Rights statement: This is an Accepted Manuscript of an article published by Taylor & Francis in Optimization 2018, available online: https://www.tandfonline.com/doi/full/10.1080/02331934.2018.1484922
Accepted author manuscript, 316 KB, PDF document
Available under license: CC BY-NC: Creative Commons Attribution-NonCommercial 4.0 International License
Final published version
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
TY - JOUR
T1 - Primal and Dual Algorithms for Optimization over the Efficient Set
AU - Liu, Zhengliang
AU - Ehrgott, Matthias
N1 - This is an Accepted Manuscript of an article published by Taylor & Francis in Optimization 2018, available online: https://www.tandfonline.com/doi/full/10.1080/02331934.2018.1484922
PY - 2018
Y1 - 2018
N2 - Optimisation over the efficient set of a multi-objective optimisation problem is a mathematical model for the problem of selecting a most preferred solution that arises in multiple criteria decision making to account for trade-offs between objectives within the set of efficient solutions. In this paper we consider a particular case of this problem, namely that of optimising a linear function over the image of the efficient set in objective space of a convex multi-objective optimisation problem. We present both primal and dual algorithms for this task.The algorithms are based on recent algorithms for solving convex multi-objective optimisation problems in objective space with suitable modifications to exploit specific properties of the problem of optimisation over the efficient set. We first present the algorithms for the case that the underlying problem is a multi-objective linear programme. We then extend them to be able to solve problems with an underlying convex multiobjective optimisation problem.We compare the new algorithms with several state of the art algorithms from the literature on a set of randomly generated instances to demonstrate that they are considerably faster than the competitors.
AB - Optimisation over the efficient set of a multi-objective optimisation problem is a mathematical model for the problem of selecting a most preferred solution that arises in multiple criteria decision making to account for trade-offs between objectives within the set of efficient solutions. In this paper we consider a particular case of this problem, namely that of optimising a linear function over the image of the efficient set in objective space of a convex multi-objective optimisation problem. We present both primal and dual algorithms for this task.The algorithms are based on recent algorithms for solving convex multi-objective optimisation problems in objective space with suitable modifications to exploit specific properties of the problem of optimisation over the efficient set. We first present the algorithms for the case that the underlying problem is a multi-objective linear programme. We then extend them to be able to solve problems with an underlying convex multiobjective optimisation problem.We compare the new algorithms with several state of the art algorithms from the literature on a set of randomly generated instances to demonstrate that they are considerably faster than the competitors.
KW - Multi-objective optimisation, optimisation over the efficient set, objective space algorithm, duality.
KW - optimisation over the efficient set
KW - objective space algorithm
KW - duality
U2 - 10.1080/02331934.2018.1484922
DO - 10.1080/02331934.2018.1484922
M3 - Journal article
VL - 67
SP - 1661
EP - 1686
JO - Optimization
JF - Optimization
SN - 0233-1934
IS - 10
ER -