Simulated Annealing Genetic Algorithm

The simulated annealing genetic algorithm is integrated into the running process of the simulated annealing algorithm, which is called the simulated annealing genetic algorithm.
Simulated Annealing AlgorithmIt is a heuristic random search algorithm based on the Monte Carlo iterative solution, it simulates the similarity between the heat balance problem in the annealing process of solids and the random search optimization problem to find the global optimal or approximate global optimal. In the process of searching for the optimal solution, in addition to the acceptable optimization solution, the simulated annealing method also has a random acceptance criterion (Metropolis criterion) that limits the acceptance of the deteriorating solution, in addition, the probability of accepting deteriorating solutions gradually tends to 0, which makes it possible for the algorithm to jump out of the local extreme region, that is, it may find the global optimal solution and ensure the convergence of the algorithm.
The process of solving the simulated annealing algorithm is as follows:
(1) random generation of the initial solution x0;
(2) initialize the annealing temperature T0;
(3) perform the following operations under temperature Tk:
· Generate a new neighborhood for the feasible solution X' and X' for the adjacent solution x;
· The difference between the calculation evaluation functions F (x') and F (x) △f = f (x')-f (x );
· New solutions are received with the probability of min {1, exp (-△f/tk)}> random [], where random [] is a random number. If the equilibrium state of temperature Tk is reached (4), otherwise (3 );
(4) reduce the temperature in a certain way. The Descent function can be defined as TK + 1 = α TK, k + 1 →, where α in [0, 1];
(5) If the convergence criterion is met, the annealing process ends; otherwise, the conversion is performed (3 ).
According to the above analysis, during the simulated annealing process, the annealing temperature controls the Optimization Direction of the solution to the minimum value, and it also uses the probability exp (-△f/tk) therefore, the algorithm can jump out of the local Extreme Point. As long as the initial temperature is high enough and the annealing process is slow enough, the algorithm can converge to the global optimal solution.