Deb, K., Pratap, A., Agarwal, S., & Meyarivan, T. A. M. T. (2002). 
A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE 
transactions on evolutionary computation, 6(2), 182-197.

Abstract
Multi-objective evolutionary algorithms (MOEAs) that use non-dominated 
sorting and sharing have been criticized mainly for: (1) their O(MN/sup 3/) 
computational complexity (where M is the number of objectives and N is 
the population size); (2) their non-elitism approach; and (3) the need 
to specify a sharing parameter. In this paper, we suggest a non-dominated 
sorting-based MOEA, called NSGA-II (Non-dominated Sorting Genetic Algorithm 
II), which alleviates all of the above three difficulties. Specifically, 
a fast non-dominated sorting approach with O(MN/sup 2/) computational 
complexity is presented. Also, a selection operator is presented that 
creates a mating pool by combining the parent and offspring populations 
and selecting the best N solutions (with respect to fitness and spread). 
Simulation results on difficult test problems show that NSGA-II is able, 
for most problems, to find a much better spread of solutions and better 
convergence near the true Pareto-optimal front compared to the Pareto-
archived evolution strategy and the strength-Pareto evolutionary algorithm - 
two other elitist MOEAs that pay special attention to creating a diverse 
Pareto-optimal front. Moreover, we modify the definition of dominance in 
order to solve constrained multi-objective problems efficiently. 
Simulation results of the constrained NSGA-II on a number of test problems, 
including a five-objective, seven-constraint nonlinear problem, are compared 
with another constrained multi-objective optimizer, and the much better 
performance of NSGA-II is observed.