arXiv subjects

Diederick Vermetten

Publications and source records attributed to Diederick Vermetten.

At least 19 recordsLinked to original sources

arXiv2026

Integer Natural Evolution Strategies

While contemporary Evolution Strategies handle integer optimization problems effectively, their adaptation mechanism is grounded in $\ell_2$-based Gaussian models, which are not native to the integer lattice. In contrast, the $\ell_1$-norm provides the natural measure of displacement on $\mathbb{Z}^n$, with the double geometric distribution as its canonical mutation operator. In this work, we derive a fully $\ell_1$-native step-size adaptation mechanism from first principles and propose an Integer Natural Evolution Strategy. We show that the DG distribution belongs to the exponential family, and that its sufficient statistic $|z|$ yields a natural-gradient signal for dispersion adaptation. By accumulating this signal via an evolution path, we obtain a fading-memory online estimator of the natural gradient, following Ollivier (2018). This establishes that DG-based step-size adaptation arises directly from the statistical structure of the mutation distribution, rather than as a discrete analog of continuous ES mechanisms. Empirical results on integer quadratic benchmarks show that \textsc{INES} learns meaningful coordinate-wise step-sizes and is competitive with integer-handling CMA-ES baselines. Its advantages are most visible in high-dimensional Ellipsoidal problems and in robust convergence at larger dimensions.

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arXiv2026

On the Influence of the Feature Computation Budget on Per-Instance Algorithm Selection for Black-Box Optimization

Per-instance algorithm selection (PIAS) takes advantage of complementarity between a set of algorithms by deciding which algorithm to run on a given instance. This decision is based on features of the instances, which, in the context of black-box optimization (BBO), require a part of the optimization budget to be computed. This raises two questions: (a) from which fraction of the budget spent on feature computation does PIAS become worth it for BBO, and (b) which fraction of the budget optimizes the tradeoff between feature accuracy and PIAS performance. To this end, we perform a broad study where PIAS with varying sampling budgets for feature computation is compared to the single best algorithm on a broad range of algorithm selection scenarios. These scenarios consist of two portfolio sizes, three problem sets, 4 dimensionalities, and 10 target budgets. We find that PIAS is viable for the majority of tested scenarios, even when as much as a quarter of the total budget is spent on feature computation. The tradeoff for the fraction of the budget spent on feature computation to maximize the benefit of PIAS is highly dependent on the specific AS scenario. Further, on average 20 percent of PIAS loss to the virtual best solver is explained by the budget spent on feature computation, highlighting the importance of properly accounting for the feature budget.

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arXiv2026

Similarity-based Portfolio Construction for Black-box Optimization

In black-box optimization, a central question is which algorithm to use to solve a given, previously unseen, problem. Selecting a single algorithm, however, entails inherent risks: inaccuracies in the selector may lead to poor choices, and even well-performing algorithms with high variance can yield unsatisfactory results in a single run. A natural remedy is to split the evaluation budget across multiple runs of potentially different algorithms. Such sequential algorithm portfolios benefit from variance reduction and complementarities between algorithms, often outperforming approaches that allocate the entire budget to a single solver. While effective portfolios can be constructed post-hoc, transferring this idea to the algorithm selection setting is non-trivial. We show that a naive portfolio constructed over the full training set already outperforms the strongest traditional baseline, the virtual best solver. We then propose a simple yet effective k-nearest-neighbor-based finetuning approach to construct portfolios tailored to unseen instances, yielding further improvements and highlighting the effectiveness of portfolio selection in fixed-budget black-box optimization.

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arXiv2026

Exploration of Pareto-preserving Search Space Transformations in Multi-objective Test Functions

Benchmark problems are an important tool for gaining understanding of optimization algorithms. Since algorithms often aim to perform well on benchmarks, biases in benchmark design provide misleading insights. In single-objective optimization, for example, many problems used to have their optimum in the center of the search domain. To remedy these issues, search space transformations have been widely adopted by benchmark suites, preventing algorithms from exploiting unintended structure. In multi-objective optimization, problem design has focused primarily on the objective space structure. While this focus addresses important aspects of the multi-objective nature of the problems, the search space structures of these problems have received comparatively limited attention. In this work, we re-emphasize the importance of transformations in the search space, and address the challenges inherent in adding transformations to boundary constraints problems without impacting the structure of the objective space. We utilized two parameterized, bijective transformations to create different instantiations of popular benchmark problems, and show how these changes impact the performance of various multi-objective optimization algorithms. In addition to the search space transformations, we show that such parameterized transformations can also be applied to the objective space, and compare their respective performance impacts.

