Local Search Methods

Local search is one of the fundamental paradigms for solving computationally hard combinatorial problems, including the constraint satisfaction problem (CSP). It provides the basis for some of the most successful and versatile methods for solving the large and difficult problem instances encountered in many real-life applications. Despite impressive advances in systematic, complete search algorithms, local search methods in many cases represent the only feasible way for solving these large and complex instances. Local search algorithms are also naturally suited for dealing with the optimisation criteria arising in many practical applications. The basic idea underlying local search is to start with a randomly or heuristically generated candidate solution of a given problem instance, which may be infeasible, sub-optimal or incomplete, and to iteratively improve this candidate solution by means of typically minor modifications. Different local search methods vary in the way in which improvements are achieved, and in particular, in the way in which situations are handled in which no direct improvement is possible. Most local search methods use randomisation to ensure that the search process does not stagnate with unsatisfactory candidate solutions and are therefore referred to as stochastic local search (SLS) methods. Prominent examples of SLS methods are randomised iterative improvement (also known as stochastic hill-climbing), evolutionary algorithms, simulated annealing, tabu search, dynamic local search and, more recently, ant colony optimisation. These classes of local search algorithms are also widely known as metaheuristics. Many SLS methods are conceptually rather simple and relatively easy to implement compared to many other techniques. At the same time, they often show excellent performance and in many cases define the state-of-the-art in the respective problems.1 Furthermore, SLS algorithms are often very flexible in that they can be easily adapted to changes in the specification of a problem. This makes them a very popular choice for solving conceptually complex application problems that are sometimes not fully formalised at the