Investigation on the choice of the initial temperature in the Simulated Annealing: A mushy state SA for TSP

It is a long time that the Simulated Annealing (SA) procedure is introduced as a non-derivative based optimization for solving NP-hard problems. Improvements from the original algorithm in the recent decade mostly concentrate on combining its initial algorithm with some heuristic methods. This is while modifications to the method are rarely happened to the initial conditions from which the annealing schedule starts. There are several parameters in the process of annealing the adjustment of which affects the overall performance. This paper focuses on the initial temperature and proposes a lower temperature with low energy to speed up the process. Such an annealing indeed starts from a mushy state rather than a quite liquid molten material. The mushy state characteristics depends on the problem that SA is being applied to solve. In this paper the Mushy State Simulated Annealing (MSSA) is applied to the Traveling Salesman Problem (TSP). The mushy state may be obtained by some simple methods like crossover elimination. A very fast version of The Wise Experiencing Traveling Salesman is also applied to initiate SA by a low-energy-low-temperature state. This fast method results in quite accurate solutions compared to other recent novel methods.