We propose an asymmetric neural network which can solve inequality-constrained combinatorial optimization problems that are difficult to solve using symmetric neural networks. In this article, a knapsack problem that is one of such the problem is solved using the proposed network. Additionally, we study condition for obtaining a valid solution. In computer simulations, we show that the condition is correct and that the proposed network produces better solutions than the simple greedy algorithm.

The Traveling Salesman Problem (TSP) can be solved by a neural network using the coding scheme based on the adjacency of city in the tour. Using this coding scheme, the neural network generates a better solution than that using other coding schemes. We, however, often get the invalid solution consisting of some subtours. In this article, we propose a method of eliminating subtours using additional neurons. On the computer simulation it is shown that we get the optimum solution by means of taking only O(n2) additional neurons and trials.

In this paper, two models for associative memory based on a measure of manhattan length are proposed. First, we propose the two-layered model which has an advantage to its implementation by using PDN. We also refer to the way to improve the recalling ability of this model against noisy input patterns. Secondly, we propose the other model which always recalls the nearest memory pattern in a measure of manhattan length by lateral inhibition. Even if a noise of input pattern is so large that the first model can not recall, this model can recall correctly against such a noisy pattern. We also confirm the performance of the two models by computer simulations.

A pseudoinverse rule, one of major rule to determine a weight matrix for associative memory, has large capacity comparing with other determining rules. However, it is wellknown that the rule has small domains of attraction of memory vectors on account of many spurious states. In this paper, we try to improve the problem by means of subtracting a constant from all diagonal elements of a weight matrix. By this method, many spurious states disappear and eigenvectors with negative eigenvalues are introduced for the orthocomplement of the subspace spanned by memory vectors. This method can be applied to two types of networks: binary network and analog network. Some computer simulations are performed for both two models. The results of the simulations show our improvement is effective to extend error correcting ability for both networks.

In this article, the autocorrelation associative neural network that is one of well-known applications of neural networks is improved to extend its capacity and error correcting ability. Our approach of the improvement is based on the consideration that negative self-feedbacks remove spurious states. Therefore, we propose a method to determine the self-feedbacks as small as possible within the range that all stored patterns are stable. A state transition rule that enables to escape oscillation is also presented because the method has a possibility of falling into oscillation. The efficiency of the method is confirmed by means of some computer simulations.