Research On Constrained Multi-Objective Optimization Algorithm Based On Evolutionary Computation

In practice,many engineering optimization problems are required to optimize multiple objective functions at the same time under certain constraints.These problems are collectively called the constrained multi-objective optimization problems.When the constraints of an optimization problem are only caused by the range of independent variables,it is also called the multi-objective optimization problem with box constraints.Among the many methods to deal with constrained multi-objective optimization problems,the algorithm based on evolutionary computation has become a research hotspot because of its simplicity and efficiency.Over the past few decades,many evolutionary algorithms have been proposed to solve different types of constrained multi-objective optimization problems.However,these algorithms still face many challenges when solving the complex ones,such as many-objective optimization problems,the problems with irregular Pareto fronts or complex constraints,and so on.In order to deal with these situations,a variety of novel constrained multi-objective optimization algorithms are proposed in this thesis.The main contributions of this thesis are as follows:1)In order to improve the performance of domination-based evolutionary algorithm in solving many-objective optimization problems,this thesis prpopses a simplex-dominance relationship with large convergence pressure.In the new simplex-dominance,any individual in the objective space correspones to a unique simplex,and the smaller the corresponding simplex,the better the convergence of the individual is considered.If there is a simplex of one contained in the simplex of another,it is said that the former simplex-dominates the latter.Compared with the traditional Pareto domination,the proposed simplex domination has greater convergence pressure.The experimental results show that the algorithm based on simplex domination converges faster than the reference-point-based evolutionary algorithm using nondominated sorting approach(denoted as NSGA-III)in dealing with many-objective optimization problems with box constraints.2)This thesis defines two indicators based on ratio and difference under the Minkovsky distance,and theoretically demonstrates that a ratio based indicator with infinite norm is the best to evaluate individual's quality.Accordingly,this thesis proposes a promising region based evolutionary algorithm(PREA)to deal with various types of box-constrained multi-objective optimization problems.In the proposed PREA,the ratio based indicator with infinite norm is first used to evaluate the fitness value of each individual,and those with the best fitness values are used to define the promising region in the objective space.Then,this thesis limits the valuable candidate solutions to those individuals located in the promising region,and others outside the promising region are excluded as poor convergence.To ensure the diversity of population,this thesis introduces a diversity maintenance mechanism based on parallel distance.In this mechanism,individuals in the objective space are vertically mapped to a unit plane,and the vertical feet between individuals are defined as their parallel distances.When the size of the candidate solution set is larger than the preset population size,the ones with the worst fitness value among the two individuals with the smallest parallel distance will be eliminated.The experimental results show that the proposed PREA performs well in solving the box-constrained multi-objective optimization problem with irregular Pareto fronts.Compared with the existing state-of-the-art algorithms,PREA has better robustness in dealing with box-constrained multi-objective optimization problems with different Pareto fronts.3)This thesis proposes a technique using multiple single criteria(TMSC)to identify valuable infeasible solutions,which can help feasible solutions to solve multi-objective optimization problems with complex constraints.In the proposed TMSC,a variety of criteria are simultaneously used to evaluate the potential value of each infeasible solution in different aspects.Those infeasible solutions that satisfy any criterion are regarded as valuable,and then are preserved and mixed with feasible solutions to solve the optimized problems.This TMSC can be easily embedded in existing evolutionary algorithms.This thesis embeds it into the self-designed algorithm PREA and record it as TMSC-EA.Numerical experiments show that TMSC-EA performs well in dealing with various constrained multi-objective optimization problems and is more robust than other existing algorithms.And TMSC-EA is the only algorithm that can deal with the problems in which the initial population is generated in the complex infeasible regions below the Pareto front.4)To prevent the population from getting stuck in local areas and losing some Pareto front fragments when solving the multi-objective optimization problems with complex constraints,it is important to guide population to evenly explore the promising areas which are not dominated by feasible solutions.To achieve this end,this thesis first introduces a cost value based distance to measure the crowding degree of each individual,and then proposes a novel constraint handling indicator to evaluate individual's quality.Theoretical studies show that the proposed indicator prefers the individuals in the promising areas.It tends to delete the one with the larger constraint violation of the two most crowded individuals in the process of reducing the population size in the promising areas.Accordingly,this thesis embeds the constraint handling indicator in the evolutionary algorithm and design an indicator based constrained multi-objective algorithm for constrained multi-objective optimization problems.Numerical experiments on several benchmark suites and real-world engineering problem show the effectiveness of the proposed algorithm.Compared with the existing six state-of-the-art constrained evolutionary multi-objective optimization algorithms,the proposed algorithm performs better in dealing with different types of constrained multi-objective optimization problems.