On the Benefits of Biased Edge-Exchange Mutation for the Multi-Criteria Spanning Tree Problem

Research has shown that for many single-objective graph problems where optimum solutions are composed of low weight sub-graphs, such as the minimum spanning tree problem (MST), mutation operators favoring low weight edges show superior performance. Intuitively, similar observations should hold for multi-criteria variants of such problems. In this work, we focus on the multi-criteria MST problem. A thorough experimental study is conducted where we estimate the probability of edges being part of non-dominated spanning trees as a function of the edges’ non-domination level or domination count, respectively. Building on gained insights, we propose several biased one-edge-exchange mutation operators that differ in the used edge-selection probability distribution (biased towards edges of low rank). Our empirical analysis shows that among different graph types (dense and sparse) and edge weight types (both uniformly random and combinations of Euclidean and uniformly random) biased edge-selection strategies perform superior in contrast to the baseline uniform edge-selection. Our findings are in particular strong for dense graphs.