Two Multi-objective Optimization Algorithms Based On Decomposition

Multi-objective optimizations widely occur in various fields,such as science and technology,production scheduling,engineering practice and so on.Because of the conflict of objectives,their results must be a set of trade-off solutions.With the development of technology,practical problems are more complex.Then it's difficult for traditional algorithms to solve them.Due to the easy principle,strong robustness and fast convergence of intelligence algorithms,they have been viewed as one hot field in multi-objective researches.In particular,as one of the most typical algorithms for multi-objective problems,multi-objective evolutionary algorithm based on decomposition(MOEA/D)has made great progress in maintaining the diversity of solutions,yet there are still some weakness such as slow convergence,poor distribution and so on.Recently,an update strategy based on objective spacial decomposition is proposed in the algorithm of multi-objective particle swarm optimization based on decomposition(MPSO/D),and provides a new idea for multi-objective optimization.However,there are still several drawbacks for the problems with complex Pareto front,such as the incomplete and non-uniform distribution of solutions and so on.To overcome these shortcomings,two improved multi-objective decomposition algorithms are proposed by integrating special decomposition and Pareto domination in this thesis.1.An improved adaptive multi-objective particle swarm optimization algorithm based on decomposition is proposed by considering the influence of parent solutions selection and population updating on the convergence of algorithm and distribution of solutions.First,to improve the convergence of algorithm,a new fitness evaluation method based on competition is designed to update parents' fitness and current population under the premise of ensuring diversity of population by decomposition strategy.Next,to avoid falling into local optimum,the personal optimum and global optimum are randomly selected from their neighbors or others to update particles with probability.Finally,to enhance the ability of algorithm to deal with complex problems,an external document is introduced to store historical elite solutions and acted as a candidate output population.2.Based on objective spacial decomposition,an adaptive decomposition multi-objective differential evolution algorithm with feedback is proposed by considering the influence of mutation operator and parameter setting on the performance of differential evolution.First,to efficiently exploit the sparse regions and promote the search performance of algorithm,a hybrid mutation operator with elite feedback is designed.In this operator,the neighborhood information of sparse individuals is used to improve exploitation at the early search stage,while the feedback information of elite individuals is employed to enhance exploration at the later search stage.Next,to improve the balance between convergence and distribution of solutions,two adaptive adjustment strategies are designed for parameters F and CR respectively,and a random perturbation is extra executed for CR.Finally,optimal solution set is output by comparing evolutionary population with external archive based on IGD.The numerical results show that proposed algorithms have more advantages in term of convergence of solution set and distribution uniformity.