k-Set frameworks in multi-criteria combinatorial optimisation
by Mark Sh. Levin
International Journal of Technology, Policy and Management (IJTPM), Vol. 11, No. 1, 2011

Abstract: This paper addresses frameworks for structuring/formulation and solving of complex discrete decision-making problems. Multi-criteria combinatorial optimisation problems based on k sets of elements (k = 1, 2, 3, 4) are examined. Firstly, for each set of elements, a multi-attribute description of elements and/or binary relation over elements is considered. Further, a combinatorial optimisation problem over a set of elements is analysed (e.g. ranking, selection, knapsack problem, ordering/scheduling, clustering, spanning trees and design of a hierarchy over elements). Secondly, binary relation over elements of two different sets can be considered (k > 1). As a result, combinatorial optimisation problems are examined, e.g. matching, assignment and allocation. Finally, generalised k-set frameworks for problem formulation are described for some application decision-making domains, e.g. 'clustering-multiple choice problem', 'clustering-assignment', 'ranking-allocation', 'assignment-multiple choice problem', 'clustering-assignment-multiple choice problem', 'clustering-clique' (multi-partite clique) and 'clustering-assignment-scheduling'. The generalised problem formulation frameworks are used at various stages of system life cycle and in many domains: system design, system improvement, system testing, system maintenance, marketing, information retrieval, multi-target assignment, multi-processor scheduling, timetabling, etc. The suggested k-set frameworks were for education.

Online publication date: Tue, 31-Mar-2015

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