Chaotic simulated annealing with augmented Lagrange for solving combinatorial optimization problems

Recent reports show that chaotic simulated annealing (CSA) can be successfully used to find the global optimum or near optimum with a set of parameters carefully chosen. However, CSA still user a penalty term to enforce solution validity us in the Hopfeld-Tank approach. This penalty method exhibits a conflict between solution quality and solution validity in the penalty approach. In addition, the relative magnitude of the penalty term often needs to be determined by trial-and-error. To overcome this disadvantage, we proposed a method which we call augmented Lagrange chaotic simulated annealing (AL-CSA). Simulation results on 48-city Traveling Salesman Problem (TSP) show that this method can maintain CSA's good solution quality while avoiding the need of penalty terms. Furthermore, convergence tame is shorter compared to CSA. The influence of Lagrange multipliers on the process of searching for global minimum is also demonstrated.