Study On Evolutionary Algorithms For Constrained Optimization And Multiobjective Optimization Problems

In scientific research and engineering applications, many problems can be formulated to different mathematical programming problems, and the traditional mathematical programming methods cannot solve the complex problems efficiently(especially the non-differentiable problems with many local optimal solutions). Evolutionary algorithms(EAs) are a kind of stochastic search algorithm which stimulates the natural selection and biological evolution in nature. EAs have attracted extensive attention of researchers due to their advantages, such as simple mechanism, easy to perform, intrinsic parallelism, strong robustness and global search ability, etc, and also been successfully used to many mathematical programming problems. In this dissertation, two kinds of complex mathematical programming problems, constrained optimization problems and multiobjective optimization problems are studied and several novel EAs are proposed for both optimization problems. The main contributions of this thesis are as follows:1. A hybrid differential evolution algorithm for constrained optimization problem(COP) is proposed. The COP is firstly converted to a bi-objective optimization problem with preference, which avoids the parameter sensitivity in penalty function methods. Secondly, a novel fitness based on reference point and weighting vector is presented,in which the reference point and the weighting vector are adjusted dynamically to balance the preference to both objective functions. At last, to speed up the convergence of the algorithm, local search based on simplex crossover is designed to search the lower left region of the feasible objective space of the bi-objective problem, where the optimal solution of the constrained optimization problem locates. The proposed hybrid algorithm is executed on standard benchmark functions, and the results show that the proposed algorithm is effective.2. For the biased bi-objective optimization model converted by COP, two evolutionary algorithms are proposed: multiobjective evolutionary algorithm based on ?-domination and biased multiobjective evolutionary algorithm based on generalized ?-properly Pareto optimal solution. In the first algorithm, comparison and selection criterion based on dynamic ?-domination is proposed, in which rational parameter isgiven to satisfy the preference of the bi-objective problem. In the second algorithm, generalized ?-properly Pareto optimal solution is given firstly; and then a biased nondominated sorting strategy is proposed based on the definition, which guarantee that the algorithms using the biased nondominated sorting strategy converge to any region on PF, avoiding the shortcoming of converging only to the middle part of PF in algorithm using ?-properly Pareto optimal solution. Numerical experiments for both algortihms show the efficiency.3. A novel bi-objective optimization model for COP is proposed, which, under proper conditions, is proved to have the unique Pareto optimal vector value. Furthermore, the preimage of the Pareto optimal vector value is shown to exactly be the optimal solution of the COP, which provided that any efficient multiobjective evolutionary algorithm can be applied to novel bi-objective model for COP. Based on the novel model, a simple differential evolution(DE) algorithm is used to solve standard benchmark problem and the results show that the novel model can effectively deal with constrained optimization problems.4. A hybrid DE algorithm is proposed for multiobjective optimization problem. Firstly, to speed up the convergence, the arithematic crossover is exerted on dominated solution to make it approach to the nondominate solutin which dominates it. And then, to maintain the diversity and aviod trapping into local optima, DE is used for nondominated solution to generate offspring. Furthermore, to get nondominated solutions located on every parts of PF, local search based on achievement scalarizing function is designed to make the search focus on sparse region where there is less nondominated solutions. Finally, to obtain a uniformly distributed archive set, the ?-dominance updating strategy is improved to overcome its disadvantage of losing the extreme solutions. Experimental results indicate that the proposed algorithm can converge efficiently to a set of evenly distributed representative solution set of Pareto optimal front for the standard test instances.