The Research On Differential Evolution Algorithm With Double Populations For Solving Constrained Optimization Problems

With the social progress and the development of science and technology, a lot ofmethods for solving constrained optimization problems (COPs) are presented.Evolutionary Algorithms (EAs) have become the focus of research for solving COPsdue to their competitive performance on complex search spaces. In EAs, thedifferential evolution (DE) is easy to understand and realize, has a few strategyparameters need to be tuned compared with other EAs, especially solving thenonlinear non-differentiable function in continuous space, it shows its robustness,ease of use and a good ability of global optimization.Firstly, this paper introduces the research background and status of the COPs.Then, the description of DE and COPs is given. Afterward, in view of DE severalaspects of work are carried out for solving COPs as follows:The scaling factor and crossover rate in strategy parameters for DE have beenimproved. The algorithm according to the size of difference vector and thedistribution of population fitness value adjusts dynamically the scaling factor andcrossover rate during the evolutionary process. And use this kind of adaptive strategyparameters could balance with global search and local search capability of thealgorithm.In most of the COPs, the fitness value of infeasible solutions around theconstraint boundary may be superior to the fitness value of most feasible solutions infeasible region. In order to use these infeasible solutions effectively, the doublepopulations search mechanism is adopted. On the one hand, it makes the individualsof the population move towards the global optimal solution and speed up theconvergence. On the other hand, it makes some infeasible individuals and feasibleindividuals of the populations exchange their information and increase the populationdiversity. Using the information of the excellent infeasible solution and the bestfeasible solution in double populations, a search space contraction mechanism isproposed. The concept of the confidence region and critical population is given. Byindividuals of critical population which evolve in the confidence region to update theindividuals of double populations is good for searching the global optimal solution.Finally, the proposed algorithm is tested on thirteen benchmark functions. Theobtained results indicate powerful global search ability and the stability.