A Novel Minimization Method for Sensor Deployment Via Heuristic 2-Sat Solution

Spectrum monitoring is a key element of spectrum management process, in which spectrum sensors are considered the most crucial component. In this paper, we discuss the problem of optimal sensor deployment for spectrum monitoring applications. Optimal sensor deployment can significantly reduce the cost of sensor deployment and improve spectrum monitoring performance and efficiency. An optimal sensor deployment technique is developed, which provides the minimized number of sensors required, as well as their locations of deployment, for monitoring transmissions by desired stations in an area of interest. The problem of optimal sensor deployment is formulated using binary linear integer programming that is solved using efficient numerical optimization algorithms. The technique is scalable in the sense that it considers the effects of pre-installed or existing spectrum sensors in the area. Finally, we apply the technique to an Ottawa area for deploying sensor to monitor all down-link transmissions in the 800 MHz Land Mobile Radio (LMR) band to demonstrate its effectiveness and performance.

As a promising technology to achieve the permanent operation of battery-powered wireless sensor devices, wireless rechargeable sensor networks (WRSNs) by radio-frequency radiation have attracted considerable attention in recent years. Determining how to save the deployment cost of WRSNs has been a hot topic. Previous scholars have mainly studied the cost of deploying chargers, thus ignoring the impact of sensor deployment on the network. Therefore, we consider the new problem of joint deployment of sensors and chargers on a two-dimensional plane, i.e., deploying the minimum number of sensors and chargers used to monitor points of interest (PoIs). Considering the interaction of deployed sensors and chargers, we divide the problem into two stages, P1 and P2. P1 addresses the sensor deployment, while P2 addresses the deployment of chargers. Both P1 and P2 have proved to be NP-hard. Meanwhile, we notice that the aggregation effect of sensors can effectively reduce the number of chargers deployed; therefore, we propose a greedy heuristic approximate solution for deploying sensors by using the aggregation effect (GHDSAE). Then, a greedy heuristic (GH) solution and a particle swarm optimization (PSO) solution are proposed for P2. The time complexity of these solutions is analyzed. Finally, extensive simulation results show that the PSO solution can always reduce the number of chargers deployed based on the GHDSAE solution sensor deployment approach. Therefore, it is more cost-effective to jointly deploy sensors and chargers by using the GHDSAE solution and the PSO solution.

We apply linear and non-linear programming to find the solutions for Nash equilibriums and Nash arbitration in game theory problems. Linear programming was shown as a viable method for solving mixed strategy zero-sum games. We review this methodology and suggest a class of zero-sum game theory problems that are well suited for linear programming. We applied this theory of linear programming to non-zero sum games. We suggest and apply a separate formulation for a maximising linear programming problem for each player. We move on the Nash arbitration method and remodel this problem as a non-linear optimisation problem. We take the game's payoff matrix and we form a convex polygon. Having found the status quo point (x*, y*), we maximise the product (x-x*)(y-y*) over the convex polygon using KTC non-linear optimisation techniques. The results give additional insights into game theory analysis.

SimplifEx: Simplifying and Explaining Linear Programs

Linear programming is a mathematical method for choosing the best product combination to maximize profit or decrease cost within the limitations of available resources. In this article, we have proposed the linear programming application for profit Maximization of a Biscuit Factory in Bangladesh. For linear programming problems, the Simplex algorithm provides a powerful computational tool, able to provide fast solution to very large-scale application. The optimization principal examined unit cost of production, the selling price and the quantity of different raw materials used in production. A model for the problem was formulated and optimum results derived using software that employed simplex method. Our main goal is to emphasize the uniqueness of linear programming modeling at the business level as an optimization technique, and to encourage manufacturing companies to employ linear programming to determine their optimal profit.

