size Migration period Migration rate Value 100 50 0.2

The genetic parameters include the population size, crossover rate (Pc), mutation rate (Pm), and the number of generations. It is hard to find the best parametric values, so the following parameters were obtained by repeated experiments. The genetic parameters are shown in

> Crossover rate(Pc)

Value 500 0.8 0.02 1,000~3,000

The suggested algorithm includes different heuristics such as swap, 2-opt, and interchange (except for RAPCC) for improvement of the solution. The swap heuristic was used to exchange each bit which selected two solutions among the five solutions generated by the parallel genetic algorithm. After applying the swap heuristic, a solution of the parallel genetic algorithm was selected by using best fitness. In a selected solution, the 2-opt heuristic performed the exchanging of two bits to enable improvement. The interchange heuristic was applied to each subsystem to exchanging sequences of bits. Finally, a solution of a hybrid parallel genetic algorithm was produced using best fitness after the application

In order to evaluate the performance of the suggested algorithm for the integer nonlinear RRAP, this study performed experiments on 33 variations of Fyffe et. al. (1968), as suggested by Nakagawa & Miyazaki (1981). In this problem, the series–parallel system is connected by

Mutation rate(Pm)

The number of generations

Fig. 7. Neighborhood structure (ring topology)

Population size

**5.1 The reliability-redundancy allocation problem (RRAP)**

Table 3. Migration parameters

**4.8 Genetic parameters**

Genetic parameter

Table 4. Genetic parameters

**4.9 Improvement solution**

of the interchange heuristic.

**5. Numerical experiments**

Table 4.

Fig. 5. Uniform crossover

#### **4.6 Mutation**

The mutation is a background operator which produces spontaneous random changes in various individuals. The mutation operator applies the uniform mutation in the suggested algorithm as shown in Fig. 6. The steps of the uniform mutation are as follows.

Fig. 6. Uniform mutation

#### **4.7 Migration**

The migration is an exchange operator to change useful information between neighbor subpopulations. Periodically, each sub-population sends its best individuals to its neighbors. When dealing with the migration, the main issues to be considered are migration parameters such as neighborhood structure, the individuals' selection for exchanging, subpopulation size, migration period, and migration rate. In the suggested algorithm, the neighborhood structure uses a ring topology as shown in Fig. 7 and the individuals' selection for exchanging is determined by the application of the fitness function. Other migration parameters are shown in Table 3.

Fig. 7. Neighborhood structure (ring topology)

Table 3. Migration parameters

### **4.8 Genetic parameters**

134 Real-World Applications of Genetic Algorithms

The mutation is a background operator which produces spontaneous random changes in various individuals. The mutation operator applies the uniform mutation in the suggested

**Step 1.** The mutation bits were selected by comparing a random number with the mutation rate after Generating a random number between 0~1 for all individual bits. **Step 2.** The value of the selected bits were substituted with a new value between 0 and the

The migration is an exchange operator to change useful information between neighbor subpopulations. Periodically, each sub-population sends its best individuals to its neighbors. When dealing with the migration, the main issues to be considered are migration parameters such as neighborhood structure, the individuals' selection for exchanging, subpopulation size, migration period, and migration rate. In the suggested algorithm, the neighborhood structure uses a ring topology as shown in Fig. 7 and the individuals' selection for exchanging is determined by the application of the fitness function. Other

algorithm as shown in Fig. 6. The steps of the uniform mutation are as follows.

maximum number of components in each subsystem.

Fig. 5. Uniform crossover

Fig. 6. Uniform mutation

migration parameters are shown in Table 3.

**4.7 Migration**

**4.6 Mutation**

The genetic parameters include the population size, crossover rate (Pc), mutation rate (Pm), and the number of generations. It is hard to find the best parametric values, so the following parameters were obtained by repeated experiments. The genetic parameters are shown in Table 4.

Table 4. Genetic parameters

### **4.9 Improvement solution**

The suggested algorithm includes different heuristics such as swap, 2-opt, and interchange (except for RAPCC) for improvement of the solution. The swap heuristic was used to exchange each bit which selected two solutions among the five solutions generated by the parallel genetic algorithm. After applying the swap heuristic, a solution of the parallel genetic algorithm was selected by using best fitness. In a selected solution, the 2-opt heuristic performed the exchanging of two bits to enable improvement. The interchange heuristic was applied to each subsystem to exchanging sequences of bits. Finally, a solution of a hybrid parallel genetic algorithm was produced using best fitness after the application of the interchange heuristic.

### **5. Numerical experiments**

### **5.1 The reliability-redundancy allocation problem (RRAP)**

In order to evaluate the performance of the suggested algorithm for the integer nonlinear RRAP, this study performed experiments on 33 variations of Fyffe et. al. (1968), as suggested by Nakagawa & Miyazaki (1981). In this problem, the series–parallel system is connected by

A Hybrid Parallel Genetic Algorithm for Reliability Optimization 137

= , *i n* = 1,2, , (18)

≤ ≤ , 1,2, , *i n* = (19)

1

*ix x*

*ij i*

*xx x*

The experimental results including component structure, reliability, cost, and weight by

