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We propose a new concept which is a generalization of fuzzy soft subset and fuzzy soft equal. Using such notions, we will be able to consider the distributive law of fuzzy soft sets. Using the distributive law of fuzzy soft sets, we point out that the distributive law of trapezoidal fuzzy soft sets as proposed by Xiao et al. (2012) is not true. The correction will further improve further extensions of the results of Xiao et al. (2012). We will also establish the generalized distributive law of trapezoidal fuzzy soft sets along with illustrative examples.

This note tries to answer issues raised in Bhardwaj and Kumar (J Optim Theory Appl 163(2): 685---696, 2014). The research summarizes that the results obtained in Khan et al. (J Optim Theory Appl 159: 536---546, 2013) are sound and correct and it fulfills all the necessary requirements of its scope and objectives.

Although flexible neural networks FNNs have been used more successfully than classical neural networks CNNs in many industrial applications, nothing is rigorously known about their properties. In fact they are not even well known to the systems and control community. In the first part of this paper, existing structures of and results on FNNs are surveyed. In the second part FNNs are examined in a theoretical framework. As a result, theoretical evidence is given for the superiority of FNNs over CNNs and further properties of the former are developed. More precisely, several fundamental properties of feedforward and recurrent FNNs are established. This includes the universal approximation capability, minimality, controllability, observability, and identifiability. In the broad sense, the results of this paper help that general use of FNNs in systems and control theory and applications be based on firm theoretical foundations. Theoretical analysis and synthesis of FNN-based systems thus become possible. The paper is concluded by a collection of topics for future work.

This paper presents an application of a customized linear programming (LP) based model predictive control strategy to the paper machine cross direction (CD) control problem. The objective of CD control is to maintain flat profiles of variables of interest by minimizing worst case deviations from setpoints (defects). These control problems can have as many as 200 actuators (inputs) and 400 sensor measurements (outputs). This large size coupled with the stringent real-time requirement of computing a control move in a few seconds poses a very challenging control problem. Computational results that demonstrate the effectiveness of this strategy will be presented. For typical disturbances this algorithm can compute provably optimal control moves for a 400 input ×400 output control problem in approximately 5 s versus approximately 90 s for a generic LP algorithm on a HP 9000/770 workstation.

The F composite fading model was recently proposed as an accurate and tractable statistical model for the characterization of the simultaneous occurrence of multipath fading and shadowing conditions encountered in realistic wireless communication scenarios. In the present contribution we capitalize on the distinct properties of this composite model to derive the achievable capacity over F composite fading channels assuming fixed rate quality of service requirements. To this end, novel exact and tractable analytic expressions are derived for both the exact and the truncated channel inversion strategies. This also enables the derivation of additional simplified approximate and asymptotic expressions for these cases, which provide meaningful insights on the effect of fading conditions on the overall system performance. This is particularly useful in the context of numerous emerging wireless applications of interest that exhibit stringent fixed rate requirements such as vehicular communications, body area networks and telemedicine, among others. acceptedVersion

We consider a one-dimensional cutting stock problem (CSP) in which the stock widths are not used to fulfill the order but kept for use in the future for the industrial-use paper production. We present a new model based on the flexible stock allocation and trim loss control to determine the production quantity. We evaluate our approach using a real data and show that we are able to solve industrial-size problems, while also addressing common cutting considerations such as aggregation of orders, multiple stock widths, and cutting different patterns on the same machine. In addition, we compare our model with others, including trim loss minimization problem (TLMP) and cutting stock problem (CSP). The results show that the proposed model outperforms the other two models regarding total flexibility and trim loss ratio.

