Identifying preferred solutions to multi-objective binary optimisation problems, with an application to the multi-objective knapsack problem

Nikolaos Argyris, José Rui Figueira, Alec Morton

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

In this paper we present a new framework for identifying preferred solutions to multi-objective binary optimisation problems. We develop the necessary theory which leads to new formulations that integrate the decision space with the space of criterion weights. The advantage of this is that it allows for incorporating preferences directly within a unique binary optimisation problem which identifies efficient solutions and associated weights simultaneously. We discuss how preferences can be incorporated within the formulations and also describe how to accommodate the selection of weights when the identification of a unique solution is required. Our results can be used for designing interactive procedures for the solution of multi-objective binary optimisation problems. We describe one such procedure for the multi-objective multi-dimensional binary knapsack formulation of the portfolio selection problem.
LanguageEnglish
Pages213-235
Number of pages23
JournalJournal of Global Optimization
Volume49
Issue number2
DOIs
Publication statusPublished - 2011

Fingerprint

Knapsack Problem
Binary
Optimization Problem
Formulation
Knapsack
Portfolio Selection
Efficient Solution
Unique Solution
Integrate
Necessary
Optimization problem
Knapsack problem

Keywords

  • knapsack problem
  • solutions
  • multi-objective
  • binary optimisation
  • application

Cite this

@article{edab4f1ca7964c0fa6b9117a8b72ca93,
title = "Identifying preferred solutions to multi-objective binary optimisation problems, with an application to the multi-objective knapsack problem",
abstract = "In this paper we present a new framework for identifying preferred solutions to multi-objective binary optimisation problems. We develop the necessary theory which leads to new formulations that integrate the decision space with the space of criterion weights. The advantage of this is that it allows for incorporating preferences directly within a unique binary optimisation problem which identifies efficient solutions and associated weights simultaneously. We discuss how preferences can be incorporated within the formulations and also describe how to accommodate the selection of weights when the identification of a unique solution is required. Our results can be used for designing interactive procedures for the solution of multi-objective binary optimisation problems. We describe one such procedure for the multi-objective multi-dimensional binary knapsack formulation of the portfolio selection problem.",
keywords = "knapsack problem, solutions, multi-objective, binary optimisation, application",
author = "Nikolaos Argyris and Figueira, {Jos{\'e} Rui} and Alec Morton",
year = "2011",
doi = "10.1007/s10898-010-9541-9",
language = "English",
volume = "49",
pages = "213--235",
journal = "Journal of Global Optimization",
issn = "0925-5001",
number = "2",

}

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.

In: Journal of Global Optimization, Vol. 49, No. 2, 2011, p. 213-235.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Identifying preferred solutions to multi-objective binary optimisation problems, with an application to the multi-objective knapsack problem

AU - Argyris, Nikolaos

AU - Figueira, José Rui

AU - Morton, Alec

PY - 2011

Y1 - 2011

N2 - In this paper we present a new framework for identifying preferred solutions to multi-objective binary optimisation problems. We develop the necessary theory which leads to new formulations that integrate the decision space with the space of criterion weights. The advantage of this is that it allows for incorporating preferences directly within a unique binary optimisation problem which identifies efficient solutions and associated weights simultaneously. We discuss how preferences can be incorporated within the formulations and also describe how to accommodate the selection of weights when the identification of a unique solution is required. Our results can be used for designing interactive procedures for the solution of multi-objective binary optimisation problems. We describe one such procedure for the multi-objective multi-dimensional binary knapsack formulation of the portfolio selection problem.

AB - In this paper we present a new framework for identifying preferred solutions to multi-objective binary optimisation problems. We develop the necessary theory which leads to new formulations that integrate the decision space with the space of criterion weights. The advantage of this is that it allows for incorporating preferences directly within a unique binary optimisation problem which identifies efficient solutions and associated weights simultaneously. We discuss how preferences can be incorporated within the formulations and also describe how to accommodate the selection of weights when the identification of a unique solution is required. Our results can be used for designing interactive procedures for the solution of multi-objective binary optimisation problems. We describe one such procedure for the multi-objective multi-dimensional binary knapsack formulation of the portfolio selection problem.

KW - knapsack problem

KW - solutions

KW - multi-objective

KW - binary optimisation

KW - application

U2 - 10.1007/s10898-010-9541-9

DO - 10.1007/s10898-010-9541-9

M3 - Article

VL - 49

SP - 213

EP - 235

JO - Journal of Global Optimization

T2 - Journal of Global Optimization

JF - Journal of Global Optimization

SN - 0925-5001

IS - 2

ER -