Solving the bi-objective multi-dimensional knapsack problem exploiting the concept of core

Mavrotas, G; Figueira, JR; Florios, K

dc.contributor.author	Mavrotas, G	en
dc.contributor.author	Figueira, JR	en
dc.contributor.author	Florios, K	en
dc.date.accessioned	2014-03-01T01:31:57Z
dc.date.available	2014-03-01T01:31:57Z
dc.date.issued	2009	en
dc.identifier.issn	0096-3003	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/19986
dc.subject	Core	en
dc.subject	Knapsack	en
dc.subject	Multi-dimensional	en
dc.subject	Multi-objective programming	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.other	Branch-and-bound algorithms	en
dc.subject.other	Computational experiment	en
dc.subject.other	Core	en
dc.subject.other	Core problems	en
dc.subject.other	Divide and conquer	en
dc.subject.other	Exact solution	en
dc.subject.other	Integer programming problems	en
dc.subject.other	Knapsack	en
dc.subject.other	Medium size	en
dc.subject.other	Multi objective	en
dc.subject.other	Multi-criteria	en
dc.subject.other	Multi-dimensional	en
dc.subject.other	Multi-objective programming	en
dc.subject.other	Multidimensional knapsack problems	en
dc.subject.other	Pareto set	en
dc.subject.other	Quality of solution	en
dc.subject.other	Solution time	en
dc.subject.other	Sub-problems	en
dc.subject.other	Trade off	en
dc.subject.other	Algorithms	en
dc.subject.other	Benchmarking	en
dc.subject.other	Computer software selection and evaluation	en
dc.subject.other	Dynamic programming	en
dc.subject.other	Integer programming	en
dc.subject.other	Linear programming	en
dc.subject.other	Multiobjective optimization	en
dc.subject.other	Problem solving	en
dc.title	Solving the bi-objective multi-dimensional knapsack problem exploiting the concept of core	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.amc.2009.08.045	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.amc.2009.08.045	en
heal.language	English	en
heal.publicationDate	2009	en
heal.abstract	This paper deals with the bi-objective multi-dimensional knapsack problem. We propose the adaptation of the core concept that is effectively used in single-objective multi-dimensional knapsack problems. The main idea of the core concept is based on the ""divide and conquer"" principle. Namely, instead of solving one problem with n variables we solve several sub-problems with a fraction of n variables (core variables). The quality of the obtained solution can be adjusted according to the size of the core and there is always a trade off between the solution time and the quality of solution. In the specific study we define the core problem for the multi-objective multi-dimensional knapsack problem. After defining the core we solve the bi-objective integer programming that comprises only the core variables using the Multicriteria Branch and Bound algorithm that can generate the complete Pareto set in small and medium size multi-objective integer programming problems. A small example is used to illustrate the method while computational and economy issues are also discussed. Computational experiments are also presented using available or appropriately modified benchmarks in order to examine the quality of Pareto set approximation with respect to the solution time. Extensions to the general multi-objective case as well as to the computation of the exact solution are also mentioned. © 2009 Elsevier Inc. All rights reserved.	en
heal.publisher	ELSEVIER SCIENCE INC	en
heal.journalName	Applied Mathematics and Computation	en
dc.identifier.doi	10.1016/j.amc.2009.08.045	en
dc.identifier.isi	ISI:000271640200012	en
dc.identifier.volume	215	en
dc.identifier.issue	7	en
dc.identifier.spage	2502	en
dc.identifier.epage	2514	en