We consider the beamformer design for multipleinput multiple-output (MISO) broadcast channels (MISO BCs) using zero-forcing dirty paper coding (ZF-DPC). Assuming a sum power constraint (SPC), most previously proposed beamformer designs are based on the QR decomposition (QRD), which is a natural choice to satisfy the ZF constraints. However, the optimality of the QRD-based design for ZF-DPC has remained unknown. In this paper, first, we analytically establish that the QRD-based design is indeed optimal for any performance measure under a SPC. Then, we propose an optimal beamformer design method for ZF-DPC with per-antenna power constraints (PAPCs), using a convex optimization framework. The beamformer design is first formulated as a rank-1-constrained optimization problem. Exploiting the special structure of the ZF-DPC scheme, we prove that the rank constraint can be relaxed and still provide the same solution. In addition, we propose a fast converging algorithm to the beamformer design problem, under the duality framework between the BCs and multiple access channels (MACs). More specifically, we show that a BC with ZF-DPC has the dual MAC with ZF-based successive interference cancellation (ZF-SIC). In this way, the beamformer design for ZF-DPC is transformed into a power allocation problem for ZF-SIC, which can be solved more efficiently. QC 20130524

A shape optimization problem for incompressible flows within a stabilized finite element framework is studied. The goal is to develop and test numerical realizations of optimal shape design problems that could be applied to non-trivial industrial problems. The resulting algorithm is applied to the optimization of the geometry of a tapered header in a paper machine headbox. Copyright © 2000 John Wiley & Sons, Ltd.

Concerning intelligent paper composition, the article puts forward an improved genetic algorithm (GA) based on the multi-population division. According to the ideas of population division, the genes of individuals in the population which control the same characters are further divided into the same sub population so that they can be performed by the genetic operators. In order to avoid the local optimum, the optimal solution of each sub population is selected to be recombined global optimum. Compared with the simple genetic algorithm (SGA), this algorithm significantly reduces the search space of the problem solution and accelerates convergence speed. Finally, the algorithm is verified in the problem of intelligent paper composition and the results indicate that the algorithm has obviously improved the quality of the intelligent paper composition compared with the SGA.

The trim-loss problem appears when a customer's demand is to be satisfied in a paper converting mill. A set of product paper reels need to be cut from raw-paper reels. The problem is by nature an integer problem and therefore gives rise to a difficult combinatorial problem. Maybe the most difficult problem beside the combinatorics, is the fact that the paper converting mill needs to adapt itself to both the customer specified widths and the raw paper widths that are delivered from a raw paper mill. This fact makes it difficult to avoid material losses during the process. In the present paper some key issues are considered as to the combining the paper mill and the paper converting mill.

The current paper presents a soft-sensor method based on belief-rule-base (BRB) system for solving the problem of tipping paper permeability measurement in the tobacco industry. Firstly, BRB is utilized to establish a model between the feature variables in the tipping paper image and the corresponding paper permeability obtained by the traditional measuring device. Unlike the traditional case of BRB, this paper adds the output attribute as the optimization parameters. In this way, the feasible solution space can be enlarged to obtain an effective BRB model. Second, in order to find the reasonable parameters of BRB in a complex nonconvex solution space, an enhanced differential evolutionary (DE) algorithm is developed to train BRB, which not only embeds a simplex method to stress the balance between the global and local search but also designs a perturbation operation and an adaptively selected mutation strategy to maintain the diversity of search direction. The test results and comparisons based on the data collected from a cigarette factory in China show that the presented method is effective and robust.

The problem of grabbing a non-tumbling satellite, addressed in this paper, is split into two subproblems, the first of determining a minimum distance collision-free path from the starting stowed pose of the space manipulator to the grabbing pose, and the second of determining a minimum time motion along this path, subject to speed and torque constraints of the manipulator. The first problem is solved using the well known A∗ algorithm, after posing path planning as a graph search problem. Different types of heuristic functions are used for the graph search, and their influence in finding the solution is discussed. The non-smooth path generated using A∗ algorithm is smoothened, and then minimum time motion subject to constraints is determined by posing it as a nonlinear programming problem and solved using an SQP algorithm. Solutions obtained for three different target satellite poses are discussed.