No. W Components structure Reliability Cost Weight 1 191 333, 11, 444, 3333, 222, 22, 111, 1111, 12, 233, 33, 1111, 11, 34 0.9868110 130 191 2 190 333, 11, 444, 3333, 222, 22, 111, 1111, 11, 233, 33, 1111, 12, 34 0.9864161 130 190 3 189 333, 11, 444, 3333, 222, 22, 111, 1111, 23, 233, 13, 1111, 11, 34 0.9859217 130 189 4 188 333, 11, 444, 3333, 222, 22, 111, 1111, 23, 223, 13, 1111, 12, 34 0.9853782 130 188 5 187 333, 11, 444, 3333, 222, 22, 111, 1111, 13, 223, 13, 1111, 22, 34 0.9846881 130 187 6 186 333, 11, 444, 333, 222, 22, 111, 1111, 23, 233, 33, 1111, 22, 34 0.9841755 129 186 7 185 333, 11, 444, 3333, 222, 22, 111, 1111, 23, 223, 13, 1111, 22, 33 0.9835049 130 185 8 184 333, 11, 444, 333, 222, 22, 111, 1111, 33, 233, 33, 1111, 22, 34 0.9829940 130 184 9 183 333, 11, 444, 333, 222, 22, 111, 1111, 33, 223, 33, 1111, 22, 34 0.9822557 129 183 10 182 333, 11, 444, 333, 222, 22, 111, 1111, 33, 333, 33, 1111, 22, 33 0.9815183 130 182 11 181 333, 11, 444, 333, 222, 22, 111, 1111, 33, 233, 33, 1111, 22, 33 0.9810271 129 181 12 180 333, 11, 444, 333, 222, 22, 111, 1111, 33, 223, 33, 1111, 22, 33 0.9802902 128 180 13 179 333, 11, 444, 333, 222, 22, 111, 1111, 33, 223, 13, 1111, 22, 33 0.9795047 126 179 14 178 333, 11, 444, 333, 222, 22, 111, 1111, 33, 222, 13, 1111, 22, 33 0.9784003 125 178 15 177 333, 11, 444, 333, 222, 22, 111, 113, 33, 223, 13, 1111, 22, 33 0.9775953 126 177 16 176 333, 11, 444, 333, 222, 22, 33, 1111, 33, 223, 13, 1111, 22, 33 0.9766905 124 176 17 175 333, 11, 444, 333, 222, 22, 13, 1111, 33, 223, 33, 1111, 22, 33 0.9757079 125 175 18 174 333, 11, 444, 333, 222, 22, 13, 1111, 33, 223, 13, 1111, 22, 33 0.9749261 123 174 19 173 333, 11, 444, 333, 222, 22, 13, 1111, 33, 222, 13, 1111, 22, 33 0.9738268 122 173 20 172 333, 11, 444, 333, 222, 22, 13, 113, 33, 223, 13, 1111, 22, 33 0.9730266 123 172 21 171 333, 11, 444, 333, 222, 22, 13, 113, 33, 222, 13, 1111, 22, 33 0.9719295 122 171 22 170 333, 11, 444, 333, 222, 22, 13, 113, 33, 222, 11, 1111, 22, 33 0.9707604 120 170 23 169 333, 11, 444, 333, 222, 22, 11, 113, 33, 222, 13, 1111, 22, 33 0.9692910 121 169 24 168 333, 11, 444, 333, 222, 22, 11, 113, 33, 222, 11, 1111, 22, 33 0.9681251 119 168 25 167 333, 11, 444, 333, 22, 22, 13, 113, 33, 222, 11, 1111, 22, 33 0.9663351 118 167 26 166 333, 11, 44, 333, 222, 22, 13, 113, 33, 222, 11, 1111, 22, 33 0.9650416 116 166

0 *ij x* ≥ , 1,2, , *i n* = , *j m* = 1,2, , , Integer (20)

1, if of the th component are used for subsystem

*ix x i i im r* = − *qq q* , ( ) 1 *im im x x q r im* = − *im* , *i n* = 1,2, ,

*x j i*

(21)

*x u*

1 *i i i im*

*y*

1

*j*

=

1 0

*ij*

where, ( ) 1 2

using a hybrid parallel genetic algorithm are shown in Table 6.

1 1 2 ln 1 *i i im*

0, otherwise *i im*

*i im*

=

1

*y*

*ix x*

=

*x x*

*i im*

1 *m*

*u u*

14 parallel subsystems and each has three or four components of choice. The objective is to maximize the reliability of the series–parallel system subject to the cost constraint of 130 and weight constraint ranging from 159 to 190. The maximum number of components is 6 in each subsystem. The component data for testing problems are listed in Table 5.

Table 5. Component data for testing problems

To use CPLEX, this study performed additional steps for transforming the integer nonlinear RRAP into an equivalent binary knapsack problem(Bae et al., 2007; Coit, 2003) as shown in Eqs. (15) to (21).

$$\text{Maximize} \quad \ln R\_S = \sum\_{i=1}^{n} \sum\_{\mathbf{x}\_{i1}=\mathbf{0}}^{\underline{u}\_i} \cdots \sum\_{\mathbf{x}\_{in}}^{\underline{u}\_i} r\_{i\mathbf{x}\_{i1}\ldots\mathbf{x}\_{in}} \cdot y\_{i\mathbf{x}\_{i1}\ldots\mathbf{x}\_{in}} \tag{15}$$

$$\text{Subject to } \sum\_{i=1}^{n} \sum\_{x\_{i1}=0}^{u\_i} \cdots \sum\_{x\_{in}}^{u\_i} \left( \sum\_{j=1}^{m} x\_{ij} \cdot c\_{ij} \right) \cdot y\_{i x\_{i1} \ldots x\_{in}} \le \mathbb{C}\_S \tag{16}$$

$$\sum\_{i=1}^{n} \sum\_{\mathbf{x}\_{i1}=0}^{\boldsymbol{u}\_{i}} \cdots \sum\_{\mathbf{x}\_{in}}^{\boldsymbol{u}\_{i}} \left( \sum\_{j=1}^{m} \boldsymbol{x}\_{ij} \cdot \boldsymbol{w}\_{ij} \right) \cdot \boldsymbol{y}\_{i\mathbf{x}\_{i1}\ldots\mathbf{x}\_{in}} \leq \boldsymbol{W}\_{\mathbf{S}} \tag{17}$$

14 parallel subsystems and each has three or four components of choice. The objective is to maximize the reliability of the series–parallel system subject to the cost constraint of 130 and weight constraint ranging from 159 to 190. The maximum number of components is 6 in

> Component choices Choice 1 Choice 2 Choice 3 Choice 4 R C W R C W R C W R C W

1 0.90 1 3 0.93 1 4 0.91 2 2 0.95 2 5 2 0.95 2 8 0.94 1 10 0.93 1 9 \* \* \* 3 0.85 2 7 0.90 3 5 0.87 1 6 0.92 4 4 4 0.83 3 5 0.87 4 6 0.85 5 4 \* \* \* 5 0.94 2 4 0.93 2 3 0.95 3 5 \* \* \* 6 0.99 3 5 0.98 3 4 0.97 2 5 0.96 2 4 7 0.91 4 7 0.92 4 8 0.94 5 9 \* \* \* 8 0.81 3 4 0.90 5 7 0.91 6 6 \* \* \* 9 0.97 2 8 0.99 3 9 0.96 4 7 0.91 3 8 10 0.83 4 6 0.85 4 5 0.90 5 6 \* \* \* 11 0.94 3 5 0.95 4 6 0.96 5 6 \* \* \* 12 0.79 2 4 0.82 3 5 0.85 4 6 0.90 5 7 13 0.98 2 5 0.99 3 5 0.97 2 6 \* \* \* 14 0.90 4 6 0.92 4 7 0.95 5 6 0.99 6 9

To use CPLEX, this study performed additional steps for transforming the integer nonlinear RRAP into an equivalent binary knapsack problem(Bae et al., 2007; Coit, 2003) as shown in

> 1 1 0 ln *i i*

= =

*Subject to* 1 1 10 1

*i im*

== =

*ix x j*

1 10 1

*i im*

== =

*ix x j*

*i i*

*n m u u*

*i i*

*n m u u*

*ix x R ry*

*n u u*

*i im*

⋅⋅ ≤

*S ix x ix x*

*i im i im*

*i im*

(16)

*ij ij ix x S*

(17)

*xc y C*

⋅⋅ ≤

1

*ij ij ix x S*

*xw y W*

*i im*

= ⋅ (15)

each subsystem. The component data for testing problems are listed in Table 5.

