Adaptive search heuristics for the generalized assignment problem

Abstract

The Generalized Assignment Problem consists of assigning a set of tasks to a set of agents at minimum cost. Each agent has a limited amount of a single resource and each task must be assigned to one and only one agent, requiring a certain amount of the agent’s resource. We present the application of a MAX-MIN Ant System (MMAS) and a greedy randomized adaptive search procedure (GRASP) to the generalized assignment problem based on hybrid approaches. The MMAS heuristic can be seen as an adaptive sampling algorithm that takes into consideration the experience gathered in earlier iterations of the algorithm. Moreover, the latter heuristic is combined with local search and tabu search heuristics to improve the search. Several neighborhoods are studied, including one based on ejection chains that produces good moves without increasing the computational effort. We present computational results of a comparative analysis of the two adaptive heuristics, followed by concluding remarks and ideas on future research in generalized assignment related problems.