![]() ![]() When applied to engineering design, an analogy is made between energy and the objective function. By examining this equation we should note two things: the probability is proportional to temperature-as the solid cools, the probability gets smaller and inversely proportional to -as the change in energy is larger the probability of accepting the change gets smaller. Where k b is the Boltzmann constant and T is the current temperature. If the change in energy is positive, the new configuration has a higher energy state however, it may still be accepted according to the Boltzmann probability factor: If the change in energy is negative, the energy state of the new configuration is lower and the new configuration is accepted. The algorithm simulates a small random displacement of an atom that results in a change in energy. In 1953 Metropolis created an algorithm to simulate the annealing process. Atoms then assume a nearly globally minimum energy state. Annealing refers to heating a solid and then cooling it slowly. ![]() Simulated annealing copies a phenomenon in nature-the annealing of solids-to optimize a complex system. ![]()
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December 2022
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