Subsystem No.

Eqs. (15) to (21).

Table 5. Component data for testing problems

 *Maximize* 1 1

$$\sum\_{\mathbf{x}\_{i1}=0}^{u\_i} \cdots \sum\_{\mathbf{x}\_{in}}^{u\_i} y\_{i\mathbf{x}\_{i1}\cdots\mathbf{x}\_{in}} = \mathbf{1} \; \text{ } i = 1 \; \text{2} \; \dots \; n \tag{18}$$

$$1 \le \sum\_{j=1}^{m} \chi\_{ij} \le u\_i \quad i = 1, 2, \cdots, n \tag{19}$$

$$\mathbf{x}\_{[i]} \ge \mathbf{0} \,, \ i = \mathbf{1}, \mathbf{2}, \cdots, \mathbf{n} \,, \ j = \mathbf{1}, \mathbf{2}, \cdots, \mathbf{m} \,, \ \text{Integer} \tag{20}$$

$$\begin{cases} \text{y}\_{i x\_{i1} \cdots x\_{in}} = \begin{cases} 1, & \text{if } x\_{ij} \text{ of the } j \text{th component are used for subsystem } i\\ 0, & \text{otherwise} \end{cases} \tag{21}$$

$$\text{where}\\
\text{, } r\_{i\mathbf{x}\_{i1}\ldots\mathbf{x}\_{im}} = \ln\left(1 - q\_{i1}^{\mathbf{x}\_{1i}} q\_{i2}^{\mathbf{x}\_{i2}} \cdots q\_{im}^{\mathbf{x}\_{im}}\right), \; q\_{im}^{\mathbf{x}\_{im}} = \left(1 - r\_{im}\right)^{\mathbf{x}\_{im}}, \; i = 1, 2, \cdots, m$$

The experimental results including component structure, reliability, cost, and weight by using a hybrid parallel genetic algorithm are shown in Table 6.

A Hybrid Parallel Genetic Algorithm for Reliability Optimization 139

16 176 0.9766905 0.9764 0.976690 0.9765 0.9766905 0.9766905 7 / 10 17 175 0.9757079 0.9753 0.975708 0.9757 0.9757079 0.9757079 9 / 10 18 174 0.9749261 0.9744 0.974788 0.9749 0.9746901 0.9749261 6 / 10 19 173 0.9738268 0.9738 0.973827 0.9738 0.9737580 0.9738268 8 / 10 20 172 0.9730266 0.9727 0.973027 0.9730 0.9730266 0.9730266 9 / 10 21 171 0.9719295 0.9719 0.971929 0.9719 0.9719295 0.9719295 7 / 10 22 170 0.9707604 0.9708 0.970760 0.9708 0.9707604 0.9707604 9 / 10 23 169 0.9692910 0.9692 0.969291 0.9693 0.9692910 0.9692910 8 / 10 24 168 0.9681251 0.9681 0.968125 0.9681 0.9681251 0.9681251 8 / 10 25 167 0.9663351 0.9663 0.966335 0.9663 0.9663351 0.9663351 8 / 10 26 166 0.9650416 0.9650 0.965042 0.9650 0.9650416 0.9650416 9 / 10 27 165 0.9637118 0.9637 0.963712 0.9637 0.9637118 0.9637118 7 / 10 28 164 0.9624219 0.9624 0.962422 0.9624 0.9624219 0.9624219 7 / 10 29 163 0.9606424 0.9606 0.959980 0.9606 0.9606424 0.9606424 8 / 10 30 162 0.9591884 0.9591 0.958205 0.9592 0.9591884 0.9591884 6 / 10 31 161 0.9580346 0.9580 0.956922 0.9580 0.9580346 0.9580346 7 / 10 32 160 0.9557144 0.9557 0.955604 0.9557 0.9557144 0.9557144 6 / 10 33 159 0.9545648 0.9546 0.954325 0.9546 0.9545648 0.9545648 8 / 10

Table 7. Comparison of CPLEX, meta-heuristics and HPGA (C=130)

and is shown in Fig. 8.

*L GA* 1( ) : MPI(%) of GA results *L TS* 2( ) : MPI(%) of TS results *L ACO* 3( ) : MPI(%) of ACO results

In order to calculate the improvement of reliability for existing studies and the suggested algorithm, a maximum possible improvement (MPI) was obtained by Eqs. from (22) to (25)

> 1( ) 100 1 *HPGA GA GA*

2( ) 100 1 *HPGA TS TS*

3( ) 100 1

4( ) 100 1 *HPGA IA IA*

*R*

*R*

*R*

*HPGA ACO ACO*

*R*

− = × − (22)

− = × − (23)

− = × − (24)

− = × − (25)

*R R L GA*

*R R L TS*

*R R L ACO*

*R R L IA*

Table 6. Experimental results by using HPGA (C=130)

The experimental results compared to the results of CPLEX and existing meta-heuristics, such as GA (Coit & Smith, 1996), TS (Kulturel-Konak et al., 2003), ACO (Liang & Smith, 2004), and IA (Chen & You, 2005) are shown in Table 6. The comparison of CPLEX, metaheuristics, and the suggested algorithm is shown in Table 7.

The suggested algorithm in all problems showed the optimal solution 6~9 times out 0f 10 runs and obtained same or superior solutions compared to the meta-heuristics. Of the results in Table 7, when compared with the meta-heuristics, 25 solutions are superior to GA, 7 solutions are superior to TS and ACO, and 9 solutions are superior to IA, respectively. The other solutions are the same. The suggested algorithm could paratactically evolve by operating several sub-populations and improve on the solution through swap, 2-opt, and interchange heuristics.

