1 BACKGROUND 1.1 Combinatorial optimization and NP-Hard problem 1.2 Traditional methods for combinatorial optimization 1.2.1 Local search 1.2.2 Genetic algorithm 1.2.3 Tabu search 1.2.4 Simulated annealing 1.3 Themes and contributions of the book 2 ARTIFICIAL NEURAL NETWORK 2.1 Biological neural network to artificial neural network 2.2 History of artificial neural network 2.3 Methods of neural networks 2.3.1 Hopfield neural network 2.3.2 Self-organizing map 2.3.3 Maximum neural network 2.3.4 Elastic net 2.4 Problems of neural network 3 IMPROVED HOPFIELD-TYPE NN WITH CHAOTIC DYNAMICS FOR MCP 3.1 Maximum clique problem 3.2 The analysis of HNN with chaotic dynamics 3.2.1 Chaotic neural networks 3.2.2 Transiently chaotic neural network 3.2.3 Relationship between TCNN and CNN 3.2.4 Analysis of parameter selection 3.3 A flexible TCNN for MCP 3.3.1 The flexible annealing strategy 3.3.2 Flexible TCNN and its dynamic analysis 3.3.3 Simulations 3.4 TCNN with filter method for MCP 3.4.1 Analysis on feasibility and adaptivity of TCNN 3.4.2 Algorithm description 3.4.3 Simulations 3.5 Delayed TCNN and its application on MCP 3.5.1 The flaw of variable delayed model 3.5.2 The delayed transiently chaotic neural network 3.5.3 Simulation 3.6 Summary 4 IMPROVED CHAOTIC MNN FOR COPS 4.1 Chaotic maximum neural network 4.2 Improved CMNN with stochastic dynamics for N-Queens 4.2.1 N-Queens problems 4.2.2 Dynamics analysis and Improvement of the CMNN with stochastic dynamics for N-Queens problems 4.2.3 Algorithm description 4.2.4 Simulations 4.3 Chaotic MNN with flexible annealing strategy for MCP 4.3.1 Improved algorithm and its dynamics analysis 4.3.2 Simulations 4.4 Summary 5 IMPROVED ELASTIC NET FOR TRAVELING SAI-ESMAN PROBLEM 5.1 Elastic net for TSP 5.2 Efficiency analysis on elastic net 5.3 The improved algorithms based on Elastic Net 5.3.1 Rebuilt clone elastic net algorithm 5.3.2 The unsupervised up-to-bottom hierarchical clustering elas. tic net algorithm 5.3.3 Simulation 5.4 Summary 6 SUMMARY AND FUTURE WORK 6.1 Summary of this book 6.2 Future work BIBLIOGRAPHY