The extension of genetic search algorithms to MOO problems requires new
concepts, such as Pareto domination ranking and fitness sharing. The goal is to
maintain the diversity in the population of solutions through successive generations.
Niching methods were introduced to reduce the effect of “random genetic drift,” and to
preserve the genetic diversity of optimal solutions. The NPGA algorithm illustrates this
approach with application to the Binh-Korn test function. The software NSGA-II can
handle real-world complex constrained MOO problems. This software package is a fast
and elitist algorithm sorting the population of parents and offspring on different ranked
fronts. A non-domination order relation prevails. An elitist search procedure guarantees
the diversity and spread of solutions. The constraint handling method differs from the
conventional methods by using a modified definition of dominance rather than penalty
parameters. NSGA-II can solve several test functions. These applications are
unconstrained test functions such as ZDT1, UF1, Kursawe and Viennet, and
constrained test functions such as SRN, Deb, and Tanaka. For these problems, we
decided to illustrate the progression of calculation at the different steps of the iteration
path.
Keywords: Crowded-comparison operator, Crowding distance, Elitist search
procedure, Kursawe’s test function, MOEA Framework, NPGA software, Niching
methods, Niche radius, NSGA-II software, Ranking process, Pareto domination
ranking, SciLab software, Selection operator, Sharing function, SRN test problem,
Tournament competition, Tanaka’s test function, UF1 test function, Viennet’s test
function.
