Search results for "Minimum-cost flow problem"
showing 4 items of 4 documents
Finding all optimal solutions to the network flow problem
1986
The problem examined in this paper is as follows: Given a feasible optimum basic solution (f.o.b.s) of the minimum cost network flow problem, find all the f.o.b.s of this problem. The existence of alternative f.o.b.s is characterized by means of elementary circuits of zero cost and length greater than two in the incremental graph associated to the given f.o.b.s. It is shown that any alternative f.o.b.s. can be obtained from the original one by circulating flow through elementary circuits belonging to a succession of incremental graphs. This result leads to the construction of an efficient algorithm to obtain all f.o.b.s. of the network flow problem.
An algorithm for the Rural Postman problem on a directed graph
1986
The Directed Rural Postman Problem (DRPP) is a general case of the Chinese Postman Problem where a subset of the set of arcs of a given directed graph is ‘required’ to be traversed at minimum cost. If this subset does not form a weakly connected graph but forms a number of disconnected components the problem is NP-Complete, and is also a generalization of the asymmetric Travelling Salesman Problem. In this paper we present a branch and bound algorithm for the exact solution of the DRPP based on bounds computed from Lagrangean Relaxation (with shortest spanning arborescence sub-problems) and on the fathoming of some of the tree nodes by the solution of minimum cost flow problems. Computation…
A decentralized solution for the constrained minimum cost flow
2010
In this paper we propose a decentralized solution to the problem of network stabilization, under flow constraints ensuring steady—state flow optimality. We propose a stabilizing strategy for network flow control with capacity constraints which drives the buffer levels arbitrarily close to a desired reference. This is a decentralized strategy optimizing the flow via the minimization of a quadratic cost of the control. A second problem characterized by non-fully connected networks is also considered, for which an exact network equilibrium is not possible. Here, the strategy, in the absence of constraints leads to a least square decentralized problem, but, unfortunately, in the presence of con…
The linear saturated decentralized strategy for constrained flow control is asymptotically optimal
2013
We present an algorithm for constrained network flow control in the presence of an unknown demand. Our algorithm is decentralized in the sense that it is implemented by a team of agents, each controlling just the flow on a single arc of the network based only on the buffer levels at the nodes at the extremes of the arc, while ignoring the actions of other agents and the network topology. We prove that our algorithm is also stabilizing and steady-state optimal. Specifically, we show that it asymptotically produces the minimum-norm flow. We finally generalize our algorithm to networks with a linear dynamics and we prove that certain least-square optimality properties still hold.