A method for generating a well-distributed Pareto set in nonlinear multiobjective optimization

Utyuzhnikov, Sergei; Fantini, Paolo; Guenov, Marin D.

doi:10.1016/j.cam.2008.03.011

Cited by 63 publications

(56 citation statements)

References 27 publications

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“…By changing θ from 0 to π/2, the rotation of the search domain is from the normal direction of the hyperplane to the direction lying on the outer part of the polygon (Utyuzhnikov et al 2009). The rotation continues until no new solution is captured.…”

Section: The Original Dsd Algorithmmentioning

confidence: 99%

“…The rotation continues until no new solution is captured. It can be shown (Utyuzhnikov et al 2009) that…”

Section: The Original Dsd Algorithmmentioning

confidence: 99%

“…In particular, this can be exploited for local approximation of the Pareto frontier (Utyuzhnikov et al 2008) and in ranking (Jaini and Utyuzhnikov 2017). Hence, it is of paramount importance to generate a well-distributed Pareto set to acquire maximum information on the Pareto surface at a minimal computational cost (Utyuzhnikov et al 2009). …”

Section: Introductionmentioning

confidence: 99%

“…In some cases, they can only capture part of the Pareto frontier (Marler and Arora 2004). The well-known classical MOO methods, which are able to approximate the whole Pareto frontier, include the Normal-Boundary Intersection (NBI) method (Dad and Dennis 1997;1998), the Normal constraint (NC) method (Messac et al 2003;Messac and Mattson 2004), the Physical Programming method (Messac 1996;Messac and Mattson 2002), and the Directed Search Domain (DSD) method (Utyuzhnikov et al 2009;Erfani and Utyuzhnikov 2011). All of these methods exploit the anchor points which are the minima of each objective in the objective space, as well as an aggregate objective function (AOF) (preference function).…”

Section: Introductionmentioning

confidence: 99%

“…The DSD method (Utyuzhnikov et al 2009;Erfani and Utyuzhnikov 2011) can be considered as an alternative approach. It introduces the affine transformation of objectives to shrink a search domain to obtain a Pareto solution in a selected area of the objective space.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A modified rotation strategy for directed search domain algorithm in multiobjective engineering optimization

Wang

Utyuzhnikov

2017

Struct Multidisc Optim

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In the real-life multiobjective optimization, it is often required to generate a well-distributed Pareto set. Only a few methods are capable of tackling such a problem in a quite general formulation. The Directed Search Domain method (DSD) proved to be efficient and, therefore, attracted much attention. In this paper, two modifications to the rotation strategy of DSD algorithm are proposed. The first modification is meant to improve its computational efficiency. The second modification is to enhance the evenness of the Pareto set with a number of additional Pareto points. These points are obtained according to some specific rotation angles calculated in a particular way. The modified approach is verified on several test cases with three objectives, including an engineering case. The proposed algorithm is compared with both the original DSD and DSD-II algorithms. It is shown that the new approach can maintain the distribution of the Pareto set at a high level with a relatively low computational cost.

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Section: The Original Dsd Algorithmmentioning

confidence: 99%

“…The rotation continues until no new solution is captured. It can be shown (Utyuzhnikov et al 2009) that…”

Section: The Original Dsd Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A modified rotation strategy for directed search domain algorithm in multiobjective engineering optimization

Wang

Utyuzhnikov

2017

Struct Multidisc Optim

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Multiresponse problems: desirability and other optimization approaches

Costa

Lourenço

2016

Journal of Chemometrics

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A diversity of multiresponse optimization methods has been introduced in the literature; however, their performance has not been thoroughly explored, and only a classical desirability‐based criterion has been commonly used. With the aim of contributing to help practitioners in selecting an effective criterion for solving multiresponse optimization problems developed under the response surface methodology framework, and thus to find compromise solutions that are technically and economically more favorable, the working ability of several easy‐to‐use criteria is evaluated and compared with that of a theoretically sound method. Four case studies with different numbers and types of responses are considered. Less‐sophisticated criteria were able to generate solutions similar to those generated by sophisticated methods, even when the objective is to depict the Pareto frontier in problems with conflicting responses. Two easy‐to‐use criteria that require less‐subjective information from the user yielded solutions similar to those of a classical desirability‐based criterion. Preference parameters range and increment impact on optimal solutions were also evaluated.

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Indicator‐based Selection in Evolutionary Multiobjective Optimization Algorithms Based On the Desirability Index

Trautmann

Wagner

Biermann

et al. 2013

Multi Criteria Decision Anal

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In multiobjective optimization, the identification of practically relevant solutions on the Pareto‐optimal front is an important research topic. Desirability functions (DFs) allow the preferences of the decision maker to be specified in an intuitive way. Recently, it has been shown for continuous optimization problems that an a priori transformation of the objectives by means of DFs can be used to focus the search of a hypervolume‐based evolutionary algorithm on the desired part of the front. In many‐objective optimization, however, the computational complexity of the hypervolume can become a crucial part. Thus, an alternative to this approach will be presented in this paper. The new algorithm operates in the untransformed objective space, but the desirability index (DI), that is, a DF‐based scalarization, will be used as the second‐level selection criterion in the non‐dominated sorting. The diversity and uniform distribution of the resulting approximation are ensured by the use of an external archive. In the experiments, different preferences are specified as DFs, and their effects are investigated. It is shown that trade‐off solutions are generated in the desired regions of the Pareto‐optimal front and with a density adaptive to the DI. The efficiency of the approach with respect to increasing objective space dimension is also analysed using scalable test functions. The convergence speed is superior to other set‐based and preference‐based evolutionary multiobjective algorithms while the approach is of low computational complexity due to cheap DI evaluations. Copyright © 2013 John Wiley & Sons, Ltd.

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A method for generating a well-distributed Pareto set in nonlinear multiobjective optimization

Cited by 63 publications

References 27 publications

A modified rotation strategy for directed search domain algorithm in multiobjective engineering optimization

A modified rotation strategy for directed search domain algorithm in multiobjective engineering optimization

Multiresponse problems: desirability and other optimization approaches

Indicator‐based Selection in Evolutionary Multiobjective Optimization Algorithms Based On the Desirability Index

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