An estimation of parameters in an energy function used in a simulated annealing method

When a combinatorial optimization problem such as the traveling salesman problem is solved by a simulated annealing method, it is common to use an energy function that consists of two kinds of terms: a cost term which should be minimized and a constraint term which expresses constraints imposed on solutions. The author proposes a method for determining appropriate values of weights of constraint terms in the annealing process. If appropriate values of parameters expressing the weights of the constraint terms are not given, only solutions which do not satisfy all constraints, or high-cost solutions, can be found. A method is presented that leads to appropriate values of these parameters and finds an optimal solution in a systematic manner. The method was applied to 10-city traveling salesman problems, and the experiments showed the effectiveness of the method.>