Mathematical Models and Algorithms for Network Flow Problems Arising in Wireless Sensor Network Applications

We examine multiple variations on two classical network flow problems, the maximum flow and minimum-cost flow problems. These two problems are well-studied within the optimization community, and many models and algorithms have been presented for their solution. Due to the unique characteristics of the problems we consider, existing approaches cannot be directly applied. The problem variations we examine commonly arise in wireless sensor network (WSN) applications. A WSN consists of a set of sensors and collection sinks that gather and analyze environmental conditions. In addition to providing a taxonomy of relevant literature, we present mathematical programming models and algorithms for solving such problems. First, we consider a variation of the maximum flow problem having node-capacity restrictions. As an alternative to solving a single linear programming (LP) model, we present two alternative solution techniques. The first iteratively solves two smaller auxiliary LP models, and the second is a heuristic approach that avoids solving any LP. We also examine a variation of the maximum flow problem having semicontinuous restrictions that requires the flow, if positive, on any path to be greater than or equal to a minimum threshold. To avoid solving a mixed-integer programming (MIP) model, we present a branch-and-price algorithm that significantly improves the computational time required to solve the problem. Finally, we study two dynamic network flow problems that arise in wireless sensor networks under non-simultaneous flow assumptions. We first consider a dynamic maximum flow problem that requires an arc to transmit a minimum amount of flow each time it begins transmission. We present an MIP for solving this problem along with a heuristic algorithm for its solution. Additionally, we study a dynamic minimum-cost flow problem, in which an additional cost is incurred each time an arc begins transmission. In addition to an MIP, we present an exact algorithm that iteratively solves a relaxed version of the MIP until an optimal solution is found

A Trapezoidal Fuzzy Membership Genetic Algorithm (TFMGA) for Energy and Network Lifetime Maximization under Coverage Constrained Problems in Heterogeneous Wireless Sensor Networks

Network lifetime maximization of Wireless Heterogeneous Wireless Sensor Networks (HWSNs) is a difficult problem. Though many methods have been introduced and developed in the recent works to solve network lifetime maximization. However, in HWSNs, the energy efficiency of sensor nodes becomes also a very difficult issue. On the other hand target coverage problem have been also becoming most important and difficult problem. In this paper, new Markov Chain Monte Carlo (MCMC) is introduced which solves the energy efficiency of sensor nodes in HWSN. At initially graph model is modeled to represent HWSNs with each vertex representing the assignment of a sensor nodes in a subset. At the same time, Trapezoidal Fuzzy Membership Genetic Algorithm (TFMGA) is proposed to maximize the number of Disjoint Connected Covers (DCC) and K-Coverage (KC) known as TFMGA-MDCCKC. Based on gene and chromosome information from the TFMGA, the gene seeks an optimal path on the construction graph model that maximizes the MDCCKC. In TFMGA gene thus focuses on finding one more connected covers and avoids creating subsets particularly. A local search procedure is designed to TFMGA thus increases the search efficiency. The proposed TFMGA-MDCCKC approach has been applied to a variety of HWSNs. The results show that the TFMGA-MDCCKC approach is efficient and successful in finding optimal results for maximizing the lifetime of HWSNs. Experimental results show that proposed TFMGA-MDCCKC approach performs better than Bacteria Foraging Optimization (BFO) based approach, Ant Colony Optimization (ACO) method and the performance of the TFMGA-MDCCKC approach is closer to the energy-conserving strategy

Energy Aware Algorithms for managing Wireless Sensor Networks

While the majority of the current Wireless Sensor Networks (WSNs) research has prioritized either the coverage of the monitored area or the energy efficiency of the network, it is clear that their relationship must be further studied in order to find optimal solutions that balance the two factors. Higher degrees of redundancy can be attained by increasing the number of active sensors monitoring a given area which results in better performance. However, this in turn increases the energy being consumed. In our research, we focus on attaining a solution that considers several optimization parameters such as the percentage of coverage, quality of coverage and energy consumption. The problem is modeled using a bipartite graph and employs an evolutionary algorithm to handle the activation and deactivation of the sensors. An accelerated version of the algorithm is also presented; this algorithm attempts to cleverly mutate the string being considered after analyzing the desired output conditions and performs a calculated crossover depending on the fitness of the parent strings. This results in a quicker convergence and a considerable reduction in the search time for attaining the desired solutions. Proficient cluster formation in wireless sensor networks reduces the total energy consumed by the network and prolongs the life of the network. There are various clustering approaches proposed, depending on the application and the objective to be attained. There are situations in which sensors are randomly dispersed over the area to be monitored. In our research, we also propose a solution for such scenarios using heterogeneous networks where a network has to self-organize itself depending on the physical allocations of sensors, cluster heads etc. The problem is modeled using a multi-stage graph and employs combinatorial algorithms to determine which cluster head a particular sensor would report to and which sink node a cluster head would report to. The solution proposed provides flexibility so that it can be applied to any network irrespective of density of resources deployed in the network. Finally we try to analyze how the modification of the sequence of execution of the two methods modifies the results. We also attempt to diagnose the reasons responsible for it and conclude by highlighting the advantages of each of the sequence