Mathematical formulations for production planning are increasing complexity, in order to improve their realism. In short-term planning, the desirable level of detail is particularly high. Exact solvers fail to generate good quality solutions for those complex models on medium- and large-sized instances within feasible time. Motivated by a real-world case study in the pulp and paper industry, this paper provides an efficient solution method to tackle the short-term production planning and scheduling in an integrated mill. Decisions on the paper machine setup pattern and on the production rate of the pulp digester (which is constrained to a maximum variation) complicate the problem. The approach is built on top of a mixed integer programming (MIP) formulation derived from the multi-stage general lotsizing and scheduling problem. It combines a Variable Neighbourhood Search procedure which manages the setup-related variables, a specific heuristic to determine the digester's production speeds and an exact method to optimize the production and flow movement decisions. Different strategies are explored to speed-up the solution procedure and alternative variants of the algorithm are tested on instances based on real data from the case study. The algorithm is benchmarked against exact procedures. (C) 2013 Elsevier Ltd. All rights reserved.

This paper presents an optimization strategy for pulp/water flow management in a paper production system. The problem is formulated at two levels - the upper/design level concerning optimal volumes of the pulp/water tower and the lower/operational level concerning how to control the system optimally with given tower volumes. At both levels of there are multiple and conflicting objectives.

This paper deals with the two-dimensional cutting stock problem with set-up cost 2CSP-S. This problem is composed of three optimisation sub-problems: a 2-D bin packing 2BP problem to place images on patterns, a linear programming LP problem to find for each pattern the number of stock sheets to be printed and a combinatorial problem to find the number of each image on each pattern. We have already developed two different metaheuristics to solve the 2CSP-S focusing on this third sub-problem: a simulated annealing and a genetic algorithm. In this article, we propose to compare these two approaches. It is important to notice that our approaches are not new packing techniques. This work was conducted for a paper industry company and experiments were realised on real and artificial data sets.

Any practical control system is affected by external signals. Some of them are “informative” (e.g. reference signals), and the others (disturbances, measurement noises etc.) are undesired as they can visibly deteriorate the system behavior. General approaches to disturbance rejection and reference tracking have been elaborated in the framework of geometric control theory, among them are disturbance decoupling control and internal model principles. These approaches, however, assume the state and control of the system to be unconstrained. To take such constraints into account, one usually has to consider optimization problems where the performance index penalizes in some way the system process. Optimization problems in presence of uncertain signals have been addressed in the context of robust control and stochastic control. Standard methods like usually provide only suboptimality of the process; the optimal value can be found for either “worst-case” signal (like in minimax H 8 -and L 1 -optimization approaches) or “on average”, assuming the external signals to be stochastic with known spectral density. In a series of his papers published in 1992-2012, Vladimir A. Yakubovich promoted the approach of universal controllers for linear-quadratic regulation (LQR) problems under uncertain signals. The term “universal” emphasizes that the controller renders the solution of the closed-loop system optimal for any external signal. Although this is not possible for arbitrary signals, in some special classes of signals the universal controllers not only exist but may even be chosen linear. The existence of linear optimal controllers has been proved for two important classes of uncertain signals, that is, polyharmonic signals with known spectrum and signals with fast decreasing spectral density. In this paper we extend the results of V.A. Yakubovich to more general classes of systems and quadratic performance indices, arising in problems of optimal oscillation damping, reference tracking and model matching.

The paper deals with the problem of defining the optimal topology for a distributed fault detection architecture for non-linear large-scale systems. A stochastic modelbased framework for diagnosis is formulated. The system structural graph is decomposed into subsystems and each subsystem is monitored by one local diagnoser. It is shown that overlapping of subsystems allows to improve the detectability properties of the monitoring architecture. Based on this theoretical result, an optimal decomposition design method is proposed, able to define the minimum number of detection units needed to guarantee the detectability of certain faults while minimizing the communication costs subject to some computation cost constraints. An algorithmic procedure is presented to solve the proposed optimal decomposition problem. Preliminary simulation results show the potential of the proposed approach. " 48 60 65

