Adaptive Scalarization Methods in Multiobjective Optimization

Eichfelder, Gabriele

doi:10.1007/978-3-540-79159-1

Cited by 310 publications

(200 citation statements)

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“…[17]- [19] and now [20] is not enough. I have dealt with several applications -but a diverse pre-image was never an issue."…”

Section: Discussionmentioning

confidence: 98%

“…However, in some real-world applications, particularly when the preference (i.e. utility function) of a decision maker is not clearly defined, a good approximation to both the PF and the PS should be required by the decision maker for facilitating their decision making as argued in [17]- [20]. For example, if two objectives f 1 and f 2 are much more important than objective v in engineering design, one often needs to first optimize f 1 and f 2 and obtain a good approximation to both the PF and the PS, then finds from the approximate PS a solution that optimizes v subject to certain constraints as their final solution.…”

Section: M X Is Called (Globally) Pareto Optimal Ifmentioning

confidence: 99%

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Approximating the Set of Pareto-Optimal Solutions in Both the Decision and Objective Spaces by an Estimation of Distribution Algorithm

Zhou¹,

Zhang

Jin

2009

IEEE Trans. Evol. Computat.

278

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Abstract-Most existing multiobjective evolutionary algorithms aim at approximating the Pareto front (PF), the distribution of the Pareto optimal solutions in the objective space. In many reallife applications, however, a good approximation to the Pareto set (PS), the distribution of the Pareto optimal solutions in the decision space, is also required by a decision maker. This paper considers a class of multiobjective optimization problems (MOPs), in which the dimensionalities of the PS and the PF manifolds are different so that a good approximation to the PF might not approximate the PS very well. It proposes a probabilistic model based multiobjective evolutionary algorithm, called MMEA, for approximating the PS and the PF simultaneously for an MOP in this class. In the modeling phase of MMEA, the population is clustered into a number of subpopulations based on their distribution in the objective space, the PCA technique is used to estimate the dimensionality of the PS manifold in each subpopulation, and then a probabilistic model is built for modeling the distribution of the Pareto optimal solutions in the decision space. Such a modeling procedure could promote the population diversity in both the decision and objective spaces. MMEA is compared with three other methods, KP1, OmniOptimizer and RM-MEDA on a set of test instances, five of which are proposed in this paper. The experimental results clearly suggest that overall, MMEA performs significantly better than the three compared algorithms in approximating both the PS and the PF.

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“…[17]- [19] and now [20] is not enough. I have dealt with several applications -but a diverse pre-image was never an issue."…”

Section: Discussionmentioning

confidence: 98%

Section: M X Is Called (Globally) Pareto Optimal Ifmentioning

confidence: 99%

Approximating the Set of Pareto-Optimal Solutions in Both the Decision and Objective Spaces by an Estimation of Distribution Algorithm

Zhou¹,

Zhang

Jin

2009

IEEE Trans. Evol. Computat.

278

View full text Add to dashboard Cite

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“…The solving of the vector (or multiobjective, multicriteria) optimization problem was analyzed in many works, e.g. [21][22]. The theory of bilevel optimization at present is intensively developing [23-27, 31].…”

Section: Limit Analysis Of Geometrically Hardening Composite Steel-comentioning

confidence: 99%

Limit Analysis of Geometrically Hardening Composite Steel-Concrete Systems / Stany Graniczne Geometrycznie Wzmacniających Się Konstrukcji Zespolonych

Alawdin¹,

Urbańska²

2023

Civil and Environmental Engineering Reports

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The paper considers some results of creating load-carrying composite systems that have uprated strength, rigidity and safety, and therefore are called geometrically (self-) hardening systems. The optimization mathematic models of structures as discrete mechanical systems withstanding dead load, monotonic or low cyclic static and kinematic actions are proposed. To find limit parameters of these actions the extreme energetic principle is suggested what result in the bilevel mathematic programming problem statement. The limit parameters of load actions are found on the first level of optimization. On the second level the power of the constant load with equilibrium preloading is maximized and/or system cost is minimized. The examples of using the proposed methods are presented and geometrically hardening composite steel-concrete system are taken into account.

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“…There are also scalarization approaches which combine properties of both groups such as the Pascoletti-Serafini scalarization [5] (for a survey of different scalarization methods, see [6], Chapter 2; for adaptive algorithms using different scalarizations, see [6], Chapter 4; for scalarizations in the context of variable ordering structures, see [7], Chapters 4 and 5).…”

Section: Prop 21 and 22)mentioning

confidence: 99%

A New Global Scalarization Method for Multiobjective Optimization with an Arbitrary Ordering Cone

Rahmo¹,

Studniarski²

2017

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We propose a new scalarization method which consists in constructing, for a given multiobjective optimization problem, a single scalarization function, whose global minimum points are exactly vector critical points of the original problem. This equivalence holds globally and enables one to use global optimization algorithms (for example, classical genetic algorithms with "roulette wheel" selection) to produce multiple solutions of the multiobjective problem. In this article we prove the mentioned equivalence and show that, if the ordering cone is polyhedral and the function being optimized is piecewise differentiable, then computing the values of a scalarization function reduces to solving a quadratic programming problem. We also present some preliminary numerical results pertaining to this new method.

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Adaptive Scalarization Methods in Multiobjective Optimization

Cited by 310 publications

References 0 publications

Approximating the Set of Pareto-Optimal Solutions in Both the Decision and Objective Spaces by an Estimation of Distribution Algorithm

Approximating the Set of Pareto-Optimal Solutions in Both the Decision and Objective Spaces by an Estimation of Distribution Algorithm

Limit Analysis of Geometrically Hardening Composite Steel-Concrete Systems / Stany Graniczne Geometrycznie Wzmacniających Się Konstrukcji Zespolonych

A New Global Scalarization Method for Multiobjective Optimization with an Arbitrary Ordering Cone

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