Explicit Control of Diversity in Differential Evolution

One of the issues that might affect the performance of Differential Evolution (DE) is premature convergence. In such cases, and especially in long-term executions, due to the nature of the reproduction phase of DE, computational resources might not be employed efficiently. In DE this issue is usually tackled by altering the reproduction phase or by attaching an external archive. However, in other fields such as in combinatorial optimization, methods that amend the replacement phase have been very successful. In this paper, two variants of DE are extended by including a replacement phase that explicitly relates the amount of diversity maintained in the population with the number of generations evolved and with the stopping criterion. One of the variants is the classic DE/rand/1/bin whereas the other one is Success-History based Adaptive DE (SHADE), a state-of-the-art approach. In the case of the classic variant, the principles employed in combinatorial optimization could be used straightforwardly. However, when integrating it with state-of-theart techniques that already incorporate mechanisms to preserve diversity, additional modifications were required. Experimental validation has been performed with the benchmarks provided for the 2013 IEEE Congress on Evolutionary Computation competition on real parameter optimization. The results of the best-ranked DE in such a competition could be improved further. Additionally, some problems that had not been solved to optimality ever by any proposal, could be successfully solved.