The paper presents a new approach to solve multifacility location problems, which is based on mixed integer programming and algorithms for minimizing differences of convex (DC) functions. The main challenges for solving the multifacility location problems under consideration come from their intrinsic discrete, nonconvex, and nondifferentiable nature. We provide a reformulation of these problems as those of continuous optimization and then develop a new DC type algorithm for their solutions involving Nesterov's smoothing. The proposed algorithm is computationally implemented via MATLAB numerical tests on both artificial and real data sets.

中文翻译：

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用DC算法解决连续多设施选址问题

本文提出了一种新的解决多设施位置问题的方法，该方法基于混合整数规划和最小化凸（DC）函数差异的算法。解决所考虑的多设施位置问题的主要挑战来自其固有的离散性，非凸性和不可微性。我们将这些问题的形式重新定义为连续优化的形式，然后针对涉及Nesterov平滑的解决方案开发新的DC类型算法。所提出的算法是通过MATLAB数值测试对人工和真实数据集进行计算实现的。