A Multifactorial Cellular Genetic Algorithm for Multimodal Multitask Optimization

Abstract

In multimodal optimization problems the main goal is to find as many global optima as possible by using a single search process. This type of optimization tasks emerges in many real-world scenarios in assorted fields including medicine, physics, and aerospace, among many others. However, addressing several multimodal optimization problems simultaneously has received little attention from the multitask optimization community to date. Even though solving different multimodal problems at the same time can largely benefit from the existing synergies among the modes of different tasks, this setup has been less studied than other optimization tasks. This work finds its inspiration in the incipient concepts of Evolutionary Multitasking and Multifactorial Optimization to propose a multifactorial Cellular Genetic Algorithm for solving multimodal optimization problems. Our designed algorithm expedites the search for the global optima of different problems at a time by including several algorithmic steps aimed at adapting the search itself as per the synergies found over the exploration of the problems' landscape. An extensive experimentation has been designed using 14 different functions from the CEC‘2013 competition on multimodal optimization benchmark. Besides evaluating the performance of the devised algorithm to retain the global optima of every function in the benchmark, we also conduct an analysis of the transfer of knowledge among such functions. Finally, we compare its performance to that of a winning proposal in this CEC‘2013 competition so as to reflect on the suitability of the multitasking paradigm to solve multimodal optimization tasks.