arXiv subjects

Diederick Vermetten

Publications and source records attributed to Diederick Vermetten.

At least 37 records · Page 2Linked to original sources

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.

cs.NE↗

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.

cs.NE↗

arXiv2024

Explainable Benchmarking for Iterative Optimization Heuristics

Benchmarking heuristic algorithms is vital to understand under which conditions and on what kind of problems certain algorithms perform well. In most current research into heuristic optimization algorithms, only a very limited number of scenarios, algorithm configurations and hyper-parameter settings are explored, leading to incomplete and often biased insights and results. This paper presents a novel approach we call explainable benchmarking. Introducing the IOH-Xplainer software framework, for analyzing and understanding the performance of various optimization algorithms and the impact of their different components and hyper-parameters. We showcase the framework in the context of two modular optimization frameworks. Through this framework, we examine the impact of different algorithmic components and configurations, offering insights into their performance across diverse scenarios. We provide a systematic method for evaluating and interpreting the behaviour and efficiency of iterative optimization heuristics in a more transparent and comprehensible manner, allowing for better benchmarking and algorithm design.

cs.NE↗

arXiv2024

Large-scale Benchmarking of Metaphor-based Optimization Heuristics

The number of proposed iterative optimization heuristics is growing steadily, and with this growth, there have been many points of discussion within the wider community. One particular criticism that is raised towards many new algorithms is their focus on metaphors used to present the method, rather than emphasizing their potential algorithmic contributions. Several studies into popular metaphor-based algorithms have highlighted these problems, even showcasing algorithms that are functionally equivalent to older existing methods. Unfortunately, this detailed approach is not scalable to the whole set of metaphor-based algorithms. Because of this, we investigate ways in which benchmarking can shed light on these algorithms. To this end, we run a set of 294 algorithm implementations on the BBOB function suite. We investigate how the choice of the budget, the performance measure, or other aspects of experimental design impact the comparison of these algorithms. Our results emphasize why benchmarking is a key step in expanding our understanding of the algorithm space, and what challenges still need to be overcome to fully gauge the potential improvements to the state-of-the-art hiding behind the metaphors.

cs.NE↗

arXiv2024

Impact of spatial transformations on landscape features of CEC2022 basic benchmark problems

When benchmarking optimization heuristics, we need to take care to avoid an algorithm exploiting biases in the construction of the used problems. One way in which this might be done is by providing different versions of each problem but with transformations applied to ensure the algorithms are equipped with mechanisms for successfully tackling a range of problems. In this paper, we investigate several of these problem transformations and show how they influence the low-level landscape features of a set of 5 problems from the CEC2022 benchmark suite. Our results highlight that even relatively small transformations can significantly alter the measured landscape features. This poses a wider question of what properties we want to preserve when creating problem transformations, and how to fairly measure them.

cs.NE↗

arXiv2023

MA-BBOB: A Problem Generator for Black-Box Optimization Using Affine Combinations and Shifts

Choosing a set of benchmark problems is often a key component of any empirical evaluation of iterative optimization heuristics. In continuous, single-objective optimization, several sets of problems have become widespread, including the well-established BBOB suite. While this suite is designed to enable rigorous benchmarking, it is also commonly used for testing methods such as algorithm selection, which the suite was never designed around. We present the MA-BBOB function generator, which uses the BBOB suite as component functions in an affine combination. In this work, we describe the full procedure to create these affine combinations and highlight the trade-offs of several design decisions, specifically the choice to place the optimum uniformly at random in the domain. We then illustrate how this generator can be used to gain more low-level insight into the function landscapes through the use of exploratory landscape analysis. Finally, we show a potential use-case of MA-BBOB in generating a wide set of training and testing data for algorithm selectors. Using this setup, we show that the basic scheme of using a set of landscape features to predict the best algorithm does not lead to optimal results, and that an algorithm selector trained purely on the BBOB functions generalizes poorly to the affine combinations.

cs.NE↗

arXiv2023

PS-AAS: Portfolio Selection for Automated Algorithm Selection in Black-Box Optimization

