On the effectiveness of genetic algorithms for the multidimensional knapsack problem

Abstract

In the Multidimensional Knapsack Problem (MKP) there are items easily identifiable as highly (lowly) profitable and likely to be chosen (not chosen) to compose high-quality solutions. For all the other items, the Knapsack Core (KC), the decision is harder. By focusing the search on the KC effective algorithms have been developed. However, the true KC is not available and most algorithms can only rely on items' efficiencies. Chu & Beasley Genetic Algorithm (CBGA), for example, uses efficiencies in a repair-operator which bias the search towards the KC. This paper shows that, as the search progresses, efficiencies lose their descriptive power and, consequently, CBGA's effectiveness decreases. As a result, CBGA rapidly finds its best solutions and stagnates. In order to circumvent this stagnation, extra information about the KC should be used to implement specific operators. Since there is a correlation between marginal probabilities in a population and efficiencies, we show that KCs can be estimated from the population during the search. By solving the estimated KCs with CPLEX, improvements were possible in many instances, evidencing CBGA's weakness to solve KCs and indicating a promising way to improve GAs for the MKP through the use of KC estimates.

Application of Pigeon Inspired Optimization for Multidimensional Knapsack Problem

“…Heuristics are problem-dependent that are designed and applicable to a problem. The research on the application of metaheuristic method to solve MKP are tabu search (Vasquez and Hao, 2001;Dammeyer andVoss, 1993, Glover andKochenberger, 1996;Vasquest andVimont, 2005, Lai et al, 2018); genetic algorithm (Khuri et al, 1994;Chu and Beasley, 1998;Berberler et al, 2013;Martins et al, 2014); simulated annealing (Leung et al, 2012;Rezoug et al, 2015); ant colony optimization (Kong et al, 2008;Ke et al, 2010;Fingler et al, 2014); particle swarm optimization (Kong et al, 2006;Hembecker et al, 2007;Wan and Nolle, 2009;Chen et al, 2010;Ktari and Chabchoub, 2013); Tisna, 2013, Chih, 2015, Haddar et al, 2016; intelligent water drops (Shah-Hosseini, 2009), binary artificial algae algorithm (Zhang et al, 2016), binary multi-verse optimizer (Baseet et al, 2019), modified flower pollination (Basset et al, 2018).…”

A randomized heuristic repair for the multidimensional knapsack problem

“…As a result, for large MKP instances, the ordering O dual is less informative for the heuristic repair which hinders its effectiveness. As shown by Martins et al [2014a], that seems to be the case for the CBGA, with the algorithm struggling to decide if core items should be put in the knapsack even in very long runs.…”

A hybrid quantum particle swarm optimization for the Multidimensional Knapsack Problem

“…Therefore, many researchers focus on heuristic and meta-heuristic search methods which can produce solutions of good qualities in a reasonable amount of time. Relevant methods include tabu search (Vasquez and Hao, 2001;Dammeyer and Voss, 1993;Glover and Kochenberger, 1996;Hanafi and Freville, 1998;Vasquez and Vimont, 2005), genetic algorithm (Chu and Beasley, 1998;Berberler et al, 2013;Martins et al, 2014), simulated annealing (Leung et al, 2012;Rezoug et al, 2015), ant colony optimization (Parra-Hernandez and Dimopoulos, 2003;Kong et al, 2008;Ke et al, 2010;Fingler et al, 2014), filter-and-fan algorithm (Khemakhem et al, 2012), particle swarm optimization (Kong et al, 2006;Wan and Nolle, 2009;Chen et al, 2010;Ktari and Chabchoub, 2013;Tisna, 2013;Beheshti et al, 2013;Chih, 2015) and so on.…”