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.
