A Metaheuristic Relying on Random Walk on a Graph for Binary Optimization Problems

Recently, evolutionary algorithms that can solve decomposable binary problems very efficiently have been developed. They are so-called model-based evolutionary algorithms, which build a model for generating solution candidates by a machine learning technique using a population. Their central procedure is linkage detection that reveals a problem structure, that is, how the entire problem consists of sub-problems. However, the model-based evolutionary algorithms have been shown to be ineffective against problems that are hard to identify their structures. Therefore, metaheuristics including evolutionary algorithms that can solve both problems quickly, reliably, and accurately are required. In this paper, toward realizing such algorithms, we propose a new model-based metaheuristic. It initially forms a graph in which a pair of a position and a value on the string of a solution candidate is a vertex and directed edges are randomly made between vertexes, and then repeats the following three steps: (1) conducting random walk on the graph, (2) producing solution candidates, and (3) reconstructing the topology of the graph. The simulation results show that the proposed metaheuristic is inferior to conventional algorithms against decomposable problems, but superior to conventional ones against problems that are hard to identify their structures.