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Given an undirected graph with weights on the edges and a set of conflicting edge pairs, the Minimum Spanning Tree Under Conflict Constraints (MSTCC) consists in finding minimum spanning tree with at most one edge of each conflicting pair and minimum cost. The problem is NP-hard and was introduces recently at literature. This paper proposes a new approach for solving MSTCC, our method is based on the GRASP metaheuristic coupled with adaptive memory programming. We test the proposed heuristic on literature’s instances with thousands of conflicts. The results indicate that the proposed algorithm was able to find all known optimal solutions and outperform the bestknown heuristics for the MSTCC.

A GRASP Approach for The Minimum Spanning Tree Under Conflict Constraints