A Collaborative Search Strategy to Solve Combinatorial Optimization and Scheduling Problems

Abstract

Since the creation of operations research as a discipline, a continued interest has been in the development of heuristics or approximation algorithms to solve complex combinatorial optimization problems. As many problems have been proven computationally intractable, the heuristic approaches become increasingly important in solving various large practical problems. The most popular heuristics that have been widely studied in literature include Simulated Annealing (SA) (Kirkpatrick 1983), Tabu Search (TS) (Glover 1986), and Genetic Algorithm (GA) (Holland 1975). Simulated annealing is a stochastic search method that explores the solution space using a hill climbing process. Tabu search, on the other hand, is a deterministic search algorithm that attempts exhaustive exploration of the neighbourhood of a solution. In contrast to the local search algorithms such as SA and TS that work with one feasible solution in each iteration, GA employs a population of solutions and is capable of both local and global search in the solution space. Despite their successes in solving many combinatorial problems, these algorithms have some limitations. For instance, SA can be easily trapped in a local optimum or may require excessive computing time to find a reasonable solution. To successfully implement a tabu search algorithm, one requires a good knowledge about the problem and its solution space to define an efficient neighbourhood structure. Genetic algorithms often converge to a local optimum prematurely and their success often relies on the efficiency of the adopted operators. Due to the deficiencies of the conventional heuristics and ever increasing demand for more efficient search algorithms, researchers are exploring two main options, developing new methods such as nature inspired metaheuristics and investigating hybrid algorithms. In recent years, a number of metaheuristics have been developed. Examples include the Greedy Randomized Adaptive Search Procedure (GRASP) (Feo & Resende, 1995; Aiex et al., 2003), Adaptive Multi Start (Boese et al., 1994), Adaptive Memory Programming (AMP) 9