A differential evolution algorithm with variable neighborhood search for multidimensional knapsack problem

Taşgetiren, M. Fatih; Pan, Quan-Ke; Kızılay, Damla; Süer, Gürsel A.

doi:10.1109/cec.2015.7257236

Cited by 18 publications

(4 citation statements)

References 58 publications

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“…VNS and its variants were applied to some knapsack problems. In several cases it is combined with another metaheuristic such that in [30] where authors considered a differential evolution algorithm with VNS to solve the multidimensional knapsack problem (MKP). It can also be combined with integer programming approaches like in [24,1] where authors deal with the MKP and the multiple-choice knapsack problem with setup, respectively.…”

Section: Constructive Heuristicsmentioning

confidence: 99%

Heuristic and exact fixation-based approaches for the discounted 0-1 knapsack problem

Wilbaut¹,

Todosijević²,

Hanafi³

et al. 2021

Preprint

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In this paper we consider the discounted 0-1 knapsack problem (DKP), which is an extension of the classical knapsack problem where a set of items is decomposed into groups of three items. At most one item can be chosen from each group and the aim is to maximize the total profit of the selected items while respecting the knapsack capacity constraint. The DKP is a relatively recent problem in the literature. We propose several efficient heuristic ways to solve the DKP using fixation techniques. One of the objectives of this work is to show that heuristic approaches dealing with the DKP can be strongly improved by using both heuristic and exact fixation rules. We propose several greedy algorithms and a new variable neighborhood search (VNS) to solve the DKP, and we evaluate the behavior of these methods on two sets of available instances when they are applied with or without fixation. Experiments show that VNS with fixation globally dominates approaches from the literature. Finally, we consider a dynamic programming-based approach where the fixation is incorporated, leading to a very efficient heuristic providing near optimal solutions and an exact approach to solve all the existing instances in less than 2 seconds.

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Section: Constructive Heuristicsmentioning

confidence: 99%

Heuristic and exact fixation-based approaches for the discounted 0-1 knapsack problem

Wilbaut¹,

Todosijević²,

Hanafi³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Similarly, the population-based methods, developed to tackle many solutions at a time are categorized into Evolutionary-based Algorithms (EAs) and Swarm Intelligence-based (SI) algorithms. Few of examples of the population-based algorithms that have been successfully utilized, modified and hybridized to solve different combinatorial optimization and engineering applications like MKP are ant algorithms [18], artificial bee colony algorithm [31], bat algorithm [45], cuckoo search algorithm [13], flower pollination algorithm [1], fruit fly optimization algorithm [26], monkey algorithm [44], differential evolution algorithm [32], genetic algorithm [28], harmony search algorithm [20]. particle swarm optimization [4,8,9,15], symbiotic organisms search algorithm [38], wind-driven optimization [43].…”

Section: Introductionmentioning

confidence: 99%

A Modified Binary Pigeon-Inspired Algorithm for Solving the Multi-dimensional Knapsack Problem

Bolaji

Okwonu

Shola

et al. 2020

Journal of Intelligent Systems

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AbstractThe pigeon-inspired optimization algorithm is a category of a newly proposed swarm intelligence-based algorithm that belongs to the population-based solution technique. The MKP is a class of complex optimization problems that have many practical applications in the fields of engineering and sciences. Due to the practical applications of MKP, numerous algorithmic-based methods like local search and population-based search algorithms have been proposed to solve the MKP in the past few decades. This paper proposes a modified binary pigeon-inspired optimization algorithm named (Modified-BPIO) for the 0 - 1 multidimensional knapsack problem (MKP). The utilization of the binary pigeon-inspired optimization (BPIO) for solving the multidimensional knapsack problem came with huge success. However, it can be observed that the BPIO converges prematurely due to lost diversity during the search activities. Given the above, the crossover operator is integrated with the landmark component of the BPIO to improve the diversity of the solution space. The MKP benchmarks from the Operations Research (OR) library are utilized to test the performance of the proposed binary method. Experimentally, it is concluded that the proposed Modified-BPIO has a better performance when compared with the BPIO and existing state-of-the-arts that worked on the same MKP benchmarks.

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“…The results obtained by them indicate that VNS is quite optimal compared to other classical algorithms to verify that if the search algorithm for multi-population variable-population environment is a feasible and effective optimization or not. Another case with research conducted by Tasgetiren et al [3] related search environment variables to solve the problem of multidimensional backpacks. The results obtained after the application of VNS are optimal with relatively short computational time.…”

Section: Introductionmentioning

confidence: 99%

Variable Neighborhoods Search for Multi-Site Production Planning

Rizki

Yuliastuti

Mahmudy

et al. 2018

JITeCS

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In the home textile industry, production planning needs to be done so that the production costs incurred by the company can be well controlled. Production planning is a problem that cannot be solved in a short time. Problems are more complex if the company has several production branches in other cities, with rules and standards that are certainly very different from one city to another. Based on this background, an algorithm is needed that can solve production planning problems for companies with many production branches in order to obtain optimal solutions. VNS is applied by the author and produces an optimal and efficient solution because the time needed is relatively short compared to the planning carried out previously by the company.

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A differential evolution algorithm with variable neighborhood search for multidimensional knapsack problem

Cited by 18 publications

References 58 publications

Heuristic and exact fixation-based approaches for the discounted 0-1 knapsack problem

Heuristic and exact fixation-based approaches for the discounted 0-1 knapsack problem

A Modified Binary Pigeon-Inspired Algorithm for Solving the Multi-dimensional Knapsack Problem

Variable Neighborhoods Search for Multi-Site Production Planning

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