A major issue while conceiving or parameterizing an optimization heuristic is to ensure an appropriate balance between exploitation and exploration of the search. Evolution strategies and neighborhood-based metaheuristics constitute relevant high-level frameworks, which ease the problem solving but are often complex to configure. Moreover, their effective behavior, according to the particularities of the search landscapes, remains difficult to grasp. In this paper, we deeply investigate the sampled walk search algorithm, which is a local search equivalent of the \((1,\lambda )\)-evolution strategy, considering that the neighborhood relation describes mutation possibilities. We specifically designed experiments to better understand the behavior of such a strategy offering a fine way to deal with the exploration versus exploitation dilemma. The main contribution is the analysis of search trajectories by evaluating and visualizing both their width (exploration) and their height (exploitation). More generally, we aim at bringing insights about the behavior of the \((1,\lambda )\)-ES in a discrete optimization context and within a fitness landscape perspective.

在构思或参数化优化启发式方法时，一个主要问题是确保搜索的开发与探索之间的适当平衡。进化策略和基于邻域的元启发法构成了相关的高级框架，这些框架虽然易于解决问题，但配置通常很复杂。此外，根据搜索环境的特殊性，它们的有效行为仍然难以掌握。在本文中，我们深入研究了样本步行搜索算法，该算法与\（（1，\ lambda）\）-进化策略，考虑到邻域关系描述了变异的可能性。我们专门设计了一些实验，以更好地了解这种策略的行为，从而为解决勘探与开发难题提供了一种很好的方法。主要的贡献是通过评估和可视化搜索轨迹的宽度（探索）和高度（开发）并对其进行可视化分析。更广泛地讲，我们旨在了解有关\（（1，\ lambda）\）- ES在离散优化上下文中以及适应度范围内的行为的见解。