A Genetic Algorithm to Solve the Multidimensional Knapsack Problem

Berberler, Murat Erşen; Guler, Asli; Nurıyev, Urfat

doi:10.3390/mca18030486

Cited by 7 publications

(5 citation statements)

References 15 publications

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“…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.…”

Section: Introductionmentioning

confidence: 98%

A hybrid quantum particle swarm optimization for the Multidimensional Knapsack Problem

Haddar

Khemakhem

Hanafi

et al. 2016

Engineering Applications of Artificial Intelligence

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Section: Introductionmentioning

confidence: 98%

A hybrid quantum particle swarm optimization for the Multidimensional Knapsack Problem

Haddar

Khemakhem

Hanafi

et al. 2016

Engineering Applications of Artificial Intelligence

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“…Metaheuristics are applied successfully to obtain the optimum or near to optimum solution for many optimization problems in the literature [31][32][33][34][35][36][37][38]. To apply metaheuristics for the optimization problem, one should define a search space for the problem.…”

Section: Introductionmentioning

confidence: 99%

Search Graph Magnification in Rapid Mixing of Markov Chains Associated with the Local Search-Based Metaheuristics

Shenoy

Pai

2021

Mathematics

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The structural property of the search graph plays an important role in the success of local search-based metaheuristic algorithms. Magnification is one of the structural properties of the search graph. This study builds the relationship between the magnification of a search graph and the mixing time of Markov Chain (MC) induced by the local search-based metaheuristics on that search space. The result shows that the ergodic reversible Markov chain induced by the local search-based metaheuristics is inversely proportional to magnification. This result indicates that it is desirable to use a search space with large magnification for the optimization problem in hand rather than using any search spaces. The performance of local search-based metaheuristics may be good on such search spaces since the mixing time of the underlying Markov chain is inversely proportional to the magnification of search space. Using these relations, this work shows that MC induced by the Metropolis Algorithm (MA) mixes rapidly if the search graph has a large magnification. This indicates that for any combinatorial optimization problem, the Markov chains associated with the MA mix rapidly i.e., in polynomial time if the underlying search graph has large magnification. The usefulness of the obtained results is illustrated using the 0/1-Knapsack Problem, which is a well-studied combinatorial optimization problem in the literature and is NP-Complete. Using the theoretical results obtained, this work shows that Markov Chains (MCs) associated with the local search-based metaheuristics like random walk and MA for 0/1-Knapsack Problem mixes rapidly.

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“…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).…”

Section: Introductionmentioning

confidence: 99%

Application of Pigeon Inspired Optimization for Multidimensional Knapsack Problem

Setiawan

Sadiyoko

Setiardjo

2020

IJIEEM

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The multidimensional knapsack problem (MKP) is a generalization of the classical knapsack problem, a problem for allocating a resource by selecting a subset of objects that seek for the highest profit while satisfying the capacity of knapsack constraint. The MKP have many practical applications in different areas and classified as a NP-hard problem. An exact method like branch and bound and dynamic programming can solve the problem, but its time computation increases exponentially with the size of the problem. Whereas some approximation method has been developed to produce a near-optimal solution within reasonable computational times. In this paper a pigeon inspired optimization (PIO) is proposed for solving MKP. PIO is one of the metaheuristic algorithms that is classified in population-based swarm intelligent that is developed based on the behavior of the pigeon to find its home although it had gone far away from it home. In this paper, PIO implementation to solve MKP is applied to two different characteristic cases in total 10 cases. The result of the implementation of the two-best combination of parameter values for 10 cases compared to particle swarm optimization, intelligent water drop algorithm and the genetic algorithm gives satisfactory results.

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A Genetic Algorithm to Solve the Multidimensional Knapsack Problem

Cited by 7 publications

References 15 publications

A hybrid quantum particle swarm optimization for the Multidimensional Knapsack Problem

A hybrid quantum particle swarm optimization for the Multidimensional Knapsack Problem

Search Graph Magnification in Rapid Mixing of Markov Chains Associated with the Local Search-Based Metaheuristics

Application of Pigeon Inspired Optimization for Multidimensional Knapsack Problem

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