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arXiv2026

How Sequential Algorithm Portfolios can benefit Black Box Optimization

In typical black-box optimization applications, the available computational budget is often allocated to a single algorithm, typically chosen based on user preference with limited knowledge about the problem at hand or according to some expert knowledge. However, we show that splitting the budget across several algorithms yield significantly better results. This approach benefits from both algorithm complementarity across diverse problems and variance reduction within individual functions, and shows that algorithm portfolios do NOT require parallel evaluation capabilities. To demonstrate the advantage of sequential algorithm portfolios, we apply it to the COCO data archive, using over 200 algorithms evaluated on the BBOB test suite. The proposed sequential portfolios consistently outperform single-algorithm baselines, achieving relative performance gains of over 14%, and offering new insights into restart mechanisms and potential for warm-started execution strategies.

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arXiv2025

Benchmarking that Matters: Rethinking Benchmarking for Practical Impact

Benchmarking has driven scientific progress in Evolutionary Computation, yet current practices fall short of real-world needs. Widely used synthetic suites such as BBOB and CEC isolate algorithmic phenomena but poorly reflect the structure, constraints, and information limitations of continuous and mixed-integer optimization problems in practice. This disconnect leads to the misuse of benchmarking suites for competitions, automated algorithm selection, and industrial decision-making, despite these suites being designed for different purposes. We identify key gaps in current benchmarking practices and tooling, including limited availability of real-world-inspired problems, missing high-level features, and challenges in multi-objective and noisy settings. We propose a vision centered on curated real-world-inspired benchmarks, practitioner-accessible feature spaces and community-maintained performance databases. Real progress requires coordinated effort: A living benchmarking ecosystem that evolves with real-world insights and supports both scientific understanding and industrial use.

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arXiv2025

A Standardized Benchmark Set of Clustering Problem Instances for Comparing Black-Box Optimizers

One key challenge in optimization is the selection of a suitable set of benchmark problems. A common goal is to find functions which are representative of a class of real-world optimization problems in order to ensure findings on the benchmarks will translate to relevant problem domains. While some problem characteristics are well-covered by popular benchmarking suites, others are often overlooked. One example of such a problem characteristic is permutation invariance, where the search space consists of a set of symmetrical search regions. This type of problem occurs e.g. when a set of solutions has to be found, but the ordering within this set does not matter. The data clustering problem, often seen in machine learning contexts, is a clear example of such an optimization landscape, and has thus been proposed as a base from which optimization benchmarks can be created. In addition to the symmetry aspect, these clustering problems also contain potential regions of neutrality, which can provide an additional challenge to optimization algorithms. In this paper, we present a standardized benchmark suite for the evaluation of continuous black-box optimization algorithms, based on data clustering problems. To gain insight into the diversity of the benchmark set, both internally and in comparison to existing suites, we perform a benchmarking study of a set of modular CMA-ES configurations, as well as an analysis using exploratory landscape analysis. Our benchmark set is open-source and integrated with the IOHprofiler benchmarking framework to encourage its use in future research.

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arXiv2025

Abnormal Mutations: Evolution Strategies Don't Require Gaussianity

The mutation process in evolution strategies has been interlinked with the normal distribution since its inception. Many lines of reasoning have been given for this strong dependency, ranging from maximum entropy arguments to the need for isotropy. However, some theoretical results suggest that other distributions might lead to similar local convergence properties. This paper empirically shows that a wide range of evolutionary strategies, from the (1+1)-ES to CMA-ES, show comparable optimization performance when using a mutation distribution other than the standard Gaussian. Replacing it with, e.g., uniformly distributed mutations, does not deteriorate the performance of ES, when using the default adaptation mechanism for the strategy parameters. We observe that these results hold not only for the sphere model but also for a wider range of benchmark problems.

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arXiv2025

Transfer Learning of Surrogate Models: Integrating Domain Warping and Affine Transformations

Surrogate models provide efficient alternatives to computationally demanding real world processes but often require large datasets for effective training. A promising solution to this limitation is the transfer of pre-trained surrogate models to new tasks. Previous studies have investigated the transfer of differentiable and non-differentiable surrogate models, typically assuming an affine transformation between the source and target functions. This paper extends previous research by addressing a broader range of transformations, including linear and nonlinear variations. Specifically, we consider the combination of an unknown input warping, such as one modeled by the beta cumulative distribution function, with an unspecified affine transformation. Our approach achieves transfer learning by employing a limited number of data points from the target task to optimize these transformations, minimizing empirical loss on the transfer dataset. We validate the proposed method on the widely used Black-Box Optimization Benchmark (BBOB) testbed and a real-world transfer learning task from the automobile industry. The results underscore the significant advantages of the approach, revealing that the transferred surrogate significantly outperforms both the original surrogate and the one built from scratch using the transfer dataset, particularly in data-scarce scenarios.

