The two-stage recombination operator and its application to the multiobjective 0/1 knapsack problem: A comparative study

Aghezzaf, Brahim; Naimi, Mohamed

doi:10.1016/j.cor.2009.02.027

Cited by 10 publications

(7 citation statements)

References 17 publications

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“…By using smoothed analysis (the specified inputs of the model are subjected to a random perturbation) Beier et al (2007) proposed a tight bound on the expected number of efficient solutions for general bi-objective integer optimization problems, which is a very interesting information within a resolution procedure. More recent research works on the {0,1}-knapsack problem considering more than two objective functions are available: Aghezzaf andNaimi (2009), Bazgan et al (2009a,b). The work by Bazgan et al (2009b) is an exact approach based on dynamic programming using several complementary dominance relations in order to discard no promising partial solutions.…”

Section: The Bi-objective {01}-knapsack Problemmentioning

confidence: 98%

“…Bazgan et al (2009a) proposed a fully polynomial approximation scheme also based in the same ideas to solve an approximation of the problem. Aghezzaf and Naimi (2009) propose a new recombination operator, which is a two-stage process preserving in the first stage the similar characteristics of the solutions to be combined and accepting the non-similar parts considering a fitness function. This approach is to be used in multi-objective evolutionary algorithms in order to enhance its performance.…”

Section: The Bi-objective {01}-knapsack Problemmentioning

confidence: 99%

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The small world of efficient solutions: empirical evidence from the bi-objective {0,1}-knapsack problem

2009

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The small world phenomenon, Milgram (1967) has inspired the study of real networks such as cellular networks, telephone call networks, citation networks, power and neural networks, etc. The present work is about the study of the graphs produced by efficient solutions of the bi-objective {0,1}-knapsack problem. The experiments show that these graphs exhibit properties of small world networks. The importance of the supported and non-supported solutions in the entire efficient graph is investigated. The present research could be useful for developing more effective search strategies in both exact and approximate solution methods of {0,1} multi-objective combinatorial optimization problems.

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Section: The Bi-objective {01}-knapsack Problemmentioning

confidence: 98%

Section: The Bi-objective {01}-knapsack Problemmentioning

confidence: 99%

The small world of efficient solutions: empirical evidence from the bi-objective {0,1}-knapsack problem

2009

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“…Numerous studies investigated performance improvement strategies for binary genetic algorithms, which are popular and can be applied in a straightforward way to solve MOKPs. Aghezzaf and Naimi (2009) improved the recombination procedure by introducing a two-stage crossover. In the first stage, the offspring is initialized in the way the similar genes of parents are inherited.…”

Section: Variationmentioning

confidence: 99%

Neuroevolution for solving multiobjective knapsack problems

Denysiuk

Gaspar‐Cunha

Delbem

2019

Expert Systems with Applications

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The multiobjective knapsack problem (MOKP) is an important combinatorial problem that arises in various applications, including resource allocation, computer science and finance. When tackling this problem by evolutionary multiobjective optimization algorithms (EMOAs), it has been demonstrated that traditional recombination operators acting on binary solution representations are susceptible to a loss of diversity and poor scalability. To address those issues, we propose to use artificial neural networks for generating solutions by performing a binary classification of items using the information about their profits and weights. As gradient-based learning cannot be used when target values are unknown, neuroevolution is adapted to adjust the neural network parameters. The main contribution of this study resides in developing a solution encoding and genotype-phenotype mapping for EMOAs to solve MOKPs. The proposal is implemented within a state-of-the-art EMOA and benchmarked against traditional variation operators based on binary crossovers. The obtained experimental results indicate a superior performance of the proposed approach. Furthermore, it is advantageous in terms of scalability and can be readily incorporated into different EMOAs.

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“…The results show that their hybrid GA can reach high-quality solutions in a little computing time. On the other hand, Aghezzaf and Naimi (2009) propose a two-stage recombination operator especially dedicated for the multi-objective variant of 0/1 MKP, in which only one offspring is generated through two stages: The similarity-preserving stage and the problem-specific knowledge stage. Their crossover operator was tested using two well-known patterns of multi-objective evolutionary algorithms.…”

Section: Introductionmentioning

confidence: 99%

“…The first is a sexual selection that improves the one proposed by Varnamkhasti and Lee (2012). The second operator is an adaptation through two new variants dedicated to 0/1 MKP, of the two-stage recombination operator proposed by Aghezzaf and Naimi (2009). The motivation behind the improvement as well as the combination of these two operators is firstly their effectiveness to solve some variants of 0/1 MKP when compared with other classical selection and crossover operators.…”

Section: Introductionmentioning

confidence: 99%

An improved sexual genetic algorithm for solving 0/1 multidimensional knapsack problem

Laabadi

Naimi

Amri

et al. 2019

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Purpose The purpose of this paper is to provide an improved genetic algorithm to solve 0/1 multidimensional knapsack problem (0/1 MKP), by proposing new selection and crossover operators that cooperate to explore the search space. Design/methodology/approach The authors first present a new sexual selection strategy that significantly improves the one proposed by (Varnamkhasti and Lee, 2012), while working in phenotype space. Then they propose two variants of the two-stage recombination operator of (Aghezzaf and Naimi, 2009), while they adapt the latter in the context of 0/1 MKP. The authors evaluate the efficiency of both proposed operators on a large set of 0/1 MKP benchmark instances. The obtained results are compared against that of conventional selection and crossover operators, in terms of solution quality and computing time. Findings The paper shows that the proposed selection respects the two major factors of any metaheuristic: exploration and exploitation aspects. Furthermore, the first variant of the two-stage recombination operator pushes the search space towards exploitation, while the second variant increases the genetic diversity. The paper then demonstrates that the improved genetic algorithm combining the two proposed operators is a competitive method for solving the 0/1 MKP. Practical implications Although only 0/1 MKP standard instances were tested in the empirical experiments in this paper, the improved genetic algorithm can be used as a powerful tool to solve many real-world applications of 0/1 MKP, as the latter models several industrial and investment issues. Moreover, the proposed selection and crossover operators can be incorporated into other bio-inspired algorithms to improve their performance. Furthermore, the two proposed operators can be adapted to solve other binary combinatorial optimization problems. Originality/value This research study provides an effective solution for a well-known non-deterministic polynomial-time (NP)-hard combinatorial optimization problem; that is 0/1 MKP, by tackling it with an improved genetic algorithm. The proposed evolutionary mechanism is based on two new genetic operators. The first proposed operator is a new and deeply different variant of the so-called sexual selection that has been rarely addressed in the literature. The second proposed operator is an adaptation of the two-stage recombination operator in the 0/1 MKP context. This adaptation results in two variants of the two-stage recombination operator that aim to improve the quality of encountered solutions, while taking advantage of the sexual selection criteria to prevent the classical issue of genetic algorithm that is premature convergence.

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The two-stage recombination operator and its application to the multiobjective 0/1 knapsack problem: A comparative study

Cited by 10 publications

References 17 publications

The small world of efficient solutions: empirical evidence from the bi-objective {0,1}-knapsack problem

The small world of efficient solutions: empirical evidence from the bi-objective {0,1}-knapsack problem

Neuroevolution for solving multiobjective knapsack problems

An improved sexual genetic algorithm for solving 0/1 multidimensional knapsack problem

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