Intelligent Algorithm For Solving Constrained Optimization Problems

The actual production of the majority of numerical optimization problems are constrained, and with thedevelopment of society, constrained optimization problems become more complex, showing a strongnonlinearity, strong constraints, multivariable and complex objective functions not differentiablecharacteristics. It is difficult to get its global optimal feasible solution. The primary task of solvingconstrained optimization problems are bound to find a suitable method of treatment, and then design anefficient algorithm. This paper focuses on solving constrained optimization problems have been studied,we propose two new constraint problem solving methods. The main work of this thesis is as follows:(1) An solving methods for constrained optimization problem based on adaptive pealty function andimproved bats algorithm is designed. An adaptive penalty function method is proposed, which both takesthe circumstances of constraint violations and characteristics of evolutionary process intoconsideration.The more frequently a constraint is violated, the more poverful it is, the larger penaltycoefficient is given to it. The more infeasible solutions in the population, the smaller the constrain shouldbe, in other words, the smaller the penalty coefficient should be, in order to keep the diversity of thepopulation. An improved bats algorithm is proposed, which generates the initial population by using theergodicity of chaos, and enhances the quality of the initial population and diversity of population. In thelocal search of bats algorithm which takes the pulse loudness into consideration, crossover operation isadded. In order to prevent the algorithm from falling into local optimal solution in the late, variationoperation is added, which ensures the diversity of the population. Then adaptive penalty function andimproved bats algorithm are mixed to solve constrained optimization problem, and4complex standard testfunctions and2practical engineering problems prove the feasibility and effectiveness of the solvingmethods for constrained optimization problem.(2) Using multi-objective method to deal with constraint conditions, an improved multi-objective geneticalgorithm is proposed to solve constrained optimization problems. The constrained optimization problem isconverted into a multi-objective optimization problem. In the evolution process, our algorithm is based onmulti-objective technique, where the population is divided into dominated and non-dominatedsubpopulation. Arithmetic crossover operator is utilized for the randomly selected individuals fromdominated and non-dominated subpopulation, respectively. The crossover operator can lead gradually theindividuals to the extreme point and improve the local searching ability. Diversity mutation operator isintroduced for non-dominated subpopulation. Through testing the performance of the proposed algorithm on8benchmark functions and3engineering optimization problems, and comparing with othermeta-heuristics, the result of simulation shows that the proposed algorithm has great ability of globalsearch.