Simulated annealing (SA) algorithms are capable of solving discrete and continuous problems. However, they are less efficient than other algorithms in solving applied problems because of their dependency on controlling parameters definition method. In the current work, a self-adaptive simulated annealing (SASA) method is presented based on entropy concept and thermodynamic laws in order to optimize the setting parameters. To provide a dynamic cooling rate and Markov chain length with a comparative relation to problem conditions, the proposed schedule utilizes thermodynamic concepts of entropy and ensemble average energy. In the proposed algorithm, simulation of the atomic motion is implemented based on velocity definition in thermodynamics and time definition in probabilistic processes. The SASA is evaluated by CEC2015 problem and compared with three other adaptive simulated annealing algorithms, a standard SA and four other metaheuristic methods using three different comparison criteria: Wilcoxon test, median, mean and standard deviation. The SASA has shown satisfactory outcomes in most unimodal, multimodal, and hybrid functions in CEC2015. It has proved to be more explorative, has obtained far better solutions, and has showed the best convergence speed compared with other algorithms when engaged in exploitation. Keywords Meta-heuristics · Self-adaptive optimization · Simulated annealing · Exploration and exploitation

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