构建可追溯最优解集的双目标优化测试集,提升算法评估可信度。
BONO-Bench: A Comprehensive Test Suite for Bi-objective Numerical Optimization with Traceable Pareto Sets
- 基于凸二次函数组合生成可控的双目标优化问题
- 20类问题支持调节变量数、最优前沿形状等特性,最优解可精确逼近
- 开源工具包支持复现,适合算法评估与对比研究
现有双目标数值优化基准测试多依赖人工构造或单目标拼接,前者缺乏现实性,后者难控性质。本文提出一种系统化问题生成方法:将理论清晰的凸二次函数组合成具有单峰或多峰结构、带或不带全局结构的优化景观。该方法可配置决策变量数、局部最优数量、帕累托前沿形状、目标空间平台区及条件度等属性,并保证最优解集可通过超体积或精确R2指标任意精度逼近。基于此,构建包含20类问题的测试套件BONO-Bench,并用于示范性基准研究。相关生成方法与测试套件已开源为Python包bonobench,支持可复现的算法评估。
原文摘要 · Abstract (English)
The evaluation of heuristic optimizers on test problems, better known as \emph{benchmarking}, is a cornerstone of research in multi-objective optimization. However, most test problems used in benchmarking numerical multi-objective black-box optimizers come from one of two flawed approaches: On the one hand, problems are constructed manually, which result in problems with well-understood optimal solutions, but unrealistic properties and biases. On the other hand, more realistic and complex single-objective problems are composited into multi-objective problems, but with a lack of control and understanding of problem properties. This paper proposes an extensive problem generation approach for bi-objective numerical optimization problems consisting of the combination of theoretically well-understood convex-quadratic functions into unimodal and multimodal landscapes with and without global structure. It supports configuration of test problem properties, such as the number of decision variables, local optima, Pareto front shape, plateaus in the objective space, or degree of conditioning, while maintaining theoretical tractability: The optimal front can be approximated to an arbitrary degree of precision regarding Pareto-compliant performance indicators such as the hypervolume or the exact R2 indicator. To demonstrate the generator's capabilities, a test suite of 20 problem categories, called \emph{BONO-Bench}, is created and subsequently used as a basis of an illustrative benchmark study. Finally, the general approach underlying our proposed generator, together with the associated test suite, is publicly released in the Python package \texttt{bonobench} to facilitate reproducible benchmarking.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。