Making the Edge-Set Encoding Fly by Controlling the Bias of Its Crossover Operator

Abstract

Edge-sets encode spanning trees directly by listing their edges. Evolutionary operators for edge-sets may be heuristic, considering the weights of edges they include in offspring, or naive, including edges without regard to their weights. Crossover operators that heuristically prefer shorter edges are strongly biased towards minimum spanning trees (MST); EAs that apply heuristic crossover generally perform poorly on spanning tree problems whose optimum solutions are not very similar to MSTs. For the edge-set encoding, a modified heuristic crossover called γ-TX implements variable bias towards low-weight edges and thus towards MSTs. The bias can be set arbitrarily between the strong bias of the heuristic crossover operator, or being unbiased. An investigation into the performance of EAs using the γ-TX for randomly created OCST problems of different types and OCST test instances from the literature present good results when setting the crossover-specific parameter γ properly. The presented results suggest that the original heuristic crossover operator of the edge-sets should be substituted by the modified γ-TX operator that allows us to control the bias towards the MST.