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arXiv2025

Transfer Learning of Surrogate Models via Domain Affine Transformation Across Synthetic and Real-World Benchmarks

Surrogate models are frequently employed as efficient substitutes for the costly execution of real-world processes. However, constructing a high-quality surrogate model often demands extensive data acquisition. A solution to this issue is to transfer pre-trained surrogate models for new tasks, provided that certain invariances exist between tasks. This study focuses on transferring non-differentiable surrogate models (e.g., random forests) from a source function to a target function, where we assume their domains are related by an unknown affine transformation, using only a limited amount of transfer data points evaluated on the target. Previous research attempts to tackle this challenge for differentiable models, e.g., Gaussian process regression, which minimizes the empirical loss on the transfer data by tuning the affine transformations. In this paper, we extend the previous work to the random forest and assess its effectiveness on a widely-used artificial problem set - Black-Box Optimization Benchmark (BBOB) testbed, and on four real-world transfer learning problems. The results highlight the significant practical advantages of the proposed method, particularly in reducing both the data requirements and computational costs of training surrogate models for complex real-world scenarios.

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arXiv2024

Stalling in Space: Attractor Analysis for any Algorithm

Network-based representations of fitness landscapes have grown in popularity in the past decade; this is probably because of growing interest in explainability for optimisation algorithms. Local optima networks (LONs) have been especially dominant in the literature and capture an approximation of local optima and their connectivity in the landscape. However, thus far, LONs have been constructed according to a strict definition of what a local optimum is: the result of local search. Many evolutionary approaches do not include this, however. Popular algorithms such as CMA-ES have therefore never been subject to LON analysis. Search trajectory networks (STNs) offer a possible alternative: nodes can be any search space location. However, STNs are not typically modelled in such a way that models temporal stalls: that is, a region in the search space where an algorithm fails to find a better solution over a defined period of time. In this work, we approach this by systematically analysing a special case of STN which we name attractor networks. These offer a coarse-grained view of algorithm behaviour with a singular focus on stall locations. We construct attractor networks for CMA-ES, differential evolution, and random search for 24 noiseless black-box optimisation benchmark problems. The properties of attractor networks are systematically explored. They are also visualised and compared to traditional LONs and STN models. We find that attractor networks facilitate insights into algorithm behaviour which other models cannot, and we advocate for the consideration of attractor analysis even for algorithms which do not include local search.

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arXiv2024

MO-IOHinspector: Anytime Benchmarking of Multi-Objective Algorithms using IOHprofiler

Benchmarking is one of the key ways in which we can gain insight into the strengths and weaknesses of optimization algorithms. In sampling-based optimization, considering the anytime behavior of an algorithm can provide valuable insights for further developments. In the context of multi-objective optimization, this anytime perspective is not as widely adopted as in the single-objective context. In this paper, we propose a new software tool which uses principles from unbounded archiving as a logging structure. This leads to a clearer separation between experimental design and subsequent analysis decisions. We integrate this approach as a new Python module into the IOHprofiler framework and demonstrate the benefits of this approach by showcasing the ability to change indicators, aggregations, and ranking procedures during the analysis pipeline.

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arXiv2024

In-the-loop Hyper-Parameter Optimization for LLM-Based Automated Design of Heuristics

Large Language Models (LLMs) have shown great potential in automatically generating and optimizing (meta)heuristics, making them valuable tools in heuristic optimization tasks. However, LLMs are generally inefficient when it comes to fine-tuning hyper-parameters of the generated algorithms, often requiring excessive queries that lead to high computational and financial costs. This paper presents a novel hybrid approach, LLaMEA-HPO, which integrates the open source LLaMEA (Large Language Model Evolutionary Algorithm) framework with a Hyper-Parameter Optimization (HPO) procedure in the loop. By offloading hyper-parameter tuning to an HPO procedure, the LLaMEA-HPO framework allows the LLM to focus on generating novel algorithmic structures, reducing the number of required LLM queries and improving the overall efficiency of the optimization process. We empirically validate the proposed hybrid framework on benchmark problems, including Online Bin Packing, Black-Box Optimization, and the Traveling Salesperson Problem. Our results demonstrate that LLaMEA-HPO achieves superior or comparable performance compared to existing LLM-driven frameworks while significantly reducing computational costs. This work highlights the importance of separating algorithmic innovation and structural code search from parameter tuning in LLM-driven code optimization and offers a scalable approach to improve the efficiency and effectiveness of LLM-based code generation.

