Incorporating preference information in interactive reference point methods for multiobjective optimization

Luque, Mariano; Miettinen, Kaisa; Eskelinen, Petri; Ruiz, Francisco

doi:10.1016/j.omega.2007.06.001

Cited by 104 publications

(63 citation statements)

References 17 publications

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“…In most of the interactive methods using achievement functions, weights are kept unaltered during the whole process and their purpose is mainly to normalize different ranges of objectives. However, these weights can have different roles (from the original idea of purely normalizing to fully preferential) as described in Ruiz et al (2008) and they can be varied to get different Pareto optimal solutions (see, for example, Luque et al (2009)). …”

Section: Basic Concepts and Notationsmentioning

confidence: 99%

NAUTILUS framework: towards trade-off-free interaction in multiobjective optimization

Miettinen

Ruiz

2016

J Bus Econ

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In this paper, we present a framework of different interactive NAU-TILUS methods for multiobjective optimization. In interactive methods, the decision maker iteratively sees solution alternatives and provides one's preferences in order to find the most preferred solution. We question the widely used setting that the solutions shown to the decision maker should all be Pareto optimal which implies that improvement in any objective function necessitates allowing impairment in some others. Instead, in NAUTILUS we enable the decision maker to make a free search without having to trade-off by starting from an inferior solution and iteratively approaching the Pareto optimal set by allowing all objective functions to improve. The framework presented consists of different modules for preference elicitation and optimization. Four main NAUTILUS method variants are introduced as well as ideas of utilizing the framework in a flexible way to derive further variants.

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Section: Basic Concepts and Notationsmentioning

confidence: 99%

NAUTILUS framework: towards trade-off-free interaction in multiobjective optimization

Miettinen

Ruiz

2016

J Bus Econ

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“…For further investigation, it is concluded that the reference point could be projected to different Pareto optimal solutions between A and B by altering weighting vectors 26 . And recently, many researchers focus on the influences of different weights on the DM preferences 17,27,28 . There are also other achievement scalarizing functions that are frequently used in literatures, for example,…”

Section: Co-published By Atlantis Press and Taylor And Francismentioning

confidence: 99%

Hybrid Multiobjective Differential Evolution Incorporating Preference Based Local Search

Dong¹,

Wang²

2014

IJCIS

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The performance of Differential Evolution (DE) for multiobjective optimization problems (MOPs) can be greatly enhanced by hybridizing with other techniques. In this paper, a new hybrid DE incorporating preference based local search is proposed. In every generation, a set of nondominated solutions is generated by DE operation. Usually these solutions distribute unevenly along the obtained nondominated set. To get solutions in the sparse region of the nondominated set, a mini population and preference based local search algorithm is specifically designed, and is used to exploit the sparse region by optimizing an achievement scalarizing function (ASF) with the dynamically adjusted reference point. As a result, multiple solutions in the sparse region can be obtained. Moreover, to retain uniformly spread nondominated solutions, an improved ε-dominance strategy, which would not delete the extreme points found during the evolution, is proposed to update the external archive set. Finally, numerical results and comparisons demonstrate the efficiency of the proposed algorithm.

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“…A budget of 10,000 function evaluations was pre-fixed and the resulting nondominated solutions were subjected to local search to guarantee (at least local) optimality. As described in [40], a reference point can be projected in a preferable direction to the DM by altering the weights of the achievement scalarizing function. Here, we altered the weight for the objective function J 1 to be 0 1, so that minimizing constraint violations is slightly preferred over the objective function J 1 .…”

Section: Numerical Experimentsmentioning

confidence: 99%

New Perspective to Continuous Casting of Steel with a Hybrid Evolutionary Multiobjective Algorithm

Sindhya

Miettinen

2011

Materials and Manufacturing Processes

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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.QC 2012020

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Incorporating preference information in interactive reference point methods for multiobjective optimization

Cited by 104 publications

References 17 publications

NAUTILUS framework: towards trade-off-free interaction in multiobjective optimization

NAUTILUS framework: towards trade-off-free interaction in multiobjective optimization

Hybrid Multiobjective Differential Evolution Incorporating Preference Based Local Search

New Perspective to Continuous Casting of Steel with a Hybrid Evolutionary Multiobjective Algorithm

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