The performance of automated algorithm selection (AAS) strongly depends on the portfolio of algorithms to choose from. Selecting the portfolio is a non-trivial task that requires balancing the trade-off between the higher flexibility of large portfolios with the increased complexity of the AAS task. In practice, probably the most common way to choose the algorithms for the portfolio is a greedy selection of the algorithms that perform well in some reference tasks of interest. We set out in this work to investigate alternative, data-driven portfolio selection techniques. Our proposed method creates algorithm behavior meta-representations, constructs a graph from a set of algorithms based on their meta-representation similarity, and applies a graph algorithm to select a final portfolio of diverse, representative, and non-redundant algorithms. We evaluate two distinct meta-representation techniques (SHAP and performance2vec) for selecting complementary portfolios from a total of 324 different variants of CMA-ES for the task of optimizing the BBOB single-objective problems in dimensionalities 5 and 30 with different cut-off budgets. We test two types of portfolios: one related to overall algorithm behavior and the `personalized' one (related to algorithm behavior per each problem separately). We observe that the approach built on the performance2vec-based representations favors small portfolios with negligible error in the AAS task relative to the virtual best solver from the selected portfolio, whereas the portfolios built from the SHAP-based representations gain from higher flexibility at the cost of decreased performance of the AAS. Across most considered scenarios, personalized portfolios yield comparable or slightly better performance than the classical greedy approach. They outperform the full portfolio in all scenarios.

cs.LG↗

arXiv2023

Comparing Algorithm Selection Approaches on Black-Box Optimization Problems

Performance complementarity of solvers available to tackle black-box optimization problems gives rise to the important task of algorithm selection (AS). Automated AS approaches can help replace tedious and labor-intensive manual selection, and have already shown promising performance in various optimization domains. Automated AS relies on machine learning (ML) techniques to recommend the best algorithm given the information about the problem instance. Unfortunately, there are no clear guidelines for choosing the most appropriate one from a variety of ML techniques. Tree-based models such as Random Forest or XGBoost have consistently demonstrated outstanding performance for automated AS. Transformers and other tabular deep learning models have also been increasingly applied in this context. We investigate in this work the impact of the choice of the ML technique on AS performance. We compare four ML models on the task of predicting the best solver for the BBOB problems for 7 different runtime budgets in 2 dimensions. While our results confirm that a per-instance AS has indeed impressive potential, we also show that the particular choice of the ML technique is of much minor importance.

cs.NE↗

arXiv2023

Computing Star Discrepancies with Numerical Black-Box Optimization Algorithms

The $L_{\infty}$ star discrepancy is a measure for the regularity of a finite set of points taken from $[0,1)^d$. Low discrepancy point sets are highly relevant for Quasi-Monte Carlo methods in numerical integration and several other applications. Unfortunately, computing the $L_{\infty}$ star discrepancy of a given point set is known to be a hard problem, with the best exact algorithms falling short for even moderate dimensions around 8. However, despite the difficulty of finding the global maximum that defines the $L_{\infty}$ star discrepancy of the set, local evaluations at selected points are inexpensive. This makes the problem tractable by black-box optimization approaches. In this work we compare 8 popular numerical black-box optimization algorithms on the $L_{\infty}$ star discrepancy computation problem, using a wide set of instances in dimensions 2 to 15. We show that all used optimizers perform very badly on a large majority of the instances and that in many cases random search outperforms even the more sophisticated solvers. We suspect that state-of-the-art numerical black-box optimization techniques fail to capture the global structure of the problem, an important shortcoming that may guide their future development. We also provide a parallel implementation of the best-known algorithm to compute the discrepancy.

cs.NE↗

arXiv2023

MA-BBOB: Many-Affine Combinations of BBOB Functions for Evaluating AutoML Approaches in Noiseless Numerical Black-Box Optimization Contexts

Extending a recent suggestion to generate new instances for numerical black-box optimization benchmarking by interpolating pairs of the well-established BBOB functions from the COmparing COntinuous Optimizers (COCO) platform, we propose in this work a further generalization that allows multiple affine combinations of the original instances and arbitrarily chosen locations of the global optima. We demonstrate that the MA-BBOB generator can help fill the instance space, while overall patterns in algorithm performance are preserved. By combining the landscape features of the problems with the performance data, we pose the question of whether these features are as useful for algorithm selection as previous studies suggested. MA-BBOB is built on the publicly available IOHprofiler platform, which facilitates standardized experimentation routines, provides access to the interactive IOHanalyzer module for performance analysis and visualization, and enables comparisons with the rich and growing data collection available for the (MA-)BBOB functions.

