A Property Preserving Method for Extending a Single-Objective Problem Instance to Multiple Objectives with Specific Correlations

A method is proposed to generate multi-objective optimization problem instances from a corresponding single-objective instance. The user of the method can specify the correlations between the generated the objectives. Different from existing instance generation methods the new method allows to keep certain properties of the original single-objective instance. In particular, we consider optimization problems where the objective is defined by a matrix, e.g., a distance matrix for the Traveling Salesperson problem (TSP) or a flow matrix for the Quadratic Assignment problem. It is shown that the method creates new distance matrices with specific correlations between each other and also have the same average distance and variance of distances as the distance matrix of the original instance. This property is important, e.g., when the influence of correlations between the objectives on the behavior of metaheuristics for the multi-objective TSP are investigated. Some properties of the new method are shown theoretically. In an empirical analysis the new method is compared with instance generation methods from the literature.

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