Dynamic Distance Minimization Problems for dynamic multi-objective optimization

In this article we propose a new dynamic multi-objective optimization problem. This dynamic Distance Minimization Problem (dDMP) functions as a benchmark problem for dynamic multi-objective optimization and is based on the static versions from the literature. The dDMP introduces a useful property and challenge for dynamic multi-objective algorithms. Not only the positions of the Pareto-optimal solutions in the search space change over time, but also the complexity of the problem can be adjusted dynamically. In addition the problem is based on a simple geometric structure, which makes it useful to visualize the search behaviour of algorithms. We describe the basic principles of the problem, and introduce the possible dynamic changes and their implementation and effects of the Pareto-optimal areas. Our experiments show how a possible instance of the dynamic DMP can be defined and how different algorithms react to the dynamic changes.