The Study And Empirical Analysis Of Neural Network Methods For Optimization Problems

Optimization problems have wide range. Many fields have various optimization problems, so solving them has important and practical meaning. Optimization problem is that we should seek variables, which can maximize or minimize the objective function under given constraint conditions. Several simple optimization problems can be solved by traditional operational research methods, but many complicated optimization problems are hard to find the optimal solution, especially the NP-Hard Problem which belongs to combinatorial optimization problems.As intelligent methods, neural networks have good self-adaptability, robustness and the searching ability of solving the non-linear complicated problems. So they have the advantage in settling difficult optimization problems. The innovation point in this dissertation lies in studying neural network methods for optimization problems from new direction, dividing optimization problems into two categories which are combinatorial optimization problems and continuous variables'optimization problems and discussing the neural network methods for these two categories of optimization problems respectively.Firstly, this dissertation discusses the neural network methods for combinatorial optimization problems. Take the TSP for example, we mainly study Hopfield Neural Network and Random Neural Network. In the process of studying Random Neural Network, we introduce DRNN to solve the TSP. Then, we study the contrast between Hopfield Neural Network and DRNN on solving the TSP from theoretical study and empirical analysis.Secondly, this dissertation studies the neural network for continuous variables'optimization problems exhaustively. We aim at the portfolio optimization problem, because it has practical meaning. In order to solve this problem, we must forecast security returns first. We use RBF Neural Network to estimate the price, because RBF Neural Network has good ability of function approximation. Then, according to the expected security returns which have been estimated, we introduce Deterministic Annealing Neural Network to find the optimal portfolio weights and make the risk minimum. Then, we use this method to analyze the securities business in China. The result shows that this method is effect.