Maximal concurrent minimal cost flow problems on extended multi-cost multi-commodity networks

The graph is a great mathematical tool, which has been effectively applied to many fields such as economy, informatics, communication, transportation, etc. It can be seen that in an ordinary graph the weights of edges and vertexes are taken into account independently where the length of a path is the sum of weights of the edges and the vertexes on this path. Nevertheless, in many practical problems, weights at vertexes are not equal for all paths going through these vertexes, but are depending on coming and leaving edges. Moreover, on a network, the capacities of edges and vertexes are shared by many goods with different costs. Therefore, it is necessary to study networks with multiple weights. Models of extended multi-cost multi-commodity networks can be applied to modelize many practical problems more exactly and effectively. The presented article studies the maximal concurrent minimal cost flow problems on multi-cost and multi-commodity networks, which are modelized as optimization problems. On the base of the algorithm to find maximal concurrent flow and the algorithm to find maximal concurrent limited cost flow, an effective polynomial approximate procedure is developed to find a good solution.

Two-dimensional phase unwrapping integrating deep learning and minimal cost flow

<p>InSAR can measure surface deformation in all-weather conditions and has been widely used to study landslides, land subsidence, and many geophysical processes. Since the phase of radar echo is measured in 2π rad modulo (wrapped), phase unwrapping is an indispensable step for InSAR, and its reliability directly determines the feasibility of deformation monitoring. However, temporal and spatial decorrelation often leads to severe noises, localized deformation or strong atmospheric turbulence may result in dense fringes, both making traditional unwrapping methods fail in acquiring continual unwrapped phases. Here, we present a deep convolutional neural network (DENet) to identify the probability of phase discontinuities between every two adjacent pixels in the interferogram and apply the probability as cost in the widely-used minimal cost flow solver to achieve phase unwrapping. To train the network effectively, we design a simulation strategy to generate sufficient training samples: the terrain-related phases are used as the background phases, and the deformation phases, atmospheric turbulence phases, and noises are superimposed to build the training samples. Unlike classical methods such as GAMMA and SNAPHU that use the coherence map as the quality index, we use the probability of phase discontinuities estimated by the DENet as the arc-cost of the minimum cost flow problem. We apply the proposed method to unwrap simulated and real interferograms and compare the results with 8 existing methods (including traditional and deep learning-based ones).  On the simulated data set, the root-mean-square error (RMSE) of the proposed method is lower than all the 8 existing methods. We also test different methods to unwrap the real Sentinel-1 interferograms and verified the reliability using ALOS-2 data with a nearly identical acquisition period. Our results show strong robustness and stability when unwrapping very large interferograms with complicated phase patterns. The proposed method takes advantages of both deep learning and traditional minimal cost flow solver, which can effectively unwrap interferograms with low coherence and/or dense fringes, providing strong potential for large-scale SAR interferometry applications.</p>

An Effective Solution Approach Based on Extension Principle for Fuzzy Minimal Cost Flow Problem

A well-known version of minimal cost flow problem with fuzzy arc costs is focused in this study. The fuzzy arc costs is applied as in most of real-world applications, the parameters have high degree of uncertainty. The goal of this problem is to determine the minimum fuzzy cost of sending and passing a specified flow value in to and from a network. A decomposition-based solution methodology is introduced to tackle this problem. The methodology applies Zadeh’s extension principle to decompose the problem to two upper bound and lower bound problems. These problems are capable of being solved for different α-cut values to construct the fuzzy cost flow value as the objective function value. The efficiency of the proposed solution methodology is studied over some well-known examples of the minimal cost flow problem. The obtained results and the procedure applied to obtain them prove the superiority of the proposed approach comparing to the previous approaches of the literature.

Multicommodity-Based Delay Analysis for Heterogeneous Wireless Services in Core Network

With the explosive growth of wireless applications, the subscribers’ requirements of QoS (Quality of Service) are increasing as well. In this paper, the upper bound of the tolerant delay of services in wireless access network is investigated, by mapping core network onto a cost-variable directed graph, where the cost is construed as the average service delay of the flows traveling in core network that depends on the current load. A multicommodity minimal cost flow mathematics problem is then derived and solved by Price-directive Decomposition and Lagrangian Relaxation. Simulations are carried out in two typical core networks and some valuable conclusions are gained.

DEGENERACY IN FUZZY LINEAR PROGRAMMING AND ITS APPLICATION

In this paper, by a definite linear function for ranking symmetric triangular fuzzy numbers, in a Fuzzy Linear Programming problem (FLP) model, we introduced a Fuzzy Degenerate Solution (FDS). In the physical meaning, occurrence of degeneracy in a Fuzzy Minimal Cost Flow Network is investigated. To prevent of falling into Cycling phenomenon in optimization process, we defined two new techniques of Cycling prevention proper to fuzzy environment.