cs.LG↗

arXiv2023

Assessing the Generalizability of a Performance Predictive Model

A key component of automated algorithm selection and configuration, which in most cases are performed using supervised machine learning (ML) methods is a good-performing predictive model. The predictive model uses the feature representation of a set of problem instances as input data and predicts the algorithm performance achieved on them. Common machine learning models struggle to make predictions for instances with feature representations not covered by the training data, resulting in poor generalization to unseen problems. In this study, we propose a workflow to estimate the generalizability of a predictive model for algorithm performance, trained on one benchmark suite to another. The workflow has been tested by training predictive models across benchmark suites and the results show that generalizability patterns in the landscape feature space are reflected in the performance space.

cs.LG↗

arXiv2023

Analysis of modular CMA-ES on strict box-constrained problems in the SBOX-COST benchmarking suite

Box-constraints limit the domain of decision variables and are common in real-world optimization problems, for example, due to physical, natural or spatial limitations. Consequently, solutions violating a box-constraint may not be evaluable. This assumption is often ignored in the literature, e.g., existing benchmark suites, such as COCO/BBOB, allow the optimizer to evaluate infeasible solutions. This paper presents an initial study on the strict-box-constrained benchmarking suite (SBOX-COST), which is a variant of the well-known BBOB benchmark suite that enforces box-constraints by returning an invalid evaluation value for infeasible solutions. Specifically, we want to understand the performance difference between BBOB and SBOX-COST as a function of two initialization methods and six constraint-handling strategies all tested with modular CMA-ES. We find that, contrary to what may be expected, handling box-constraints by saturation is not always better than not handling them at all. However, across all BBOB functions, saturation is better than not handling, and the difference increases with the number of dimensions. Strictly enforcing box-constraints also has a clear negative effect on the performance of classical CMA-ES (with uniform random initialization and no constraint handling), especially as problem dimensionality increases.

cs.NE↗

arXiv2023

Challenges of ELA-guided Function Evolution using Genetic Programming

Within the optimization community, the question of how to generate new optimization problems has been gaining traction in recent years. Within topics such as instance space analysis (ISA), the generation of new problems can provide new benchmarks which are not yet explored in existing research. Beyond that, this function generation can also be exploited for solving complex real-world optimization problems. By generating functions with similar properties to the target problem, we can create a robust test set for algorithm selection and configuration. However, the generation of functions with specific target properties remains challenging. While features exist to capture low-level landscape properties, they might not always capture the intended high-level features. We show that a genetic programming (GP) approach guided by these exploratory landscape analysis (ELA) properties is not always able to find satisfying functions. Our results suggest that careful considerations of the weighting of landscape properties, as well as the distance measure used, might be required to evolve functions that are sufficiently representative to the target landscape.

cs.NE↗

arXiv2023

When to be Discrete: Analyzing Algorithm Performance on Discretized Continuous Problems

The domain of an optimization problem is seen as one of its most important characteristics. In particular, the distinction between continuous and discrete optimization is rather impactful. Based on this, the optimizing algorithm, analyzing method, and more are specified. However, in practice, no problem is ever truly continuous. Whether this is caused by computing limits or more tangible properties of the problem, most variables have a finite resolution. In this work, we use the notion of the resolution of continuous variables to discretize problems from the continuous domain. We explore how the resolution impacts the performance of continuous optimization algorithms. Through a mapping to integer space, we are able to compare these continuous optimizers to discrete algorithms on the exact same problems. We show that the standard $(μ_W, λ)$-CMA-ES fails when discretization is added to the problem.

