A new optimization algorithm based on a combination of particle swarm optimization, convergence and divergence operators for single-objective and multi-objective problems

Particle swarm optimization (PSO) is a randomized and population-based optimization method that was inspired by the flocking behaviour of birds and human social interactions. In this work, multi-objective PSO is modified in two stages. In the first stage, PSO is combined with convergence and divergence operators. Here, this method is named CDPSO. In the second stage, to produce a set of Pareto optimal solutions which has good convergence, diversity and distribution, two mechanisms are used. In the first mechanism, a new leader selection method is defined, which uses the periodic iteration and the concept of the particle's neighbour number. This method is named periodic multi-objective algorithm. In the second mechanism, an adaptive elimination method is employed to limit the number of non-dominated solutions in the archive, which has influences on computational time, convergence and diversity of solution. Single-objective results show that CDPSO performs very well on the complex test functions in terms of solution accuracy and convergence speed. Furthermore, some benchmark functions are used to evaluate the performance of periodic multi-objective CDPSO. This analysis demonstrates that the proposed algorithm operates better in three metrics through comparison with three well-known elitist multi-objective evolutionary algorithms. Finally, the algorithm is used for Pareto optimal design of a two-degree of freedom vehicle vibration model. The conflicting objective functions are sprung mass acceleration and relative displacement between sprung mass and tyre. The feasibility and efficiency of periodic multi-objective CDPSO are assessed in comparison with multi-objective modified NSGAII.