An improved grammatical evolution approach for generating perturbative heuristics to solve combinatorial optimization problems

Abstract

Search methodologies such as hyper-heuristics have been successfully used to automate the generation of perturbative heuristics to solve combinatorial optimization problems. However, the domain of automated generation of perturbative heuristics has generally not been well researched and very few works have actually been conducted in the area. In addition, most of the proposed hyper-heuristic methods in the literature simply recombine already existing and human-derived low-level perturbative heuristics (or primitive heuristic components) with various move acceptance criteria to generate the new perturbative heuristics instead of producing the heuristics from scratch. As a result, these methods cannot be applied to problem domains where the human-derived low-level heuristics are not available. The study presented in this paper addresses this issue by proposing an improved approach, based on our previous work, that generates good quality reusable perturbative heuristics from scratch. While this new approach also uses grammatical evolution to generate the heuristics from a set of basic actions and components of the solution (as in our previous work), the grammar has been substantially extended and includes new methods for selecting solution components, conditional constructs, utilizes some information from the solution space as well as extends the syntax of the basic actions in order to cover a wider range of heuristics. Furthermore, the new approach has been applied to a new problem domain, i.e. the boolean satisfiability problem, in addition to the examination timetabling and vehicle routing problems investigated in the earlier work. The experimental results show that the new approach not only generates better perturbative heuristics than those produced in our earlier work, it also produces results that are competitive with those obtained by currently existing generation perturbative hyper-heuristics that have been applied to the benchmark sets in the three domains.