Multiple Tasks for Multiple Objectives: A New Multiobjective Optimization Method via Multitask Optimization

Handling conflicting objectives and finding multiple Pareto optimal solutions are two challenging issues in solving multiobjective optimization problems (MOPs). Inspired by the efficiency of multitask optimization (MTO) in finding multiple optimal solutions of multitask optimization problem (MTOP), we propose to treat MOP as a MTOP and solve it by using MTO. By transforming the MOP into a MTOP, not only that the difficulty in handling conflicting objectives can be avoided, but also that MTO can help efficiently find well-distributed multiple optimal solutions for MOP. With the above idea, this paper proposes a new multiobjective optimization method via MTO, with the following three contributions. Firstly, a theorem is proposed to theoretically show the relationship between MOP and MTOP and how MOP can be transformed into a MTOP. Secondly, based on the theoretical analysis, a multiple tasks for multiple objectives (MTMO) framework is proposed for solving MOP efficiently. Thirdly, a MTMO-based evolutionary algorithm is developed to solve MOP, together with two novel strategies. One is a target point estimation strategy for transforming the MOP into a MTOP automatically and accurately. The other is an archive-based implicit knowledge transfer strategy for efficiently transferring knowledge across multiple tasks to enhance the optimization results of multiple tasks together. The superiority of the proposed algorithm is validated in extensive experiments on 15 MOPs with objective numbers varying from 3 to 20 and with six state-of-the-art algorithms as competitors. Therefore, solving MOP and even many-objective optimization problem via MTO is a new, promising, and efficient method.