Exact Solution Algorithms for Multi-dimensional Multiple-choice Knapsack Problems

Ghassemi-Tari, Farhad; Hendizadeh, Hamed; Hogg, Gary L.

doi:10.9734/cjast/2018/40420

Cited by 6 publications

(6 citation statements)

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“…Ghassemi‐Tari et al. (2018) propose a depth‐first branch‐and‐bound approach for solving the MMKP. Nodes are selected based on a discriminating criterion.…”

Section: Relevant Literature On the Mmkpmentioning

confidence: 99%

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Simple strategies that generate bounded solutions for the multiple‐choice multi‐dimensional knapsack problem: a guide for OR practitioners

Dellinger

Song

et al. 2022

Int Trans Operational Res

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The multiple‐choice multi‐dimensional knapsack problem (MMKP) is an NP‐hard generalization of the classic 0–1 knapsack problem. The MMKP has a variety of important industrial and business applications. Approximate solution approaches characteristically give no guarantees on solution quality. Exact solution approaches usually generate solutions that are guaranteed to be close to the optimum but typically take excessive computation times—one to several hours have been recorded in the literature. In this article, we use both simple single‐step and multiple step strategies to demonstrate how a commercial software package (Gurobi in this case) can easily be used to generate guaranteed tightly bounded solutions for 293 MMKP instances commonly tested in the literature. These four simple strategies that require no problem‐specific algorithms are shown to perform competitively with the five best published algorithms for the MMKP. Since no problem‐specific coding is required, these simple strategies are easy for operations research practitioners to use.

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“…Ghassemi‐Tari et al. (2018) propose a depth‐first branch‐and‐bound approach for solving the MMKP. Nodes are selected based on a discriminating criterion.…”

Section: Relevant Literature On the Mmkpmentioning

confidence: 99%

“…This approach can be used either as an exact procedure or heuristically. Ghassemi-Tari et al (2018) propose a depth-first branch-and-bound approach for solving the MMKP. Nodes are selected based on a discriminating criterion.…”

Section: Mathematical Programming-based Solution Approachesmentioning

confidence: 99%

Simple strategies that generate bounded solutions for the multiple‐choice multi‐dimensional knapsack problem: a guide for OR practitioners

Dellinger

Song

et al. 2022

Int Trans Operational Res

View full text Add to dashboard Cite

show abstract

“…The reduction of a solution space and enumeration of a smaller number of nodes in BB based algorithms have been onerous in finding solutions for various knapsack problems. However, Tari [52] presented an algorithmic procedure based on the BB with three different selective branching mechanisms for the reduction of the solution space to derive an optimal solution of the Multi-dimensional Multi-choice Knapsack problem.…”

Section: ) Exact Algorithmsmentioning

confidence: 99%

A Comparative Study of Meta-Heuristic Optimization Algorithms for 0 – 1 Knapsack Problem: Some Initial Results

et al. 2019

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In this paper, we present some initial results of several meta-heuristic optimization algorithms, namely, genetic algorithms, simulated annealing, branch and bound, dynamic programming, greedy search algorithm, and a hybrid genetic algorithm-simulated annealing for solving the 0-1 knapsack problems. Each algorithm is designed in such a way that it penalizes infeasible solutions and optimizes the feasible solution. The experiments are carried out using both low-dimensional and high-dimensional knapsack problems. The numerical results of the hybrid algorithm are compared with the results achieved by the individual algorithms. The results revealed the superior performances of the branch and bound dynamic programming, and hybrid genetic algorithm with simulated annealing methods over all the compared algorithms. This performance was established by taking into account both the algorithm computational time and the solution quality. In addition, the obtained results also indicated that the hybrid algorithm can be applied as an alternative to solve smalland large-sized 0-1 knapsack problems.INDEX TERMS Knapsack problem, genetic algorithms, simulated annealing, branch and bound, dynamic programming, greedy search algorithm, hybrid IGA-SA.

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“…Parra-Hernandez and Dimopoulos [7] extended the idea of their heuristic approach for the MKP to the MMKP. Over the last 10 years, studies of the MMKP have focused on iterative heuristics [16][17][18][19], branch-and-bound methods [20,21], Lagrangian relaxation [22][23][24], linear programming relaxation [25], reformulation/reduction [25][26][27][28], Pareto-algebraic heuristics [20,29], approximate core [30], core-based exact algorithm [31], two-phase kernel search [32], meta-heuristics such as genetic algorithm [33], swarm intelligence [23,[34][35][36][37], estimation of distribution algorithm [38], simulated annealing [39], tabu search [40], etc.…”

Section: Introductionmentioning

confidence: 99%

A Memetic Algorithm with a Novel Repair Heuristic for the Multiple-Choice Multidimensional Knapsack Problem

2022

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We propose a memetic algorithm for the multiple-choice multidimensional knapsack problem (MMKP). In this study, we focus on finding good solutions for the MMKP instances, for which feasible solutions rarely exist. To find good feasible solutions, we introduce a novel repair heuristic based on the tendency function and a genetic search for the function approximation. Even when the density of feasible solutions over the entire solution space is very low, the proposed repair heuristic could successfully change infeasible solutions into feasible ones. Based on the proposed repair heuristic and effective local search, we designed a memetic algorithm that performs well on problem instances with a low density of feasible solutions. By performing experiments, we could show the superiority of our method compared with previous genetic algorithms.

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Exact Solution Algorithms for Multi-dimensional Multiple-choice Knapsack Problems

Cited by 6 publications

References 0 publications

Simple strategies that generate bounded solutions for the multiple‐choice multi‐dimensional knapsack problem: a guide for OR practitioners

Simple strategies that generate bounded solutions for the multiple‐choice multi‐dimensional knapsack problem: a guide for OR practitioners

A Comparative Study of Meta-Heuristic Optimization Algorithms for 0 – 1 Knapsack Problem: Some Initial Results

A Memetic Algorithm with a Novel Repair Heuristic for the Multiple-Choice Multidimensional Knapsack Problem

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