We analyze the two combinatorial problems of Dominating Set and Vertex Coloring regarding what kind of local optima are present for various instances. For a variety of graph classes each, we determine whether the induced landscapes are unimodal, plateau-unimodal (all optima are just one plateau), equimodal (all local optima are global) or truly multimodal. We do this for two different neighborhood operators, one based on making only a single change and one also allowing swaps (interchanging two parts of the solution).

翻译：本文针对支配集和顶点着色这两个组合问题，分析了不同实例中局部最优解的存在类型。对于多种图类，我们分别判定其诱导景观是单峰的、高原单峰的（所有最优解仅为一个高原）、等峰的（所有局部最优解均为全局最优）还是真正的多峰的。我们基于两种不同的邻域算子进行此项分析：一种仅允许单次改动，另一种则允许交换操作（即互换解的两个部分）。