A combined scalarizing method for multiobjective programming problems

Rastegar, Narges; Khorram, Esmaile

doi:10.1016/j.ejor.2013.11.020

Cited by 19 publications

(12 citation statements)

References 28 publications

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“…At the same time, such a generalization of Proposition 5.1, as well as obtaining the first-order optimality conditions in (14), is not so straightforward, because the directional derivatives of the goal functions have a cumbersome form. Another topic to be investigated is the finding of the properly optimal solutions to (1) (for the definition, see, e.g., [6]). In this connection, the following two approaches seem promising: first, analyzing the objective function equal to a weighted sum of objectives and additional variables (the so-called surplus and slack variables) like in [6,Theorem 3.4]; second, a modification of Proposition 3.1, which is based on the use of the scalar function G(x) introduced in (10).…”

Section: Perspectivesmentioning

confidence: 99%

“…Another topic to be investigated is the finding of the properly optimal solutions to (1) (for the definition, see, e.g., [6]). In this connection, the following two approaches seem promising: first, analyzing the objective function equal to a weighted sum of objectives and additional variables (the so-called surplus and slack variables) like in [6,Theorem 3.4]; second, a modification of Proposition 3.1, which is based on the use of the scalar function G(x) introduced in (10). These extensions of Propositions 3.1, 4.1, 5.1, and 5.2, along with finding a method for determination of a solution to equation (11), seem the directions for further research.…”

Section: Perspectivesmentioning

confidence: 99%

“…There is a large variety of methods for determination of Pareto-optimal solutions and their generalizations, in which the optimality is understood with respect to various kinds of preference cones, Miettinen [3] and Jahn [4]. Many of them are based on a scalarization approach [3,[5][6][7] that transforms the initial problem into a single-objective optimization problem. Usually, it involves some parameters that are changed in order to detect different Pareto-optimal points: weights in the linear scalarization function in [6] or, more generally, a composition of the vector objective function and a linear functional from the dual cone of the preference (ordering) cone; and norm parameter for L p -scalarization in Nikulin et al [7].…”

Section: Introductionmentioning

confidence: 99%

“…Many of them are based on a scalarization approach [3,[5][6][7] that transforms the initial problem into a single-objective optimization problem. Usually, it involves some parameters that are changed in order to detect different Pareto-optimal points: weights in the linear scalarization function in [6] or, more generally, a composition of the vector objective function and a linear functional from the dual cone of the preference (ordering) cone; and norm parameter for L p -scalarization in Nikulin et al [7]. Another group of methods for approximating the Pareto frontier for various decision problems with a small number of objectives (mainly, two) are provided in Ruzika and Wiecek [8].…”

Section: Introductionmentioning

confidence: 99%

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A Note on Optimality Conditions for Multi-objective Problems with a Euclidean Cone of Preferences

Golubin

2014

J Optim Theory Appl

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The paper suggests a new-to the best of the author's knowledgecharacterization of decisions, which are optimal in the multi-objective optimization problem with respect to a definite proper preference cone, a Euclidean cone with a prescribed angular radius. The main idea is to use the angle distances between the unit vector and points of utility space. A necessary and sufficient condition for the optimality in the form of an equation is derived. The first-order necessary optimality conditions are also obtained.

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Section: Perspectivesmentioning

confidence: 99%

Section: Perspectivesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Note on Optimality Conditions for Multi-objective Problems with a Euclidean Cone of Preferences

Golubin

2014

J Optim Theory Appl

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“…After conversion to the singleobjective problem, two different optimization algorithms are applied to solve this problem. Weighted (linear) sum method is the oldest and best known approach for solving multiobjective optimization problems [22]. The scalarization formula of weighted sum method is given at the following equation.…”

Section: Methods and Techniquesmentioning

confidence: 99%

Multiobjective PID controller design for active suspension system: scalarization approach

Altınöz¹

2018

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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In this study, the PID tuning method (controller design scheme) is proposed for a linear quarter model of active suspension system installed on the vehicles. The PID tuning scheme is considered as a multiobjective problem which is solved by converting this multiobjective problem into single objective problem with the aid of scalarization approaches. In the study, three different scalarization approaches are used and compared to each other. These approaches are called linear scalarization (weighted sum), epsilon-constraint and Bensons methods. The objectives of multiobjective optimization are selected from the time-domain properties of the transient response of the system which are overshoot, rise time, peak time and error (in total there are four objectives). The aim of each objective is to minimize the corresponding property of the time response of the system. First, these four objective is applied to the scalarization functions and then single objective problem is obtained. Finally, these single objective problems are solved with the aid of heuristic optimization algorithms. For this purpose, four optimization algorithms are selected, which are called Particle Swarm Optimization, Differential Evolution, Firefly, and Cultural Algorithms. In total, twelve implementations are evaluated with the same number of iterations. In this study, the aim is to compare the scalarization approaches and optimization algorithm on active suspension control problem. The performance of the corresponding cases (implementations) are numerically and graphically demonstrated on transient responses of the system.

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An Innovative GA for VCIM Production Scheduling Optimisation

Dao

2017

Springer Theses

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A combined scalarizing method for multiobjective programming problems

Cited by 19 publications

References 28 publications

A Note on Optimality Conditions for Multi-objective Problems with a Euclidean Cone of Preferences

A Note on Optimality Conditions for Multi-objective Problems with a Euclidean Cone of Preferences

Multiobjective PID controller design for active suspension system: scalarization approach

An Innovative GA for VCIM Production Scheduling Optimisation

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