A reduction dynamic programming algorithm for the bi-objective integer knapsack problem

•Introduce size reduction and upper bound reduction based on the core concept.•Construct the mixed network consisting of items with different upper bounds.•Develop an efficient dynamic programming algorithm based on the mixed network.•Conduct the time complexity analysis for the reduction procedures...

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Vydané v:European journal of operational research Ročník 231; číslo 2; s. 299 - 313
Hlavní autori: Rong, Aiying, Figueira, José Rui
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Amsterdam Elsevier B.V 01.12.2013
Elsevier Sequoia S.A
Predmet:
Algorithms
Approximation
Core concept
Dominance relation
Dynamic programming
Effectiveness studies
Integer knapsack problem
Integer programming
Integers
Knapsack problem
Mathematical functions
Mathematical models
Multi-objective programming
Networks
Pareto optimum
State reduction
Upper bounds
Dominance relation
Multi-objective programming
Dynamic programming
State reduction
Integer knapsack problem
Core concept
ISSN:0377-2217, 1872-6860
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Shrnutí:•Introduce size reduction and upper bound reduction based on the core concept.•Construct the mixed network consisting of items with different upper bounds.•Develop an efficient dynamic programming algorithm based on the mixed network.•Conduct the time complexity analysis for the reduction procedures.•Conduct the time and space analysis for the developed algorithm. This paper presents a backward state reduction dynamic programming algorithm for generating the exact Pareto frontier for the bi-objective integer knapsack problem. The algorithm is developed addressing a reduced problem built after applying variable fixing techniques based on the core concept. First, an approximate core is obtained by eliminating dominated items. Second, the items included in the approximate core are subject to the reduction of the upper bounds by applying a set of weighted-sum functions associated with the efficient extreme solutions of the linear relaxation of the multi-objective integer knapsack problem. Third, the items are classified according to the values of their upper bounds; items with zero upper bounds can be eliminated. Finally, the remaining items are used to form a mixed network with different upper bounds. The numerical results obtained from different types of bi-objective instances show the effectiveness of the mixed network and associated dynamic programming algorithm.
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ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2013.05.045