Multiobjective Sequential Transfer Optimization: Benchmark Problems and Preliminary Results

In cases of frequent problem-solving of multiobjective optimization tasks from a domain due to changing conditions or problem features, a growing number of individual tasks will be solved and stored in a database, providing an opportunity for a target task at hand to achieve better optimization performance through knowledge transfer from the previously-solved tasks, which is also known as sequential transfer optimization. Despite a variety of transfer algorithms that have been developed over the years, the research on the design of benchmark problems for evaluating such algorithms received far less attention. Oftentimes, the source and target tasks in existing test problems are manually assembled or extended from specific practical problems, limiting their ability to represent the diverse yet complex source-target similarity relationships in real-world problems. In light of this, we propose design methods to generate multiobjective sequential transfer optimization problems (MSTOPs) systematically in this work, wherein the Pareto manifolds of individual tasks and the manifold-based similarity between the tasks can be customized with ease, enabling a broad spectrum of representation of the diverse similarity relationships between the source-target Pareto manifolds of MSTOPs. Lastly, a benchmark suite with 12 test problems is developed using the proposed methods, which would serve as an arena for electing superior multiobjective sequential transfer optimization algorithms. The source code is available at https://github.com/XmingHsueh/MSTOP.