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- Hartikainen, Markus, 1981-, et al.
(författare)
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Constructing a Pareto front approximation for decision making
- 2011
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Ingår i: Mathematical Methods of Operations Research. - : Springer Berlin/Heidelberg. - 1432-2994 .- 1432-5217. ; 73:2, s. 209-234
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Tidskriftsartikel (refereegranskat)abstract
- An approach to constructing a Pareto front approximation to computationally expensive multiobjective optimization problems is developed. The approximation is constructed as a sub-complex of a Delaunay triangulation of a finite set of Pareto optimal outcomes to the problem. The approach is based on the concept of inherent nondominance. Rules for checking the inherent nondominance of complexes are developed and applying the rules is demonstrated with examples. The quality of the approximation is quantified with error estimates. Due to its properties, the Pareto front approximation works as a surrogate to the original problem for decision making with interactive methods.
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| 3. |
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| 4. |
- Luque, Mariano, et al.
(författare)
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Global Formulation for Interactive Multiobjective Optimization
- 2011
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Ingår i: OR Spectrum. - : Springer-Verlag New York. - 0171-6468 .- 1436-6304. ; 33:1, s. 27-48
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Tidskriftsartikel (refereegranskat)abstract
- Interactive methods are useful and realistic multiobjective optimization techniques and, thus, many such methods exist. However, they have two important drawbacks when using them in real applications. Firstly, the question of which method should be chosen is not trivial. Secondly, there are rather few practical implementations of the methods. We introduce a general formulation that can accommodate several interactive methods. This provides a comfortable implementation framework for a general interactive system. Besides, this implementation allows the decision maker to choose how to give preference information to the system, and enables changing it anytime during the solution process. This change-of-method option provides a very flexible framework for the decision maker.
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| 6. |
- Miettinen, Kaisa, 1965-, et al.
(författare)
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A new hybrid mutation operator for multiobjective optimization with differential evolution
- 2011
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Ingår i: Soft Computing - A Fusion of Foundations, Methodologies and Applications. - : Springer. - 1432-7643 .- 1433-7479. ; 15:10, s. 2041-2055
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Tidskriftsartikel (refereegranskat)abstract
- Differential evolution has become one of the most widely used evolutionary algorithms in multiobjective optimization. Its linear mutation operator is a simple and powerful mechanism to generate trial vectors. However, the performance of the mutation operator can be improved by including a nonlinear part. In this paper, we propose a new hybrid mutation operator consisting of a polynomial-based operator with nonlinear curve tracking capabilities and the differential evolution’s original mutation operator, for the efficient handling of various interdependencies between decision variables. The resulting hybrid operator is straightforward to implement and can be used within most evolutionary algorithms. Particularly, it can be used as a replacement in all algorithms utilizing the original mutation operator of differential evolution. We demonstrate how the new hybrid operator can be used by incorporating it into MOEA/D, a winning evolutionary multiobjective algorithm in a recent competition. The usefulness of the hybrid operator is demonstrated with extensive numerical experiments showing improvements in performance compared with the previous state of the art.
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| 8. |
- Miettinen, Kaisa, 1965-, et al.
(författare)
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New Perspective to Continuous Casting of Steel with a Hybrid Evolutionary Multiobjective Algorithm
- 2011
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Ingår i: Materials and Manufacturing Processes. - : Taylor & Francis. - 1042-6914 .- 1532-2475. ; 26:3, s. 481-492
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Tidskriftsartikel (refereegranskat)abstract
- In this article, we present a new perspective in solving computationally demanding problems such as the optimal control of the continuous casting of steel. We consider a multiobjective formulation of the optimal control of the surface temperature of the steel strand with five objectives, where constraint violations are minimized as objectives because no feasible solutions exist otherwise. A hybrid evolutionary multiobjective algorithm (HNSGA-II) is used to overcome discrepancies of evolutionary multiobjective optimization algorithms such as slow convergence and lack of convergence proof to the Pareto front. HNSGA-II uses NSGA-II as an underlying evolutionary multiobjective algorithm and an achievement scalarization function to scalarize objective functions for local search, which improves the population and speeds up the convergence. This is important because most evolutionary multiobjective algorithms are known to have difficulties with five objective functions. The algorithm is used to generate a set of Pareto solutions showing different trade-offs. However, it is difficult to generate Pareto solutions showing all the different trade-offs with a finite small population size. Hence, we use the preference information related to constraint violations in the weights of the achievement scalarization function to generate solutions with different trade-offs in preferable regions of the Pareto front. In addition, we use clustering and present typical solutions of different clusters so that the most preferred solution to be implemented can easily be identified. We demonstrate the approach and compare the results to previous studies.
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| 9. |
- Miettinen, Kaisa, 1965-, et al.
(författare)
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Wastewater treatment : New insight provided by interactive multiobjective optimization
- 2011
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Ingår i: Decision Support Systems. - : Elsevier. - 0167-9236 .- 1873-5797. ; 51:2, s. 328-337
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we describe a new interactive tool developed for wastewater treatment plant design. The tool is aimed at supporting the designer in designing new wastewater treatment plants as well as optimizing the performance of already available plants. The idea is to utilize interactive multiobjective optimization which enables the designer to consider the design with respect to several conflicting evaluation criteria simultaneously. This is more important than ever because the requirements for wastewater treatment plants are getting tighter and tighter from both environmental and economical reasons. By combining a process simulator to simulate wastewater treatment and an interactive multiobjective optimization software to aid the designer during the design process, we obtain a practically useful tool for decision support. The applicability of our tool is illustrated with a case study related to municipal wastewater treatment where three conflicting evaluation criteria are considered.
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| 10. |
- Podkopaev, D., et al.
(författare)
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Handling preferences in the "pre-conflicting" phase of decision making processes under multiple criteria
- 2011
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Ingår i: Algorithmic Decision Theory Second International Conference, ADT 2011, Piscataway, NJ, USA, October 26-28, 2011. Proceedings. - Berlin, Heidelberg : Springer Berlin/Heidelberg. - 9783642248726 ; , s. 234-246
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Konferensbidrag (refereegranskat)abstract
- Multiple criteria decision making (MCDM) literature concentrates on the concept of conflicting objectives, which is related to focusing on the need of trading off. Most approaches to eliciting preferences of the decision maker (DM) are built accordingly on contradistinguishing different attainable levels of objectives. We propose to pay attention to the non-conflicting aspects of decision making allowing the DM to express preferences as a desirable direction of consistent improvement of objectives. We show how such preference information combined with a dominance relation principle results in a Chebyshev-type scalarizing model, which can be used in early stages of decision making processes for deriving preferred solutions without trading off.
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