Annealed Differential Evolution

Differential evolution (DE) has recently emerged as a leading methodology for global search and optimization over continuous, high-dimensional spaces. It has been successfully applied to a wide variety of nearly intractable engineering problems. However, the DE and its variants usually employ a deterministic selection mechanism that always allows the better solution to survive to the next generation. This often prevents DE from escaping local optima at the early stages of search over a multi-modal fitness landscape and leads to a premature convergence. The present work proposes to improve the accuracy and convergence speed of DE by introducing a stochastic selection mechanism. The idea of a conditional acceptance function (that allows accepting inferior solutions with a gradually decaying probability) is borrowed from the realm of the simulated annealing (SA). In addition, the work proposes a center of mass based mutation operator and a decreasing crossover rate in DE. Performance of the resulting hybrid algorithm has been compared with three state-of-the-art adaptive DE schemes. The method is shown to be statistically significantly better on a six-function test-bed and one difficult engineering optimization problem with respect to the following performance measures: solution quality, time to find the solution, frequency of finding the solution, and scalability.