A multi-criteria approach to approximate solution of multiple-choice knapsack problem

We propose a method for finding approximate solutions to multiple-choice knapsack problems. To this aim we transform the multiple-choice knapsack problem into a bi-objective optimization problem whose solution set contains solutions of the original multiple-choice knapsack problem. The method relies...

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Bibliographic Details
Published in:Computational optimization and applications Vol. 70; no. 3; pp. 889 - 910
Main Authors: Bednarczuk, Ewa M., Miroforidis, Janusz, Pyzel, Przemysław
Format: Journal Article
Language:English
Published: New York Springer US 01.07.2018
Springer Nature B.V
Subjects:
Branch & bound algorithms
Computation
Convex and Discrete Geometry
Dynamic programming
Greedy algorithms
Knapsack problem
Management Science
Mathematics
Mathematics and Statistics
Multiple choice
Operations Research
Operations Research/Decision Theory
Optimization
Statistics
Multi-objective optimization
Knapsack
Linear scalarization
Multiple-choice knapsack
ISSN:0926-6003, 1573-2894
Online Access:Get full text
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Summary:We propose a method for finding approximate solutions to multiple-choice knapsack problems. To this aim we transform the multiple-choice knapsack problem into a bi-objective optimization problem whose solution set contains solutions of the original multiple-choice knapsack problem. The method relies on solving a series of suitably defined linearly scalarized bi-objective problems. The novelty which makes the method attractive from the computational point of view is that we are able to solve explicitly those linearly scalarized bi-objective problems with the help of the closed-form formulae. The method is computationally analyzed on a set of large-scale problem instances (test problems) of two categories: uncorrelated and weakly correlated. Computational results show that after solving, in average 10 scalarized bi-objective problems, the optimal value of the original knapsack problem is approximated with the accuracy comparable to the accuracies obtained by the greedy algorithm and an exact algorithm. More importantly, the respective approximate solution to the original knapsack problem (for which the approximate optimal value is attained) can be found without resorting to the dynamic programming. In the test problems, the number of multiple-choice constraints ranges up to hundreds with hundreds variables in each constraint.
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ISSN:0926-6003
1573-2894
DOI:10.1007/s10589-018-9988-z