A Hybrid Parallel Genetic Algorithm for Reliability Optimization 139

27 165 333, 11, 444, 333, 22, 22, 11, 113, 33, 222, 11, 1111, 22, 33 0.9637118 117 165 28 164 333, 11, 44, 333, 222, 22, 11, 113, 33, 222, 11, 1111, 22, 33 0.9624219 115 164 29 163 333, 11, 44, 333, 22, 22, 13, 113, 33, 222, 11, 1111, 22, 33 0.9606424 114 163 30 162 333, 11, 44, 333, 22, 22, 11, 113, 33, 222, 13, 1111, 22, 33 0.9591884 115 162 31 161 333, 11, 44, 333, 22, 22, 11, 113, 33, 222, 11, 1111, 22, 33 0.9580346 113 161 32 160 333, 11, 44, 333, 22, 22, 11, 111, 33, 222, 13, 1111, 22, 33 0.9557144 112 160 33 159 333, 11, 44, 333, 22, 22, 11, 111, 33, 222, 11, 1111, 22, 33 0.9545648 110 159

The experimental results compared to the results of CPLEX and existing meta-heuristics, such as GA (Coit & Smith, 1996), TS (Kulturel-Konak et al., 2003), ACO (Liang & Smith, 2004), and IA (Chen & You, 2005) are shown in Table 6. The comparison of CPLEX, meta-

The suggested algorithm in all problems showed the optimal solution 6~9 times out 0f 10 runs and obtained same or superior solutions compared to the meta-heuristics. Of the results in Table 7, when compared with the meta-heuristics, 25 solutions are superior to GA, 7 solutions are superior to TS and ACO, and 9 solutions are superior to IA, respectively. The other solutions are the same. The suggested algorithm could paratactically evolve by operating several sub-populations and improve on the solution through swap, 2-opt, and

1 191 0.9868110 0.9867 0.986811 0.9868 0.9868110 0.9868110 8 / 10 2 190 0.9864161 0.9857 0.986416 0.9859 0.9864161 0.9864161 7 / 10 3 189 0.9859217 0.9856 0.985922 0.9858 0.9859217 0.9859217 9 / 10 4 188 0.9853782 0.9850 0.985378 0.9853 0.9853297 0.9853782 8 / 10 5 187 0.9846881 0.9844 0.984688 0.9847 0.9844495 0.9846881 8 / 10 6 186 0.9841755 0.9836 0.984176 0.9838 0.9841755 0.9841755 9 / 10 7 185 0.9835049 0.9831 0.983505 0.9835 0.9834363 0.9835049 8 / 10 8 184 0.9829940 0.9823 0.982994 0.9830 0.9826980 0.9829940 9 / 10 9 183 0.9822557 0.9819 0.982256 0.9822 0.9822062 0.9822557 7 / 10 10 182 0.9815183 0.9811 0.981518 0.9815 0.9815183 0.9815183 9 / 10 11 181 0.9810271 0.9802 0.981027 0.9807 0.9810271 0.9810271 8 / 10 12 180 0.9802902 0.9797 0.980290 0.9803 0.9802902 0.9802902 9 / 10 13 179 0.9795047 0.9791 0.979505 0.9795 0.9795047 0.9795047 9 / 10 14 178 0.9784003 0.9783 0.978400 0.9784 0.9782085 0.9784003 7 / 10 15 177 0.9775953 0.9772 0.977474 0.9776 0.9772429 0.9775953 8 / 10

Reliability Number

HPGA (This study)

of optimal by HPGA (10 runs)

Table 6. Experimental results by using HPGA (C=130)

interchange heuristics.

No. W

heuristics, and the suggested algorithm is shown in Table 7.

CPLEX GA TS ACO IA

In order to calculate the improvement of reliability for existing studies and the suggested algorithm, a maximum possible improvement (MPI) was obtained by Eqs. from (22) to (25) and is shown in Fig. 8.

$$L1 \text{(GA)} = \frac{R\_{HPGA} - R\_{GA}}{1 - R\_{GA}} \times 100 \tag{22}$$

$$L2\text{(TS)} = \frac{R\_{HPGA} - R\_{TS}}{1 - R\_{TS}} \times 100\tag{23}$$

$$L\mathcal{B}(ACO) = \frac{R\_{HPGA} - R\_{ACO}}{1 - R\_{ACO}} \times 100\tag{24}$$

$$L4(IA) = \frac{R\_{HPGA} - R\_{IA}}{1 - R\_{IA}} \times 100\tag{25}$$

*L GA* 1( ) : MPI(%) of GA results *L TS* 2( ) : MPI(%) of TS results *L ACO* 3( ) : MPI(%) of ACO results

A Hybrid Parallel Genetic Algorithm for Reliability Optimization 141

The suggested algorithm presented optimal solutions in all large-scale problems. For the experimental results of large-scale problems 1~4, the suggested algorithm showed the optimal solutions 4~8 times out of 10 runs. The optimal solution to large-scale problem 5

In order to evaluate the performance of the suggested algorithm for the reliability allocation problem with multiple-choice, this study performed experiments by using the Nahas & Nourelfath (2005) and the Kim et al. (2008) examples in series. The Nahas & Nourelfath (2005) examples consist of four examples: examples 1, 2, and 3 consist of 15 subsystems with 60, 80, and 100 components, respectively, and example 4 consists of 25 subsystems with 166 components. The budgets are \$1,000, \$900, \$1,000, and \$1,400, respectively. Examples by the Kim et al. (2008) consist of two large-scale examples (examples 5 and 6). Large-scale examples are presented through connecting the system data of example 4. Examples 5 and 6 consist of 100 and 200 subsystems with budgets of \$7,200~\$7,650 and \$14,400~\$15,100,

To use CPLEX, this study performed an additional step for transforming the nonlinear

The experimental results of examples 1~4 including component structure, reliability, and

cost by using CPLEX and a hybrid parallel genetic algorithm are shown in Table 9.

1 1 1 1 ln ln ln *n m n m S ij ij ij ij i j i j R rx x r* = = = = = ⋅= ⋅

CPLEX HPGA

∏ (26)

Reliability Component structure Reliability Cost

3-3-3-5-2-3-2-2-3-1-2-3-4-

3-3-3-5-2-3-2-2-3-1-2-3-4-

2-3-3-4-2-3-2-2-3-1-2-3-3-

2-2-2-3-4-3-2 0.857054 990

4-1-2-3-4-3-1 0.915042 900

3-2-2-4-4-4-2 0.965134 995

4-1-2-3-3-4-2-3-2-2-3-1 0.865439 1,395

3-1-3-3-3-4-2-3-2-2-3-1 0.865439 1,395

4-1-3-3-3-5-3-3-2-2-3-1 0.865439 1,400

**5.2 The reliability allocation problem with component choices (RAPCC)**

objective function into the linear function as shown in Eq. (26).

Number of

4 25 166 1,400 0.865439

components budget

1 15 60 1,000 0.857054 3-4-5-2-3-3-2-3-

2 15 80 900 0.915042 3-3-3-4-2-3-3-2-

3 15 100 1,000 0.965134 3-3-4-4-3-3-2-2-

Table 9. Experimental results of examples 1~4 by using CPLEX and HPGA

As found in Table 9, the suggested algorithm presented the optimal solutions in examples 14 and obtained a new optimal solution (3-3-3-5-2-3-2-2-3-1-2-3-4-3-1-3-3-3-4-2-3-2-2-3-1) in

was obtained by HPGA in 1 out of 10 runs.

respectively.

No. Number of subsystems

example 4.

