EMT-ReMO: Evolutionary Multitasking for High-Dimensional Multi-Objective Optimization via Random Embedding

Abstract

Since multi-objective optimization (MOO) involves multiple conflicting objectives, the high dimensionality of the solution space has a much more severe impact on multi-objective problems than single-objective optimization. Taking the advantage of random embedding, some related works have been proposed to scale derivative-free MOO methods to high-dimensional functions. However, with the premise of "low effective dimensionality", a single randomly embedded subspace cannot guarantee the effectiveness of obtained solutions. Taking this cue, we propose an evolutionary multitasking paradigm for multi-objective optimization via random embedding (EMT-ReMO) to enhance the efficiency and effectiveness of current embedding-based methods in solving high-dimensional optimization problems with low effective dimensions. In EMT-ReMO, the target problem is firstly embedded into multiple low-dimensional subspaces by using different random embeddings, aiming to build up a multi-task environment for identifying the underlying effective subspace. Then the implicit multi-objective evolutionary multitasking is performed with seamless knowledge transfer to enhance the optimization process. Experimental results obtained on six high-dimensional MOO functions with or without low effective dimensions have confirmed the effectiveness as well as the efficiency of the proposed EMT-ReMO.