Solving multiobjective, multiconstraint knapsack problems using mathematical programming and evolutionary algorithms

Florios, K; Mavrotas, G; Diakoulaki, D

dc.contributor.author	Florios, K	en
dc.contributor.author	Mavrotas, G	en
dc.contributor.author	Diakoulaki, D	en
dc.date.accessioned	2014-03-01T01:34:37Z
dc.date.available	2014-03-01T01:34:37Z
dc.date.issued	2010	en
dc.identifier.issn	0377-2217	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/20777
dc.subject	Branch and bound	en
dc.subject	Evolutionary algorithms	en
dc.subject	Knapsack problem	en
dc.subject	Multiobjective	en
dc.subject.classification	Management	en
dc.subject.classification	Operations Research & Management Science	en
dc.subject.other	Adaptive parameters	en
dc.subject.other	Approximate algorithms	en
dc.subject.other	Branch and bound	en
dc.subject.other	Branch and bounds	en
dc.subject.other	Branching heuristics	en
dc.subject.other	Constraint methods	en
dc.subject.other	Data sets	en
dc.subject.other	Degree of approximation	en
dc.subject.other	Epsilon-constraint method	en
dc.subject.other	Exact algorithms	en
dc.subject.other	General purpose	en
dc.subject.other	Knapsack problem	en
dc.subject.other	Knapsack problems	en
dc.subject.other	Meta heuristics	en
dc.subject.other	Multi objective evolutionary algorithms	en
dc.subject.other	Multi-constraints	en
dc.subject.other	Multi-criteria	en
dc.subject.other	Multiobjective	en
dc.subject.other	NSGA-II	en
dc.subject.other	Objective functions	en
dc.subject.other	Operational research	en
dc.subject.other	Pareto front	en
dc.subject.other	Specific problems	en
dc.subject.other	Adaptive algorithms	en
dc.subject.other	Approximation algorithms	en
dc.subject.other	Heuristic methods	en
dc.subject.other	Integer programming	en
dc.subject.other	Linear programming	en
dc.subject.other	Multiobjective optimization	en
dc.subject.other	Evolutionary algorithms	en
dc.title	Solving multiobjective, multiconstraint knapsack problems using mathematical programming and evolutionary algorithms	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.ejor.2009.06.024	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.ejor.2009.06.024	en
heal.language	English	en
heal.publicationDate	2010	en
heal.abstract	In this paper, we solve instances of the multiobjective multiconstraint (or multidimensional) knapsack problem (MOMCKP) from the literature. with three objective functions and three constraints. We use exact as well as approximate algorithms. The exact algorithm is a properly modified version of the multicriteria branch and bound (MCBB) algorithm, which is further customized by suitable heuristics. Three branching heuristics and a more general purpose composite branching and construction heuristic are devised. Comparison is made to the published results from another exact algorithm, the adaptive epsilon-constraint method [Laumanns, M., Thiele, L, Zitzler, E., 2006. An efficient, adaptive parameter variation scheme for Metaheuristics based on the epsilon-constraint method. European journal of operational Research 169, 932-942], using the same data sets. Furthermore, the same problems are solved using standard multiobjective evolutionary algorithms (MOEA), namely, the SPEA2 and the NSGAII. The results from the exact case show that the branching heuristics greatly improve the performance of the MCBB algorithm, which becomes faster than the adaptive epsilon-constraint. Regarding the performance of the MOEA algorithms in the specific problems, SPEA2 outperforms NSGAII in the degree of approximation of the Pareto front, as measured by the coverage metric (especially for the largest instance). (C) 2009 Elsevier B.V. All rights reserved.	en
heal.publisher	ELSEVIER SCIENCE BV	en
heal.journalName	European Journal of Operational Research	en
dc.identifier.doi	10.1016/j.ejor.2009.06.024	en
dc.identifier.isi	ISI:000272073100002	en
dc.identifier.volume	203	en
dc.identifier.issue	1	en
dc.identifier.spage	14	en
dc.identifier.epage	21	en