A Comparison of Encodings and Algorithms for Multiobjective Minimum Spanning Tree Problems

Finding minimum-weight spanning trees (MST) in graphs is a classic problem in operations research with important applications in network design. The basic MST problem can be solved eeciently, but the degree constrained and multiobjective versions are NP-hard. Current approaches to the degree-constrained single objective MST include Raidl's evolutionary algorithm (EA) which employs a direct tree encoding and associated operators, and Knowles and Corne's encoding based on a modiied version of Prim's algorithm. Approaches to the multiobjective MST include various approximate constructive techniques from operations research, along with Zhou and Gen's recent evolutionary algorithm using a Pr ufer based encoding. In this paper we apply (appropriately modiied) the best of recent methods for the (degree-constrained) single objective MST problem to the multiobjective MST problem, and compare with a method based on Zhou and Gen's approach. Our evolutionary computation approaches, using the diierent encodings, involve a new population-based variant of Knowles and Corne's PAES algorithm. We nd the direct encoding to considerably outperform the Pr ufer encoding. And we nd that a simple iterated approach, based on Prim's algorithm modiied for the multiobjective MST, also signiicantly outperforms the Pr ufer encoding.