The Hopfield neural network is attracting attention as a high‐speed solver for optimization and other problems. However, it contains a problem in that the network may not arrive at the globally optimal solution but stops at a locally optimal solution unless the initial state is selected appropriately. In other words, the selection of the initial state is important in solving a problem using the Hopfield neural network. This paper considers the real number partition problem, the problem of finding the k largest elements from a given set of real numbers, given integer k. A network to solve this problem is constructed. It is shown that the network arrives at the globally optimal solution if the initial state satisfies a certain condition. Its basin also is examined. As an application example of the network, the sorting problem is considered.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Information Systems
- Hardware and Architecture
- Computational Theory and Mathematics