运筹学最大最小,运筹学最大流最小费用问题谁会( 三 ) _生活百科

Then, on the basis of the new flow to continue to check and adjust. This iteration continues until no adjustment may be, they will have the minimum cost maximum flow. The characteristics of this line of thought is to maintain the feasibility of the problem (always maintain maximum flow), to promote optimal. Solution to another and in front of the maximum flow algorithm, introduced a similar line of thought, first of all, given the general flow as the initial flow of zero. The cost of the flow to zero, of course, is the smallest cost. And then find a source to the Meeting Point by flow chain, but by the requirements of this chain must be a stream flow of all chain costs by a minimum. If we can find out by flow chain, the chain in the flow by increasing flow, a new flow. The flow will be treated as the initial flow, continue to search for links by increasing stream flow. This iteration continues, until found by flow chain, then the flow is the minimum cost maximum flow. Idea of the characteristics of this algorithm is to maintain the optimal solution of (each of the new fees are the smallest stream flow), but gradually close to the feasible solution (up to maximum flow is a feasible solution when).
As a result of the second algorithm and has introduced close to the maximum flow algorithm and the algorithm by finding the minimum cost flow chain, can be turned into a source to find the shortest path to the Meeting Point, so this algorithm here.
In this algorithm, in order to seek to increase the minimum cost flow chain, the current flow of each, accompanied by the need to establish a network flow by the flow network. For example, Figure 1 is a network G of minimum cost flow, next to parameters c (e), f (e), w (e), and Figure 2 is the network flow by the flow network G '. By the peak-flow network and the same as the original network. By the following principles in accordance with the establishment of the network edge flow: If G in the edge (u, v) is not enough traffic, that is, f (u, v) 0, then G' in the building edge (v, u ), to empower the w '(v, u) =- w (u, v). The establishment of the network by streaming, you can seek in this network to the Meeting Point source shortest path, as decided by flow path, and then in the original network by flow in this path. Here, the use of maximum flow algorithm is still the principle of increasing flow, but the cost must be selected by the smallest chain by stream flow.
Calculation, there is a need to address the problem. This is the stream network by G 'the right to have a negative side, thus labeling law can not be directly applied to find x to y of the shortest path, using the right of other negative side computing network approach to the shortest path x to y to find the shortest path, will greatly reduce the computational efficiency. In order to still use the labeling method to calculate the shortest path, each flow set up by the network to achieve the shortest path, the network G can be the right of w (e) an amendment to do so by the stream to build the network will not be a negative right side, and guarantee the shortest path does not change. This modified method described below.
When the flow value is zero, the first built by the shortest path for flow network, the result of non-negative right side, of course, can be used to calculate labeling law. In order to increase flow network after the establishment of a negative time is not right side of the approach taken is to have stream G edge (f (e)> 0) the right to w (e) amendment to 0. To this end, each time a flow network obtained by the shortest path, the following computing G in the right side of the new w "(u, v):
w "(u, v) = L (u)-L (v) + w (u, v) (*)
Where L (u), L (v) - calculation of G 'of the shortest path x to y when u and v the value of the label. For the first time if the shortest path (u, v) is the flow path by the edge, then, according to the shortest path algorithm must have L (v) = L (u) + w '(u, v) = L (u) + w (u, v), substituting into (*) type must