Application of Advance Constrained Simplex Method for MIMO Systems in Quantum Communication Networks

This paper first describes advanced constrained simplex method (advanced complex method), then it shows that this complex procedure has any problems when it’s taken for finding the maximum of a general nonlinear function of several variables within a constrained region is described in wireless communication systems, especially for multiple-input multiple-out (MIMO Configuration). Next advanced constrained simplex method is described how to resolve the problem of the multiple-input multiple-out, and shown how to be efficient compared with the complex method and the simplex method by some simulations. And this wireless network design can be used to MIMO systems in Quantum Communication networks. The feature of technology by which the system told by this paper can get optimum solution by a little search number of times compared with a conventional system in the MIMO environment with more than one optimal value, and is at the place. This system was applied to the Quantum network environment by this paper. This can achieve more compact than the conventional Quantum network environment

Modified Network Simplex Method to Solve a Sheltering Network Planning and Management Problem

This dissertation considers sheltering network planning and operations for natural disaster preparedness and responses with a two-stage stochastic program. The first phase of the network design decides the locations, capacities and held resources of new permanent shelters. Both fixed costs for building a new permanent shelter and variable costs based on capacity are considered. Under each disaster scenario featured by the evacuee demand and transportation network condition, the flows of evacuees and resources to shelters, including permanent and temporary ones, are determined in the second stage to minimize the transportation and shortage/surplus costs. Typically, a large number of scenarios are involved in the problem and cause a huge computational burden. The L-shaped algorithm is applied to decompose the problem into the scenario level with each sub-problem as a linear program. The Sheltering Network Planning and Operation Problem considered in this dissertation also has a special structure in the second-stage sub-problem that is a minimum cost network flow problem with equal flow side constraints. Therefore, the dissertation also takes advantages of the network simplex method to solve the response part of the problem in order to solve the problem more efficiently. This dissertation investigates the extending application of special minimum cost equal flow problem. A case study for preparedness and response to hurricanes in the Gulf Coast region of the United States is conducted to demonstrate the usage of the model including how to define scenarios and cost structures. The numerical experiment results also verify the fast convergence of the L-shaped algorithm for the model

On Combinatorial Network Flows Algorithms and Circuit Augmentation for Pseudoflows

There is a wealth of combinatorial algorithms for classical min-cost flow problems and their simpler variants like max flow or shortest path problems. It is well-known that many of these algorithms are related to the Simplex method and the more general circuit augmentation schemes: prime examples are the network Simplex method, a refinement of the primal Simplex method, and min-mean cycle canceling, which corresponds to a steepest-descent circuit augmentation scheme. We are interested in a deeper understanding of the relationship between circuit augmentation and combinatorial network flows algorithms. To this end, we generalize from the consideration of primal or dual flows to so-called pseudoflows, which adhere to arc capacities but allow for a violation of flow balance. We introduce `pseudoflow polyhedra,' in which slack variables are used to quantify this violation, and characterize their circuits. This enables the study of combinatorial network flows algorithms in view of the walks that they trace in these polyhedra, and in view of the pivot rules for the steps. In doing so, we provide an `umbrella,' a general framework, that captures several algorithms. We show that the Successive Shortest Path Algorithm for min-cost flow problems, the Shortest Augmenting Path Algorithm for max flow problems, and the Preflow-Push algorithm for max flow problems lead to (non-edge) circuit walks in these polyhedra. The former two are replicated by circuit augmentation schemes for simple pivot rules. Further, we show that the Hungarian Method leads to an edge walk and is replicated, equivalently, as a circuit augmentation scheme or a primal Simplex run for a simple pivot rule