Differential Evolution Algorithms For Constrained Optimization

Constrained optimization problems(COPs) are mathematical programming problemsfrequently encountered in practice. Solving COPs has become an important researcharea of evolutionary computation in recent years. Differential evolutionary(DE) hasattracted more and more attention due to its simple principle, less controlled parametersand strong robustness.However it is unconstrained essentially,constraint-handlingtechniques need to be introduced to solve COPs.Therefore,research on the performanceof constrained DE from two basic aspects(i.e.,constraint-handling techniques anddifferential evolutionary algorithms) can contribute to the basic theory research as wellas later application.In this paper,a brief description of the research background and the development ofDE is firstly given,and detailed of the principle,the improvement strategy， theadvantages over other algorithms and application.Then the constraint-handlingtechniques based on evolutionary computation are classifiedly reviewed. Finally twoimproved algorithms combined composite DE(CoDE) with two different techniques areproposed.The first is based on penalty functions,which uses the adaptive penalty function asconstraint-handling technique, introduces distance as fitness function and evaluates thedistance according to the feasible rate, combined with CoDE to reserve the betterindividuals.Thus keeps diversity of the population,also guides the search process eithertoward finding more feasible solutions or favor in search for optimal solutions.Experimental results show that the new method exhibits better adaptivity and strongerglobal optimization ability compared to similar algorithms.The second is based on multiobjective,which converts COPs into multiobjectiveoptimization problems(MOPs) in which two objective are considered:the first is tooptimal the original objective function,and the second is to minimize the degree ofconstraint violation.It attempts to optimal MOPs through multiobjective optimizationtechniques,which consists of two main components:the population evolution model andthe infeasible solution replacement mechanism.The former evolves population withCoDE as the search engine,in which employs Pareto dominance to compare theindividuals to preserve the preferred in the population.The latter is used to improve thequality and feasibility of the individuals, with the purpose of guiding the populationtoward promising solutions and the feasible region simultaneously. Experimental resultsshow that the proposed algorithm has higher accuracy and stronger ability of global optimization.