 *Maximize*

*L IA* 4( ) : MPI(%) of IA results *RHPGA* : system reliability by HPGA

*RGA* : system reliability by GA

*RTS* : system reliability by TS

*RACO* : system reliability by ACO

*RIA* : system reliability by IA

Fig. 8. MPI

The suggested algorithm improved system reliability better than existing studies except for TS in the 1st~20th test problems in which the weight was heavy. In addition, HPGA found superior system reliability compared to TS in the 29th~32th test problems in which the weight was light. The other solutions are almost the same.

Through the experiment, this study found that the performance of HPGA is superior to the existing meta-heuristics. In order to evaluate the performance of HPGA in large-scale problems, 5 more problems are presented through connecting the system data of testing problem 1 (C=190, W=191) in series systems. The large-scale problems consist of 28 subsystems (C=260, W=382), 42 subsystems (C=390, W=573), 56 subsystems (C=520, W=764), 70 subsystems (C=650, W=955) in series systems. After 10 runs using HPGA, the results compared with the optimal solution by CPLEX are shown in Table 8.

Table 8. Experimental results of the large-scale problems

The suggested algorithm improved system reliability better than existing studies except for TS in the 1st~20th test problems in which the weight was heavy. In addition, HPGA found superior system reliability compared to TS in the 29th~32th test problems in which the

Through the experiment, this study found that the performance of HPGA is superior to the existing meta-heuristics. In order to evaluate the performance of HPGA in large-scale problems, 5 more problems are presented through connecting the system data of testing problem 1 (C=190, W=191) in series systems. The large-scale problems consist of 28 subsystems (C=260, W=382), 42 subsystems (C=390, W=573), 56 subsystems (C=520, W=764), 70 subsystems (C=650, W=955) in series systems. After 10 runs using HPGA, the

results compared with the optimal solution by CPLEX are shown in Table 8.

subsystems C W CPLEX HPGA (10 runs)

1 14 130 191 0.9868110 0.9868110 0.000021 8 / 10 2 28 260 382 0.9740720 0.9740720 0.000147 6 / 10 3 42 390 573 0.9612374 0.9612374 0.000564 4 / 10 4 56 520 764 0.9488162 0.9488162 0.001095 1 / 10 5 70 650 955 0.9370413 0.9370413 0.001732 1 / 10

Max S.D. Number of optimal

weight was light. The other solutions are almost the same.

Table 8. Experimental results of the large-scale problems

*L IA* 4( ) : MPI(%) of IA results

Fig. 8. MPI

No. Number of

*RHPGA* : system reliability by HPGA *RGA* : system reliability by GA *RTS* : system reliability by TS *RACO* : system reliability by ACO *RIA* : system reliability by IA

The suggested algorithm presented optimal solutions in all large-scale problems. For the experimental results of large-scale problems 1~4, the suggested algorithm showed the optimal solutions 4~8 times out of 10 runs. The optimal solution to large-scale problem 5 was obtained by HPGA in 1 out of 10 runs.

### **5.2 The reliability allocation problem with component choices (RAPCC)**

In order to evaluate the performance of the suggested algorithm for the reliability allocation problem with multiple-choice, this study performed experiments by using the Nahas & Nourelfath (2005) and the Kim et al. (2008) examples in series. The Nahas & Nourelfath (2005) examples consist of four examples: examples 1, 2, and 3 consist of 15 subsystems with 60, 80, and 100 components, respectively, and example 4 consists of 25 subsystems with 166 components. The budgets are \$1,000, \$900, \$1,000, and \$1,400, respectively. Examples by the Kim et al. (2008) consist of two large-scale examples (examples 5 and 6). Large-scale examples are presented through connecting the system data of example 4. Examples 5 and 6 consist of 100 and 200 subsystems with budgets of \$7,200~\$7,650 and \$14,400~\$15,100, respectively.

To use CPLEX, this study performed an additional step for transforming the nonlinear objective function into the linear function as shown in Eq. (26).

$$\text{Maximize } \cdot \ln R\_S = \ln \left\{ \prod\_{i=1}^{n} \left( \sum\_{j=1}^{m} r\_{ij} \cdot \mathbf{x}\_{ij} \right) \right\} = \sum\_{i=1}^{n} \sum\_{j=1}^{m} \mathbf{x}\_{ij} \cdot \ln r\_{ij} \tag{26}$$

The experimental results of examples 1~4 including component structure, reliability, and cost by using CPLEX and a hybrid parallel genetic algorithm are shown in Table 9.

Table 9. Experimental results of examples 1~4 by using CPLEX and HPGA

As found in Table 9, the suggested algorithm presented the optimal solutions in examples 14 and obtained a new optimal solution (3-3-3-5-2-3-2-2-3-1-2-3-4-3-1-3-3-3-4-2-3-2-2-3-1) in example 4.

A Hybrid Parallel Genetic Algorithm for Reliability Optimization 143

14,400 0.802546 0.802218 0.000425 -0.1661 0.802218 0 -0.1661 0.802364 0.000110 -0.0922

14,450 0.806496 0.806167 0.000396 -0.1700 0.806167 0 -0.1700 0.806251 0.000076 -0.1266

14,550 0.814290 0.813792 0.000352 -0.2682 0.813792 0 -0.2682 0.813792 0.000182 -0.2682

14,600 0.818299 0.817388 0.000391 -0.5014 0.817798 0.000053 -0.2757 0.817984 0.000003 -0.1734

14,700 0.826207 0.824787 0.000709 -0.8171 0.825364 0.000142 -0.4851 0.825774 0.000325 -0.2491

14,800 0.833851 0.833428 0.000891 -0.2546 0.833510 0.000026 -0.2052 0.833604 0.000450 -0.1487

14,650 0.822160 0.821656 0.000891 -0.2834 0.821656 0 -0.2834 0.822160 0 0

14,750 0.830105 0.829263 0.000815 -0.4956 0.829427 0.000026 -0.3991 0.830105 0.000407 0

14,850 0.837614 0.837448 0.000824 -0.1022 0.837614 0 0 0.837614 0 0

14,900 0.841310 0.840805 0.000786 -0.3182 0.841310 0.000107 0 0.841310 0 0

14,950 0.844856 0.844009 0.000506 -0.5459 0.844856 0.000215 0 0.844856 0 0

15,000 0.848500 0.848332 0.000610 -0.1109 0.848500 0.000027 0 0.848500 0 0

15,050 0.852076 0.851991 0.000722 -0.0575 0.852076 0 0 0.852076 0 0

15,100 0.855751 0.855582 0.000679 -0.1172 0.855751 0 0 0.855751 0 0

As shown in Table 11, the result of SA and TS gave the optimal solution 2 and 6 times out of the 10 cases, respectively. The suggested algorithm found the optimal solution 8 times for the same cases and it showed the same or superior MPI compared to that of SA and TS. As the results in Table 12 show that, when compared with TS and the reoptimization procedure (TS+SA), the suggested algorithm gave the optimal solution 9 times out of the 15 cases and showed the same or superior MPI than TS and the reoptimization procedure (TS+SA). This is because the suggested algorithm could parallelly evolve by operating several sub-

Throughout the experiment, this study found that performance of HPGA is superior to existing meta-heuristics. This study has generated one more example, example 7, which is presented through connecting the system data of example 4 in series. Example 7 consists of 1,000 subsystems with \$90,000\$99,000 budgets. After 10 runs using CPLEX and HPGA in example 7, the experimental results including the maximum, standard deviation values, and

Table 12. Experimental results of example 6 by using CPLEX and HPGA (10 runs)

populations and improve the solution through swap and 2-opt heuristics.

maximum possible improvement (MPI) are shown in Table 13.

