A synchronous reference point-based interactive method for stochastic multiobjective programming

Stochastic multiobjective programming models are highly complex problems, due to the presence of random parameters, together with several conflicting criteria that have to be optimized simultaneously. Even the widely used concept of efficiency has to be redefined for these problems. The use of inter...

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Vydáno v:OR Spectrum Ročník 34; číslo 4; s. 763 - 784
Hlavní autoři: Luque, M., Ruiz, F., Cabello, J. M.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer-Verlag 01.10.2012
Springer
Springer Nature B.V
Témata:
Algorithms
Business and Management
Calculus of Variations and Optimal Control; Optimization
Decision making
Expected values
Interactive
Mathematical analysis
Mathematical models
Methods
Objectives
Operations Research/Decision Theory
Probability
Programming
Random variables
Regular Article
Stochasticity
Synchronous
Interactive methods
Minimum risk efficiency
Probability efficiency
Reference point
Multiobjective programming
Stochastic programming
ISSN:0171-6468, 1436-6304
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Shrnutí:Stochastic multiobjective programming models are highly complex problems, due to the presence of random parameters, together with several conflicting criteria that have to be optimized simultaneously. Even the widely used concept of efficiency has to be redefined for these problems. The use of interactive procedures can somehow ease this complexity, allowing the decision maker to learn about the problem itself, and to look for his most preferred solution. Reference point schemes can be adapted to stochastic problem, by asking the decision maker to provide, not only desirable levels for the objectives, but also the desired probability to achieve these values. In this paper, we analyze the different kinds of achievement scalarizing functions that can be used in this environment, and we study the efficiency (in the stochastic sense) of the different solutions obtained. As a result, a synchronous interactive method is proposed for a class of stochastic multiobjective problems, where only the objective functions are random. Several solutions can be generated by this new method, making use of the same preferential information, using the different achievement scalarizing functions. The preferential information (levels and probabilities for the objectives) is incorporated into the achievement scalarizing functions in a novel way to generate the new solutions. The special case of linear normal problems is addressed separately. The performance of the algorithm is illustrated with a numerical example.
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ISSN:0171-6468
1436-6304
DOI:10.1007/s00291-011-0236-5