Overview of multiobjective particle swarm optimization algorithm

In the real world, the development model of optimization problems tends to be diversified and large scale. Therefore, optimization technologies are facing severe challenges in terms of nonlinearity, multi-dimensionality, intelligence, and dynamic programming. Multiobjective optimization problems have multiple conflicting objective functions, so the unique optimal solution is impossible to obtain when optimizing, and multiple objective values must be considered to obtain a compromise optimal solution set. When traditional optimization methods treat complex multiobjective problems, such as those with nonlinearity and high dimensionality, good optimization results are difficult to ensure or even infeasible. The evolutionary algorithm is a method that simulates the natural evolution process and is optimized via group search technology. It has the characteristics of strong robustness and high search efficiency. Inspired by the foraging behavior of bird flocks in nature, the particle swarm optimization algorithm has a simple implementation, fast convergence, and unique updating mechanism. With its outstanding performance in the single-objective optimization process, particle swarm optimization has been successfully extended to multiobjective optimization, and many breakthrough research achievements have been made in combinatorial optimization and numerical optimization. Consequently, the multiobjective particle swarm algorithm has far-reaching research value in theoretical research and engineering practice. As a meta-heuristic optimization algorithm, particle swarm optimization is widely used to solve multiobjective optimization problems. This paper summarized the advanced strategies of the multiobjective particle swarm optimization algorithm. First, the basic theories of multiobjective optimization and particle swarm optimization were reviewed. Second, the difficult problems involving multiobjective optimization were analyzed. Third, the achievements in recent years were summarized from five aspects: optimal particle selection strategies, diversity maintenance mechanisms, convergence improvement measures, coordination methods between diversity and convergence, and improvement schemes of iterative formulas, parametric and topological structure. Finally, the problems to be solved and the future research direction of the multiobjective particle swarm optimization algorithm were presented.