Multi-objetive optimization problem mapping based on algorithmic parameter rankings

Each of multi-objective optimization problems has its own problem characteristics, and the appropriate evolutionary algorithm and its algorithmic parameters generally depend on each problem. So far optimization problems have been roughly categorized by characteristics of internal functions such as the multimodality, the ill-scaledness, the non-separability. Therefore, it has been difficult to represent fine-grained problem similarities among a variety of problems. To visually represent similarities of different optimization problems and appropriate algorithmic parameters for each problem domain having a similar problem characteristic, this work proposes a method to map multi-objective optimization problems into a two-dimensional space and visualize appropriate algorithmic parameters all over the two-dimensional problem map. The proposed method uses a set of uniformly distributed algorithmic parameters used in an evolutionary algorithm, ranks them based on their search performance for each problem and use the differences of the parameter rankings among problems as problem similarities. Experimental results using 35 kinds of problems derived from DTLZ models show that the proposed method can map similar problems closely and different problems far in the two-dimensional problem map and visually represent appropriate parameters all over the problem map.