Evolutionary Sequential Transfer Optimization for Objective-Heterogeneous Problems

Evolutionary sequential transfer optimization is a paradigm that leverages search experience from solved source optimization tasks to accelerate the evolutionary search of a target task. Even though many algorithms have been developed, they mainly focus on objective-homogeneous problems, where the source and target tasks possess a similar number of objectives. In this work, we explore objective-heterogeneous problems, in which knowledge transfers across single-objective optimization problems (SOPs), multi-objective optimization problems (MOPs), and many-objective optimization problems (MaOPs). Objective-heterogeneous problems challenge the existing methods due to the diverse search and objective spaces between the source and the target task. To address this issue, we present a decision variable analysis-based transfer method that can conduct knowledge transfer across problems with the different numbers of objectives. We first separate decision variables of MOPs and MaOPs into convergence-related variables (CVs) and diversity-related variables (DVs), according to their roles while treating variables of SOPs as CVs. Then, we propose a convergence transfer module to transfer knowledge of CVs to speed up the convergence. It aligns both solutions and fitness ranks for preserving fitness rank consistency between the source and target tasks, whereby accelerating search speed. Besides, a diversity transfer module is presented to refine the distribution of DVs to maintain the population diversity. Experimental results on objective-heterogeneous test problems and a real-world case study have demonstrated the effectiveness of the proposed algorithm.