With the advent of paralleling and implementation of restructuring in the power market, some routine rules and patterns of traditional market should be accomplished in a way different from the past. To this end, the unit commitment (UC) scheduling that has once been aimed at minimizing operating costs in an integrated power market, is metamorphosed to profit based unit commitment (PBUC) by adopting a new schema, in which generation companies (GENCOs) have a common tendency to maximize their own profit. In this paper, a novel optimization technique called imperialist competitive algorithm (ICA) as well as an improved version of this evolutionary algorithm are employed for solving the PBUC problem. Moreover, traditional binary approach of coding of initial solutions is replaced with an improved integer based coding method in order to reduce computational complexity and subsequently ameliorate convergence procedure of the proposed method. Then, a sub-ICA algorithm is proposed to obtain optimal generation power of thermal units. Simulation results validate effectiveness and applicability of the proposed method on two scenarios: (a) a set of unimodal and multimodal standard benchmark functions, (b) two GENCOs consist of 10 and 100 generating units. fuel consumption coefficient of unit (i) fuel consumption coefficient of unit (i) fuel consumption coefficient of unit (i) cost of imperialist (n) cost of country (n) cost function of unit i ($); for units with ON status, (C i (P (i,t))= a i + b i *P (i,t) + c i *P (i,t) 2 normalized cost of nth imperialist cold start-up cost of unit i ($/h) cooling constant of unit i (h) ramp down rate of unit i (MW/h) cost of best obtained solution at last iteration of algorithm hot start-up cost of unit i ($/h) initial state of unit i (h) commitment state of unit i at time t number of decades of main/sub algorithm total number of generating units number of colonies number of imperialists initial number of colonies of empire n a chaotic vector produced by a chose map total system demand at time t (MW/h) positions of a colony at the current decade positions of an imperialist at the current decade positions of a colony at the next decade maximum active generation of unit i (MW/h) maximum response rate limited active power output of unit i at time t minimum active generation of unit i (MW/h) maximum response rate limited active power output of unit i at time t generation of unit i at time t (MW/h) a randomly generated number within [0,1] total revenue ($) start-up cost of unit i at time t ($) stopping criterion of the algorithm, when it converges into 10−6 tolerance dispatch period (h) total cost of generation ($) total cost of imperialist empire n minimum OFF time of unit i (h) minimum ON time of unit i (h) ramp up rate of unit i (MW/h) a vector that is directed toward the imperialist locations and starts from the previous location of the colony |{v 1}|=1 a vector perpendicular to vector V 1 time duration for which unit i has been OFF at time t (h) time duration for which unit i has been ON at time t (h) colonies’ corporation factor in imperialist’ power a chaotic number between zero and one generated by a specific mapping method assimilation weight factor deviation limit from the original direction prosperity value of empire i forecasted market price for energy at time t ($/MWh) probability of imperialist i 
An ICA based approach for solving profit based unit commitment problem market