An “evolutionary neural network (ENN)” is presented for the max cut problem of an undirected graph G(V, E) in this paper. The goal of the NP-hard problem is to find a partition of V into two disjoint subsets such that the cut size be maximized. The cut size is the sum of weights on edges in E whose endpoints belong to different subsets. The ENN combines the evolutionary initialization scheme of the neural state into the energy minimization criteria of the binary neural network. The performance of ENN is evaluated through simulations in randomly weighted complete graphs and unweighted random graphs with up to 1000 vertices. The results show that the evolutionary initialization scheme drastically improves the solution quality. ENN can always find better solutions than the maximum neural network, the mean field annealing, the simulated annealing, and the greedy algorithm

A three-stage algorithm of combining sequential heuristic methods into a parallel neural network is presented for the channel assignment problem in cellular mobile communication systems in this paper. The goal of this NP-complete problem is to find a channel assignment to requested calls with the minimum number of channels subject to interference constraints between channels. The three-stage algorithm consists of: 1) the regular interval assignment stage; 2) the greedy assignment stage; and 3) the neural-network assignment stage. In the first stage, the calls in a cell determining the lower bound on the total number of channels are assigned channels at regular intervals. In the second stage, the calls in a cell with the largest degree and its adjacent cells are assigned channels by a greedy heuristic method. In the third stage, the calls in the remaining cells are assigned channels by a binary neural network, The performance is verified through solving well-known benchmark problems, Especially for Sivarajan's benchmark problems, our three-stage algorithm first achieves the lower bound solutions in all of the 13 instances, while the computation time is comparable with existing algorithms.

A multicast packet switching system can replicate a packet in the window of each input port to send out the copies from different output ports simultaneously. In order to maximize the throughput, a combinatorial optimization problem must be solved in real time of finding a switching configuration which does not only satisfy the constraints on the system, but also maximizes the number of copies under transmission demands. In this paper, we focus on the one-shot scheduling problem where all the copies of selected packets must be sent out simultaneously. We propose the neural network composed of W/spl times/N binary neurons for the problem in the W-window-N-input-port system. The motion equation is newly defined with three heuristic methods. We verify the performance through simulations in up to 3-window-1000-input-port systems, where our binary neural network provides the better performance than the existing methods so as to reduce the delay time under practical situations.

In a multicast packet switching system, multiple output ports can send out packets simultaneously by means of the packet copying function. In realizing such a switching system, the transmission pattern must be determined for successively arising transfer requests, so that the number of transmitted packets is maximized, while satisfying the constraints. This paper considers the one-shot scheduling problem formulated by Chen and colleagues, where all copies of the same packet are sent at the same time, and proposes a new solution method using a neural network. In the proposed solution method using the neural network, the binary neuron, which is suited to the digital techniques and hardware implementation, is employed together with the synchronous update scheme. In order to improve the convergence performance and the accuracy of the solution, an operational equation with an additional heuristic term and a coefficient setting procedure taking account of transfer requests are proposed. By simulations for cases of up to 1000 ports, it is shown that the proposed solution method using the neural network is better in deriving the solution than the conventional method. It is also shown that the considered problem is NP -hard. © 1999 Scripta Technica, Electron Comp Jpn Pt 3, 83(3): 12–21, 2000

In a multihop radio network, packets are transmitted from course nodes to destination nodes by activating several links between nodes. Each node can either send a packet to, or receive a packet from, at most one of its adjacent nodes simultaneously. To minimize the transmission time for given requests, the problems must be solved by selecting a transmission route for each request (the routing problem) and by finding a link activation schedule (the link activation problem). The routing problem is decomposed into two subproblems: the candidate extraction problem and the route selection problem. In this paper, we propose a neural network algorithm using the maximum neuron model for the route selection problem. We verify through simulations that our algorithm finds better solutions in a shorter time than the existing algorithms. We also probe the NP-hardness of this problem. © 1999 Scripta Technica, Electr Eng Jpn, 129(2): 78–86, 1999

