A parametric segmented multifactorial evolutionary algorithm based on a three-phase analysis

Evolutionary multitasking optimization, which concentrates on solving multiple tasks simultaneously, has been a core area of interest for researchers in recent years. Existing Multifactorial Evolutionary Algorithms (MFEA) are quite dependent on the synergy among the tasks. Consequently, solving multiple tasks is prone to fall into local traps when the optimization enters a certain stage. The objective of this paper is to investigate these problems in more detail and provide corresponding solutions. Specifically, we propose a three-stage analysis method that divides the multitasking optimization problem into three stages and explain the MFEA features according to the individual distribution in each stage, based on which we further develop a Parametric Segmented Multifactorial Evolutionary Algorithm (PS-MFEA) and apply a precise search strategy in the algorithm. Additionally, we propose both a reinitialization mechanism and a backtracking mechanism to avoid local optima. We conduct a comprehensive experiment on two test sets of benchmark problems with different similarity levels and the discrete combinatorial optimization tasks of the traveling salesman problem. The results demonstrate that using PS-MFEA can obtain better performances in both test sets and solve practical problems.