Multi-Criterion Optimization in Minimum Spanning Trees

The Extreme Point Deterministic Algorithm (EPDA), proposed for the multicriterion minimum spanning tree problem, is applicable to more than two criteria and can determine large Pareto fronts comprising of both supported and non-supported efficient solutions, unlike many existing algorithms. EPDA is validated against an exhaustive search for small problems (four to ten nodes, two and three criteria); and compared with the algorithm proposed by Steiner and Radzik for larger problems (up to 300 nodes in two criteria). Scalability of EPDA is further demonstrated by applying it to graphs of up to 100 nodes in three criteria. Experimental results using benchmark hard instances generated by algorithms from literature show that EPDA finds the true Pareto fronts for small instances of the problem and that it is more efficient than existing algorithms for larger instances tested in terms of front occupation, scalability and large number of non-supported efficient solutions found. Therefore, it can be used in decision-aid tools in the field of network architecture and design as well as in network operations and management when several objectives have to be optimised. Moreover, fronts calculated by EPDA can serve as reference for testing other algorithms in particular evolutionary-based approaches.