Local optima networks (LONs) have recently been used to analyse subfunction structure in problems which contain strong linkage. However, many questions remain: for example, it is not known how LON subfunction structure relates to optimiser performance on the underlying problems. In addition, the potential of using the associated features to distinguish between classes of problem is not well understood. Therefore we address these gaps. We construct LONs in two different ways, propose a new set of features (which are based upon the structure of subfunction argument sets), and investigate the associations with performance of three state-of-the-art optimisers. The results indicate that the subfunction-related features may depend on the LON construction algorithm and that some of them are useful for separating problem classes. Also, the proposed features seem to relate to the performance of some optimisers for some problem-operator combinations. The approach and the findings together not only provide new insight about the interplay between the studied problems and optimisers, but also lay the groundwork for possible online LON-based operator adaptation in the future.
The L_∞ star discrepancy of a point set is a measure for how uniformly a point set is distributed in a given space. Point sets of low star discrepancy are used as designs of experiments, as initial designs for Bayesian optimization algorithms, for quasi-Monte Carlo integration methods, and many other applications. Recent work has shown that classical constructions such as Sobol’, Halton, or Hammersley sequences can be outperformed by large margins when considering point sets of fixed sizes rather than their asymptotic behavior when the number of points tends to infinity. These results, highly relevant to the aforementioned applications, raise the question of how much existing constructions can be improved through size-specific optimization. In this work, we study this question for the 3-dimensional setting, focusing on how well the so-called Kronecker construction performs for various set sizes n. We show that, for settings with at least 500 points, optimizing the two configurable parameters of its construction using evolutionary computation approaches such as CMA-ES yields point sets whose discrepancy values outperform those of the previously best-known sets. Using the algorithm configuration technique Irace, we then derive parameters that yield new state-of-the-art discrepancy values for whole ranges of set sizes. An investigation of the problem landscapes using exploratory landscape analysis reveals that the problem is highly multimodal and that some of its characteristics differ substantially from the 24 BBOB functions.
Local Optima Networks (LONs) are established graph-based models for landscape analysis, yet their methodological maturity in continuous optimisation lags behind their combinatorial counterparts. This study investigates the challenges of constructing LONs for the Black-Box Optimisation Benchmark (BBOB) suite using a basin-hopping framework. We first identify a critical sampling anomaly—spurious local optima on theoretically unimodal functions—and suggest that vanishing gradients are the primary cause, proposing specific parameters to mitigate this behaviour. To improve high-dimensional interpretability, we introduce an integrated topographic visualisation that superimposes the LON graph onto a reconstructed fitness surface. This approach extends the intuition of 2d heatmaps to higher dimensions, capturing both connectivity and topography. Finally, we characterise the 5d BBOB suite using an expanded set of LON features. Comparative analysis reveals that LON-derived metrics outperform traditional landscape features for 3 of the 4 optimisers tested, suggesting that graph-based models capture structural nuances distinct from traditional metrics. These results contribute to establish the LON framework as a complementary quantitative and visualisation tool to characterise continuous optimisation landscapes.
Comparing multiple optimization algorithms across problem instances involves understanding not only which algorithm is best on average, but how instance characteristics shift relative performance over time. The PolarBear framework identifies Pareto-optimal anytime algorithms via scale-free Bayesian ranking models, but pools all instances into a single marginal comparison, discarding structure that could inform algorithm selection at deployment. We extend its temporal Plackett-Luce model with an ANOVA decomposition of latent utilities: algorithm performance over time is decomposed into a global baseline, main effects of instance characteristics, and their interactions, all modeled as time-varying processes. Factor levels are explicitly modeled independently, making the decomposition an analytical tool rather than a predictive model. We develop a diagnostic toolkit for the fitted posterior: Shapley information values quantify the decision-theoretic gain from learning each factor, log-lifts reveal how each factor level shifts performance ratings relative to the global baseline, and conditional anytime Pareto sets identify specialist algorithms that emerge under specific conditions. We demonstrate the framework on the BBOB benchmark suite, decomposing anytime performance of a diverse algorithm portfolio into effects of function identity and dimensionality. Clustering the level-specific deviations from the global baseline produces a data-driven problem taxonomy grounded in algorithmic performance rather than landscape properties.
