Search results
Results from the WOW.Com Content Network
The minimum-cost flow problem (MCFP) is an optimization and decision problem to find the cheapest possible way of sending a certain amount of flow through a flow network. A typical application of this problem involves finding the best delivery route from a factory to a warehouse where the road network has some capacity and cost associated.
q(i, j) = the minimum cost to reach square (i, j). Starting at rank n and descending to rank 1 , we compute the value of this function for all the squares at each successive rank. Picking the square that holds the minimum value at each rank gives us the shortest path between rank n and rank 1 .
The generalized travelling salesman problem, also known as the "travelling politician problem", deals with "states" that have (one or more) "cities", and the salesman must visit exactly one city from each state. One application is encountered in ordering a solution to the cutting stock problem in order to minimize knife changes.
In mathematical optimization, the network simplex algorithm is a graph theoretic specialization of the simplex algorithm. The algorithm is usually formulated in terms of a minimum-cost flow problem. The network simplex method works very well in practice, typically 200 to 300 times faster than the simplex method applied to general linear program ...
The assignment problem consists of finding, in a weighted bipartite graph, a matching of a given size, in which the sum of weights of the edges is minimum. If the numbers of agents and tasks are equal, then the problem is called balanced assignment. Otherwise, it is called unbalanced assignment. [1] If the total cost of the assignment for all ...
The goal is to bring the system, from an arbitrary initial state, to a state with the minimum possible energy. Simulated annealing searching for a maximum. The objective here is to get to the highest point. In this example, it is not enough to use a simple hill climb algorithm, as there are many local maxima. By cooling the temperature slowly ...
1. In the minimum-cost flow problem, each edge (u,v) also has a cost-coefficient a uv in addition to its capacity. If the flow through the edge is f uv, then the total cost is a uv f uv. It is required to find a flow of a given size d, with the smallest cost. In most variants, the cost-coefficients may be either positive or negative.
The problem can be solved e.g. by minimizing . A common linearization of this problem is the minimization of the maximum utilization , where. In the minimum cost multi-commodity flow problem, there is a cost for sending a flow on . You then need to minimize. In the maximum multi-commodity flow problem, the demand of each commodity is not fixed ...