Numerical results for the multiobjective trust region algorithm MHT

Thomann, Jana; Eichfelder, Gabriele

doi:10.1016/j.dib.2019.104103

Cited by 10 publications

(5 citation statements)

References 9 publications

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“…The heuristic approaches from Section 3 have been implemented in Matlab R2017a and tested on 20 test problems from [19,Tab. 1], [20]: BK1, CL1, IM1, T1, LE1, Schaffer2, VU1, FF (n = 2, 3, 4, 5), Jin1 (n = 2, 3, 5), lovison1 (constrained and unconstrained), lovison4 (constrained and unconstrained) and T4 (n = 2, 3). For reasons of comparison, the test problems do not contain expensive black box functions, but are all given analytically.…”

Section: Results Of Numerical Testsmentioning

confidence: 99%

“…We summarize the findings and present individual results exemplarily. For more details on numerical tests for the method MHT and the test instances, see [19,20].…”

Section: Results Of Numerical Testsmentioning

confidence: 99%

“…The trust region algorithm, presented in [18,19,20] and called MHT, is designed to consider such multi-objective heterogeneous optimization problems, where one of the objectives is an expensive black-box function. The simulation only gives function values.…”

Section: Introductionmentioning

confidence: 99%

“…This leads to single-objective subproblems, which have to be solved, and have the structure of the well-known Tammer-Weidner functional [11]. However, the algorithm MHT proposed in [19,20] calculates only one efficient solution, to be more concrete, accumulation points of the generated sequence of iteration points satisfy a necessary optimality criteria to be a locally optimal solution. The method is not designed to find a representation of the Pareto front.…”

Section: Introductionmentioning

confidence: 99%

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Representation of the Pareto front for heterogeneous multi-objective optimization

2019

J. Appl. Numer. Optim.

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Optimization problems with multiple objectives which are expensive, i. e., where function evaluations are time consuming, are difficult to solve. Finding at least one locally optimal solution is already a difficult task. In case only one of the objective functions is expensive while the others are cheap, for instance, analytically given, this can be used in the optimization procedure. Using a trust-region approach and the Tammer-Weidner-functional for finding descent directions, in [19] an algorithm was proposed which makes use of the heterogeneity of the objective functions. In this paper, we present three heuristic approaches, which allow to find additional optimal solutions of the multiobjective optimization problem and by that representations at least of parts of the Pareto front. We present the related theoretical results as well as numerical results on some test instances.

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Section: Results Of Numerical Testsmentioning

confidence: 99%

“…We summarize the findings and present individual results exemplarily. For more details on numerical tests for the method MHT and the test instances, see [19,20].…”

Section: Results Of Numerical Testsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Representation of the Pareto front for heterogeneous multi-objective optimization

2019

J. Appl. Numer. Optim.

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“…An initial study [45], comparing MHT against a weighted sum-based approach and direct multisearch for multiobjective optimization, concluded that the proposed approach can yield good results.…”

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confidence: 99%

Heterogeneous Objectives: State-of-the-Art and Future Research

Allmendinger¹,

Knowles²

2021

Preprint

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Multiobjective optimization problems with heterogeneous objectives are defined as those that possess significantly different types of objective function components (not just incommensurable in units or scale). For example, in a heterogeneous problem the objective function components may differ in formal computational complexity, practical evaluation effort (time, costs, or resources), determinism (stochastic vs deterministic), or some combination of all three. A particularly challenging variety of heterogeneity may occur by the combination of a time-consuming laboratorybased objective with other objectives that are evaluated using faster computer-based calculations. Perhaps more commonly, all objectives may be evaluated computationally, but some may require a lengthy simulation process while others are computed from a relatively simple closed-form calculation. In this chapter, we motivate the need for more work on the topic of heterogeneous objectives (with reference to real-world examples), expand on a basic taxonomy of heterogeneity types, and review the state of the art in tackling these problems. We give special attention to heterogeneity in evaluation time (latency) as this requires sophisticated approaches. We also present original experimental work on estimating the amount of heterogeneity in evaluation time expected in many-objective problems, given reasonable assumptions, and survey related research threads that could contribute to this area in future.

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Heterogeneous Objectives: State-of-the-Art and Future Research

Allmendinger

Knowles

2023

Natural Computing Series

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Numerical results for the multiobjective trust region algorithm MHT

Cited by 10 publications

References 9 publications

Representation of the Pareto front for heterogeneous multi-objective optimization

Representation of the Pareto front for heterogeneous multi-objective optimization

Heterogeneous Objectives: State-of-the-Art and Future Research

Heterogeneous Objectives: State-of-the-Art and Future Research

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