Multi-objective optimization is one of the main problems in engineering practice and scientific research,its main characteristic is that each object may be mutually restricted,so the result is often a group of solutions that non-dominance.One solution is better for a certain object,but it is worse for other objects.The set of all these non-dominance solutions is called the Pareto optimal solution set.The traditional method of solving multi-objective optimization is simple and efficient,but it also has many defects,especially the high-dimensional multi-objective optimization problems(the problem with more than three objects).Therefore,how to design an efficient optimization algorithm has become one of the research topics of scholars.Particle swarm optimization(PSO)algorithm is a new evolutionary algorithm developed in recent years.Because of its clear principle,simple structure,and easy implementation,it has received extensive attention since its proposal and has been widely used for objective optimization,neural networks,pattern recognition and other fields.Our works mainly focus on the application of particle swarm optimization for multi-objective.The main research work and achievements are as follows: Firstly,this paper introduces the research background and significance,the mathematical models and related concepts of multi-objective optimization problems,and the research status of multi-objective optimization algorithms.Secondly,introduced the particle swarm algorithm principle and mathematical model,the research status of the multi-objective particle swarm optimization algorithm.Then,compared with classical multi-objective evolutionary algorithms,we propoesd a multi-objective particle swarm optimization based on multi-strategies(M-MOPSO)algorithm for solving low-dimensional multi-objective optimization problems.Many scholars have proposed a corresponding algorithm for deal with high-dimensional multi-objective optimization problems verification of its effectiveness,we also proposed a multi-objective particle swarm optimization algorithm based on indicator and direction vectors(IDMOPSO)for many-objective problems and verify its validity.For M-MOPSO algorithm,the integrated strategies are:(a)individual replacement strategy based on Pareto dominance;(b)the speed update method based on two strategies to balance local and global search capability;(c)hybrid gaussian mutation strategy avoidance algorithm fall into a local optimum;(d)The non-dominance solution generated during the process of evolutionary management based on index-based archival update.For IDMOPSO algorithm,we have made significant improvements to the standard MOPSO.The improved key operators are:(a)processing of particles jumping out of the search space;(b)personal-best particle selection is improved;(c)improvements are made in the selection of grobal-best particle;(d)improvements are made in the updating and maintenance of external archive.The experiment compares the IDMOPSO algorithm with classical evolutionary algorithms for solving high-dimensional multi-objective optimization problems.The experimental data is verified to verify the effectiveness of the IDMOPSO algorithm in dealing with many-objective problems.Finally,summarize the whole paper,describe the main research work done in this paper,and points out the deficiencies of our work,and last give a brief description of the future research direction. |