arXiv:2608.08898cs.NEcs.AI2026-08

用代码复杂度衡量优化问题难度,快速预测算法表现。

A New Approach to Characterising Optimisation Problems Using Programmatic Representation and Complexity Measures

论文配图:A New Approach to Characterising Optimisation Problems Using Programmatic Representation and Complexity Measures
图 1 · 摘自论文原文
  • 将目标函数写成程序,用Halstead体积衡量代码复杂度
  • 复杂度越高,算法性能越差,相关性显著为负
  • 无需采样搜索空间,计算快,适合自动分析

优化问题实例的特征刻画是理解算法行为与性能的关键,有助于算法选择与配置。本文提出一种新方法:将问题实例以程序形式实现,通过代码复杂度来表征问题难度。核心思想是目标函数的代码复杂度与其搜索景观复杂度相关。我们采用Halstead体积作为代码复杂度指标,可快速通过现有库计算,相当于程序熵的简化版本。在BBOB优化基准套件和简单前馈神经网络训练任务上验证了该方法。结果显示,该复杂度度量与算法性能呈显著负相关,具有作为算法选择等元特征的潜力。该方法不需对搜索空间采样,对变换不变,且计算高效,可作为现有特征刻画方法的补充。

原文摘要 · Abstract (English)

Characterising optimisation problem instances is a fundamental part of understanding the behaviour and performance of different algorithms as well as providing information for algorithm selection and configuration. In this paper we propose a novel approach to problem characterisation based on the representation of instances when implemented as a program. The intuition is that the complexity of the code required to express an objective function should relate to the complexity of the search landscape. We identify the Halstead volume as a measure of code complexity, which can be seen as a simplified version of the entropy of the program. Given a code implementation of the objective function, the Halstead volume and entropy can be quickly calculated using existing libraries. We apply the proposed complexity measures to the well-known BBOB optimisation problem suite and the simple feed-forward neural network training task. We also show that the measures are negatively correlated with algorithm performance and therefore show potential as predictive meta-features for algorithm selection and other problem analysis. We envisage the proposed measures as complementary to other problem characterisation approaches, but with the advantages of not requiring any sampling of the search space, being invariant to transformations, and being very quick to calculate automatically.

优化问题代码复杂度算法选择元特征

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。