Metaheuristics Based on Solution Construction

Abstract

In section 3.1.1 we saw how randomization can make constructive search methods better than pure greedy methods, because the danger of being too eager is dampened a little. We called this approach randomized adaptive search. Now we want to explain a metaheuristic which is based on this idea. It is called Greedy Randomized Adaptive Search Procedure (GRASP, cf [70, 170]). As it is a constructive search method, it starts with an empty solution and adds solution elements to a partial solution until it is complete. It may be argued, this is exactly the way a greedy construction method works, but there are subtle differences, which are pointed out now. Greedy methods do not perform search, they construct a single solution in an iterative fashion by evaluating all remaining solution elements and according to their performance add them to the partial solution. Elements are added as long as the solution is improved. If this is not the case anymore, the construction is stopped and the final solution is returned. Hence greedy methods do not perform search.