Guided genetic algorithm for the multidimensional knapsack problem

Abstract

Genetic Algorithm (GA) has emerged as a powerful method for solving a wide range of combinatorial optimisation problems in many fields. This paper presents a hybrid heuristic approach named Guided Genetic Algorithm (GGA) for solving the Multidimensional Knapsack Problem (MKP). GGA is a two-step memetic algorithm composed of a data pre-analysis and a modified GA. The pre-analysis of the problem data is performed using an efficiency-based method to extract useful information. This prior knowledge is integrated as a guide in a GA at two stages: to generate the initial population and to evaluate the produced offspring by the fitness function. Extensive experimentation was carried out to examine GGA on the MKP. The main GGA parameters were tuned and a comparative study with other methods was conducted on well-known MKP data. The real impact of GGA was checked by a statistical analysis using ANOVA, t-Test and Welch's t-Test. The obtained results showed that the proposed approach largely improved standard GA and was highly competitive with other optimisation methods.

An OR practitioner’s solution approach to the multidimensional knapsack problem

“…each time) and have the program return the best overall solution out of the five best solutions obtained by TLBO. Recently, Rezoug et al (2018) presented a guided genetic algorithm (GGA) to solve the MKP. In their paper, using the 270 MKPs from Beasley's OR-Library, Rezoug et al (2018) report in their Table 10 how their GGA performed compared to 9 solution approaches from the literature.…”

“…Some recent (since 2011) examples applied to solve the MKP include: harmony search (HS)-based approaches by Kong et al (2015) and Rezoug and Boughaci (2016), particle swarm optimization (PSO)-based approaches by Labed et al (2011) and Kang (2012), a shuffled complex evolution algorithm by Baroni and Varejao (2015). fruit fly optimization algorithm by Meng and Pan (2017), or a guided genetic algorithm (GGA) approach by Rezoug et al (2018). In order to solve the MKP, earlier papers discussed a genetic algorithm by Chu and Beasley (1998) and heuristic approaches by Moraga et al (2005), Akçay et al (2007) and Boyer et al (2009).…”

“…In this paper, we used 270 test problems available in Beasley's OR-Library to measure the performance of our TLBO algorithm for the MKP. Furthermore, Rezoug et al (2018) recently summarized in their Table 10, how 10 solution approaches for the MKP performed on these same 270 test problems. TLBO performed competitively with the 10 solution approaches reported in Rezoug et al (2018).…”

“…Furthermore, Rezoug et al (2018) recently summarized in their Table 10, how 10 solution approaches for the MKP performed on these same 270 test problems. TLBO performed competitively with the 10 solution approaches reported in Rezoug et al (2018). Specifically, on the problems with the largest number of constraints (usually considered more difficult to solve), TLBO outperformed all but two of the 10 solution procedures, while its results on the best two solution procedures were comparable without the need for time-consuming parameter fine-tuning.…”

“…That will be followed by a discussion of the adaptation of this metaheuristic to solve the MKP. Then empirical results will be used to compare our TLBO solutions of the 270 Beasley test problems with the 10 solution approaches that are compared in Rezoug et al(2018). Finally, a brief summary will be provided.…”