- Email: [email protected]
Neural network parallel computing
lqeurocomputing 6 (1994) 257-259 Elsevier
257
NEUCOM 305
Book reviews Material to be included in this section can be submitted to: Prof. C. Gielen, Department of Medical Physics and Biophysics, University of Nijmegen, Geert Grooteplein Noord 21, 6525 EZ Nijmegen, The Netherlands. Tel: 31 80 614 242, fax: 31 80 541 435, email: [email protected]
Neural Network Parallel Computing, by Yoshiyasu Takefuji. Kluwer Academic Publlshers, Boston, 1992. ISBN 0-7923-9190-X. 225 pp, price: US $ 65. The book Neural Network Parallel Computing by Yoshiyasu Takefuji is an extremely interesting book. The stated purpose of the book is to encourage further investigation in neural networks for optimization by demonstrating the capability of neural networks for solving a variety of computational problems. Presented are many neural network architectures and algorithms in a variety of fields including computer-aided VLSI design, operations research, molecular biology, and computer science. The book has an interesting structure in that it presents some software and an example of the N-Queen problem at the beginning of the book and then proceeds to examples of the use of neural networks and finally toward the end of the book to mathematical theory. Organized in 14 chapters, the book explores applications of neural network for optimizations most by dealing with the application to the optimization of geometric problems of academic and practical interest, such as scheduling, routing, sequencing, sorting, tiling, map coloring, chess game strategy, and RNA secondary structure. Each chapter briefly defines a problem and then gives an example of its solution. For each application the performance of the proposed solution is compared with that of standard, documented solutions thus giving the reader an excellent insight into the efficiency of the algorithm used. At the end of each chapter some selected problems and a list of references are provided. The book is for the reader who wants to use neural networks methods to solve a particular problem such as the routing problem in a VLSI design. The algorithms presented involve simulating first-order differential equations (the motion equation of neural networks) that model the dynamic nature of the systems in the problems. The first order Euler method is widely used in the book to simulate the differential equations numerically. Chapter 1 introduces the reader a neural network model to help understand a basic neural network approach for solving the general optimization problem. The model solves the Nqueen problem with the goal being to locate N queens on an N by N chessboard where any pair of queens do not command each other. The proposed neural network model addresses the limitations of the traditional approaches in which the convergence rate dramatically degraded with the problem size. This first chapter also highlights two important issues: (1) How to 0925-2312/94/:K~7.00 (~) 1994 - Elsevier Science B.V. All rights reserved
258
Book reviews
construct a neural representation from a given problem, and (2) How to formulate the motion equation considering the necessary and sufficient constraints and/or the cost function from the problem. Chapter 2 examines the scheduling problem traffic in order to maximize the throughput time and minimize the waiting time of the traffic. This chapter highlights the importance of the hysteresis property used to reduce the complicated oscillatory behaviors of neural dynamics for solving optimization problems. The hysteresis helps to shorten drastically the convergence time to the global minimum. The simulations indicate an interesting behavior: the solution quality of the system does not degrade with the problem size. Chapter 3 provides a neural network algorithm to solve a map coloring problem in which a set of regions are to be colored with a limited set of colors, but the regions that are sharing a common boundary are not of the same color. A scaling method for the coefficients in the motion equation is given that allows the state of the system to escape from the local minimum and to converge to the global minimum. An important result from more than one thousand sets of simulations, is that the number of iterations was observed as not being strongly influenced by the problem size. Chapter 4 describes an algorithm for solving graph planarization problems that can be used in designing printed circuits boards and routing VLSI circuit. The proposed algorithm has very good performance in terms of convergence rate. Chapter 5 involves a channel routing problem, a major issue in automatic layout design of VLSI circuits and printed circuit boards. The simulation results support the consistency of the algorithm and show that the primary goal for finding the near optimum solution in parallel processing is successfully achieved in terms of the computer time and the solution quality. The conclusion is that the flexibility of this algorithm can easily be accommodated to the future advancement of the VLSI technology. In Chapter 6, neural networks are used for solving the ribonucleic (RNA) secondary structure, an important contribution to both molecular biology and manufacturing. The simulation results demonstrated that the proposed algorithms are both promising and practical. Chapter 7 presents an algorithm for finding a knight's tour on a chessboard (this algorithm is a contribution since no general method has been given to this problem in the last century). The average simulation takes less than one hundred steps, but the larger the problem the more often the state of the system converged to an unsatisfactory solution. This application shows the importance of the hysteresis, since without the hysteresis property the state of the system tends to oscillate. Chapter 8 introduces an algorithm to solve the spare allocation problems. Spare allocation is widely used in manufacturing memory chips to provide reparability of faulty cells and enhance the production yield. The simulation results show that the number of iterations and the frequency of the convergence are not determined by the problem size. In Chapter 9, new parallel algorithms