A new mixed integer programming approach for optimization over the efficient set of a multiobjective linear programming problem

Lu, Kuan; Mizuno, Shinji; Shi, Jianming

doi:10.1007/s11590-020-01554-7

Cited by 8 publications

(5 citation statements)

References 19 publications

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“…Note that the convergence of the models (20), ( 21) and ( 24), (25) under the condition that ∑ K k=1 Q k is positive definite matrix. Thus, these models can not solve linear programming problems which limits their application.…”

Section: Comparing With Some Existing Modelsmentioning

confidence: 99%

“…It is clear that this model is not stable. The single objective problem is also solved by using neural network in (24) and (25). From Figure 3, we see that this model is not suitable for solving the MOLP problem.…”

Section: Numerical Simulationsmentioning

confidence: 99%

“…Antunes et al in Reference 24 debated on five multi‐objective interactive methods for MOLP problems, which are representative of different strategies of search. Lu et al in Reference 25 solved an equivalent mixed integer programming problem to compute an optimal solution to the MOLP problems. Shao and Ehrgott in Reference 21 proposed an approximation version of Benson's algorithm to sandwich the extended feasible set of an MOLP with an outer approximation and an inner approximation.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Comparing With Some Existing Modelsmentioning

confidence: 99%

Section: Numerical Simulationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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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“…The optimization function J consists of two parts: the predictive control output ˆ( 1) 15) is a multi-objective optimization problem with constraints [26,27], the efficient set method can be used to solve it [28]. In order to facilitate the solution by the efficient set method, the relevant constraints can be organized as:…”

Section: Nh Inmentioning

confidence: 99%

Data-Driven Predictive Control With Switched Subspace Matrices for an SCR System

et al. 2022

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Selective catalytic reduction (SCR) systems are distributed systems with strong timevarying parameter characteristics such that an accurate model for it is difficult to establish. Its control task simultaneously achieving high NO x conversion efficiency and low 3 NH slip is a typical multi-objective and multi-constraint problem, which is suitable to be solved in the framework of the model predictive control (MPC). However, how to find a data-driven identification method based on the dynamic characteristics of an SCR system and a corresponding MPC method for satisfying its emission requirements remain a formidable challenge. The sufficient identification for the traditional identification method with fixed subspace model requires an excessively high order subspace matrix, such that a degradation in real-time performance is caused and the generality of the method under non-identification conditions is limited. In this paper, utilizing the transient data of the SCR system under the WHTC cycle, a novel identification method for some lower order subspace matrices excited by the segmented data referring to the dynamic of the ammonia coverage ratio is established. A corresponding predictive controller with the switched subspace matrices according to working conditions is designed in order to further improve its real-time performance, generality and robustness. The simulation results show that under the identification condition the proposed predictive controller compared to the traditional method can improve the emissions of NO x and 3 NH , that under the non-identification condition the proposed predictive controller can also improve the emissions and its optimization effects have better robustness to uncertainties of the transient cycle, and that the proposed predictive controller saves an significant computation time.

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“…There have been researches on the problem of optimizing over Pareto outcome set in the case the objectives of Problem (VM) are linear or convex. Benson [5] proposed an outcome-based algorithm in linear case, followed by some variations of Branch-and-Bound algorithms in [8] and a new mixed integer programming approach proposed by Lu et al in [20]. On the other hand, the case of convex objectives was considered by Muu in [23].…”

mentioning

confidence: 99%

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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A new mixed integer programming approach for optimization over the efficient set of a multiobjective linear programming problem

Cited by 8 publications

References 19 publications

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

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

Data-Driven Predictive Control With Switched Subspace Matrices for an SCR System

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

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