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Design of test problems for discrete estimation of distribution algorithms

Two types of problem structures, overlapping and conflict structures, are challenging for the estimation of distribution algorithms (EDAs) to solve. To test the capabilities of different EDAs of dealing with overlapping and conflict structures, some test problems have been proposed. However, the upper-bound of the degree of overlap and the effect of conflict have not been fully investigated. This paper investigates how to properly define the degree of overlap and the degree of conflict to reflect the difficulties of problems for the EDAs. A new test problem is proposed with the new definitions of the degree of overlap and the degree of conflict. A framework for building the proposed problem is presented, and some model-building genetic algorithms are tested by the problem. This test problem can be applied to further researches on overlapping and conflict structures.