An outcome space algorithm for optimization over the weakly efficient set of a multiple objective nonlinear programming problem

Benson, Harold P.

doi:10.1007/s10898-011-9786-y

Cited by 21 publications

(23 citation statements)

References 31 publications

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“…A branch and bound technique also plays an essential role in the algorithm of [3]. This algorithm is designed for globally optimising a finite, convex function over the weakly efficient set of a nonlinear multi-objective optimisation problem that has nonlinear objective functions and a convex, non-polyhedral feasible region.…”

Section: Outcome Space Algorithmmentioning

confidence: 99%

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Primal and dual algorithms for optimization over the efficient set

Liu

Ehrgott

2018

Optimization

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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. Keywords:Multi-objective optimisation, optimisation over the efficient set, objective space algorithm, duality.

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Section: Outcome Space Algorithmmentioning

confidence: 99%

“…A relaxed problem is used to find upper bounds by using a convex combination of the vertices of the simplex. The reader is referred to [3] for more details.…”

Section: Outcome Space Algorithmmentioning

confidence: 99%

Primal and dual algorithms for optimization over the efficient set

Liu

Ehrgott

2018

Optimization

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“…. Benson [2,3,4] argues that generating the Pareto outcome set requires less computational effort than generating the Pareto set itself since in mathematical models, the number of objectives is often fewer than the number of variables. Moreover, in practical issues, decision makers naturally base on the objective values rather than on variable values to select the best option.…”

mentioning

confidence: 99%

“…Thoai [30] then proposed a decomposition Branch-and-Bound algorithm, while he also considered concave approach in [31]. A cutting-plane algorithm was proposed by Benson in [3], extended by Kim et al in [17]. Bonnel et al [6] then proposed a deterministic algorithm, while Liu et al [18] developed Benson's approach to propose primal and dual algorithms.…”

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confidence: 99%

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Optimizing over Pareto set of semistrictly quasiconcave vector maximization and application to stochastic portfolio selection

Vượng¹,

Thang²

2023

JIMO

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<p style='text-indent:20px;'>Optimization over Pareto set of a semistrictly quasiconcave vector maximization problem has many applications in economics and technology but it is a challenging task because of the nonconvexity of objective functions and constraint sets. In this article, we propose a novel approach, which is a Branch-and-Bound algorithm for maximizing a composite function <inline-formula><tex-math id="M1">\begin{document}$ \varphi(f(x)) $\end{document}</tex-math></inline-formula> over the non-dominated solution set of the <inline-formula><tex-math id="M2">\begin{document}$ p $\end{document}</tex-math></inline-formula>-objective programming problem, where <inline-formula><tex-math id="M3">\begin{document}$ p\geq 2, p \in \mathbb{N}, $\end{document}</tex-math></inline-formula> the function <inline-formula><tex-math id="M4">\begin{document}$ \varphi $\end{document}</tex-math></inline-formula> is increasing and the objective function <inline-formula><tex-math id="M5">\begin{document}$ f $\end{document}</tex-math></inline-formula> is semistrictly quasiconcave. By utilizing the nice properties of Pareto set to define the partitions of branch and bound scheme, the proposed algorithms are promised to be more accurate and efficient than ones using the multi-objective evolutionary approach such as NSGA-III. This is validated by some computational experiments. The Stochastic Portfolio Selection Problem is chosen as an application of our algorithm, where Sharpe ratio is a semistrictly quasiconcave objective function.</p>

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Utilizing a projection neural network to convex quadratic multi‐objective programming problems

Jahangiri

Nazemi

2023

Adaptive Control & Signal

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Summary In this paper, we propose a projection neural network model for solving convex quadratic multi‐objective optimization problem (CQMOP). The CQMOP is first converted into an equivalent convex nonlinear programming problem by the means of the weighted sum method, where the Pareto optimal solutions are calculated via different values of weights. A neural network model is then constructed for solving the obtained convex problem. It is shown that the presented neural network is stable in the sense of Lyapunov and is globally convergent. Simulation results are given to illustrate the global convergence and performance of the suggested model. Both theoretical and numerical approaches are studied. Numerical results are in good agreement with the proved theoretical concepts.

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An outcome space algorithm for optimization over the weakly efficient set of a multiple objective nonlinear programming problem

Cited by 21 publications

References 31 publications

Primal and dual algorithms for optimization over the efficient set

Primal and dual algorithms for optimization over the efficient set

Optimizing over Pareto set of semistrictly quasiconcave vector maximization and application to stochastic portfolio selection

Utilizing a projection neural network to convex quadratic multi‐objective programming problems

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