Empirical Analysis of the Dynamic Binary Value Problem with IOHprofiler

TL;DR

This work addresses dynamic optimization by focusing on the Dynamic Binary Value (DBV) benchmark and its integration into the IOHprofiler benchmarking platform. It develops practical, theory-inspired benchmarks and conducts large-scale empirical studies to understand how mutation, crossover, population size, and environmental update frequency shape performance under dynamic settings. Key findings include a mutation-rate threshold $\chi_0$ separating efficient $O(N \log N)$ performance from exponential-time behavior, a strong influence of weight-distributions over instance specifics, and non-monotone effects of update frequency on problem difficulty, all demonstrated within a reproducible, modular framework. The results establish a productive theory-practice loop and provide a reusable platform for future investigations into dynamic optimization algorithms.

Abstract

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.

Figures (7)

• Figure 1: Dimenionality 1000, SHAP-values for each of the varied parameter settings. For selection, red corresponds to plus-selection. For the function version, red corresponds to the rank-based version.
• Figure 2: Dimensionality 1000, number of evaluations (log-scaled) needed to reach optimum given different mutation rates.
• Figure 3: Dimensionality 1000, relative number of correct bits after the budget (1000 times $N$) is used, given different mutation rates.
• Figure 4: Dimensionality 1000, some selected ERT curves for different mutation rates (rank-based function).
• Figure 5: Dimensionality 1000, number of evaluations (log-scaled) needed to reach optimum, on the rank-based functions, given different number of parents and mutation after crossover setting. Crossover probability is $0.5$.