用精确方法和启发式方法求解符号罗马控制和符号全罗马控制问题
Solving the signed Roman domination and signed total Roman domination problems with exact and heuristic methods
摘要：
本文研究了符号罗马控制和符号全罗马控制问题。对于每个问题，我们提出了两个整数线性规划（ILP）公式，约束规划（CP）公式和可变邻域搜索（VNS）方法。我们提出的ILP配方和多面体的研究，我们表明，两个模型松弛多面体的正确性证明是等价的。VNS使用专门设计的罚函数，允许稍微不可行的解决方案的外观。这些解决方案的接受将整个搜索过程引向长期有希望的领域。所有提出的方法进行了大量的实例测试。实验结果表明，对于大多数中小规模的实例，它们都达到了最优解。这两种ILP模型都被证明比其他两种方法更成功。
英文摘要：
In this paper we deal with the signed Roman domination and signed total Roman domination problems. For each problem we propose two integer linear programming (ILP) formulations, the constraint programming (CP) formulation and variable neighborhood search (VNS) method. We present proofs for the correctness of the ILP formulations and a polyhedral study in which we show that the polyhedrons of the two model relaxations are equivalent. VNS uses specifically designed penalty function that allows the appearance of slightly infeasible solutions. The acceptance of these solutions directs the overall search process to the promising areas in the long run. All proposed approaches are tested on the large number of instances. Experimental results indicate that all of them reach optimal solutions for the most of small and middle scale instances. Both ILP models have proven to be more successful than the other two methods.
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