Identifying preferred solutions to Multi-Objective Binary Optimisation problems, with an application to the Multi-Objective Knapsack Problem

Argyris, Nikolaos; Figueira, José Rui; Morton, Alec

doi:10.1007/s10898-010-9541-9

Cited by 12 publications

(8 citation statements)

References 33 publications

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“…where A is de…ned by a set of constraints on weights (for example, perhaps the weight associated with population 1 may be less than or equal to the three quarters of the weight associated with population 2). As it happens, algorithms for …nding A-e¢ cient solutions to MCO problems have been an active area for research in recent years (Liesiö et al, 2007;Argyris et al, 2011).…”

Section: De…nitionmentioning

confidence: 99%

“…Indeed, while algorithms for multicriteria linear programs have been well-known for some time (Steuer, 1986), algorithms for multicriteria integer and combinatorial problems are very much a live research …eld (Ehrgott and Gandibleux, 2000;Alves and Clímaco, 2007). To identify the A-e¢ cient solutions for problem (14) we use a computer code which implements the algorithm described in Argyris et al (2011). The idea of the algorithm is form a single combinatorial optimisation problem with both choice of alternative x and weights A k variable, and solve multiple times, progressively cutting o¤ solutions after they have been identi…ed.…”

Section: Analysis Of the Discrete Versionmentioning

confidence: 99%

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Aversion to health inequalities in healthcare prioritisation: A multicriteria optimisation perspective

Morton

2014

Journal of Health Economics

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In this paper we discuss the prioritisation of healthcare projects where there is a concern about health inequalities, but the decision maker is reluctant to make explicit quantitative value judgements and the data systems only allow the measurement of health at an aggregate level. Our analysis begins with a standard welfare economic model of healthcare resource allocation. We show how - under the assumption that the healthcare projects under consideration have a small impact on individual health--the problem can be reformulated as one of finding a particular subset of the class of efficient solutions to an implied multicriteria optimisation problem. Algorithms for finding such solutions are readily available, and we demonstrate our approach through a worked example of treatment for clinical depression.

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Section: De…nitionmentioning

confidence: 99%

Section: Analysis Of the Discrete Versionmentioning

confidence: 99%

Aversion to health inequalities in healthcare prioritisation: A multicriteria optimisation perspective

Morton

2014

Journal of Health Economics

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“…The second column of Table 7 shows the result of the first step of the proposed procedure (Section 3.3) for comparing portfolios. That is, the PROMETHEE V classical solution given by (6), in which, c = p = 14. The third and fourth columns correspond to results of the second step.…”

Section: C-optimum Promethee V Applicationmentioning

confidence: 99%

“…Some alternatives have positive scores (net flows) and others have negative scores. Mavrotas et al(2006) mention that this issue was not clarified in previous studies on PROMETHEE V, since all the signs of the net flow should be positive in the objective function in(6). They suggest transforming all the net flows from PROMETHEE II into non-negative scores by changing the scaling of the net flows, with the following transformation:…”

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confidence: 99%

Portfolio Selection of Information Systems Projects Using Promethee v With C-Optimal Concept

Almeida¹,

Almeida²,

Costa³

2014

Pesqui. Oper.

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This paper presents a multicriteria decision model for selecting a portfolio of information system (IS) projects, which integrates strategic and organizational view within a multicriteria decision structure. The PROMETHEE V method, based on outranking relations is applied, considering the c-optimal concept in order to overcome some scaling problems found in the classical PROMETHEE V approach. Then, a procedure is proposed in order to make a final analysis of the c-optimal portfolios found as a result of using PROMETHEE V. Also, the organizational view is discussed, including some factors that may influence decision making on IS projects to be included in the portfolio, such as adding the company's strategic vision and technical aspects that demonstrate how IS contributes value to a company's business.

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“…Several studies have been proposed as for example in [5], [38], [39] and [49]. Often the aim is to define a new methodology to tackle these problems as in [4], [6] or [40].…”

Section: Introductionmentioning

confidence: 99%

A general space-time model for combinatorial optimization problems (and not only)

Barbati

Corrente

Greco

2020

Omega

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We consider the problem of defining a strategy consisting of a set of facilities taking into account also the location where they have to be assigned and the time in which they have to be activated. The facilities are evaluated with respect to a set of criteria. The plan has to be devised respecting some constraints related to different aspects of the problem such as precedence restrictions due to the nature of the facilities. Among the constraints, there are some related to the available budget. We consider also the uncertainty related to the performances of the facilities with respect to considered criteria, and plurality of stakeholders participating to the decision. The considered problem can be seen as the combination of some prototypical operations research problems: knapsack problem, location problem and project scheduling. Indeed, the basic brick of our model is a variable x ilt which takes value 1 if facility i is activated in location l at time t, and 0 otherwise. Due to the conjoint consideration of a location and a time in the decision variables, what we propose can be seen as a general space-time model for operations research problems. We discuss how such a model permits to handle complex problems using several methodologies including multiple attribute value theory and multiobjective optimization. With respect to the latter point, without any loss of the generality, we consider the compromise programming and an interactive methodology based on the Dominance-based Rough Set Approach. We illustrate the application of our model with a simple didactic example.

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Identifying preferred solutions to Multi-Objective Binary Optimisation problems, with an application to the Multi-Objective Knapsack Problem

Abstract: Multi-objective optimisation, Efficient solutions, Preferred solutions, Knapsack problems, Interactive procedures, Multi-criteria portfolio selection,

Cited by 12 publications

References 33 publications

Aversion to health inequalities in healthcare prioritisation: A multicriteria optimisation perspective

Aversion to health inequalities in healthcare prioritisation: A multicriteria optimisation perspective

Portfolio Selection of Information Systems Projects Using Promethee v With C-Optimal Concept

A general space-time model for combinatorial optimization problems (and not only)

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