基于混沌神经网络的优化技术研究

So far many heurestic optimization approaches have been proposed. This project aims to solve the continuous optimization problems and some combinatorial optimization problems based on neural network and chaotic neural network. This is because there exists much potentiality for studying in these areas, and a few accomplishments have been obtained, especially in the continuous nonlinear optimization problems based on chaotic neural network. Pointing at that this project obtained the following accomplishments possessing creativeness: 1. Proposed a universal neural network model to solve linear programming; 2. Proposed a universal neural network model to solve both quadratic programming and linear programming; 3. Proposed three chaotic neural network models for solving global optimization of nonlinear programming: (a) A chaotic noise annealing neural network model; (b) A chaotic double-annealing neural network model; (c) A chaotic parameters disturbance annealing neural network model. The common merits of the three models are stability, reliability, high precision and overcoming the drawback of the existing similar models that the adjustments of the parameters are difficult in these models. 4. Proposed two neural algorithms for solving global optimization of nonlinear programming: (a) A neural network optimization algorithm based on annealing strategy of parameters disturbance; (b) A global optimization algorithm based on neural network with trust region strategy. 5. Proposed some algorithms for solving several combinatorial optimization problems based on chaotic neural network (CNN): (a) Two CNN algorithms for solving assignment problems; (b) A CNN algorithm for solving Job-shop schedule problems; (c) A CNN algorithm for solving four-coloring map problems and k-colorability problems; (d) A CNN algorithm for solving the shortest path problem; (e) A CNN algorithm for solving general 0-1 integer programming. 6. Proposed a fast CNN algorithm for solving four-coloring map problems; 7. Proposed a chaotic search method for a class of combinatorial optimization problems. This project provides the linear and nonlinear optimization problems and several combinatorial optimization problems with several new powerful tools.

优化技术是管理现代化的有力工具。传统的优化算法收敛慢且对某些非线性问题甚至不收敛。80年代采用的神经网络求解算法收敛快速但易陷入局部极小点。本研究拟采用近年来掀起的混沌神经网络模型求解，可使收敛快速且可达全局极小点并同初始条件无关。拟研究一般的非线性规划及组合优化问题求解算法。本成果将对优化技术提供一种新的强有力的工具。