**4. Mixed simulated annealing**

By overcoming the mentioned shortcoming, we proposed a mixed simulated annealing (MSA) to speed up traditional simulated annealing (SA) and 2-stage SA. The basic idea is to improve the global search ability and to speed up the search process by a special crossover operator, which uses the information of past solutions. Just like SA and 2-stage SA, MSA is an iterative improvement method and a stochastic algorithm. The main difference between 2-stage SA and MSA is the special crossover operator to use a part of configuration of the current best and to reduce the informational waste. Although we can get a rough solution by producing solutions randomly, it is with low improving efficiency. The proposed crossover operator has a search direction, which is based on the configuration from past good solutions, to get high improving efficiency.

The intuitive comparison shows several intuitive advantage of MSA comparing with traditional SA and 2-stage SA. For global search ability, 2-stage SA is better than traditional SA due to big changes in the first stage, and MSA is even better than 2-stage SA due to the crossover operator and even bigger changes in the first stage. Traditional SA and 2-stage SA do not use past experience, while MSA is using past good solutions by using the crossover operator.