cs.NE↗

arXiv2023

Modular Differential Evolution

New contributions in the field of iterative optimisation heuristics are often made in an iterative manner. Novel algorithmic ideas are not proposed in isolation, but usually as an extension of a preexisting algorithm. Although these contributions are often compared to the base algorithm, it is challenging to make fair comparisons between larger sets of algorithm variants. This happens because even small changes in the experimental setup, parameter settings, or implementation details can cause results to become incomparable. Modular algorithms offer a way to overcome these challenges. By implementing the algorithmic modifications into a common framework, many algorithm variants can be compared, while ensuring that implementation details match in all versions. In this work, we propose a version of a modular framework for the popular Differential Evolution (DE) algorithm. We show that this modular approach not only aids in comparison, but also allows for a much more detailed exploration of the space of possible DE variants. This is illustrated by showing that tuning the settings of modular DE vastly outperforms a set of commonly used DE versions which have been recreated in our framework. We then investigate these tuned algorithms in detail, highlighting the relation between modules and performance on particular problems.

cs.NE↗

arXiv2023

Deep-BIAS: Detecting Structural Bias using Explainable AI

Evaluating the performance of heuristic optimisation algorithms is essential to determine how well they perform under various conditions. Recently, the BIAS toolbox was introduced as a behaviour benchmark to detect structural bias (SB) in search algorithms. The toolbox can be used to identify biases in existing algorithms, as well as to test for bias in newly developed algorithms. In this article, we introduce a novel and explainable deep-learning expansion of the BIAS toolbox, called Deep-BIAS. Where the original toolbox uses 39 statistical tests and a Random Forest model to predict the existence and type of SB, the Deep-BIAS method uses a trained deep-learning model to immediately detect the strength and type of SB based on the raw performance distributions. Through a series of experiments with a variety of structurally biased scenarios, we demonstrate the effectiveness of Deep-BIAS. We also present the results of using the toolbox on 336 state-of-the-art optimisation algorithms, which showed the presence of various types of structural bias, particularly towards the centre of the objective space or exhibiting discretisation behaviour. The Deep-BIAS method outperforms the BIAS toolbox both in detecting bias and for classifying the type of SB. Furthermore, explanations can be derived using XAI techniques.

cs.NE↗

arXiv2023

Using Affine Combinations of BBOB Problems for Performance Assessment

Benchmarking plays a major role in the development and analysis of optimization algorithms. As such, the way in which the used benchmark problems are defined significantly affects the insights that can be gained from any given benchmark study. One way to easily extend the range of available benchmark functions is through affine combinations between pairs of functions. From the perspective of landscape analysis, these function combinations smoothly transition between the two base functions. In this work, we show how these affine function combinations can be used to analyze the behavior of optimization algorithms. In particular, we highlight that by varying the weighting between the combined problems, we can gain insights into the effects of added global structure on the performance of optimization algorithms. By analyzing performance trajectories on more function combinations, we also show that aspects such as the scaling of objective functions and placement of the optimum can greatly impact how these results are interpreted.

cs.NE↗

arXiv2023

Performance comparison of optimization methods on variational quantum algorithms

Variational quantum algorithms (VQAs) offer a promising path toward using near-term quantum hardware for applications in academic and industrial research. These algorithms aim to find approximate solutions to quantum problems by optimizing a parametrized quantum circuit using a classical optimization algorithm. A successful VQA requires fast and reliable classical optimization algorithms. Understanding and optimizing how off-the-shelf optimization methods perform in this context is important for the future of the field. In this work, we study the performance of four commonly used gradient-free optimization methods: SLSQP, COBYLA, CMA-ES, and SPSA, at finding ground-state energies of a range of small chemistry and material science problems. We test a telescoping sampling scheme (where the accuracy of the cost-function estimate provided to the optimizer is increased as the optimization converges) on all methods, demonstrating mixed results across our range of optimizers and problems chosen. We further hyperparameter tune two of the four optimizers (CMA-ES and SPSA) across a large range of models and demonstrate that with appropriate hyperparameter tuning, CMA-ES is competitive with and sometimes outperforms SPSA (which is not observed in the absence of hyperparameter tuning). Finally, we investigate the ability of an optimizer to beat the `sampling noise floor' given by the sampling noise on each cost-function estimate provided to the optimizer. Our results demonstrate the necessity for tailoring and hyperparameter-tuning known optimization techniques for inherently-noisy variational quantum algorithms and that the variational landscape that one finds in a VQA is highly problem- and system-dependent. This provides guidance for future implementations of these algorithms in the experiment.

quant-ph↗