Abstract
Various methods for the optimal synthesis of systems have been developed, for example, the optimal synthesis of chemical processing system. However, published works for the synthesis of optimal network flow systems are very scarce.
On the other hand, the importance of a matroid theory has been increasingly recognized recently as an effective approach to the combinatorial optimization problem.
In this paper, a network system was chosen as the subject to the study. An optimal flow problem is first formulated. The problem is to find a maximum flow having as proportional to the given weights distribution of flows as possible. The value of weights to be given will be assigned so that the desired distribution of flows with respect to multiple sources and sinks are obtained. Secondly, it has been indicated that the optimal synthesis problem can be solved by utilizing the weight vectors as a means of the structure parameters.
A synthesis method has been proposed with the two level approach which determines the optimal values of the evaluation function by varying the distribution of flows with respect to multiple sources and sinks in a network.
A characteristic of the proposed method is that difficulties on the numerical computation for a large scale problem can be avoided.
In order to prove the validity of the proposed methods, illustrative examples are solved to see how they work.