14,500 0.810301 0.809890 0.000519 -0.2167 0.809970 0 -0.1745 0.810301 0.000094 0

TS TS+SA Reoptimization HPGA (This Study)

Max S.D. %MPI Max S.D. %MPI Max S.D. %MPI

Budget CPLEX

After 10 runs using HPGA in examples 14, the experimental results including maximum, average and standard deviation values were compared with existing meta-heuristics such as ACO (Nahas & Nourelfath, 2005), SA (Kim et al., 2004), and TS (Kim et al., 2008). The comparison of meta-heuristics and the suggested algorithm is shown in Table 10.

Table 10. Experimental results of examples 1~4 by using CPLEX and HPGA

The suggested algorithm in examples 14 generated the optimal solutions without standard deviation and showed the same or superior solution compared to meta-heuristics.

In order to evaluate the performance of HPGA in large-scale problems, this study performed experiments by using examples in series as suggested by the Kim et al. (2008). After 10 runs using CPLEX and HPGA in examples 5 and 6, experimental results including maximum, standard deviation values, and maximum possible improvement (MPI) compared with existing meta-heuristics such as simulated annealing, tabu search, and reoptimization procedure by the Kim et al. (2008) are shown in Tables 11 and 12. The MPI was obtained by Eq. (27).

$$\%MPI = \frac{\{Max - CPLEX\}}{\{1 - CPLEX\}} \times 100\tag{27}$$

Table 11. Experimental results of example 5 by using CPLEX and HPGA (10 runs)

After 10 runs using HPGA in examples 14, the experimental results including maximum, average and standard deviation values were compared with existing meta-heuristics such as ACO (Nahas & Nourelfath, 2005), SA (Kim et al., 2004), and TS (Kim et al., 2008). The

ACO SA TS HPGA

Max Ave. S.D. Max Ave. S.D. Max Ave. S.D. Max Ave. S.D. 1 0.85705 0.85705 0 0.85705 0.85705 0 0.857054 0.857054 0 0.857054 0.857054 0 2 0.91504 0.91504 0 0.91504 0.91504 0 0.915042 0.915042 0 0.915042 0.915042 0 3 0.96512 0.96439 0.00050 0.96513 0.96503 0.00033 0.965134 0.965134 0 0.965134 0.965134 0 4 0.86543 0.86491 0.00038 0.86543 0.86536 0.00025 0.865439 0.865439 0 0.865439 0.865439 0

The suggested algorithm in examples 14 generated the optimal solutions without standard

In order to evaluate the performance of HPGA in large-scale problems, this study performed experiments by using examples in series as suggested by the Kim et al. (2008). After 10 runs using CPLEX and HPGA in examples 5 and 6, experimental results including maximum, standard deviation values, and maximum possible improvement (MPI) compared with existing meta-heuristics such as simulated annealing, tabu search, and reoptimization procedure by the Kim et al. (2008) are shown in Tables 11 and 12. The MPI was obtained by

> ( ) % 100 (1 ) *Max CPLEX MPI*

7,200 0.895758 0.895575 0.001342 -0.1756 0.895758 0.000312 0 0.895758 0.001017 0 7,250 0.900167 0.899438 0.001050 -0.7302 0.899984 0.000305 -0.1833 0.899984 0.000236 -0.1833 7,300 0.904599 0.903866 0.001027 -0.7683 0.904414 0.000390 -0.1939 0.904599 0.000529 0 7,350 0.908866 0.908405 0.001202 -0.5058 0.908866 0.000480 0 0.908866 0.000424 0 7,400 0.913154 0.912601 0.000499 -0.6368 0.913064 0.000337 -0.1036 0.913114 0.000107 -0.0461 7,450 0.917184 0.916815 0.000510 -0.4456 0.917093 0.000494 -0.1099 0.917184 0.000229 0 7,500 0.921141 0.920770 0.000743 -0.4705 0.921141 0.000365 0 0.921141 0.000156 0 7,550 0.925023 0.925023 0.000590 0 0.925023 0.000502 0 0.925023 0.000172 0 7,600 0.929013 0.928269 0.000696 -1.0481 0.929013 0.000445 0 0.929013 0 0 7,650 0.931526 0.931526 0.000388 0 0.931526 0 0 0.931526 0 0

Table 11. Experimental results of example 5 by using CPLEX and HPGA (10 runs)

*CPLEX*

− = × − (27)

SA TS HPGA (This Study) Max S.D. %MPI Max S.D. %MPI Max S.D. %MPI

(This study)

comparison of meta-heuristics and the suggested algorithm is shown in Table 10.

Table 10. Experimental results of examples 1~4 by using CPLEX and HPGA

deviation and showed the same or superior solution compared to meta-heuristics.

No.

Eq. (27).

Budget CPLEX

Table 12. Experimental results of example 6 by using CPLEX and HPGA (10 runs)

As shown in Table 11, the result of SA and TS gave the optimal solution 2 and 6 times out of the 10 cases, respectively. The suggested algorithm found the optimal solution 8 times for the same cases and it showed the same or superior MPI compared to that of SA and TS. As the results in Table 12 show that, when compared with TS and the reoptimization procedure (TS+SA), the suggested algorithm gave the optimal solution 9 times out of the 15 cases and showed the same or superior MPI than TS and the reoptimization procedure (TS+SA). This is because the suggested algorithm could parallelly evolve by operating several subpopulations and improve the solution through swap and 2-opt heuristics.

Throughout the experiment, this study found that performance of HPGA is superior to existing meta-heuristics. This study has generated one more example, example 7, which is presented through connecting the system data of example 4 in series. Example 7 consists of 1,000 subsystems with \$90,000\$99,000 budgets. After 10 runs using CPLEX and HPGA in example 7, the experimental results including the maximum, standard deviation values, and maximum possible improvement (MPI) are shown in Table 13.

