带可靠性约束的最小生成森林问题的求解
Solution of minimum spanning forest problems with reliability constraints
摘要：
我们提出了可靠性约束的k根最小生成森林，一个相关的最优化问题，其目的是找到一个k根最小成本森林，连接给定的客户到一些供应顶点，在这样的方式，客户和供应顶点之间的每一条路径上的最小所需的可靠性是满足和成本是最小的。边的可靠性是指该边不发生故障的概率，而路径的可靠性是该路径上各边可靠性的乘积，该问题在电信、电力和交通等领域的网络设计中有相关的应用。对于它的解决方案，我们提出了一个混合整数线性规划模型，和一个自适应的大邻域搜索元启发式调用几个震动和局部搜索算子。大量的计算测试证明，元启发式算法可以在很短的计算时间内提供高质量的解决方案。
英文摘要：
We propose the reliability constrained k-rooted minimum spanning forest, a relevant optimization problem whose aim is to find a k-rooted minimum cost forest that connects given customers to a number of supply vertices, in such a way that a minimum required reliability on each path between a customer and a supply vertex is satisfied and the cost is a minimum. The reliability of an edge is the probability that no failure occurs on that edge, whereas the reliability of a path is the product of the reliabilities of the edges in such path. The problem has relevant applications in the design of networks, in fields such as telecommunications, electricity and transports. For its solution, we propose a mixed integer linear programming model, and an adaptive large neighborhood search metaheuristic which invokes several shaking and local search operators. Extensive computational tests prove that the metaheuristic can provide good quality solutions in very short computing times.
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