Study On Evolutionary Algorithms For Constrained Multi-objective Optimization Problems

There are many real-world optimization problems involving multiple objectives and constraints.For instance,the product design problem aims to minimize the cost and maximize the quality of products subjecting to due time.Over the last two decades,evolutionary algorithms have been widely employed to solve constrained multi-objective optimization problems and gained a lot of outstanding research findings,and become the most popular methods,where differential evolution(DE)algorithm is one of the most representative evolutionary algorithms.However,with the increasing number of objectives and the more complex constraints,the existing constrained multi-objective evolutionary algorithms have some defects such as poor diversity,slow convergence and a serious waste of computing resources.Therefore,it is urgent to design efficient and practical constrained multi-objective evolutionary algorithms to solve complex constrained multi-objective optimization problems.Balancing objective optimization and constraint satisfaction is crucial for solving constrained multi-objective optimization problems.For constrained multi-objective evolutionary algorithms,it is necessary to maintain the diversity,feasibility and convergence of the population for striking the balance.Aiming at dynamically balancing constraints and objectives in the process of population evolution,this thesis proposes several improved constrained multi-objective evolutionary algorithms and the main work are summarized as follows:1.A constrained multi-objective evolutionary algorithm based on the correlation between objectives and constraints is developed.The proposed method mainly contains two stages:the learning stage and the evolving stage.In the learning stage,the correlation between each objective and all constraints is obtained through DE.In the evolving stage,the original constrained multi-objective optimization problem is first decomposed into a set of single-objective constrained subproblems,which is optimized through the DE cooperative framework.Each subpopulation performed the specific constrained DE to optimize the assigned subproblem,whose fitness function is constructed by the obtained correlation.For the archive population,an update mechanism is designed to solve the original constrained multi-objective optimization problem.Experimental studies on two benchmark suites demonstrate the superiority of the proposed algorithm over 5 state-of-the-art algorithms.2.An adaptive two-stage constrained multi-objective evolutionary algorithm is presented.In the process of population evolution,the proposed algorithm adaptively switches the two stages by different fitness evaluation strategies to dynamically strike the balance between constraints and objectives,especially for solving complex constrained Pareto front(CPF)problems.One stage focuses on objective optimization,namely ensuring the diversity of the population,and forces to the population quickly cross the infeasible region into the feasible region;the other stage emphasizes the constraints’ satisfaction,namely maintaining the feasibility of the population,and drives the population to converge to the real CPF as soon as possible.A mutation operator of DE is also designed to guide the population evolution.Experimental results on a set of benchmark problems demonstrate that the proposed algorithm achieves higher convergence accuracy for solving complex problems than the other 4 competitive algorithms;Meanwhile,the algorithm is also employed for several benchmark problems in the other two suites,and the experimental results show that the algorithm achieves good generality.3.A constrained many-objective evolutionary algorithm based on hybrid selection strategy is proposed.The novel correlation between objectives and constraints is firstly defined.Additionally,a hybrid selection strategy using the correlation is designed to guide the population to approach the CPF.It is verified on the benchmark problems and applied to the real-world problem,urban water supplement distribution network optimization.The experimental results on both test problems and the real-world problem show the superiority of the proposed algorithm over 4 state-of-the-art algorithms.