The Maximal Covering Problem with Some Negative Weights

This article presents the maximal covering problem on a network when some of the weights can be negative. Integer programming formulations are proposed and tested with ILOG CPLEX. Heuristic algorithms, an ascent algorithm, and simulated annealing are proposed and tested. The simulated annealing approach provides the best results for a data set comprising 40 problems. Este articulo presenta un caso del problema de cubrimiento o cobertura maxima en una red cuando algunos de los pesos son negativos. Para dicho caso se propone el uso de formulaciones programacion lineal de enteros. El metodo es evaluado con el programa de optimizacion ILOG CPLEX. Tambien se proponen y evaluan dos algoritmos heuristicos -un algoritmo ascendente y un algoritmo de recocido (temple) simulado. Este ultimo ofrece los mejores resultados para un conjunto de datos compuesto por 40 problemas. 本文讨论了网络中存在负权情况下的最大覆盖问题，提出了该问题整数规划算法，并基于ILOG CPLEX 软件进行了算法实现；对包含40个最大覆盖问题的数据集，分别采用上升算法和模拟退火算法这两种启发式算法进行求解与测试，结果表明模拟退火算法能够获得最好的结果。

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