When constructing a regression model, the primary problem faced by the researcher is that it is not clear what the equation of connection between the explained and explanatory variables should be. This initial stage of construction the selection of the model structural specification is called. When choosing a regression specification in parallel, the question arises of which explanatory variables should be included in the equation. This is the problem of variables selection in regression models. Its essence is to single out from the set of “candidates” for inclusion a subset of the most informative of them based on some quality criterion. The article is devoted to the problem of variables selection in regression models estimated using the ordinary least squares. The previously proposed approach to selection a given number of variables based on mixed 0–1 linear programming is considered. The unknown parameters in this problem are the beta coefficients of standardized regression and Boolean variables that are responsible for the occurrence of factors in the model. The optimal values ​​of unknown parameters are found on the basis of maximizing the value of the coefficient of determination of regression. Unfortunately, to solve the problem under consideration, it is required to manually set the number of selected factors, which is often impossible to determine in advance. Therefore, the goal was to formalize the problem so that as a result of its solution the optimal number of selected regressors was also determined. For this purpose, the adjusted determination coefficient, depending on the number of model factors, was used as the objective function. As a result, the problem of mixed integer linear programming was formulated. The unknown parameters in it are still beta coefficients and Boolean variables, as well as an integer variable – the number of regressors. Based on data on prices and characteristics of sedans and hatchbacks of the American automobile industry, a computational experiment was carried out confirming the correctness of the developed mathematical apparatus. The problem formalized in this work in the form of a mixed integer linear programming looks more preferable from a computational point of view than the same problem formalized in modern scientific literature as a mixed quadratic linear programming.

Many planning problems involve choosing a set of optimal decisions for a system in the face of uncertainty of elements that may play a central role in the way the system is analyzed and operated. During the past decade, there has been a renewed interest in the modelling, analysis, and solution of such problems due to a remarkable development of both new theoretical results and novel computational techniques in stochastic optimization. A prominent approach is to develop upper and lower bounding approximations to the problem along with procedures to sharpen bounds until an acceptable tolerance is satisfied. The contributions of this dissertation are concerned with the latter approach. The thesis first studies the stochastic linear programming problem with randomness in both the objective coefficients and the constraints. A convex concave saddle property of the value function is utilized to derive new bounding techniques which generalize previously known results. These approximations require discretizing bounded domains of the random variables in such a way that tight upper and lower bounds result. Such techniques will prove attractive with the recent advances in large scale linear programming. The above results are also extended to obtain new upper and lower bounds when the domains of random variables are unbounded. While these bounds are tight, the approximating models are large-scale deterministic linear programs. In particular, with a proposed order-cone decomposition for the domains, these linear programs are well-structured, thus enabling one to use efficient techniques for solution, such as parallel computation. The thesis next considers convex stochastic programs. Using aggregation concepts from the deterministic literature, new bounds are developed for the problem which are computable using standard convex programming algorithms. Finally, the discussion is focused on a stochastic convex program arising in a certain resource allocation problem. Exploiting the problem structure, bounds are developed via the Karush-Kuhn-Tucker conditions. Rather than discretizing domains, these approximations advocate replacing difficult multidimensional integrals by a series of simple univariate integrals. Such practice allows one to preserve differentiability properties so that smooth convex programming methods can be applied for solution.

In this paper we propose a general Linear Programming (LP) based formulation and solution methodology for obtaining optimal solution to the load distribution problem in divisible load scheduling. We exploit the power of the versatile LP formulation to propose algorithms that yield exact solutions to several very general load distribution problems for which either no solutions or only heuristic solutions were available. We consider both star (single-level tree) networks and linear daisy chain networks, having processors equipped with front-ends, that form the generic models for several important network topologies. We consider arbitrary processing node availability or release times and general models for communication delays and computation time that account for constant overheads such as start up times in communication and computation. The optimality of the LP based algorithms is proved rigorously.

In the wireless sensor networks, sensor deployment and coverage are the vital parameter that impacts the network lifetime. Network lifetime can be increased by optimal placement of sensor nodes and optimizing the coverage with the scheduling approach. For sensor deployment, heuristic algorithm is proposed which automatically adjusts the sensing range with overlapping sensing area without affecting the high degree of coverage. In order to demonstrate the network lifetime, we propose a new heuristic algorithm for scheduling which increases the network lifetime in the wireless sensor network. Further, the proposed heuristic algorithm is compared with the existing algorithms such as ant colony optimization, artificial bee colony algorithm and particle swarm optimization. The result reveals that the proposed heuristic algorithm with adjustable sensing range for sensor deployment and scheduling algorithm significantly increases the network lifetime.

