Incomplete Solution Representations and Decoders

Abstract

Representing candidate solutions in a metaheuristic in an indirect way and using a decoding algorithm for obtaining corresponding actual solutions is a commonly applied technique to transform a more complex search space, possibly with constraints that are difficult to handle, into one where standard local search neighborhoods can be more easily applied. The decoding algorithm used here may also be a more advanced, “intelligent” procedure that solves part of the whole problem. This leads us further to incomplete solution representations, where a metaheuristic essentially acts on only a subset of the decision variables, while the decoder augments the missing parts in an optimal or reasonably good way.We study this general approach by considering the Generalized Minimum Spanning Tree (GMST) problem as an example and investigate two different decoder-based variable neighborhood search approaches relying on complementary incomplete representations and respective efficient decoders. Ultimately, a combined approach is shown to perform best.