In this article, we focus on solving the power dominating set problem and its connected version. These problems are frequently used for finding optimal placements of phasor measurement units in power systems. We present an improved integer linear program (ILP) for both problems. In addition, a greedy constructive algorithm and a local search are developed. A greedy randomised adaptive search procedure (GRASP) algorithm is created to find near optimal solutions for large scale problem instances. The performance of the GRASP is further enhanced by extending it to the novel fixed set search (FSS) metaheuristic. Our computational results show that the proposed ILP has a significantly lower computational cost than existing ILPs for both versions of the problem. The proposed FSS algorithm manages to find all the optimal solutions that have been acquired using the ILP. In the last group of tests, it is shown that the FSS can significantly outperform the GRASP in both solution quality and computational cost.

中文翻译：

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固定集合搜索适用于功率支配集合问题

在本文中，我们着重解决功率支配集问题及其连接版本。这些问题通常用于寻找电力系统中相量测量单元的最佳位置。我们针对这两个问题提出了一种改进的整数线性程序（ILP）。此外，还开发了贪婪的构造算法和局部搜索。创建一个贪婪的随机自适应搜索过程（GRASP）算法，以查找大规模问题实例的近似最优解。通过将GRASP扩展到新颖的固定集搜索（FSS）元启发式方法，可以进一步提高其性能。我们的计算结果表明，针对该问题的两个版本，建议的ILP的计算成本均比现有ILP的计算成本低得多。提出的FSS算法设法找到使用ILP已获得的所有最佳解决方案。在最后一组测试中，表明FSS在解决方案质量和计算成本上都可以大大优于GRASP。