Domination landscape in evolutionary algorithms and its applications

Evolutionary algorithms (EAs) are usually required to solve problems based on domination relationship among solutions. Often, the domination relationship is almost the sole source of knowledge that EAs can utilize, especially when the problem solving engine concerned is taken as a black box. In this paper, the domination landscape (DL), onto which an optimization problem (OP) can be mapped, is introduced. A DL may correspond to a cluster of OPs, implying that a class of OPs may have the same DL. To illustrate DL, we consider its representation as a directed graph, with its corresponding matrix and function. Of the various properties of DL, the domination-preserving property is used for the analysis of DL-equivalent OPs, and for the basis for classification of OPs. Taking DL as a tool for theoretical analysis, parameters determination for fitness scaling, the convergence property of EAs and the analysis of robustness in light of fitness noise are presented. The study of DL in this paper establishes the necessary theoretical foundation for future applications of DL equality and similarity based optimization.