**3. Simulated annealing**

SA resembles the cooling process of molten metal through annealing (slow cooling process). At high temperature (*T*), the atoms in the molten metal can move freely with respect to each other, but as the temperature is reduced, the movement of the atoms gets restricted. The atoms start to get arranged and finally form crystals having the minimum possible energy which depends on the cooling rate. If the temperature is reduced at a very fast rate, the crystalline state may not be achieved at all and, instead, the system may end up in a polycrystalline state, which may have a higher energy state than the crystalline state. Therefore, in order to achieve the absolute minimum energy state, the temperature should be reduced at a slow rate [16].

From the optimization point of view, this physical process is analogous to the determination of near-global or global optimum solutions. The energy of the atoms represents the objective function and the final ground state corresponds to the global minimum of the objective function. The analogy between the physical system and the optimization problem is shown in Table 1 [17].


**Table 1.** Analogy between simulated annealing and optimization.

The basic steps of canonical SA are presented in Figure 2 and described in the following subsections [18].

**Figure 2.** Simulated Annealing algorithm flowchart (*NI* is the number of iterations).
