On the Biobjective Adjacent Only Quadratic Spanning Tree Problem

The adjacent only quadratic minimum spanning tree problem is an NP-hard version of the minimum spanning tree where the costs of interaction effects between every pair of adjacent edges are included in the objective function. This paper addresses the biobjective version of this problem. A Pareto local search algorithm is proposed. The algorithm is applied to a set of 108 benchmark instances. The results are compared to the optimal Pareto front generated by a branch and bound algorithm, which is a multiobjective adaptation of a well known algorithm for the mono-objective case.