Visual mapping of multi-objective optimization problems and evolutionary algorithms

This work proposes a method to map optimization problems and evolutionary search algorithms into a two-dimensional space, respectively. In the research domain of evolutionary optimization, benchmark optimization problems and search algorithms have been evolved cooperatively so far. A variety of benchmark problems are essential for the research of search algorithms. However, there is difficulty to quantitatively and visually represent differences among benchmark problems. Also, there is the same difficulty in describing differences among search algorithms. The proposed method maps optimization problems based on the difference in the search algorithm ranking on each optimization problem. Also, the proposed method maps search algorithms based on the difference in the problem ranking on each search algorithm. In the experiment, we use 26 kinds of multi-objective optimization problems included in the ZDT, DTLZ, and WFG benchmark suites and 29 kinds of evolutionary search algorithms. As a result, we show that similarities of the internal functions are reflected in the position of each problem on the optimization problem map, and the similarities of the design principles of search algorithms are reflected in the position of each search algorithm on the search algorithm map.