A Hybrid Parallel Genetic Algorithm for Reliability Optimization 145

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Table 13. Experimental results of example 7 by using CPLEX and HPGA (10 runs)

As shown in Table 13, the suggested algorithm presented the optimal solution in 3 times out of 10 cases. While the budget increased, the suggested algorithm found the near-optimal solution.

### **6. Conclusions**

This study suggested mathematical programming models and a hybrid parallel genetic algorithm for reliability optimization with resource constraints. The experimental results compared HPGA with existing meta-heuristics and CPLEX, and evaluated the performance of the suggested algorithm.

The suggested algorithm presented superior solutions to all problems (including large-scale problems) and found that the performance is superior to existing meta-heuristics. This is because the suggested algorithm could paratactically evolve by operating several subpopulations and improve the solution through swap, 2-opt, and interchange (except for RAPCC) heuristics.

The suggested algorithm would be able to be applied to system design with a reliability goal with resource constraints for large scale reliability optimization problems.

### **7. References**

90,000 0.831082 0.830757 0.000681 -0.1924 91,000 0.847706 0.846918 0.000594 -0.5174 92,000 0.860003 0.859647 0.000317 -0.2543 93,000 0.871659 0.871516 0.000183 -0.2228 94,000 0.883369 0.883275 0.000262 -0.0806 95,000 0.895226 0.895185 0.000208 -0.0391 96,000 0.904832 0.904832 0.000079 0 97,000 0.913836 0.913791 0.000055 -0.0522 98,000 0.920716 0.920716 0.000016 0 99,000 0.924869 0.924869 0 0

Table 13. Experimental results of example 7 by using CPLEX and HPGA (10 runs)

As shown in Table 13, the suggested algorithm presented the optimal solution in 3 times out of 10 cases. While the budget increased, the suggested algorithm found the near-optimal

This study suggested mathematical programming models and a hybrid parallel genetic algorithm for reliability optimization with resource constraints. The experimental results compared HPGA with existing meta-heuristics and CPLEX, and evaluated the performance

The suggested algorithm presented superior solutions to all problems (including large-scale problems) and found that the performance is superior to existing meta-heuristics. This is because the suggested algorithm could paratactically evolve by operating several subpopulations and improve the solution through swap, 2-opt, and interchange (except for

The suggested algorithm would be able to be applied to system design with a reliability goal

Ait-Kadi, D. & Nourelfath, M. (2001). Availability Optimization of Fault-Tolerant Systems,

Bae, C. O.; Kim, H. G.; Kim, J. H.; Son, J. Y. & Yun, W. Y. (2007). Solving the Redundancy

*International Journal of Industrial Engineering*, Special Issue, pp.315-323. Bellman, R. & Dreyfus, S. (1958). Dynamic Programming and the Reliability of Multicomponent Devices, *Operations Research*, Vol.6, No.2, pp.200-206.

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Allocation Problem with Multiple Component Choice using Metaheuristics,

with resource constraints for large scale reliability optimization problems.

*Management (IEPM 2001)*, Quebec, Canada, August, 2001.

HPGA Max S.D. %MPI

Budget CPLEX

solution.

**6. Conclusions**

RAPCC) heuristics.

**7. References**

of the suggested algorithm.

**7**

*Malaysia*

**Hybrid Genetic Algorithm-Support Vector**

**Machine Technique for Power Tracing in**

*Universiti Teknologi Malaysia (UTM), Universiti Malaysia Perlis (UniMAP) and*

The electric power industry is under deregulation in response to changes in the law, technology, market and competition. The aim of deregulation is to optimize the system welfare by introducing competitive environment, mainly among the power producers. Developing fair and transparent power flow and loss allocation method has been an active

In the last decades, several power flow tracing algorithms have been proposed in literature mainly from physical flow approach (Bialek & Tam, 1996; Wu et al., 2000; Sulaiman et al., 2008; Pantos et al., 2005) and circuit theory approach (Teng, 2005; Wen-Chen et al., 2004; Mustafa et al., 2008a; Lo & Alturki, 2006). The concept of proportional sharing principle has been proposed by (Bialek & Tam, 1996). This approach has a drawback in handling the transmission losses by introducing fictitious nodes on every lossy branch which will causes the expansion of distribution matrix. The graph method was proposed by (Wu et al., 2000) where the method is basically using the searching technique of the paths and routes from a particular generator to a particular load. The adaptation of the methods from (Bialek & Tam, 1996) and (Wu et al., 2000) has been proposed in (Sulaiman et al., 2008) for tracing the power and loss in deregulated power system. However, the main disadvantage of this approach is it cannot be applied for the circular power flow system. Modification of (Bialek & Tam, 1996) has been done in (Pantos et al., 2005) to trace the real and reactive power by introducing decoupled power flow to overcome the lossy system problem. This method introduces equivalent model of a line for reactive power tracing. The effects of line charging to original generators and loads are integrated. Nevertheless, the actual power contribution

The uses of circuit theory in power tracing have been introduced in (Teng, 2005; Wen-Chen et al., 2004; Mustafa et al., 2008a; Lo & Alturki, 2006). In (Teng, 2005), a method that applies

topic of research, with many transactions taking place at any time.

from generators to loads has been ignored.

\* Corresponding Author

**1. Introduction**

**Deregulated Power Systems**

*Universiti Kebangsaan Malaysia (UKM)*

Mohd Wazir Mustafa, Mohd Herwan Sulaiman\*, Saifulnizam Abd. Khalid and Hussain Shareef


*2.2.7 Porosity measurements of the 97MXC coatings*

Porosity is a defining physical characteristic of the deposits obtained by thermal spray, due to the presence of interlamellar voids and interconnection channels between them. It is expressed by the degree of porosity of the deposit, measured in percentages, [48]. In the case of the 97MXC coatings, the porosity was investigated by image analysis of the transversal section of the specimens, using the IQ Materials software (Japan).

In **Figure 19** it is presented the variation of the average porosity of the 97MXC deposits with the compressed air pressure passing through the primary circuit - for different values of the current intensity that supplies the electric arc.

