一种求解最小双费用流问题的算法

多目标优化是网络最优化的一个重要子问题。通过实际应用案例，抽象出一种带容量限制的双费用权网络模型，并由此提出了相应的最小双费用流问题。之后，借鉴网络分层的思想，根据双费用权网络的特点设计出一个求解该问题的双层原始对偶算法，并严谨地证明了算法的正确性，估计出算法的复杂度为O(n2v0)。此外，对算法进行了推广改进，使其能求解一般k费用权网络中的最小k费用流问题。最后，通过一个实例来演示算法的执行。

An algorithm to solving minimum double-cost flow problem

Multi-objective optimization is a critical part of network optimization. The paper derives a minimum double cost flow problem in double-cost network model with limitations on capacity from a practical case. According to the thought of hierarchy and the feature of double-cost network, the corresponding minimum double-cost flow problem is introduced and a two-layer primal dual algorithm is proposed to solve it. The correctness of our algorithm is proved and its complexity is estimated as O(n2v0). Besides, the algorithm is improved to solve the minimum k cost flow problem in k-cost network. Finally, a case is used to exhibit how the algorithm works.