Adaptive Constraint Handling Techniques And Their Application For Evolutionary Optimization

The practical science and engineering optimization problems such as the design of pressure vessels are often restricted by physical constraints or functional requirements.Evolutionary algorithm,as a population-based optimization method,has the advantages of strong robustness and high search efficiency.But the evolutionary algorithm is a kind of unconstrained search technology,so it is the key to solve the constrained optimization problems by using evolutionary algorithm to design effective constraint handling method.The traditional penalty function method and the promising stochastic ranking method are two main methods to deal with the constrained optimization.But the penalty function method and the stochastic ranking method exist the problem that the penalty factor and the penalty probability are difficult to set,and they all have the risk of under-punishment or over-punishment.In this paper,the dynamic probability and annealing ideas are introduced respectively based on the analysis of the shortcomings of the classical stochastic ranking method,and two adaptive constraint methods are proposed which are dynamic stochastic ranking and annealing stochastic ranking.On the other hand,on the basis of deeply revealing the theoretical relationship between the penalty function method and decomposition-based aggregate function in the bi-objective optimization,bi-objective decomposition-based constraint handling method is proposed to avoid the difficulty of setting up the penalty factor.The main research work of this paper is summarized as follows:1.A dynamic stochastic ranking constraint handling method is proposed by introducing the dynamic punishment probability,which makes the penalty probability adaptively adjusted according to the evolutionary process and reduces the risk that the fixed probability may cause the population to converge to an infeasible region.2.An annealing stochastic ranking constraint handling method is proposed by referring to the Metropolis acceptance criterion in the process of annealing.It comprehensively considers the factors such as the difference of degree of constraint violation between individuals and the evolution process of the population when the degree of constraint violation is chosen as the basis of comparison,so that the individual who has a larger degree of constraint violation can have a chance to be reserved in an adaptive probability,thus improving the diversity of population in the evolutionary process and the global search ability of population.3.The bi-objective decomposition-based constraint handling method is proposed on the basis of deeply revealing the theoretical relationship between the penalty function method and decomposition-based aggregate function in the bi-objective optimization.This method divides the bi-objective space conically by using the conical area evolutionary algorithm and adopts double population structure to search several conical sub-regions in parallel according to the conical area.It avoids the difficulty of setting up the penalty factor and makes full use of the effective information of Pareto front to guide the population to the global optimal solution.4.In this paper,dynamic stochastic ranking method,annealing stochastic ranking method and bi-objective decomposition-based method are used to compare the experiment and performance evaluation of 13 constrained optimization benchmarks and pressure vessel design and Himmelblau non-linear programming.Experimental results on standard benchmarks and two engineering problems show that three proposed methods of this paper have higher solution quality than the stochastic ranking method,and the constraint handling performance of bi-objective decomposition-based method is best of the three methods.