Evolutionary multitasking in combinatorial search spaces: A case study in capacitated vehicle routing problem

Multifactorial optimization (MFO) is a new paradigm proposed recently for evolutionary multi-tasking. In contrast to traditional evolutionary optimization approaches, which focus on solving only a single optimization problem at a time, MFO was proposed to solve multiple optimization problems simultaneously. It is contended that the concept of evolutionary multi-tasking provides the scope for implicit knowledge transfer of useful traits across different but related problem domains, thereby enhancing the evolutionary search for problem-solving. With the aim of evolutionary multi-tasking, multifactorial evolutionary algorithm (MFEA) was proposed in [1], and demonstrated efficient multi-tasking performances on several problem domains, including continuous, discrete, and the mixtures of continuous and combinatorial tasks. To solve different problems, the design of unified solution representations and effective problem specific decoding operators are required in MFEA. In particular, the random-key unified representation and the sorting based decoding operator were presented in MFEA for multi-tasking in the context of vehicle routing problem. However, problems such as ineffective solution representation and decoding are existed in this unified representation, which would deteriorate the multi-tasking performance of MFEA. Taking this cue, in this paper, we propose an improved MFEA (P-MFEA) with a permutation based unified representation and a split based decoding operator. To evaluate the efficacy of the proposed P-MFEA, comparison against the traditional single task evolutionary search paradigm on 12 multi-tasking capacitated vehicle routing problems is presented and discussed.