This paper investigates what properties a neighbourhood requires to support beneficial local search. We show that neighbourhood locality, and a reduction in cost probability towards the optimum, support a proof that search among neighbours is more likely to find an improving solution in a single search step than blind search. This is the first paper to introduce such a proof. The concepts underlying these properties are illustrated on a satisfiability problem class, and on travelling salesman problems. Secondly, for a given cost target t, we investigate a combination of blind search and local descent termed local blind descent, and present various conditions under which the expected number of steps to reach a cost better than t using local blind descent, is proven to be smaller than with blind search. Experiments indicate that local blind descent, given target cost t, should switch to local descent at a starting cost that reduces as t approaches the optimum.

翻译：本文研究邻域需要具备何种性质才能支持有益的局部搜索。我们证明，邻域局部性以及向最优解方向成本降低的概率，共同支持以下结论：在单次搜索步骤中，通过邻域搜索找到改进解的可能性高于盲目搜索。这是首次提出此类证明的论文。这些性质的基本概念通过可满足性问题类别和旅行商问题进行了阐释。其次，针对给定成本目标t，我们研究了一种结合盲目搜索与局部下降的方法（称为局部盲目下降），并提出了多种条件。在这些条件下，经证明，使用局部盲目下降达到优于t成本的期望步数少于盲目搜索。实验表明，在给定目标成本t的情况下，局部盲目下降应在起始成本处切换至局部下降，且该起始成本随t趋近最优解而降低。