A noise annealing neural network for global optimization

Abstract

This paper deals with a neural network model for global optimization. The model presented can solve nonlinear constrained optimization problems with continuous decision variables. Incorporating the noise annealing concept, the model is able to produce such a solution which is the global optima of the original task with probability close to 1. After a brief outline of some existing globally optimizing neural networks we introduce the stochastic neural model called noise annealing neural network which is based on Wong's diffusion iiiachine and can be regarded as an extension of the canonical nonlinear programming neural network by Kennedy and Chua. The usefulness of the model developed is supported by analytical investigations and coinputer simulations.

Application of stereoscopic tracking velocimetry for experimental and numerical investigation of directional solidification

“…Here, we present the results for further refinement of the technique in searching the absolute minimum and comparison of the performances. The stochastic neural network as described by Wong [13] and Biro et al [14], which can be utilized to enhance our global optimization, was obtained by adding Gaussian noise to the input of the Hopfield network. That is…”

A noise annealing neural network for hydroelectric generation scheduling with pumped-storage units

“…Numerous techniques based on analogies to statistical physics are designed for avoiding local optima [14]- [16]. In the case of discrete optimization such a network is the mean field neural network.…”

An Efficient Solving the Travelling Salesman Problem : Global Optimization of Neural Networks by Using Hybrid Method

“…While some researchers tried to find more appropriate parameters in the energy function (Aiyer et al, 1990;Baba, 1989;Biro et al, 1996;Burke, 1994;Gall & Zisssimopoulos, 1999;Gee & Prager, 1995;Hegde et al, 1988;Hopfield & Tank, 1985;Huang, 2005;Sharbaro, 1994;Wilson & Pawley, 1988), others hoped to get better energy functions (Baba, 1989). To date, research work has been extended to every aspect of the Hopfield model (Aarts & Laarhoven, 1985;Abe et al, 1992;Aiyer et al, 1990;Baba, 1989;Biro et al, 1996;Burke, 1994;Hegde et al, 1988;Hopfield & Tank, 1985;Sharbaro, 1994;Wilson & Pawley, 1988), and it is now clear how to correctly map problems onto the network so that invalid solutions never emerge. As for the quality of obtained solutions, while there are indications that the Hopfield model is solely suitable for solving Euclidean TSPs of small size (Wilson & Pawley, 1988), some researchers argue it is unreasonable to take the TSP as the benchmark to measure the optimization ability of the Hopfield model (Sharbaro, 1994).…”

“…In terms of the geometric structure of the distribution of the cities and the symmetry of distances between a pair of cities, the TSP can be classified into several categories (Aiyer et al, 1990;Baba, 1989;Biro et al, 1996;Burke, 1994;Gee & Prager, 1995;Hegde et al, 1988;Sharbaro, 1994;Wilson & Pawley, 1988). The Hopfield model for the TSP is built of n * n neurons.…”

“…Most of the researches have been concentrated on the improvement of either the convergence speed or the convergence rate to the global minimum in consideration of the weight parameter of the energy function, etc. But there are few that try to solve both global convergence and speedup by simultaneously setting the initial neuron outputs (Baba, 1989;Biro et al, 1996;Gall & Zissimopoulos 1999;Gee & Prager, 1995;Heung, 2005). This chapter proposes an efficient method for improving the convergence performances of the NN by applying a global optimization method.…”