for sorting and searching are introduced. The notable quality of the proposed neural network algorithms is that two and only two iterations are required regardless of the size of the problem. Chapter 10 examines an algorithm to solve tiling problems that can be used for placement of components or cells in a VLSI chip, designing and compacting printing circuit boards, and solving a variety of two- or three-dimension packing problems. It is important to note that few sequential algorithms have been reported to solve this problem. Chapters 11 and 12 give a short theoretical presentation to help the reader understand the principles and theory underlying neural networks. Chapter 11 gives a flavor of human brain organization and functioning, and discusses its modeling into neural networks via digital and analog circuits. Chapter 12 summarizes the important mathematical background involved in the neural computing for optimization problems, and introduces four neuron models. Chapter 13 extends the discussion by pointing out some forthcoming interesting applications of neural
Book reviews
259
networks to communication and graph problems, and envisages the future of neural networks for optimization problems. Chapter 14 concludes the presentation with an introduction to the theory of conjunctoids and artificial learning. In summary this book will serve as a valuable reference book to researchers and practicing engineers, who are interested in doing work using neural networks concepts in a variety of interesting applications in optimization. The book achieves its goal, i.e. to demonstrate the capability of neural networks as a technique for solving a variety of computational optimization problems over the best known algorithms or the best-methods if they exist. This book is a useful addition to the neural networks literature. First, it provides a large number of references to the most relevant literature in parallel computations. The major asset of this book is to bring insight to the task of solving a variety of real-world problems to a reader often overwhelmed with too theoretical concepts. This book is clear and accessible, and can be addressed to a broad readership; even to readers that just entered or are entering this field of research. Written explanations and appropriate illustrations help the reader elucidate the concepts and relations. The problems at the end of each chapter are helpful in applying and deepening the concepts and relations. It also contains Turbo Pascal programs that are ready to run, and easy to implement algorithms. In addition, directions for the development of software simulators on a variety of platforms from UNIX stations to PCs or Macintosh machines are provided. It is important to note that a parallel machine is not required, because the programs provided simulate the behavior of a parallel machine using a sequential computer. Catherine Roze
Department of Industrial Technology, University of North Dakota, Box 7118, Grand Forks, ND 58202, USA. Email: [email protected] Dr. Joe Hootman
Professor, Department of Electrical Engineering, University of North Dakota, Box 8155, Grand Forks, ND 58202, USA.
257
NEUCOM 305
Book reviews Material to be included in this section can be submitted to: Prof. C. Gielen, Department of Medical Physics and Biophysics, University of Nijmegen, Geert Grooteplein Noord 21, 6525 EZ Nijmegen, The Netherlands. Tel: 31 80 614 242, fax: 31 80 541 435, email: [email protected]
Neural Network Parallel Computing, by Yoshiyasu Takefuji. Kluwer Academic Publlshers, Boston, 1992. ISBN 0-7923-9190-X. 225 pp, price: US $ 65. The book Neural Network Parallel Computing by Yoshiyasu Takefuji is an extremely interesting book. The stated purpose of the book is to encourage further investigation in neural networks for optimization by demonstrating the capability of neural networks for solving a variety of computational problems. Presented are many neural network architectures and algorithms in a variety of fields including computer-aided VLSI design, operations research, molecular biology, and computer science. The book has an interesting structure in that it presents some software and an example of the N-Queen problem at the beginning of the book and then proceeds to examples of the use of neural networks and finally toward the end of the book to mathematical theory. Organized in 14 chapters, the book explores applications of neural network for optimizations most by dealing with the application to the optimization of geometric problems of academic and practical interest, such as scheduling, routing, sequencing, sorting, tiling, map coloring, chess game strategy, and RNA secondary structure. Each chapter briefly defines a problem and then gives an example of its solution. For each application the performance of the proposed solution is compared with that of standard, documented solutions thus giving the reader an excellent insight into the efficiency of the algorithm used. At the end of each chapter some selected problems and a list of references are provided. The book is for the reader who wants to use neural networks methods to solve a particular problem such as the routing problem in a VLSI design. The algorithms presented involve simulating first-order differential equations (the motion equation of neural networks) that model the dynamic nature of the systems in the problems. The first order Euler method is widely used in the book to simulate the differential equations numerically. Chapter 1 introduces the reader a neural network model to help understand a basic neural network approach for solving the general optimization problem. The model solves the Nqueen problem with the goal being to locate N queens on an N by N chessboard where any pair of queens do not command each other. The proposed neural network model addresses the limitations of the traditional approaches in which the convergence rate dramatically degraded with the problem size. This first chapter also highlights two important issues: (1) How to 0925-2312/94/:K~7.00 (~) 1994 - Elsevier Science B.V. All rights reserved
258
Book reviews
