Fundamentals of Multicriteria Optimization

Stadler, W.

doi:10.1007/978-1-4899-3734-6_1

Cited by 66 publications

(36 citation statements)

References 9 publications

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“…Here, i represents a function's position in the preferred sequence, and F j ðx Ã j Þ represents the optimum of the jth objective function, found in the jth iteration (Stadler 1988).…”

Section: Coping With Multiple Objectivementioning

confidence: 99%

A robust multi-objective global supplier selection model under currency fluctuation and price discount

2016

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Robust supplier selection problem, in a scenario-based approach has been proposed, when the demand and exchange rates are subject to uncertainties. First, a deterministic multi-objective mixed integer linear programming is developed; then, the robust counterpart of the proposed mixed integer linear programming is presented using the recent extension in robust optimization theory. We discuss decision variables, respectively, by a two-stage stochastic planning model, a robust stochastic optimization planning model which integrates worst case scenario in modeling approach and finally by equivalent deterministic planning model. The experimental study is carried out to compare the performances of the three models. Robust model resulted in remarkable cost saving and it illustrated that to cope with such uncertainties, we should consider them in advance in our planning. In our case study different supplier were selected due to this uncertainties and since supplier selection is a strategic decision, it is crucial to consider these uncertainties in planning approach.

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“…Here, i represents a function's position in the preferred sequence, and F j ðx Ã j Þ represents the optimum of the jth objective function, found in the jth iteration (Stadler 1988).…”

Section: Coping With Multiple Objectivementioning

confidence: 99%

A robust multi-objective global supplier selection model under currency fluctuation and price discount

2016

View full text Add to dashboard Cite

show abstract

“…permutations of , , must be checked. Let us apply Proposition 2 to find the solution of an unconstrained MOOP with three quadratic objective functions with two of them being those defined by (11a) and (11b) and the third defined by 3 ( 1 , 2 ) = …”

Section: Proposition 2 Let E Be the Unit Vector Defined By E = ∇ (P)mentioning

confidence: 99%

“…Bold points at the Pareto set boundary were found with the same method applied to the functions 1 (X), 2 (X), 3 (X) taken in pairs. According to Proposition 1, in such cases, the Pareto set is necessarily a curve.…”

Section: Proposition 3 Consider a Moop Involving Quadratic Functionsmentioning

confidence: 99%

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Multiobjective Optimization Involving Quadratic Functions

Augusto

Bennis

Caro³

2014

Journal of Optimization

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Multiobjective optimization is nowadays a word of order in engineering projects. Although the idea involved is simple, the implementation of any procedure to solve a general problem is not an easy task. Evolutionary algorithms are widespread as a satisfactory technique to find a candidate set for the solution. Usually they supply a discrete picture of the Pareto front even if this front is continuous. In this paper we propose three methods for solving unconstrained multiobjective optimization problems involving quadratic functions. In the first, for biobjective optimization defined in the bidimensional space, a continuous Pareto set is found analytically. In the second, applicable to multiobjective optimization, a condition test is proposed to check if a point in the decision space is Pareto optimum or not and, in the third, with functions defined in n-dimensional space, a direct noniterative algorithm is proposed to find the Pareto set. Simple problems highlight the suitability of the proposed methods.

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“…More promising approaches are available. 82 Perhaps these will American Institute of Aeronautics and Astronautics ultimately prove useful for applications to aerodynamic multipoint optimization.…”

Section: Fig 13 Simultaneous Analysis and Design (Sand) Algorithmmentioning

confidence: 99%

Multidisciplinary design optimization techniques - Implications and opportunities for fluid dynamics research

Zang

Green

1999

30th Fluid Dynamics Conference

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A challenge for the fluid dynamics community is to adapt to and exploit the trend towards greater multidisciplinary focus in research and technology. The past decade has witnessed substantial growth in the research field of Multidisciplinary Design Optimization (MDO). MDO is a methodology for the design of complex engineering systems and subsystems that coherently exploits the synergism of mutually interacting phenomena. As evidenced by the papers, which appear in the biannual AIAA/USAF/NASA/ISSMO Symposia on Multidisciplinary Analysis and Optimization, the MDO technical community focuses on vehicle and system design issues. This paper provides an overview of the MDO technology field from a fluid dynamics perspective, giving emphasis to suggestions of specific applications of recent MDO technologies that can enhance fluid dynamics research itself across the spectrum, from basic flow physics to full configuration aerodynamics.

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Fundamentals of Multicriteria Optimization

Cited by 66 publications

References 9 publications

A robust multi-objective global supplier selection model under currency fluctuation and price discount

A robust multi-objective global supplier selection model under currency fluctuation and price discount

Multiobjective Optimization Involving Quadratic Functions

Multidisciplinary design optimization techniques - Implications and opportunities for fluid dynamics research

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