We consider precoder design for maximizing the weighted sum rate (WSR) of successive zero-forcing dirty paper coding (SZF-DPC). For this problem, the existing precoder designs often assume a sum power constraint (SPC) and rely on the singular value decomposition (SVD). The SVD-based designs are known to be optimal but require high complexity. We first propose a low-complexity optimal precoder design for SZF-DPC under SPC, using the QR decomposition. Then, we propose an efficient numerical algorithm to find the optimal precoders subject to per-antenna power constraints (PAPCs). To this end, the precoder design for PAPCs is formulated as an optimization problem with a rank constraint on the covariance matrices. A well-known approach to solve this problem is to relax the rank constraints and solve the relaxed problem. Interestingly, for SZF-DPC, we are able to prove that the rank relaxation is tight. Consequently, the optimal precoder design for PAPCs is computed by solving the relaxed problem, for which we propose a customized interior-point method that exhibits a superlinear convergence rate. Two suboptimal precoder designs are also presented and compared to the optimal ones. We also show that the proposed numerical method is applicable for finding the optimal precoders for block diagonalization scheme.

We consider the beamformer design for zero-forcing dirty paper coding (ZF-DPC), a suboptimal transmission technique for MISO broadcast channels (MISO BCs). For the sum rate maximization problem under a total power constraint, the existing beamformer designs in the literature are based on the QR decomposition (QRD), which is used to satisfy the ZF constraints. However, the optimality of the QRD-based design has been unknown previously. In this paper, we prove that the QRD-based design is optimal for ZF-DPC for any performance measure under a sum power constraint. For the per-antenna power constraints, the QRD-based designs become suboptimal, and we propose an optimal design, using a convex optimization framework. Low-complexity suboptimal designs are also presented, and numerically shown to achieve a significant fraction of the sum rate provided by the optimal design.

A simple yet generic approach is presented to extract the growth and breakage kinetics from the temporal data of heterogeneous cell population. The moment form of the one-dimensional population balance equation is directly solved by a MATLAB solver for linear systems to extract the kinetics. The corresponding systems of linear equations are, however, highly underdetermined and ill-conditioned. To address this, the problem is regularized by assuming a suitable upper bound of the solution. The range between minimum and maximum possible values of the solution is discretized into several sub-intervals. The system is then solved against each sub-interval, whose values are used as lower and upper bounds in a suitable MATLAB solver and a local solution is obtained in all these ranges. The final solution is then computed by taking average of all solutions having residual norms less than a particular threshold. To validate the method, the results of the inverse technique are compared and discussed against two theoretical experiments.

Recent results in the literature have provided connections between the so-called turnpike property, near optimality of closed-loop solutions using model predictive control schemes, and strict dissipativity. An important feature of these results is that strict dissipativity provides a checkable condition for the other two properties. These results relate to optimal control problems with undiscounted stage cost. Motivated by applications in economics, we consider optimal control problems with discounted stage cost and define a notion of discounted strict dissipativity. As in the undiscounted case, we show that discounted strict dissipativity provides a checkable condition for various properties of the solutions of the optimal control problem associated with the appropriately defined discounted available storage function.

An optimization problem regarding water removal in the press section of a paper machine is considered in this work. The proposed model tries to minimize a cost function comprising the replacement of the felts in the press section, the cost of energy to operate the press and the cost of energy in the drying section, while satisfying the constraints of water mass balance in the process. The model is classified as a mixed-integer nonlinear program (MINLP) in which the most important decisions are: a) the sequence of paper to produce or when to produce the paper; b) the need to exchange the felts; and c) when to exchange the felts. Numerical examples are presented to illustrate the performance of the model.

Dirty paper coding scheme (DPC) is known to be a capacity achieving transmission technique in downlink multiuser MIMO channels. As a suboptimal solution to DPC, a precoding technique called successive zero-forcing dirty paper coding (SZF-DPC) has been proposed recently. The condition for the existence of the precoding matrices in SZF-DPC restricts the capability of supporting multiple users simultaneously. Thus, a user scheduling algorithm is needed to achieve multiuser diversity in SZF-DPC as the number of users grows. In this paper, we propose three low-complexity suboptimal scheduling algorithms to exploit the multi-user diversity gain for SZF-DPC. The first algorithm greedily maximizes the true sum capacity. The second algorithm is based on eigenvalues that are closely related to the true capacity. The third algorithm relies on the diagonal elements of the effective channel matrix since we realize a strong relationship between the eigenvalues and diagonal entries of a Hermitian matrix. Simulation results of several cases show that the proposed scheduling algorithms can obtain a significant fraction of sum capacity of the optimal solution.

