Guided Local Search: An Illustrative Example in Function Optimisation

Guided Local Search originally proposed by Voudouris and Tsang [29] is a general optimisation technique suitable for a wide range of combinatorial optimisation problems. Successful applications of the technique so far include practical problems such as Frequency Allocation [29], Workforce Scheduling [28] and Vehicle Routing [2, 18] and also classic problems such as the Travelling Salesman Problem (TSP) and the Quadratic Assignment Problem (QAP) [30]. Guided Local Search (GLS) belongs to a class of techniques known as Metaheuristics [22, 23, 25]. Prominent members of this class include Tabu Search [712], Simulated Annealing [1, 5, 19, 21], GRASP [6], Genetic Algorithms [4, 14, 24], Scatter Search [8] and others. Metaheuristics aim at enhancing the performance of heuristic methods in solving large and difficult combinatorial optimisation problems. In the case of GLS, the main focus is on the exploitation of problem and search-related information to effectively guide local search heuristics in the vast search spaces of NP-hard optimisation problems. This is achieved by augmenting the objective function of the problem to be minimised with a set of penalty terms which are dynamically manipulated during the search process to steer the heuristic to be guided. Higher goals, such as the distribution of the search effort to the areas of the search space according to the promise of these areas to contain high quality solutions, can be expressed and pursued. GLS is closely related to the Frequency-Based Memory approaches introduced in Tabu Search [9, 13], extending these approaches to take into account the quality of structural parts of the solution and also react to feedback from the local optimisation heuristic under guidance. In this paper, we provide an illustrative example of how GLS works by explaining its use for solving an a non-convex optimisation problem.