A New and More Challenging Compositive Multi-Task Optimization Problem Test Suite

Evolutionary multi-task optimization (EMTO) is a recently emerging topic in the research area of evolutionary computation, aiming at solving multiple different optimization tasks simultaneously. Recently, with the development of EMTO, many multi-task optimization problem (MTOP) benchmark test suites have been proposed. However, these MTOP test suites are not sufficiently challenging. That is, the tasks in these MTOPs always have the same dimensionality and the aligned dimensions of the tasks can have related physical meanings or similar optimal values. To address these disadvantages of existing MTOP test suites, we propose a new and more challenging compositive MTOP (cMTOP) test suite. There are ten cMTOP instances in this test suite and each instance contains two tasks. These cMTOP instances are more challenging with three properties. First, the tasks in each cMTOP have different numbers of dimensions. Second, to make the aligned dimensions of two tasks have irrelated physical meanings, each task is a composition function composed of several basic functions. Third, each task in cMTOP is shifted and rotated to make the aligned dimensions of the two tasks have different optimal values. Based on these properties, the proposed cMTOP test suite is more challenging and can better evaluate the performance of EMTO algorithms. Finally, we analyze the performance of several state-of-the-art EMTO algorithms on this new and challenging cMTOP test suite.