Abstract
<p class="zhengwen">This paper proposes a hybrid genetic algorithm method for optimizing constrained black box functions utilizing shrinking box and exterior penalty function methods (SBPGA). The constraints of the problem were incorporated in the fitness function of the genetic algorithm through the penalty function. The hybrid method used the proposed Variance-based crossover (VBC) and Arithmetic-based mutation (ABM) operators; moreover, immigration operator was also used. The box constraints constituted a hyperrectangle that kept shrinking adaptively in the light of the revealed information from the genetic algorithm about the optimal solution. The performance of the proposed algorithm was assessed using 11 problems which are used as benchmark problems in constrained optimization literatures. ANOVA along with a success rate performance index were used to analyze the model.</p>Based on the results, we believe that the proposed method is fairly robust and efficient global optimization method for Constrained Optimization Problems whether they are continuous or discrete.
Highlights
Global optimization for Black-box functions, BBF, is still demanding even with the great advances in computational power of the modern computers as it is used in many applications including finite element analysis and computational fluid dynamics
Fitting response surfaces has been used extensively in the literature to carry out MBDO (Camp (1955), Carroll & Fiacco(1961), Picheny, Wagner, Ginsbourger (2012), Pierskalla (1968)., Ramadan, S. & Ramadan, K. (2012), Regis & Shoemaker (2005)) such that the response surfaces were used to visualize the relationship between the values of the variables and the objective function values
The number of chromosomes in the initial population is equal to the population size PopSize which is related to the total generation number TGN as follows: PopSize = γ × TGN, (8)
Summary
Global optimization for Black-box functions, BBF, is still demanding even with the great advances in computational power of the modern computers as it is used in many applications including finite element analysis and computational fluid dynamics. The principle behind penalty-based methods is that any violation in the constraints must make the objective function value infeasible. The exterior penalty function is designed such that a sequence of infeasible points is generated to lead to the optimal solution for the COP (Kramer (2010)) This method utilizes the maximum function to incorporate the constraints into the objective function and makes the resulting UCOP a non smooth problem. A free sampling algorithm and easyhybrid global optimization method is proposed to solve COP using the stochastic genetic algorithm method and the deterministic shrinking box method. A hybrid GA with Variance-based crossover VBC and Arithmetic-based mutation ABM operators along with a fitness function of the form Equation (3) will be used in the context of shrinking box method. This combination of stochastic-deterministic nature of the proposed method is aimed to increase the global and local search capabilities of the proposed method
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