Multi-objective Minimum Spanning Trees

Abstract

In this chapter, we analyze multi-objective evolutionary algorithms (MOEAs) on an NP-hard multi-objective combinatorial optimization problem, namely the multi-objective minimum spanning tree problem. Many successful evolutionary algorithms have been proposed for this problem (Knowles and Corne, 2001; Zhou and Gen, 1999). In Chapter 5, we showed that stochastic search algorithms are able to compute minimum spanning trees in expected polynomial time. The analysis is based on the investigation of the expected multiplicative distance decrease (where the distance is measured as the weight difference between the current solution and an optimal one) and serves as a starting point for the analysis of the multi-objective minimum spanning tree problem.