In the present paper, the effects of cake thickness and time on the efficiency of brown stock washer of the paper mill are studied by using mathematical model of pulp washing for the species of sodium and lignin ions. The mechanism of the diffusion‐ dispersion washing of the bed of the pulp fibers is mathematically modeled by the basic material balance and adsorption isotherm is used to describe the equilibrium between the concentration of the solute in the liquor and concentration of the solute on the fibers. To study the parametric effect, numerical solutions of the axial domain of the system governed by partial differential equations (transport and isotherm equations) for different boundary conditions are obtained by the “pdepe” solver in MATLAB source code. The effects of both the parameters are shown by three dimensional graphical representation as well as concentration profiles.

A production optimization problem concerned with the water removal in the press section in a paper machine is considered in the present paper. The proposed model seeks to determine the planning of production of paper in order to minimize a cost function that consists of replacement of the felts in the press section, cost of energy to operate the press and cost of energy in the drying section. The proposed model corresponds a mixed-integer nonlinear programming (MINLP) where the most important decisions in the paper machine are: a) the sequence of paper to produce, or when to produce the paper, b) the need to exchange the felts, and c) when to exchange the felts. Numerical examples are presented to illustrate the performance of the model. This work was developed considering a real case with data from a Brazilian paper plant.

or preparing Multi-objective formulations are a realistic models for many complex engineering, AI, mathematical and optimization problems etc. Customized genetic algorithms have been expressed as effective to determine best solutions to these problems. In many real-life problems, there are many conflicts to each other towards objective, and mainly by taking single objective to optimizing a particular solution can give unacceptable result with respective to other objective. An inevitable features of Genetic Algorithm are to generate set of solutions for multi objective problem with satisfying objective at acceptance level without dominating to any other solution. Genetic Algorithm is used in maximization as well as minimization of function. This paper tried to show an overview and tutorial is presented how Genetic Algorithm is best to solve the maximization of function for given function. This feature make Genetic Algorithm very unique from traditional genetic algorithms. Roulette-Wheel selection method is adopted to calculate fitness function and other functions. KeywordsAlgorithm, optimization and its techniques, Multi- objective functions, conclusion.

A Galerkin-based family of numerical formulations is presented for solving nonlinear optimal control problems. This paper introduces a family of direct methods that calculate optimal trajectories by discretizing the system dynamics using Galerkin numerical techniques and approximate the cost function with Gaussian quadrature. In this numerical approach, the analysis is based on L 2 -norms. An important result in the theoretical foundation is that the feasibility and consistency theorems are proved for problems with piecewise continuous controls. Galerkin methods may be formulated in a number of ways that allow for eficiency and/or improved accuracy while solving a wide range of optimal control problems with a variety of state and control constraints. Numerical formulations using Legendre test functions are derived. One formulation allows for a weak enforcement of boundary conditions, which imposes end conditions only up to the accuracy of the numerical approximation itself. Finally, a numerical example is shown to demonstrate the exponential convergence of Galerkin optimal control.

This article proposes an Enhanced Memetic Differential Evolution (EMDE) for designing digital filters which aim at detecting defects of the paper produced during an industrial process. Defect detection is handled by means of two Gabor filters and their design is performed by the EMDE. The EMDE is a novel adaptive evolutionary algorithm which combines the powerful explorative features of Differential Evolution with the exploitative features of three local search algorithms employing different pivot rules and neighborhood generating functions. These local search algorithms are the Hooke Jeeves Algorithm, a Stochastic Local Search, and Simulated Annealing. The local search algorithms are adaptively coordinated by means of a control parameter that measures fitness distribution among individuals of the population and a novel probabilistic scheme. Numerical results confirm that Differential Evolution is an efficient evolutionary framework for the image processing problem under investigation and show that the EMDE performs well. As a matter of fact, the application of the EMDE leads to a design of an efficiently tailored filter. A comparison with various popular metaheuristics proves the effectiveness of the EMDE in terms of convergence speed, stagnation prevention, and capability in detecting solutions having high performance.

