Dynamic multiobjective optimization problems: test cases, approximations, and applications

After demonstrating adequately the usefulness of evolutionary multiobjective optimization (EMO) algorithms in finding multiple Pareto-optimal solutions for static multiobjective optimization problems, there is now a growing need for solving dynamic multiobjective optimization problems in a similar manner. In this paper, we focus on addressing this issue by developing a number of test problems and by suggesting a baseline algorithm. Since in a dynamic multiobjective optimization problem, the resulting Pareto-optimal set is expected to change with time (or, iteration of the optimization process), a suite of five test problems offering different patterns of such changes and different difficulties in tracking the dynamic Pareto-optimal front by a multiobjective optimization algorithm is presented. Moreover, a simple example of a dynamic multiobjective optimization problem arising from a dynamic control loop is presented. An extension to a previously proposed direction-based search method is proposed for solving such problems and tested on the proposed test problems. The test problems introduced in this paper should encourage researchers interested in multiobjective optimization and dynamic optimization problems to develop more efficient algorithms in the near future.