In this paper, we consider an automatic warehouse, in which rc-k palettes are arranged two-dimensionally on a grid with r rows c columns. The palettes in the warehouse can slide independently and simultaneously with the use of k spaces, unless they come into collision. Then, we show the minimum number of sliding operations required to move a specified palette to a specified position, where one sliding operation is a set of slides of palettes which are executed simultaneously in a unit time withouto any collision.

Let G be a simple graph and α be an automorphism of G. A spanning tree T of G is said to be α-invariant if α is also an automorphism of T. We give a necessary and sufficient condition for a connected graph G to have an α-invariant spanning tree.

Genetic algorithms have been shown to be very useful in a variety of search and optimization problems. In this paper, we propose a modified genetic channel router. We adopt the compatible crossover operator and newly designed compatible mutation operator in order to search solution space more effectively, where vertical constraints are integrated. By carefully selected fitness function forms and optimized genetic parameters, the current version speeds up benchmarks on average about 5.83 times faster than that of our previous version. Moreover the total convergence to optimal solutions for benchmarks can be always obtained.

A neural network model for solving channel routing problem is proposed and described. Channel routing problem is one of the most important and popular phases of computer aided design of VLSI chips. Since the problem is NP-complete, many heuristic algorithms with various routing conditions have been proposed for the last decade. Recently, J.J. Hopfield has demonstrated that a neural network can provide a heuristic technique for solving optimization problem. This paper describes how channel routing problem can be solved by a neural network model proposed by Hopfield. A brief summary of Hopfield neural network model, how to construct a neural network for solving channel routing problem, and results of digital computer simulation are described. Our results show that the neural network could provide good solutions of channel routing problem. For example, it computes a solution of the number of horizontal tracks 31 for the difficult example" and by using simple compaction algorithm the solution can be improved to 28, which is optimal within our channel routing strategy.

Genetic algorithms have been shown to be very useful in a variety of search and optimization problems. In this paper we present a genetic algorithm for maximum independent set problem. We adopt a permutation encoding with a greedy decoding to solve the problem. The DIMACS benchmark graphs are used to test our algorithm. For most graphs solutions found by our algorithm are optimal, and there are also a few exceptions that solutions found by the algorithm are almost as large as maximum clique sizes. We also compare our algorithm with a hybrid genetic algorithm, called GMCA, and one of the best existing maximum clique algorithms, called CBH. The exiperimental results show that our algorithm outperformed two of the best approaches by GMCA and CBH in final solutions.

This paper presents two kinds of simplification methods for incompletely specified sequential machines. The strategy of the methods is that as many states in original machines are covered in the simplification processes as possible. The purpose of the methods is to derive a simplified machine having either the largest maximal compatible set or its subset. With the methods, one of the minimal machines can not be always derived, but a near-minimal machine can be obtained more quickly with less memory, since they need not derive all the compatible sets. In this paper, the effectiveness of the methods is checked by applying them to simplification problems of incompletely specified machines generated by using random numbers, and of the MCNC benchmark machines. The experimental results show that our methods can derive a simplified machine quickly, especially for machines having a great number of states or don't care rate.

Evolution programs have been shown to be very useful in a variety of search and optimization problems, however, until now, there has been little attempt to apply evolution programs to channel routing problem. In this paper, we present an exolution program and identify the key points which are essential to successfully applying evolution programs to channel routing problem. We also indicate how integrating heuristic information related to the problem under consideration helps in convergence on final solutions and illustrate the validity of out approach by providing experimental results obtained for the benchmark tests. compared with the optimal solutions.

A new state reduction method of incompletely specified sequential machines is proposed in this paper. The method is based on a genetic algorithm implementing a dormant mechanism. MCNC benchmark machines are simplified by using this method to evaluate the method. The experimental results show that machines of almost the same number of states as the minimum ones can be derived by this method.

Genetic algorithms have been shown to be very useful in a variety of search and optimization problems. In this paper, we describe the implementation of genetic algorithms for channel routing problems and identify the key points which are essential to making full use of the population of potential solutions, that is one of the characteristics of genetic algorithms. Three efficient crossover techniques which can be divided further into 13 kinds of crossover operators have been compared. We also extend our previous work with ability to deal with dogleg case by simply splitting multi-terminal nets into a series of 2-terminal subnets. It routes the Deutsch's difficult example with 21 tracks without any detours.