Hyperheuristic Approaches for Multiobjective Optimisation

In multiobjective optimisation the aim is to find solutions that represent a compromise between the various (sometimes conflicting) criteria used to evaluate the quality of solutions. A solution x is said to be non-dominated with respect to a set of solutions S if there is no other solution in S that is, as good as x in all the criteria and better than x in at least one of the criteria. In Pareto optimisation the goal is to find a set of solutions that is representative of the whole trade-off surface, i.e. non-dominated solutions that are a good approximation to the Pareto optimal front [5]. The present work proposes the use of hyperheuristics to improve the ability of local search-based metaheuristics to produce non-dominated fronts that are uniformly distributed over the desired trade-off surface. A hyperheuristic can be thought at as, basically, a heuristic that manages the application of a set of heuristics in order to solve an optimisation problem [1]. By using a hyperheuristic approach, the neighbourhood exploration can be targeted in order to guide the search towards the desired regions of the trade-off surface. This strategy takes into consideration the localization of the current solution(s) in the objective space and the ability of each neighbourhood exploration heuristic to achieve improvements on each of the objectives. That is, a hyperheuristic systematically tries to apply the neighbourhood exploration heuristic that improves on 'poor' objectives while maintaining the quality of 'rich' objectives on a given solution. This is a novel approach for tackling the problem of achieving a good coverage of the desired trade-off surface in multiobjective combinatorial optimisation.