In this paper the design of heat recovery systems for paper machines is studied by means of a sequential modular flow-sheeting program. The program is used for economical optimization of the heat recovery system with respect to its design variables. In the optimization, the objective function, calculated by the flow-sheeting program, is mapped to an approximate model, which is repeatedly updated and optimized. The values of the design variables used in the mapping are provided by factorial experiments. Analyses have predicted that considerable steam savings can be obtained if the heat recovery systems that are designed by the use of current standard practice are replaced by optimized systems. The early venture profit of the system can usually be increased by about 5% by means of optimization.

We investigate the one-dimensional cutting-stock problem integrated with the lot-sizing problem in the context of paper industries. The production process in paper mill industries consists of producing raw materials characterized by rolls of paper and cutting them into smaller rolls according to customer requirements. Typically, both problems are dealt with in sequence, but if the decisions concerning the cutting patterns and the production of rolls are made together, it can result in better resource management. We investigate Dantzig–Wolfe decompositions and develop column generation techniques to obtain upper and lower bounds for the integrated problem. First, we analyze the classical column generation method for the cutting-stock problem embedded in the integrated problem. Second, we propose the machine decomposition that is compared with the classical period decomposition for the lot-sizing problem. The machine decomposition model and the period decomposition model provide the same lower bound, which is recognized as being better than the linear relaxation of the classical lot-sizing model. To obtain feasible solutions, a rounding heuristic is applied after the column generation method. In addition, we propose a method that combines an adaptive large neighborhood search and column generation method, which is performed on the machine decomposition model. We carried out computational experiments on instances from the literature and on instances adapted from real-world data. The rounding heuristic applied to the first column generation method and the adaptive large neighborhood search combined with the column generation method are efficient and competitive.

This study examines a two-stage two-dimensional cutting stock problem encountered by a paper mill company. The problem includes various machine-related and operational constraints based on real-world situations. Paper products are manufactured using two major cutting processes. Each cutting machine has a specific minimum and maximum width for input and output rolls and is limited by the maximum number of rolls it can cut at the same time. A mathematical model is presented to formally address the problem and an efficient multiple-choice knapsack-based heuristic algorithm is proposed to solve the problem. To demonstrate the efficiency of the proposed heuristic algorithm, computational experiments are conducted on test data-set generated from real-world data provided by a large paper mill company in the Republic of Korea.

The industrial treatment of waste paper in order to regain valuable fibers from which recovered paper can be produced, involves several steps of preparation. One important step is the separation of stickies that are normally attached to the paper. If not properly separated, remaining stickies reduce the quality of the recovered paper or even disrupt the production process. For the mechanical separation process of fibers from stickies a separator screen is used. This machine has one input feed and two output streams, called the accept and the reject. In the accept the fibers are concentrated, whereas the reject has a higher concentration of stickies. The machine can be controlled by setting its reject rate. But even when the reject rate is set properly, after just a single screening step, the accept still has too many stickies, or the reject too many fibers. To get a better separation, several separators have to be assembled into a network. From a mathematical point of view this problem can be seen as a multi-commodity network flow design problem with a nonlinear, controllable distribution function at each node. We present a nonlinear mixed-integer programming model for the simultaneous selection of the network’s topology and the optimal setting of each separator. Numerical results are obtained via different types of linearization of the nonlinearities and the use of mixed-integer linear solvers, and compared with state-of-the-art global optimization software.

