发表机构
School of Electrical Engineering and Computer Science, University of Queensland; Department of Decision Sciences, University of South Africa（昆士兰大学电气工程与计算机科学学院; 南非大学决策科学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出基于程序表示与Halstead体积等代码复杂度度量的优化问题表征新方法，在BBOB套件和神经网络训练任务中验证其与算法性能负相关，可作为算法选择的预测元特征。
AI 中文摘要
优化问题实例的表征是理解不同算法的行为与性能、为算法选择与配置提供信息的基础环节。本文提出一种基于实例的程序实现形式进行问题表征的新方法，其核心思路是：表达目标函数所需代码的复杂度应与搜索空间的复杂度相关。我们将Halstead体积（一种可视为程序熵简化版本的代码复杂度度量）作为研究对象，给定目标函数的代码实现，可通过现有库快速计算Halstead体积与熵。我们将所提复杂度度量应用于知名的BBOB优化问题套件及简单的前馈神经网络训练任务，结果显示这些度量与算法性能呈负相关，因此具备作为算法选择及其他问题分析的预测元特征的潜力。我们认为所提度量是对其他问题表征方法的补充，且具有无需对搜索空间进行采样、对变换具有不变性、自动计算速度极快的优势。
英文摘要
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.
