Using the idea of expanded core for the exact solution of bi-objective multi-dimensional knapsack problems

Mavrotas, G; Figueira, JR; Antoniadis, A

dc.contributor.author	Mavrotas, G	en
dc.contributor.author	Figueira, JR	en
dc.contributor.author	Antoniadis, A	en
dc.date.accessioned	2014-03-01T01:37:31Z
dc.date.available	2014-03-01T01:37:31Z
dc.date.issued	2011	en
dc.identifier.issn	0925-5001	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/21538
dc.subject	Core	en
dc.subject	Exact algorithm	en
dc.subject	Knapsack problem	en
dc.subject	Multi-objective programming	en
dc.subject.classification	Operations Research & Management Science	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.other	Branch-and-bound algorithms	en
dc.subject.other	Core	en
dc.subject.other	Core problems	en
dc.subject.other	Divide and conquer	en
dc.subject.other	Exact algorithms	en
dc.subject.other	Exact solution	en
dc.subject.other	Knapsack problems	en
dc.subject.other	Multi objective	en
dc.subject.other	Multidimensional knapsack problems	en
dc.subject.other	Multiobjective programming	en
dc.subject.other	Pareto optimal solutions	en
dc.subject.other	Pareto set	en
dc.subject.other	Single objective	en
dc.subject.other	Sub-problems	en
dc.subject.other	Approximation algorithms	en
dc.subject.other	Integer programming	en
dc.subject.other	Linear programming	en
dc.subject.other	Multiobjective optimization	en
dc.subject.other	Pareto principle	en
dc.subject.other	Problem solving	en
dc.title	Using the idea of expanded core for the exact solution of bi-objective multi-dimensional knapsack problems	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/s10898-010-9552-6	en
heal.identifier.secondary	http://dx.doi.org/10.1007/s10898-010-9552-6	en
heal.language	English	en
heal.publicationDate	2011	en
heal.abstract	We propose a methodology for obtaining the exact Pareto set of Bi-Objective Multi-Dimensional Knapsack Problems, exploiting the concept of core expansion. The core concept is effectively used in single objective multi-dimensional knapsack problems and it 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). In the multi-objective case, the general idea is that we start from an approximation of the Pareto set (produced with theMulti-Criteria Branch and Bound algorithm, using also the core concept) and we enrich this approximation iteratively. Every time an approximation is generated, we solve a series of appropriate single objective Integer Programming (IP) problems exploring the criterion space for possibly undiscovered, new Pareto Optimal Solutions (POS). If one or more new POS are found, we appropriately expand the already found cores and solve the new core problems. This process is repeated until no new POS are found from the IP problems. The paper includes an educational example and some experiments. © Springer Science+Business Media, LLC. 2010.	en
heal.publisher	SPRINGER	en
heal.journalName	Journal of Global Optimization	en
dc.identifier.doi	10.1007/s10898-010-9552-6	en
dc.identifier.isi	ISI:000288456900004	en
dc.identifier.volume	49	en
dc.identifier.issue	4	en
dc.identifier.spage	589	en
dc.identifier.epage	606	en