The restoration of regular paper fragments can be solved just as the Traveling Salesman Problem. Paper pretreatment and edge matching are the main steps during the restoration process, which contain binarization, screening between the left and right boundary depending the width of paper margins. For some longer paper fragments, the transverse splicing can be realized with Greed Algorithm. But the algorithm will get a non-ideal restoration for more fine paper fragments. Therefore the noise-suppressed processing before clustering from line to line through projection is essential in order to make sure that the regular English fragments can get the regularity like Chinese characters. The two experiments get an 100% correct rates when using the method combining the improved genetic algorithm for traveling salesman problem.combining the improved genetic algorithm for traveling salesman problem.

In this paper, we address some computational challenges arising in complex simulation-based design optimization problems. High computational cost, black-box formulation and stochasticity are some of the challenges related to optimization of design problems involving the simulation of complex mathematical models. Solving becomes even more challenging in case of multiple conflicting objectives that must be optimized simultaneously. In such cases, application of multiobjective optimization methods is necessary in order to gain an understanding of which design offers the best possible trade-off. We apply a three-stage solution process to meet the challenges mentioned above. As our case study, we consider the integrated design and control problem in paper mill design where the aim is to decrease the investment cost and enhance the quality of paper on the design level and, at the same time, guarantee the smooth performance of the production system on the operational level. In the first stage of the three-stage solution process, a set of solutions involving different trade-offs is generated with a method suited for computationally expensive multiobjective optimization problems using parallel computing. Then, based on the generated solutions an approximation method is applied to create a computationally inexpensive surrogate problem for the design problem and the surrogate problem is solved in the second stage with an interactive multiobjective optimization method. This stage involves a decision maker and her/his preferences to find the most preferred solution to the surrogate problem. In the third stage, the solution best corresponding that of stage two is found for the original problem. peerReviewed

Improved streamflow forecasting is considered an important task for researchers and water resources managers. However, streamflow forecasting is often challenging owing to the complexity of hydrologic systems. The accuracy of streamflow forecasting mainly depends on the input data from rainfall. Hence, this is important to make the estimation of rainfall as accurate as possible result in achieve an economical design of watershed management, water budget studies, reservoir operation, and flood forecasting and control. Most of the previous research was highlighted, an optimal rain gauge network is necessary to provide high quality rainfall estimates. The goal of this paper is to provide a concise review of several studies on the optimal design of a rain gauge network models to enhance the accuracy of streamflow forecasting. This study had two components. First, the design of an optimal rain gauge network using the kriging-based geostatistical approach based on the variance reduction framework. Second, the uses of optimization technique for minimizing the kriging variance in order to optimize rain gauge networks. Additionally, a discussion of both techniques to design an optimal rain gauge network is presented. A well designed rain gauge network is capable of providing accurate rainfall estimates with an optimal number of rain gauge network density. This paper closes with a set of recommendations for what observations and capabilities are needed in the future to advance our understanding of an optimal rain gauge network design and their location for improving the estimate of aerial rainfall.

A Dirty Paper Coding (DPC) based transmission scheme for the Gaussian multiple-input multiple-output (MIMO) cognitive radio channel (CRC) is studied when there is imperfect and perfect channel knowledge at the transmitters (CSIT) and the receivers, respectively. In particular, the problem of optimizing the sum-rate of the MIMO CRC over the transmit covariance matrices is dealt with. Such an optimization, under the DPC-based transmission strategy, needs to be performed jointly with an optimization over the inflation factor. To this end, first the problem of determination of inflation factor over the MIMO channel $Y=H_1 X + H_2 S + Z$ with imperfect CSIT is investigated. For this problem, two iterative algorithms, which generalize the corresponding algorithms proposed for the channel $Y=H(X+S)+Z$, are developed. Later, the necessary conditions for maximizing the sum-rate of the MIMO CRC over the transmit covariances for a given choice of inflation factor are derived. Using these necessary conditions and the algorithms for the determination of the inflation factor, an iterative, numerical algorithm for the joint optimization is proposed. Some interesting observations are made from the numerical results obtained from the algorithm. Furthermore, the high-SNR sum-rate scaling factor achievable over the CRC with imperfect CSIT is obtained., To be presented at ISIT 2009, Seoul, S. Korea