Local search is a fundamental tool in the development of heuristic algorithms. A neighborhood operator takes a current solution and returns a set of similar solutions, denoted as neighbors. In best improvement local search, the best of the neighboring solutions replaces the current solution in each iteration. On the other hand, in first improvement local search, the neighborhood is only explored until any improving solution is found, which then replaces the current solution. In this work we propose a new strategy for local search that attempts to avoid low-quality local optima by selecting in each iteration the improving neighbor that has the fewest possible attributes in common with local optima. To this end, it uses inequalities previously used as optimality cuts in the context of integer linear programming. The novel method, referred to as delayed improvement local search, is implemented and evaluated using the travelling salesman problem with the 2-opt neighborhood and the max-cut problem with the 1-flip neighborhood as test cases. Computational results show that the new strategy, while slower, obtains better local optima compared to the traditional local search strategies. The comparison is favourable to the new strategy in experiments with fixed computation time or with a fixed target.

局部搜索是开发启发式算法的基本工具。邻域算子采用当前解并返回一组相似的解，表示为邻域。在最佳改进局部搜索中，相邻解决方案中的最佳解决方案在每次迭代中替换当前解决方案。另一方面，在第一次改进局部搜索中，只探索邻域直到找到任何改进的解决方案，然后替换当前的解决方案。在这项工作中，我们提出了一种新的局部搜索策略，该策略试图通过在每次迭代中选择与局部最优具有最少可能属性的改进邻居来避免低质量局部最优。为此，它使用以前用作整数线性规划上下文中的最优切割的不等式。新颖的方法，称为延迟改进局部搜索，使用具有 2-opt 邻域的旅行商问题和具有 1-flip 邻域的 max-cut 问题作为测试用例来实现和评估。计算结果表明，与传统的局部搜索策略相比，新策略虽然速度较慢，但​​获得了更好的局部最优解。在固定计算时间或固定目标的实验中，这种比较有利于新策略。