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中文摘要：
将投资限制引入经典约束p-中位问题，提出带投资的约束p-中位问题，该问题更适用于交通、物流等领域的设施选址。在深入分析带投资约束p-中位问题的数学模型的基础上，首先提出了适用于该问题求解的局部搜索策略；其次，将局部搜索策略与拉格朗日启发式算法和蚁群算法相结各，设计了求解该问题的拉格朗日混合蚁群算法。实验结果表明，带投资的约束p-中位问题能够根据投资金额规划不同的投资方案；且提出的混合蚁群算法较大程度上提高了蚁群算法和拉格朗日启发式算法的求解精度，具有较好的收敛性。
英文摘要：
This paper presented a capacitated p-median problem with investment constraint called extended capacitated p-median problem （ECPMP）, which was more suitable for facility location areas such as transportation and logistics. Furthermore, this paper firstly developed a local search method based on the properties of ECPMP＇s mathematical model. Secondly, it proposed a new hybrid ant colony algorithm for the ECPMP by combining the local search method, Lagrangian heuristic algorithm and ant colony algorithm. The numerical results not only show that the ECPMP can present different investment plans according to the amount of investment, but also disclose that the hybrid algorithm can perform better than the ant colony algorithm and Lagrangian heuristic algorithm in terms of solution precision and rate of convergence.
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