A Hybrid Ant Colony Algorithm with a Local Search for the Strongly Correlated Knapsack Problem

Large combinatorial optimization problems may be overly complex to be processed by a single type of algorithm. This explains the growing interest of researchers in the hybrid resolution. The hybridization of algorithms aims to take advantage of each one benefits, thereby achieving better results. In this paper, a hybrid metaheuristic is proposed to solve one of the most complex variants of the knapsack problem which is the Strongly Correlated Knapsack Problem (SCKP). The proposed approach combines a proposed Ant Colony Optimization algorithm (ACO) with a 2 opt algorithm. The proposed ACO scheme used combines two ant algorithms: the MAX-MIN Ant System and the Ant Colony System. At a first stage, our proposed ACO aims to solve the SCKP to optimality. In case an optimal solution is not found, a proposed 2 opt algorithm is used. Even if the 2 opt heuristic fails to find the optimal solution, it would hopefully improve the solution quality by reducing the gap between the found solution and the optimum. The proposed algorithm was tested on a set of instances and compared with classical and recent methods reported in the literature.