Improve Theoretical Upper Bound of Jumpk Function by Evolutionary Multitasking

Abstract

Recently, the concept of evolutionary multitasking has emerged in the field of evolutionary computation as a promising approach to exploit the latent synergies among distinct optimization problems automatically. Many experimental studies have shown multifactorial evolutionary algorithm (MFEA), an implemented algorithm of evolutionary multitasking, can outperform the traditional optimization approaches of solving each task independently on handling synthetic and real-world multi-task optimization (MTO) problems in terms of solution quality and computation resource. However, as far as we know, there exists no study demonstrating the superiority of evolutionary multitasking from the aspect of theoretical analysis. In this paper, we propose a simple (4+2) MFEA to optimize the benchmarks Jumpk and LeadingOnes functions simultaneously. Our theoretical analysis shows that the upper bound of expected running time for the proposed algorithm on the Jumpk function can be improved to O(n2 + 2k) while the best upper bound for single-task optimization on this problem is O(nk-1). Moreover, the upper bound of expected running time to optimize LeadingOnes function is not increased. This result indicates that evolutionary multitasking is probably a promising approach to deal with some problems which traditional optimization methods can't well tackle. This paper provides an evidence of the effectiveness of the evolutionary multitasking from the aspect of theoretical analysis.