For solving combinatorial optimisation problems with metaheuristics, different search operators are applied for sampling new solutions in the neighbourhood of a given solution. It is important to understand the relationship between operators for various purposes, e.g., adaptively deciding when to use which operator to find optimal solutions efficiently. However, it is difficult to theoretically analyse this relationship, especially in the complex solution space of combinatorial optimisation problems. In this paper, we propose to empirically analyse the relationship between operators in terms of the correlation between their local optima and develop a measure for quantifying their relationship. The comprehensive analyses on a wide range of capacitated vehicle routing problem benchmark instances show that there is a consistent pattern in the correlation between commonly used operators. Based on this newly proposed local optima correlation metric, we propose a novel approach for adaptively selecting among the operators during the search process. The core intention is to improve search efficiency by preventing wasting computational resources on exploring neighbourhoods where the local optima have already been reached. Experiments on randomly generated instances and commonly used benchmark datasets are conducted. Results show that the proposed approach outperforms commonly used adaptive operator selection methods.

翻译：针对使用元启发式方法求解组合优化问题，需要采用不同的搜索算子在给定解的邻域内采样新解。理解算子之间的关系对于多种目标（例如自适应地决定何时使用何种算子以高效寻找最优解）具有重要意义。然而，在复杂的组合优化问题解空间中，从理论上分析这种关系存在困难。本文提出通过算子局部最优之间的相关性来经验性地分析算子关系，并开发了一种量化该关系的度量方法。通过对一系列带容量约束的车辆路径问题基准实例的全面分析，发现常用算子之间的相关性存在一致的模式。基于新提出的局部最优相关性度量，我们提出了一种在搜索过程中自适应选择算子的新方法。其核心目标是避免在局部最优已探明的邻域上浪费计算资源，从而提升搜索效率。在随机生成的实例和常用基准数据集上的实验表明，所提出的方法优于常用的自适应算子选择方法。