Multiobjective Multitask Optimization With Multiple Knowledge Types and Transfer Adaptation

Evolutionary multitasking (EMT) exploits the correlation among different tasks to help handle them through knowledge transfer (KT) techniques in evolutionary algorithms. In this area, multiobjective multitask optimization (MO-MTO) utilizes EMT to solve multiple multiobjective optimization tasks simultaneously. The key to addressing MO-MTO problems (MO-MTOPs) is to transfer appropriate knowledge among optimization tasks to assist the multiobjective evolutionary process. Both the type and the amount of knowledge can significantly affect the KT process. To achieve better KT behavior, we propose a multiple knowledge types and transfer adaptation (MKTA) framework for handling MO-MTOPs. The MKTA framework incorporates multiple types of knowledge in order to obtain comprehensive KT performance. It also provides transfer adaptation strategies to control: 1) the type of knowledge and 2) the amount of knowledge for KT via parameter adaptation approaches, thereby mitigating negative KT. Furthermore, we propose an evolution-path-model-based knowledge type and incorporate the existing unified-search-space-based knowledge type to form the knowledge pool for MKTA. Finally, the MKTA framework is coupled with a ranking-based differential evolution operator to constitute the complete algorithm MTDE-MKTA. In the experimental study, MTDE-MKTA outperformed ten advanced algorithms on 39 benchmark MO-MTOPs and six groups of realworld application problems.

I. Introduction

Multiobjective optimization problems (MOPs), are widespread in the production and life of the real world [1], [2]. An MOP usually contains two or more conflicting objective functions and the goal is to obtain a set of Pareto optimal solutions for decision making [3]. Evolutionary algorithms (EAs) have achieved remarkable success in solving MOPs due to the nature of population evolution. EAs that handle MOPs are called multiobjective EAs (MOEAs). Multiobjective methods in MOEAs usually use three methods: 1) nondominated sorting [3], [4]; 2) decomposition [5]; and 3) indicator [6] methods. The evolutionary operator for generating offspring is also an important part of MOEAs. The evolutionary operators are most often genetic algorithm (GA) [3], differential evolution (DE) [7], particle swarm optimization (PSO) [8], and evolutionary strategy (ES) [9].