When to use Integer Programming Software to solve large multi-demand multidimensional knapsack problems: a guide for operations research practitioners

Song, Myung Soon; Emerick, Brooks; Lu, Yun; Vasko, Francis J.

doi:10.1080/0305215x.2021.1933965

Cited by 5 publications

(5 citation statements)

References 13 publications

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“…In fact, in a recent article, Song et al. (2021) demonstrated that there are MDMKPs from the literature with as few as 100 variables that did not obtain even a feasible solution after an hour of execution time using CPLEX (12.9) on a standard PC. Therefore, in general, the authors do not expect the simple single‐step strategy to be beneficial for solving all COPs.…”

Section: Mmkp Empirical Resultsmentioning

confidence: 99%

“…Additionally, in Dellinger et al (2021), both Gurobi and CPLEX were used to solve the GAP instances, and there was no statistically significant difference in solution quality or execution times between Gurobi and CPLEX. Using classification tree analysis, Song et al (2021) classify multi-demand MKPs (MDMKPs) as either easy, moderate, or difficult to solve based on predicted execution time to solve the MDMKP on a standard PC. Dellinger et al (2022) customized SSIT strategies to solve MDMKPs based on their difficulty classification.…”

Section: Multiple Pass Mode (Ssit Methodology)mentioning

confidence: 99%

“…Using classification tree analysis, Song et al. (2021) classify multi‐demand MKPs (MDMKPs) as either easy, moderate, or difficult to solve based on predicted execution time to solve the MDMKP on a standard PC. Dellinger et al.…”

Section: Overview Of the Simple Strategies For Solving Mmkps With Gurobimentioning

confidence: 99%

“…It is common for difficult combinatorial optimization problems (COPs) to require excessive computing time when simple single-step strategies such as BCASE1 or BCASE2 are used. In fact, in a recent article, Song et al (2021) demonstrated that there are MDMKPs from the literature with as few as 100 variables that did not obtain even a feasible solution after an hour of execution time using CPLEX (12.9) on a standard PC. Therefore, in general, the authors do not expect the simple single-step strategy to be beneficial for solving all COPs.…”

Section: Multiple-step Strategies Ssit1mentioning

confidence: 99%

See 3 more Smart Citations

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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Section: Mmkp Empirical Resultsmentioning

confidence: 99%

Section: Multiple Pass Mode (Ssit Methodology)mentioning

confidence: 99%

Section: Overview Of the Simple Strategies For Solving Mmkps With Gurobimentioning

confidence: 99%

Section: Multiple-step Strategies Ssit1mentioning

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

Self Cite

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show abstract

“…More benefits of SSIT are detailed in [19]. Successful applications of SSIT to solve several binary integer programs (BIP) have been documented in the literature [14][15][16][17][18][19]. For these applications, SSIT typically generates solutions guaranteed to be within 0.1% of the optimums in about 60 seconds on standard PCs.…”

Section: Methodsmentioning

confidence: 99%

Using general-purpose integer programming software to generate bounded solutions for the multiple knapsack problem: a guide for or practitioners

Shively-Ertas

Lu²,

Song³

et al. 2023

Int. J. Ind. Optim.

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An NP-Hard combinatorial optimization problem that has significant industrial applications is the Multiple Knapsack Problem. If approximate solution approaches are used to solve the Multiple Knapsack Problem there are no guarantees on solution quality and exact solution approaches can be intricate and challenging to implement. This article demonstrates the iterative use of general-purpose integer programming software (Gurobi) to generate solutions for test problems that are available in the literature. Using the software package Gurobi on a standard PC, we generate in a relatively straightforward manner solutions to these problems in an average of less than a minute that are guaranteed to be within 0.16% of the optimum. This algorithm, called the Simple Sequential Increasing Tolerance (SSIT) algorithm, iteratively increases tolerances in Gurobi to generate a solution that is guaranteed to be close to the optimum in a short time. This solution strategy generates bounded solutions in a timely manner without requiring the coding of a problem-specific algorithm. This approach is attractive to management for solving industrial problems because it is both cost and time effective and guarantees the quality of the generated solutions. Finally, comparing SSIT results for 480 large multiple knapsack problem instances to results using published multiple knapsack problem algorithms demonstrates that SSIT outperforms these specialized algorithms.

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Verifying new instances of the multidemand multidimensional knapsack problem with instance space analysis

Scherer,

Hill,

Lunday

et al. 2024

Computers & Operations Research

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When to use Integer Programming Software to solve large multi-demand multidimensional knapsack problems: a guide for operations research practitioners

Cited by 5 publications

References 13 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

Using general-purpose integer programming software to generate bounded solutions for the multiple knapsack problem: a guide for or practitioners

Verifying new instances of the multidemand multidimensional knapsack problem with instance space analysis

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