Discrete Optimization Estimation of flows in flow networks
نویسندگان
چکیده
Let G be a directed graph with an unknown flow on each edge such that the following flow conservation constraint is maintained: except for sources and sinks, the sum of flows into a node equals the sum of flows going out of a node. Given a noisy measurement of the flow on each edge, the problem we address, which we call the MOST PROBABLE FLOW ESTIMATION problem (MPFE), is to estimate the most probable assignment of flow for every edge such that the flow conservation constraint is maintained. We provide an algorithm called DY-MPFE for solving the MPFE problem when the measurement error is Gaussian (GAUSSIAN-MPFE). The algorithm works in O(jEj + jVj) when the underlying undirected graph of G is a 2-connected planar graph, and in O(jEj + jVj) when it is a 2-connected serial-parallel graph or a tree. This result is applicable to any MINIMUM COST FLOW problem for which the cost function is se(Xe le) for edge e where le and se are constants, and Xe is the flow on edge e. We show that for all topologies, the GAUSSIANMPFE s precision for each edge is analogous to the equivalent resistance measured in series to this edge in an electrical network built by replacing every edge with a resistor reflecting the measurement s precision on that edge. 2005 Elsevier B.V. All rights reserved.
منابع مشابه
Estimation of Discharge over the Submerged Compound Sharp-Crested Weir using Artificial Neural Networks and Genetic Programming
Truncated sharp crested weirs are used to measure flow rate and control upstream water surface in irrigation canals and laboratory flumes. The main advantages of such weirs are ease of construction and capability of measuring a wide range of flows with sufficient accuracy. Artificial neural networks (ANNs) and genetic programming (GP) have recently been used for estimation of hydraulic data. In...
متن کاملOptimal energy management of the photovoltaic based distribution networks considering price responsive loads, energy storage systems and convex power flows.
Nowadays, presence of photovoltaic systems in distribution network is not without challenge and it may not have economic productivity for the system under the lack of optimal management. Energy storage systems are able to cope with this problem. Therefore, in this paper, a new method is proposed for energy management of the distribution networks in order to show that how presence of the energy ...
متن کاملA Novel Method for Designing and Optimization of Networks
In this paper, system planning network is formulated with mixed-integer programming. Two meta-heuristic procedures are considered for this problem. The cost function of this problem consists of the capital investment cost in discrete form, the cost of transmission losses and the power generation costs. The DC load flow equations for the network are embedded in the constraints of the mathematica...
متن کاملMulti-objective optimization of discrete time–cost tradeoff problem in project networks using non-dominated sorting genetic algorithm
The time–cost tradeoff problem is one of the most important and applicable problems in project scheduling area. There are many factors that force the mangers to crash the time. This factor could be early utilization, early commissioning and operation, improving the project cash flow, avoiding unfavorable weather conditions, compensating the delays, and so on. Since there is a need to allocate e...
متن کاملA new energy-based method for 3D motion estimation of incompressible PIV flows
Estimation of motion has many applications in fluid analysis. A lot of work has been carried out using Particle Image Velocimetry (PIV) to design experiments which capture and measure the flow motion using 2D images. Recent technological advances allow capturing 3D PIV image sequences of moving particles. In this paper, we deal with incompressible fluid flows which are a large class of physical...
متن کامل