Move acceptance in local search metaheuristics for cross-domain search

•Classification of local search metaheuristics based on their move acceptance methods.•A concise overview of local search metaheuristics in relevant classes.•Cross-domain performance comparison of 8 local search metaheuristics from each class.•Simulated annealing (SA) has the best performance over 45 instances from 9 domains.•Parameters of SA needs re-tuning for each domain to achieve this performance. Metaheuristics provide high-level instructions for designing heuristic optimisation algorithms and have been successfully applied to a range of computationally hard real-world problems. Local search metaheuristics operate under a single-point based search framework with the goal of iteratively improving a solution in hand over time with respect to a single objective using certain solution perturbation strategies, known as move operators, and move acceptance methods starting from an initially generated solution. Performance of a local search method varies from one domain to another, even from one instance to another in the same domain. There is a growing number of studies on ‘more general’ search methods referred to as cross-domain search methods, or hyper-heuristics, that operate at a high-level solving characteristically different problems, preferably without expert intervention. This paper provides a taxonomy and overview of existing local search metaheuristics along with an empirical study into the effects that move acceptance methods, as components of single-point based local search metaheuristics, have on the cross-domain performance of such algorithms for solving multiple combinatorial optimisation problems. The experimental results across a benchmark of nine different computationally hard problems highlight the shortcomings of existing and well-known methods for use as components of cross-domain search methods, despite being re-tuned for solving each domain.