Systems and Computers in JapanVolume 30, Issue 13 p. 52-60 A proposal of a greedy neural network for route assignments in multihop radio networks Takayuki Baba, Takayuki Baba Department of Informatics and Mathematical Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Japan 560-0043Search for more papers by this authorNobuo Funabiki, Nobuo Funabiki Department of Informatics and Mathematical Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Japan 560-0043Search for more papers by this authorSeishi Nishikawa, Seishi Nishikawa Department of Informatics and Mathematical Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Japan 560-0043Search for more papers by this author Takayuki Baba, Takayuki Baba Department of Informatics and Mathematical Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Japan 560-0043Search for more papers by this authorNobuo Funabiki, Nobuo Funabiki Department of Informatics and Mathematical Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Japan 560-0043Search for more papers by this authorSeishi Nishikawa, Seishi Nishikawa Department of Informatics and Mathematical Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Japan 560-0043Search for more papers by this author First published: 04 November 1999 https://doi.org/10.1002/(SICI)1520-684X(19991130)30:13<52::AID-SCJ6>3.0.CO;2-VAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract In a radio communications network, all of the nodes cannot communicate with each other directly. Then packets are transferred from a source node to a destination node through several nodes. Therefore, we need to schedule transfer timing at each node, and communications routes must be assigned to minimize the total transfer time when many packet transfers are requested. This problem is divided into two problems: the communications route assignment problem and the scheduling problem. The former problem is subdivided into the communication route candidate extraction problem and the communication route selection problem. This paper first proposes an evaluation function (Cost) which gives the lowest limit of the total transfer time for the communication route assignment problem. Next this paper proposes a k-shortest route extraction procedure for the communication route extraction problem. This procedure is based on the k-shortest route algorithm. It prevents extraction of a route whose number of hops is more than the upper limit, sets an appropriate number of extraction routes, prevents loops, and prevents redundant route extraction. We also propose a greedy neural network procedure for the communication route selection problem. This procedure introduces the ω function into the operation equation of the neuron initial value setting based on the number of hops and a cost minimization term for the evaluation function. The procedure uses an appropriate termination condition for iterative computation. It also uses the first-order maximum neuron. Through simulations of 500-vertex communication network examples, the proposed procedure has the merits of high precision, short computation, and smaller number of computations in a region. © 1999 Scripta Technica, Syst Comp Jpn, 30(13): 52–60, 1999 Volume30, Issue1330 November 1999Pages 52-60 RelatedInformation

A novel neural network approach called gradual neural network (GNN) is presented for segmented channel routing in field programmable gate arrays (FPGA's). FPGA's contain predefined segmented channels for net routing, where adjacent segments in a track can be interconnected through programmable switches for longer segments. The goal of the FPGA segmented channel routing problem, known to be NP-complete, is to find a conflict-free net routing with the minimum routing cost. The GNN for the N-net-M-track problem consists of a neural network of NxM binary neurons and a gradual expansion scheme. The neural network satisfies the constraints of the problem, while the gradual expansion scheme seeks the cost minimization by gradually increasing activated neurons. The energy function and the motion equation are newly defined with heuristic methods. The performance is verified through solving 30 instances, where GNN finds better solutions than existing algorithms within a constant number of iteration steps.

The graph partitioning problem is an NP hard problem of deriving the partitioning of each vertex such that the total sum of the edge weights among the groups is minimized and the total sum of the vertex weights in each group is less than the upper limit. In this paper, a neural network solution is proposed in which the binary neurons are used for the graph 2-partitioning problem. In the present neural network, an energy function that is applicable to graphs both with and without edge and vertex weights is defined. For improvement of solution accuracy, shaking terms are introduced into the operating equation. To evaluate the solution search capability of the present method, simulations are carried out for random graphs, together with the KL method proposed by Kernighan and Lin, and the FM method proposed by Fiduccia and Mattheyses. From the simulation results, it is shown that the solutions obtained by the present method are the best. © 1999 Scripta Technica, Electron Comm Jpn Pt 3, 82(12): 34–42, 1999

A novel neural network approach called "Evolutionary Neural Network (ENN)" is presented for the module orientation problem. The goal of this NP-complete problem is to minimize the total wire length by flipping circuit modules with respect to their vertical and/or horizontal axes of symmetry. In order to achieve high quality VLSI systems, it is strongly desired to solve the problem as quickly as possible in the design cycle. Based on the concept of the genetic algorithm, the evolutionary initialization scheme on neuron states is introduced so as to provide a high quality solution within a very short time. The performance of ENN is compared with three heuristic algorithms through simulations on 20 examples with up to 500 modules. The results show that ENN can find the best solutions in the shortest time.

A novel neural network approach using the maximum neuron model is presented for N-queens problems. The goal of the N-queens problem is to find a set of locations of N queens on an N×N chessboard such that no pair of queens commands each other. The maximum neuron model proposed by Takefuji et al. has been applied to two optimization problems where the optimization of objective functions is requested without constraints. This paper demonstrates the effectiveness of the maximum neuron model for constraint satisfaction problems through the N-queens problem. The performance is verified through simulations in up to 500-queens problems on the sequential mode, the N-parallel mode, and the N2-parallel mode, where our maximum neural network shows the far better performance than the existing neural networks.

A constraint resolution scheme of the Hopfield neural network named "neuron mask" is presented for a class of combinatorial optimization problems. Neuron mask always satisfies constraints of selecting a solution candidate from each group so as to force the state of the neural network into a solution space. This paper presents the definition of neuron mask and the introduction into the neural network through the N-queens problem. The performance is verified by simulations on three computation modes, where neuron mask improves the performance of the neural network.