construct a neural representation from a given problem, and (2) How to formulate the motion equation considering the necessary and sufficient constraints and/or the cost function from the problem. Chapter 2 examines the scheduling problem traffic in order to maximize the throughput time and minimize the waiting time of the traffic. This chapter highlights the importance of the hysteresis property used to reduce the complicated oscillatory behaviors of neural dynamics for solving optimization problems. The hysteresis helps to shorten drastically the convergence time to the global minimum. The simulations indicate an interesting behavior: the solution quality of the system does not degrade with the problem size. Chapter 3 provides a neural network algorithm to solve a map coloring problem in which a set of regions are to be colored with a limited set of colors, but the regions that are sharing a common boundary are not of the same color. A scaling method for the coefficients in the motion equation is given that allows the state of the system to escape from the local minimum and to converge to the global minimum. An important result from more than one thousand sets of simulations, is that the number of iterations was observed as not being strongly influenced by the problem size. Chapter 4 describes an algorithm for solving graph planarization problems that can be used in designing printed circuits boards and routing VLSI circuit. The proposed algorithm has very good performance in terms of convergence rate. Chapter 5 involves a channel routing problem, a major issue in automatic layout design of VLSI circuits and printed circuit boards. The simulation results support the consistency of the algorithm and show that the primary goal for finding the near optimum solution in parallel processing is successfully achieved in terms of the computer time and the solution quality. The conclusion is that the flexibility of this algorithm can easily be accommodated to the future advancement of the VLSI technology. In Chapter 6, neural networks are used for solving the ribonucleic (RNA) secondary structure, an important contribution to both molecular biology and manufacturing. The simulation results demonstrated that the proposed algorithms are both promising and practical. Chapter 7 presents an algorithm for finding a knight's tour on a chessboard (this algorithm is a contribution since no general method has been given to this problem in the last century). The average simulation takes less than one hundred steps, but the larger the problem the more often the state of the system converged to an unsatisfactory solution. This application shows the importance of the hysteresis, since without the hysteresis property the state of the system tends to oscillate. Chapter 8 introduces an algorithm to solve the spare allocation problems. Spare allocation is widely used in manufacturing memory chips to provide reparability of faulty cells and enhance the production yield. The simulation results show that the number of iterations and the frequency of the convergence are not determined by the problem size. In Chapter 9, new parallel algorithms for sorting and searching are introduced. The notable quality of the proposed neural network algorithms is that two and only two iterations are required regardless of the size of the problem. Chapter 10 examines an algorithm to solve tiling problems that can be used for placement of components or cells in a VLSI chip, designing and compacting printing circuit boards, and solving a variety of two- or three-dimension packing problems. It is important to note that few sequential algorithms have been reported to solve this problem. Chapters 11 and 12 give a short theoretical presentation to help the reader understand the principles and theory underlying neural networks. Chapter 11 gives a flavor of human brain organization and functioning, and discusses its modeling into neural networks via digital and analog circuits. Chapter 12 summarizes the important mathematical background involved in the neural computing for optimization problems, and introduces four neuron models. Chapter 13 extends the discussion by pointing out some forthcoming interesting applications of neural
Book reviews
259
networks to communication and graph problems, and envisages the future of neural networks for optimization problems. Chapter 14 concludes the presentation with an introduction to the theory of conjunctoids and artificial learning. In summary this book will serve as a valuable reference book to researchers and practicing engineers, who are interested in doing work using neural networks concepts in a variety of interesting applications in optimization. The book achieves its goal, i.e. to demonstrate the capability of neural networks as a technique for solving a variety of computational optimization problems over the best known algorithms or the best-methods if they exist. This book is a useful addition to the neural networks literature. First, it provides a large number of references to the most relevant literature in parallel computations. The major asset of this book is to bring insight to the task of solving a variety of real-world problems to a reader often overwhelmed with too theoretical concepts. This book is clear and accessible, and can be addressed to a broad readership; even to readers that just entered or are entering this field of research. Written explanations and appropriate illustrations help the reader elucidate the concepts and relations. The problems at the end of each chapter are helpful in applying and deepening the concepts and relations. It also contains Turbo Pascal programs that are ready to run, and easy to implement algorithms. In addition, directions for the development of software simulators on a variety of platforms from UNIX stations to PCs or Macintosh machines are provided. It is important to note that a parallel machine is not required, because the programs provided simulate the behavior of a parallel machine using a sequential computer. Catherine Roze
Department of Industrial Technology, University of North Dakota, Box 7118, Grand Forks, ND 58202, USA. Email: [email protected] Dr. Joe Hootman
Professor, Department of Electrical Engineering, University of North Dakota, Box 8155, Grand Forks, ND 58202, USA.