Walsh-based surrogate-assisted multi-objective combinatorial optimization: A fine-grained analysis for pseudo-boolean functions

Derbel, Bilel; Pruvost, Geoffrey; Liefooghe, Arnaud; Vérel, Sebástien; Zhang, Qingfu

doi:10.1016/j.asoc.2023.110061

Cited by 3 publications

(3 citation statements)

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“…Surrogate model based on Walsh functions [38], building multivariate polynomial models (see next Section 2.2), have proven to be effective in various contexts including interpolation where precise learning of Walsh coefficients is necessary [14], numerical simulations with some noise [25], and in multiobjective combinatorial optimization [13].…”

Section: Surrogate Model For Combinatorial Optimizationmentioning

confidence: 99%

“…In this section, the quality of the sparse Walsh surrogate models is compared to the quality of the full Walsh surrogate [25]. We follow the sparse regression method based on the classical LASSO-LARS algorithm from [25,23,13] to estimate the parameters of the Walsh expansion which contains all terms of order below a given degree k, so called full Walsh expansion of degree k in this article. Figure 6 (left) compares the R 2 coefficient of determination (part of explained variance) of the different surrogate models: full Walsh expansion of degree 1, and of degree 2, and the sparse Walsh model with lag = 4 of degree 2, and of degree 3.…”

Section: Sparse Walsh Model Qualitymentioning

confidence: 99%

“…The design of a surrogate by an expert would push to select the most important variables interactions which influence the objective function. Heuristically based on knowledge of the optimization problems, some researchers propose to bound the degree of the Walsh expansion [6,14,13], but the number of terms can still be too large compare to the sample size. In feature selection machine learning problems [26], where the goal is to select the most important predictors for a machine learning algorithm, block model [33,4] is used which supposes that the features are clustered into families of variables.…”

mentioning

confidence: 99%

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Sparse Surrogate Model for Optimization: Example of the Bus Stops Spacing Problem

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Combinatorial optimization problems can involve computationaly expensive fitness function, making their resolution challenging. Surrogate models are one of the effective techniques used to solve such black-box problems by guiding the search towards potentially good solutions. In this paper, we focus on the use of surrogate based on multinomial approaches, particularly based on Walsh functions, to tackle pseudo-Boolean problems. Although this approach can be effective, a potential drawback is the growth of the polynomial expansion with problem dimension. We introduce a method for analyzing real-world combinatorial black-box problems defined through numerical simulation. This method combines Walsh spectral analysis and polynomial regression. Consequently, we propose a sparse surrogate model that incorporates selected, relevant terms and is simpler to optimize. To demonstrate our approach, we apply it to the bus stop spacing problem, an exemplary combinatorial pseudo-Boolean challenge.

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Section: Surrogate Model For Combinatorial Optimizationmentioning

confidence: 99%

Section: Sparse Walsh Model Qualitymentioning

confidence: 99%

mentioning

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Surrogate-assisted evolutionary algorithms for expensive combinatorial optimization: a survey

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As potent approaches for addressing computationally expensive optimization problems, surrogate-assisted evolutionary algorithms (SAEAs) have garnered increasing attention. Prevailing endeavors in evolutionary computation predominantly concentrate on expensive continuous optimization problems, with a notable scarcity of investigations directed toward expensive combinatorial optimization problems (ECOPs). Nevertheless, numerous ECOPs persist in practical applications. The widespread prevalence of such problems starkly contrasts the limited development of relevant research. Motivated by this disparity, this paper conducts a comprehensive survey on SAEAs tailored to address ECOPs. This survey comprises two primary segments. The first segment synthesizes prevalent global, local, hybrid, and learning search strategies, elucidating their respective strengths and weaknesses. Subsequently, the second segment furnishes an overview of surrogate-based evaluation technologies, delving into three pivotal facets: model selection, construction, and management. The paper also discusses several potential future directions for SAEAs with a focus towards expensive combinatorial optimization.

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Scalable benchmarks and performance measures for dynamic multi-objective optimization

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Walsh-based surrogate-assisted multi-objective combinatorial optimization: A fine-grained analysis for pseudo-boolean functions

Cited by 3 publications

References 38 publications

Sparse Surrogate Model for Optimization: Example of the Bus Stops Spacing Problem

Sparse Surrogate Model for Optimization: Example of the Bus Stops Spacing Problem

Surrogate-assisted evolutionary algorithms for expensive combinatorial optimization: a survey

Scalable benchmarks and performance measures for dynamic multi-objective optimization

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