A neural network approach called the ''Gradual Neural Network (GNN)'' for the time slot assignment problem in the TDM multicast switching system is presented in this paper. The goal of this NP-complete problem is to find an assignment of packet transmission requests into a minimum number of time slots. A packet can be transmitted from one source to several destinations simultaneously by its replication. A time slot represents a switching configuration of the system with unit time for each packer transmission through an I/O line. The GNN consists of the binary neural network and the gradual expansion scheme. The binary neural network satisfies the constraints imposed on the system by solving the motion equation, whereas the gradual expansion scheme minimizes the number of required time slots by gradually expanding activated neurons. The performance is evaluated through simulations in practical size systems, where the GNN finds far better solutions than the best existing algorithm.

A three stage algorithm of heuristic search methods and a neural network is presented for the channel assignment problem in cellular mobile communication systems. This NP complete problem requires us to find a channel assignment to requested calls with the minimum number of channels subject to interference constraints between channels. The proposed algorithm consists of: (1) the regular interval assignment stage, (2) the greedy assignment stage, and (3) the neural network assignment stage. The performance is evaluated through benchmark problems, where our algorithm finds the optimum or near optimum solutions in all the instances

This paper presents a binary Hopfield neural network approach for finding a broadcasting schedule in a low-altitude satellite system. Our neural network is composed of simple binary neurons on the synchronous parallel computation, which is greatly suitable for implementation on a digital machine. With the help of heuristic methods, the neural network of a maximum of 200000 neurons can always find near-optimum solutions on a conventional workstation in our simulations

A digital neural network approach is presented for the multilayer channel routing problem with the objective of crosstalk minimization in this paper. As VLSI fabrication technology advances, the reduction of crosstalk between interconnection wires on a chip has gained important consideration in VLSI design, because of the closer interwire spacing and the circuit operation ar higher frequencies. Our neural network is composed of N x M x L digital neurons with one-bit output and seven-bit input for the N-net-M-track-2L-layer problem using a set of integer parameters, which is greatly suitable fur the implementation on digital technology. The digital neural network directly seeks a routing solution of satisfying the routing constraint and the crosstalk constraint simultaneously The heuristic methods are effectively introduced to improve the convergence property. The performance is evaluated through solving 10 benchmark problems including Deutsch difficult example in 2-10 layers. Among the existing neural networks, the digital neural network first achieves the lower bound solution in terms of the number of tracks in any instance. Through extensive simulation runs, it provides the best maximum crosstalks of nets for valid routing solutions of the benchmark problems in multilayer channels.

A new algorithm for multilayer over-the-cell channel routing problems using two neural networks is presented in this paper. In the multilayer over-the-cell channel routing problem, signal nets may be placed not only in the multilayer channel between two cells, but also on the multilayer routing area over the cells. The goal of our algorithm is to route all the given nets in both routing areas with the minimum number of tracks in the channel. Our algorithm consists of four steps: (1) extracting nets for the over-the-cell routing, (2) routing nets in the multilayer over-the-cell routing area by the neural network, (3) transforming nets for the channel routing and (4) routing nets in the multilayer channel by the neural network. The performance of our algorithm was verified through seven benchmark problems with 1–4 layers for the over-the-cell and 2–8 layers for the channel. The simulation results support the flexibility of our algorithm in the multilayer over-the-cell channel routing problem.

A neural network of massively interconnected digital neurons is presented For the total coloring problem in this paper. Given a graph G(V, E), the goal of this NP-complete problem is to find a color assignment on the vertices in V and the edges in E with the minimum number of colors such that no adjacent or incident pair of elements in V and E receives the same color. A graph coloring is a basic combinatorial optimization problem for a variety of practical applications. The neural network consists of(Nf Al).L neurons for the N-verlex-M-edge-L-color problem. Using digital neurons of binary outputs and range-limited non-negative integer inputs with a set of integer parameters, our digital neural network is greatly suitable for the implementation on digital circuits. The performance is evaluated through simulations in random graphs with the lower bounds on the number of colors. With a help of heuristic methods, the digital neural network of up to 530, 656 neurons always finds a solution in the NP-complete problem within a constant number of iteration steps on the synchronous parallel computation.

This paper presents a binary neural network approach for the net assignment problem in the over-the-cell routing model in VLSI layout design. The goal of the problem for one cell row and two adjacent channels is to assign a subset of nets in the cell row such that the total channel density is minimized without violating the capacity constraint, the selection constraint, and the routing constraint. The neural network is composed of NM binary neurons for the N-net-M-track problem. Unlike the existing algorithm, our neural network finds an assignment of all the nets either in the cell row or in two channels simultaneously. The performance is verified through simulations in seven benchmark problems for channel routing. With the help of four heuristic methods, the neural network can find near-optimum solutions on the synchronous parallel computation

This paper presents a binary neural network approach for link activation problems in multihop radio networks. The goal of the NP-complete problems is to find a conflict-free link activation schedule with the minimum number of time slots for specified communication requirements. The neural network is composed of NxM binary neurons for scheduling N links in M time slots. The energy functions and the motion equations are newly defined with heuristic methods. The simulation results through 14 instances with up to 419 links show that the neural network not only surpasses the best existing neural network in terms of the convergence rate and the computation time, but also can solve large scale instances within a constant number of iteration steps.