We present several techniques that use distances between candidate solutions to achieve intensification in Local Search (LS) algorithms. An important drawback of classical LS is that after visiting a very high-quality solution the search process can “forget about it” and continue towards very different areas. We propose a method that works on top of a given LS to equip it with a form of memory so as to record the highest-quality visited areas (spheres). More exactly, this new method uses distances between candidate solutions to perform a coarse–grained recording of the LS trajectory, i.e., it records a number of discovered spheres. The (centers of the) spheres are kept sorted in a priority queue in which new centers are continually inserted as in insertion-sort algorithms. After thoroughly investigating a sphere, the proposed method resumes the search from the first best sphere center in the priority queue. The resulting LS trajectory is no longer a continuous path, but a tree-like structure, with closed branches (already investigated spheres) and open branches (as-yet-unexplored spheres). We also explore several other techniques relying on distances, e.g., in Section 2.3, we show how to use distance information to prevent the search from looping indefinitely on large (quasi-)plateaus. Experiments on three problems based on different encodings (partitions, vectors and permutations) confirm the intensification potential of the proposed ideas.

中文翻译：

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距离指导的本地搜索

我们提出了几种使用候选解决方案之间的距离来实现局部搜索（LS）算法中的强化的技术。传统LS的一个重要缺点是，在访问了非常高质量的解决方案之后，搜索过程可能会“忘记它”并继续朝着非常不同的领域发展。我们提出一种在给定的LS上工作的方法，为它配备某种形式的内存，以便记录最高质量的访问区域（球体）。更确切地说，这种新方法使用候选解之间的距离来执行LS轨迹的粗粒度记录，即，它记录了许多发现的球体。球体的（中心）在优先级队列中保持排序，在该队列中，像插入排序算法一样，不断插入新的中心。在彻底研究了一个球体之后，提出的方法从优先级队列中的第一个最佳球体中心继续搜索。产生的LS轨迹不再是连续路径，而是树状结构，具有封闭的分支（已经研究过的球体）和开放的分支（尚未开发的球体）。我们还将探索其他一些依赖于距离的技术，例如在2.3节中，我们展示了如何使用距离信息来防止搜索在大（准）高原上无限循环。基于不同编码（分区，向量和排列）的三个问题的实验证实了所提出思想的增强潜力。