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arXiv2024

Sampling in CMA-ES: Low Numbers of Low Discrepancy Points

The Covariance Matrix Adaptation Evolution Strategy (CMA-ES) is one of the most successful examples of a derandomized evolution strategy. However, it still relies on randomly sampling offspring, which can be done via a uniform distribution and subsequently transforming into the required Gaussian. Previous work has shown that replacing this uniform sampling with a low-discrepancy sampler, such as Halton or Sobol sequences, can improve performance over a wide set of problems. We show that iterating through small, fixed sets of low-discrepancy points can still perform better than the default uniform distribution. Moreover, using only 128 points throughout the search is sufficient to closely approximate the empirical performance of using the complete pseudorandom sequence up to dimensionality 40 on the BBOB benchmark. For lower dimensionalities (below 10), we find that using as little as 32 unique low discrepancy points performs similar or better than uniform sampling. In 2D, for which we have highly optimized low discrepancy samples available, we demonstrate that using these points yields the highest empirical performance and requires only 16 samples to improve over uniform sampling. Overall, we establish a clear relation between the $L_2$ discrepancy of the used point set and the empirical performance of the CMA-ES.

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arXiv2024

Quantifying Individual and Joint Module Impact in Modular Optimization Frameworks

This study explores the influence of modules on the performance of modular optimization frameworks for continuous single-objective black-box optimization. There is an extensive variety of modules to choose from when designing algorithm variants, however, there is a rather limited understanding of how each module individually influences the algorithm performance and how the modules interact with each other when combined. We use the functional ANOVA (f-ANOVA) framework to quantify the influence of individual modules and module combinations for two algorithms, the modular Covariance Matrix Adaptation (modCMA) and the modular Differential Evolution (modDE). We analyze the performance data from 324 modCMA and 576 modDE variants on the BBOB benchmark collection, for two problem dimensions, and three computational budgets. Noteworthy findings include the identification of important modules that strongly influence the performance of modCMA, such as the~\textit{weights\ option} and~\textit{mirrored} modules for low dimensional problems, and the~\textit{base\ sampler} for high dimensional problems. The large individual influence of the~\textit{lpsr} module makes it very important for the performance of modDE, regardless of the problem dimensionality and the computational budget. When comparing modCMA and modDE, modDE undergoes a shift from individual modules being more influential, to module combinations being more influential, while modCMA follows the opposite pattern, with an increase in problem dimensionality and computational budget.

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arXiv2024

Avoiding Redundant Restarts in Multimodal Global Optimization

Naïve restarts of global optimization solvers when operating on multimodal search landscapes may resemble the Coupon's Collector Problem, with a potential to waste significant function evaluations budget on revisiting the same basins of attractions. In this paper, we assess the degree to which such ``duplicate restarts'' occur on standard multimodal benchmark functions, which defines the \textit{redundancy potential} of each particular landscape. We then propose a repelling mechanism to avoid such wasted restarts with the CMA-ES and investigate its efficacy on test cases with high redundancy potential compared to the standard restart mechanism.

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arXiv2024

Empirical Analysis of the Dynamic Binary Value Problem with IOHprofiler

Optimization problems in dynamic environments have recently been the source of several theoretical studies. One of these problems is the monotonic Dynamic Binary Value problem, which theoretically has high discriminatory power between different Genetic Algorithms. Given this theoretical foundation, we integrate several versions of this problem into the IOHprofiler benchmarking framework. Using this integration, we perform several large-scale benchmarking experiments to both recreate theoretical results on moderate dimensional problems and investigate aspects of GA's performance which have not yet been studied theoretically. Our results highlight some of the many synergies between theory and benchmarking and offer a platform through which further research into dynamic optimization problems can be performed.

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arXiv2024

Impact of Training Instance Selection on Automated Algorithm Selection Models for Numerical Black-box Optimization

The recently proposed MA-BBOB function generator provides a way to create numerical black-box benchmark problems based on the well-established BBOB suite. Initial studies on this generator highlighted its ability to smoothly transition between the component functions, both from a low-level landscape feature perspective, as well as with regard to algorithm performance. This suggests that MA-BBOB-generated functions can be an ideal testbed for automated machine learning methods, such as automated algorithm selection (AAS). In this paper, we generate 11800 functions in dimensions $d=2$ and $d=5$, respectively, and analyze the potential gains from AAS by studying performance complementarity within a set of eight algorithms. We combine this performance data with exploratory landscape features to create an AAS pipeline that we use to investigate how to efficiently select training sets within this space. We show that simply using the BBOB component functions for training yields poor test performance, while the ranking between uniformly chosen and diversity-based training sets strongly depends on the distribution of the test set.

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