Evolution strategy algorithms are nature-inspired methods. The differential evolution (DE) algorithm is stochastic population-based. The differential evolution strategy consists of subsequent recombination of solutions. Operators such as crossover, mutation, and selection change the composition and the performances of the population. This method for solving SOO problems was extended to MOO problems. In this case, more properties were required, such as promoting the diversity of solutions and performing elitism. Contrary to other genetic algorithms, DE algorithm relies on the mutation operation, rather than crossover operation. DE algorithm is implemented in Mathematica® software among other numerical methods for single-objective optimization problems. Two examples illustrate the computations with Mathematica®, the bivariate Rosenbrock’s test function, and a highly multimodal test function drawn from Mathematica®. Test function ZDT6 shows the application of DE algorithm for solving a multi-objective optimization problem with three decision variables and two objectives.
Keywords: Crowding distance, Differential evolution, DE algorithm, Diversity promoting, Elitism, External archive, Fitness sharing, Genetic operators, Mathematica®, Multimodal test function, Primary vector, Recombination, Rosenbrock’s test function, Selection procedure, Target vector, Trial vector, Weighted difference, ZDT6 test function.