Review of key results in metaheuristic methods

In this chapter, we discuss another class of heuristics, which are known as metaheuristic methods [36]. An iteration in metaheuristic methods typically aims to improve the current feasible solution, with the initial solution given by the user. Some well-known metaheuristic methods are iterative improvement, simulated annealing, tabu search, and genetic algorithms [36]. For certain type of problems, metaheuristic methods could be very effective.

The so-called iterative improvement (or basic local search) method tries to find a better solution in each iteration by searching in the neighborhood of the current solution, and terminates when a better solution cannot be found. It has been shown that the performance of iterative improvement methods for combinatorial optimization problems may not be satisfactory [19]. This can be explained by the fact that this method tends to stop as soon as it finds a local optimum.

Compared to iterative improvement, simulated annealing (SA) [1] has an explicit strategy to escape from local optima. The basic idea of SA is to allow a move (with a probability) even if it may tentatively result in a solution of worse quality than the current solution. There is also a cooling procedure in SA, which decreases such randomness (or diversification) as time passes. As the cooling proceeds, SA gradually converges to a simple iterative improvement algorithm, which guarantees convergence. The performance of SA is sensitive to the initial solution and the neighborhood structure (in addition to the cooling procedure).