Due to the importance of linear algebra and matrix operations in data analytics, there is significant interest in using relational query optimization and processing techniques for evaluating (sparse) linear algebra programs. In particular, in recent years close connections have been established between linear algebra programs and relational algebra that allow transferring optimization techniques of the latter to the former. In this paper, we ask ourselves which linear algebra programs in MATLANG correspond to the free-connex and q-hierarchical fragments of conjunctive first-order logic. Both fragments have desirable query processing properties: free-connex conjunctive queries support constant-delay enumeration after a linear-time preprocessing phase, and q-hierarchical conjunctive queries further allow constant-time updates. By characterizing the corresponding fragments of MATLANG, we hence identify the fragments of linear algebra programs that one can evaluate with constant-delay enumeration after linear-time preprocessing and with constant-time updates. To derive our results, we improve and generalize previous correspondences between MATLANG and relational algebra evaluated over semiring-annotated relations. In addition, we identify properties on semirings that allow to generalize the complexity bounds for free-connex and q-hierarchical conjunctive queries from Boolean annotations to general semirings.

A big challenge of designing and implementing a monitoring system for distributed systems such as the computational grid is how to quickly and dynamically deploy and manage a large collection of monitoring sensors. Currently available monitoring systems often use the static sensor deployment mechanism, which makes the sensor deployment quite difficult and inefficient. We have developed an agent-based grid monitoring system that enables fast, dynamic, and on- demand sensor deployment and management. The monitoring system perfectly solves the problem of fast and dynamic sensor deployment using dynamic sensor loading mechanism. In addition, the monitoring system uses software agent technology to solve the problem of dynamic and on-demand sensor management.

Linear and dynamic programming formulations are introduced for optimizing the placement of distributed best management practices (BMPs) at the watershed scale. The results of linear programming optimization of infiltration-based stormwater management BMPs are compared with the results of genetic algorithm (GA)optimization using a nonlinear distributed model. Additionally, linear and dynamic programming optimization of sediment-trapping BMPs are compared with GA optimization using a nonlinear distributed model. The results indicate that the solution to stormwater peak-flow reduction is influenced primarily by distributed-flow arrival time, and a linear programming analog to a nonlinear optimization model can efficiently reproduce much of the same solution structure. Linear and dynamic programming solutions to the storm sediment-management problem indicate natural sediment trapping is an important consideration, and a solution to the sediment-management-optimization problem can be efficiently found ...

The Panggak Darat Irrigation Area in Lingga Regency can irrigate 134.05 ha of rice fields. The problem that often occurs is that irrigation areas are not fully optimal for agricultural product productivity, so that an effort can be made to minimize the shortage of irrigation water and/or minimize the deviation of water release that can result from an optimal pattern of irrigation operations. The purpose of this study is to obtain an optimal operating pattern with better operating performance than the existing (planning). The analytical method used is an optimization technique using the LINDO program (linear programming). The objective function is to minimize the shortage of irrigation water. Evaluation of the operational performance of the optimized and existing reservoirs is carried out using simulation techniques. The results showed that the optimal operating pattern was obtained from the Objective Function with an average total release of reservoir water of 3.20 million m3, which can meet 100% of the irrigation water Requirements of an area of 134.05 ha of irrigation area that must be irrigated. The reliability of the optimization results is in the form of 100% irrigation reliability with a planting intensity of 300% with a rice-rice cropping pattern where the existing (planning) is a rice-rice-bero cropping pattern or a rice-bero cropping pattern with a cropping intensity of 200%. Optimization results from the objective function of minimizing the shortage of irrigation water provide better operating performance than the existing conditions, so as to increase agricultural productivity.

Neural Network Optimisation of Remotely Sensed Maize Leaf Nitrogen with a Genetic Algorithm and Linear Programming using Five Performance Parameters

The sensor relocation problem (SR problem) is an important issue in wireless sensor networks (WSNs). The main difference between SR problem and sensor deployment (SD) problem is that SR problem has a strict response time requirement. Because the SD problem occurs during network initialization, so there is no strict response time requirement. The SD problem is solved as long as the required coverage level is met. However, the SR problem occurs during operation of WSNs, we need to minimize the impact on the surveillance task while replacing faulty sensors with redundant sensors. In this paper, we revisit the SR problem in mobile WSNs. In terms of response time and moving distance, the proposed algorithm moves redundant sensors to faulty sensors and coverage holes by cascaded movement. It also considers the estimated value of network lifetime in the planning of cascading schedule. Hence, the SR problems caused by inappropriate cascading schedules can be avoided. Overall, the proposed SR algorithm has the following features: 1) shorter response time; 2) shorter moving distances; 3) smaller number of requesting places; and 4) longer network lifetime. The performance evaluation done in this paper has confirmed its superior performances in all these aspects.