Learning Task Relationships in Evolutionary Multitasking for Multiobjective Continuous Optimization

Multiobjective multifactorial optimization (MO-MFO), rooted in a multitasking environment, is an emerging paradigm wherein multiple distinct multiobjective optimization problems are solved together. This article proposes an evolutionary multitasking algorithm with learning task relationships (LTR) for MO-MFO. In the proposed algorithm, a procedure of LTR is well designed. The decision space of each task is treated as a manifold, and all decision spaces of different tasks are jointly modeled as a joint manifold. Then, through solving a generalized eigenvalue decomposition problem, the joint manifold is projected to a latent space while keeping the necessary features for all tasks and the topology of each manifold. Finally, the task relationships are represented as the joint mapping matrix, which is composed of multiple mapping functions, and they are utilized for information transfer across different decision spaces during the evolutionary process. In the empirical experiments, the performance of the proposed algorithm is verified and compared with several state-of-the-art solvers for MO-MFO on three suites of MO-MFO test problems. Empirical results demonstrate that the proposed algorithm surpasses other competitors on most test instances, and can well tackle complicated MO-MFO problems which involve distinct optimization tasks with heterogeneous decision spaces.

Automated summary

In this article, an evolutionary multitasking algorithm with learning task relationships is proposed for multiobjective multifactorial optimization (MO-MFO). The algorithm models the decision spaces of different tasks as a joint manifold and utilizes a joint mapping matrix to transfer information across different decision spaces. Experimental results demonstrate its superior performance compared to other state-of-the-art solvers in tackling complex MO-MFO problems involving heterogeneous decision spaces.