We contribute to the theoretical understanding of randomized search heuristics for dynamic problems. We consider the classical vertex coloring problem on graphs and investigate the dynamic setting where edges are added to the current graph. We then analyze the expected time for randomized search heuristics to recompute high quality solutions. The (1+1) Evolutionary Algorithm and RLS operate in a setting where the number of colors is bounded and we are minimizing the number of conflicts. Iterated local search algorithms use an unbounded color palette and aim to use the smallest colors and, consequently, the smallest number of colors. We identify classes of bipartite graphs where reoptimization is as hard as or even harder than optimization from scratch, i.e., starting with a random initialization. Even adding a single edge can lead to hard symmetry problems. However, graph classes that are hard for one algorithm turn out to be easy for others. In most cases our bounds show that reoptimization is faster than optimizing from scratch. We further show that tailoring mutation operators to parts of the graph where changes have occurred can significantly reduce the expected reoptimization time. In most settings the expected reoptimization time for such tailored algorithms is linear in the number of added edges. However, tailored algorithms cannot prevent exponential times in settings where the original algorithm is inefficient.

我们有助于对动态问题的随机搜索启发式的理论理解。我们考虑图上的经典顶点着色问题，并研究将边添加到当前图的动态设置。然后我们分析随机搜索启发式重新计算高质量解决方案的预期时间。(1+1) 进化算法和 RLS 在颜色数量有界的设置中运行，我们正在最小化冲突的数量。迭代局部搜索算法使用无界调色板，旨在使用最小的颜色，因此使用最少的颜色。我们确定了二部图的类别，其中重新优化与从头开始优化一样困难甚至更难，即从随机初始化开始。即使添加一条边也会导致严重的对称问题。然而，对于一种算法来说很难的图类对于其他算法来说却很容易。在大多数情况下，我们的界限表明重新优化比从头优化更快。我们进一步表明，将变异算子调整到发生变化的图形部分可以显着减少预期的重新优化时间。在大多数设置中，此类定制算法的预期重新优化时间与添加的边数呈线性关系。但是，在原始算法效率低下的设置中，定制算法无法防止指数时间。我们进一步表明，将变异算子调整到发生变化的图形部分可以显着减少预期的重新优化时间。在大多数设置中，此类定制算法的预期重新优化时间与添加的边数呈线性关系。但是，在原始算法效率低下的设置中，定制算法无法防止指数时间。我们进一步表明，将变异算子调整到发生变化的图形部分可以显着减少预期的重新优化时间。在大多数设置中，此类定制算法的预期重新优化时间与添加的边数呈线性关系。但是，在原始算法效率低下的设置中，定制算法无法防止指数时间。