Generating properly efficient points in multi-objective programs by the nonlinear weighted sum scalarization method

Zarepisheh, Masoud; Khorram, Esmaile; Pardalos, Pãnos M.

doi:10.1080/02331934.2012.671819

Cited by 9 publications

(4 citation statements)

References 26 publications

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“…In [25], Zarepisheh et al have proved, given integer l > 0, the set of properly efficient solutions of (1) coincides with that of the following problem min…”

Section: Proper Efficiency and Transformationmentioning

confidence: 99%

Proper efficiency, scalarization and transformation in multi-objective optimization: Unified approaches

Zamani¹,

Soleimani-damaneh²

2019

Preprint

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In this paper, we investigate the relationships between proper efficiency and the solutions of a general scalarization problem in multi-objective optimization. We provide some conditions under which the solutions of the dealt with scalar program are properly efficient and vice versa. We also show that, under some conditions, if the considered general scalar problem is unbounded, then the original multi-objective problem does not have any properly efficient solution. In another part of the work, we investigate a general transformation of the objective functions which preserves proper efficiency. We show that several important results existing in the literature are direct consequences of the results of the present paper.

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“…In [25], Zarepisheh et al have proved, given integer l > 0, the set of properly efficient solutions of (1) coincides with that of the following problem min…”

Section: Proper Efficiency and Transformationmentioning

confidence: 99%

Proper efficiency, scalarization and transformation in multi-objective optimization: Unified approaches

Zamani¹,

Soleimani-damaneh²

2019

Preprint

View full text Add to dashboard Cite

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“…Sometimes, the solutions of multiobjective optimization problems, which are obtained by the algorithms based on weighted sum method, are not well distributed in the Pareto optimal front. Studies can be found in this field [4,32]. However, the algorithm in this paper is for multiobjective engineering optimization problems, which do not require even-distributed Pareto optimal solutions in the Pareto optimal front.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…Combining with some gradient methods, a scalar method can easily obtain the optimum by iterations. Typical multiobjective scalar methods include traditional weighted sum method [3,4], constraint method [5], NBI [6], and multiobjective automatic weighted sum method [7]. With the continuous development, more and more new scalar methods have emerged in this field [8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

An Efficient Hybrid Algorithm for Multiobjective Optimization Problems with Upper and Lower Bounds in Engineering

Yang

et al. 2015

Mathematical Problems in Engineering

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Generally, the inconvenience of establishing the mathematical optimization models directly and the conflicts of preventing simultaneous optimization among several objectives lead to the difficulty of obtaining the optimal solution of a practical engineering problem with several objectives. So in this paper, a generate-first-choose-later method is proposed to solve the multiobjective engineering optimization problems, which can set the number of Pareto solutions and optimize repeatedly until the satisfactory results are obtained. Based on Frisch’s method, Newton method, and weighed sum method, an efficient hybrid algorithm for multiobjective optimization models with upper and lower bounds and inequality constraints has been proposed, which is especially suitable for the practical engineering problems based on surrogate models. The generate-first-choose-later method with this hybrid algorithm can calculate the Pareto optimal set, show the Pareto front, and provide multiple designs for multiobjective engineering problems fast and accurately. Numerical examples demonstrate the effectiveness and high efficiency of the hybrid algorithm. In order to prove that the generate-first-choose-later method is rapid and suitable for solving practical engineering problems, an optimization problem for crash box of vehicle has been handled well.

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“…Generalized treatments with applications, in this topic, exist in previous works. [6][7][8][9][10] On the other hand, complex mathematical programming problems were initially studied by Levinson,11 in a particular linear form. Henceforward, several topics of the optimization theory were extended to complex space (see Elbrolosy 12 for example).…”

Section: Introductionmentioning

confidence: 99%

Extensions of proper efficiency in complex space

Youness

Elbrolosy

2017

Math Methods in App Sciences

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MSC Classification: 90C25; 90C29; 90C30; 90C46 In this paper, we extend proper efficiency concepts for a vector optimization problem in complex space. The relationships among the concepts due to Benson, Borwein, Kuhn-Tucker, and Geoffrion have been discussed under some convexity and constraints qualification conditions. The necessary and sufficient conditions for a feasible point to be a properly efficient solution are established.The results are generalizations of the concepts of proper efficiency and their related theorems from real to complex space and complete the existing ones.

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Generating properly efficient points in multi-objective programs by the nonlinear weighted sum scalarization method

Cited by 9 publications

References 26 publications

Proper efficiency, scalarization and transformation in multi-objective optimization: Unified approaches

Proper efficiency, scalarization and transformation in multi-objective optimization: Unified approaches

An Efficient Hybrid Algorithm for Multiobjective Optimization Problems with Upper and Lower Bounds in Engineering

Extensions of proper efficiency in complex space

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