What if we increase the number of objectives? Theoretical and empirical implications for many-objective combinatorial optimization

Allmendinger, Richard; Jaszkiewicz, Andrzej; Liefooghe, Arnaud; Tammer, Christiane

doi:10.1016/j.cor.2022.105857

Cited by 16 publications

(9 citation statements)

References 81 publications

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“…Some examples of such scalarizations are the weighted sum [31] and the ε-constraint problem [32]. It is important to explain that these two examples of scalarization approach are special cases of the nonlinear scalarizing functional presented in (NLSF); see, e.g., [14,29].…”

Section: Existence Results For (Mop) In Reflexive Banach Preimage Spa...mentioning

confidence: 99%

“…, n, R j is the convex subset of the solution set χ Eff (G(R 2 ); R q + ). Under certain assumptions concerning the parameters in the scalarizing functional (NLSF) that are to be chosen by the decision maker corresponding to his preferences, we adapt here the preamble presented in [14] as follows:…”

Section: 32mentioning

confidence: 99%

“…In what follows, we make use of the following proposition, whose general form can be seen in [14], to solve Problem (SSP) with q = 8. Proposition 5.2.…”

Section: 32mentioning

confidence: 99%

“…In Section 5, we perform optimization over the set of efficient elements of a multi-objective location problem. By applying the characterization of the nonlinear scalarizing functional introduced by Gerstewitz [13] in [14], a single solution from the set of efficient elements which corresponds to the preferences of the decision maker is generated. Finally, the paper concludes in Section 6 with some remarks and future research goals.…”

Section: Introductionmentioning

confidence: 99%

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Existence results and optimization over the set of efficient solutions in vector-valued approximation theory

2023

J. Nonlinear Var. Anal.

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Continuity of the objective functions and compactness of their domain are classical assumptions widely used to obtain existence results for solutions of optimization problems. Due to the lack of compactness in general spaces, under some moderate assumptions concerning the objective function and the feasible set, we derive existence results for vector-valued optimization problems and corresponding results for associated scalarized problems in this paper. Furthermore, we apply our results to special vector-valued approximation problems, especially to multi-objective location problems where the whole set of efficient solutions can be generated by a geometric primal-dual algorithm. Moreover, by using the nonlinear scalarizing functional introduced by Gerstewitz, we perform an optimization according to the preferences of a decision maker on the generated set of efficient solutions from which we derive a single solution of this set that corresponds to the preferences of the decision maker.

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Section: Existence Results For (Mop) In Reflexive Banach Preimage Spa...mentioning

confidence: 99%

Section: 32mentioning

confidence: 99%

“…In what follows, we make use of the following proposition, whose general form can be seen in [14], to solve Problem (SSP) with q = 8. Proposition 5.2.…”

Section: 32mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Existence results and optimization over the set of efficient solutions in vector-valued approximation theory

2023

J. Nonlinear Var. Anal.

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“…Similarly, an aspect that is kept for future work is the investigation of heterogeneous MNK landscapes with more than two objectives. Addressing many-objective problems constitutes a formidable challenge [4] and heterogeneous MOPs do not seem to be an exception in this respect.…”

Section: Discussionmentioning

confidence: 99%

Multi-objective NK landscapes with heterogeneous objectives

Cosson

Santana

Derbel

et al. 2022

Proceedings of the Genetic and Evolutionary Computation Conference

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HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

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Efficient Approximation of Expected Hypervolume Improvement Using Gauss-Hermite Quadrature

Rahat

Chugh

Fieldsend

et al. 2022

Lecture Notes in Computer Science

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Many methods for performing multi-objective optimisation of computationally expensive problems have been proposed recently. Typically, a probabilistic surrogate for each objective is constructed from an initial dataset. The surrogates can then be used to produce predictive densities in the objective space for any solution. Using the predictive densities, we can compute the expected hypervolume improvement (EHVI) due to a solution. Maximising the EHVI, we can locate the most promising solution that may be expensively evaluated next. There are closed-form expressions for computing the EHVI, integrating over the multivariate predictive densities. However, they require partitioning of the objective space, which can be prohibitively expensive for more than three objectives. Furthermore, there are no closed-form expressions for a problem where the predictive densities are dependent, capturing the correlations between objectives. Monte Carlo approximation is used instead in such cases, which is not cheap. Hence, the need to develop new accurate but cheaper approximation methods remains. Here we investigate an alternative approach toward approximating the EHVI using Gauss-Hermite quadrature. We show that it can be an accurate alternative to Monte Carlo for both independent and correlated predictive densities with statistically significant rank correlations for a range of popular test problems.

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What if we increase the number of objectives? Theoretical and empirical implications for many-objective combinatorial optimization

Cited by 16 publications

References 81 publications

Existence results and optimization over the set of efficient solutions in vector-valued approximation theory

Existence results and optimization over the set of efficient solutions in vector-valued approximation theory

Multi-objective NK landscapes with heterogeneous objectives

Efficient Approximation of Expected Hypervolume Improvement Using Gauss-Hermite Quadrature

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