As expected, the variation of the average porosity of the 97MXC coatings presents a decreasing tendency both by the increasing of the compressed air pressure value and by the increasing of the current intensity value. Thus, it is observed that

**155**

*Hard Alloys with High Content of WC and TiC—Deposited by Arc Spraying Process*

for the same value of the intensity of the electric current, when the compressed air pressure increases, the average porosity of the deposits decreases by up to 12%. The effect of increasing the temperature of the arc achieved by increasing the electric current determines the reduction of the average porosity by a maximum of 28%. It can be stated that between the two process parameters: compressed air pressure and electric current intensity, the latter has a "dramatic" influence on the deposition

The studies, carried out in this paper, demonstrate that qualitative deposits of hard alloys, containing WC and TiC, can be obtained by arc spray process, using a

The increase of the electric arc temperature, due to the increase of the current intensity favors the decomposition of some chemical compounds (TiC, FeB, WC), respectively the appearance of hard chemical compounds of type W2C and of complex carbides of type eta: FeW3C, Fe3W3C and Fe6W6C; the accentuated melting of the additional material and the formation of small particles with low inertia, capable to fix in the surface roughness determine the increase of the adhesion of the deposits of hard alloys and the reduction of the porosity in relatively large limits

The pressure of the compressed air passing through the primary circuit determines the increase of the velocity of the sprayed particles [33], respectively their better fixation in the asperities of the substrate surface. This aspect justifies the adhesion increasing, the average porosity reducing of the coatings (by up to 12%), and the increasing of the microhardness of the coatings - at the increasing of the

The presence, inside the coatings of hard chemical compounds, type WC and W2C - incorporated in the carbide matrix (FeW)xC, as well as compounds TiC, FeCr, and FeB, permits improving the wear behavior of deposits, underlined through the stability of the friction torque, the increasing of the coefficient of

classic spray device equipped with a conical nozzle system.

*DOI: http://dx.doi.org/10.5772/intechopen.94605*

density of 97MXC.

**3. Conclusions**

(up to 28%).

compressed air pressure.

**Conflict of interest**

friction and obtaining a low wear rate.

The authors declare no conflict of interest.

**Figure 19.** *Average porosity variation of 97MXC coatings with the compressed air pressure.*

for the same value of the intensity of the electric current, when the compressed air pressure increases, the average porosity of the deposits decreases by up to 12%. The effect of increasing the temperature of the arc achieved by increasing the electric current determines the reduction of the average porosity by a maximum of 28%. It can be stated that between the two process parameters: compressed air pressure and electric current intensity, the latter has a "dramatic" influence on the deposition density of 97MXC.


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**21**

*Belgium*

**Immunotherapy for Malignant Gliomas:**

Since many decades, medical doctors and researchers have been intrigued by the possible beneficial contribution of the immune system in the long-lasting combat against cancer. Both in the cellular and humoral immunity arms, powerful tools are available to target the cancer cell. Moreover, the gradual shift of a focus on aspecific reinforcement of the innate immune system towards a specifically activated adaptive immunity in order to reject cancer cells has dominated the field of the last 10 to 20 years(1). Restorative immunotherapy in which cytokine balances are restored or reset and aspecific adoptive immunotherapy using e.g. natural killer (NK) cells or lymphokine-activated killer (LAK) cells are classical representations of the first wave. Specific adoptive immunotherapy using ex vivo activated antitumor cytotoxic T cells and especially active specific immunotherapy ('cancer vaccines') are representative for the second wave. Thorough changes in the underlying basic immunology mechanism guide these novel approaches. To date, only the different variants of cancer vaccines are able to induce an immunological memory, as such being the only approach potentially protecting the patients for future cancer re-challenges(2). A perceived low rate of classical objective responses, restricted to volume changes of a measurable tumor burden, has been the principal body of criticism

Several new insights however, especially focusing on changes in the micro-environment of the tumors, are only starting to be unraveled. Without any doubt, they're already now revealing much more than the previous tips of the curtains. Nowadays, converging evidence is being gained in a rapid way, for the need to move towards a third wave of immunotherapy approaches, those of the multimodal integrated immunotherapy paradigms, considering all the relevant players in the complex field of tumor

The idea to actively prime cytotoxic T cells to specifically kill a tumor target cell has become a well established scientific fact. Several approaches all aiming to induce specifically activated, tumor-rejecting effector T cells have been investigated and found to be reproducible and reliable technologies. Genetically engineered tumor cells but especially autologous dendritic cells charged with tumor associated antigens have become the most

**2. Proof of the principle: A solid body of preclinical evidence**

**1. Introduction**

against these therapies.

immunology.

**A Roadmap for the Future**

S. De Vleeschouwer and SW. Van Gool

*Catholic University Leuven*

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*2.6. Durability*

In order to develop new biocomposite insulating materials, it is necessary to ensure the durability conditions to ensure the commercial product can be reached. However, there are only a few papers that study the durability of long-term tests in those materials. The longevity of bio-composites can be impacted by various forms of biological degradation, such as mold growth, as well as environmental factors like fluctuations in temperature and humidity [105].

Investigating the water absorption characteristics of biocomposites is crucial, given the weak water resistance of biomaterial. For biocomposites used outdoors in construction applications, their water absorbency is a critical factor affecting their mechanical properties and dimensional stability [126].

Hemp fibers also present low stability against contact with water, which sees their Young's modulus reduced by 50% after immersion in water [127]. Moreover, using a 100% vegetable material increases the risk of mold growing in high humidity conditions [115]. Mold growth can be relieved by increasing the pH of the material, as is the case with hempcrete, which has anti-fungal properties [61].

In the case of VFRCM (vegetal fabric reinforced cementitious matrix), the issue arises from the alkaline hydrolysis resulting from the production of Ca(OH)2 during cement hydration. The calcium adsorption is pH dependent, and the pectin contained in fibers can react with calcium ions in an alkaline environment [128]. Moreover, a reduction in compressive strength has been observed in hempcrete when using Ca(OH)2 treated hemp stalks compared to untreated ones [129,130]. To incorporate a material that is rich in Al2O3 and SiO2 can mitigate the degradation of the hemp fibers. This material should have the ability to consume Ca(OH)2 during mortar hydration [131]. Alternatively, the fiber can undergo physical or chemical treatment. To extend these findings to vegetable binders, it is crucial to ensure compatibility between the hemp stalk and the vegetal binder to achieve optimal results.

To prevent the degradation of the biomaterials, a solution is to introduce a coating in order to protect the material against environmental effects. To increase the water resistance of these materials, surface coatings such as NaOH, silane, and epoxy have been studied, which reduce the moisture absorption of the fibers [132–135].

In one research work, a vegetal coating is proposed by coating a bamboo particle with pine resin, obtaining a hydrophobic material after treatment; in addition, after the coating, bamboo particles become a stable material against the environment [136]. Nevertheless, the pine resin worsens the fire resistance properties. Arabic gum also presents good results as a coating in cases of humidity and fire, although it cannot be used in direct contact with water since Arabic gum is soluble in water, so when the layer is in direct contact, the protective coating is removed until the material is uncoated [137]. Although these coatings increase the durability of the material, no studies have been found that investigate how the insulating properties behave when these coatings are added.

The coating would not only have the function of protecting the material, but also of stabilizing the interior moisture. Since moisture has a great impact on the insulating properties, as seen in the previous sections.