  The present study proposes a multi-objective framework for structure
selection of nonlinear systems which are represented by polynomial NARX models.
This framework integrates the key components of Multi-Criteria Decision Making
(MCDM) which include preference handling, Multi-Objective Evolutionary
Algorithms (MOEAs) and a posteriori selection. To this end, three well-known
MOEAs such as NSGA-II, SPEA-II and MOEA/D are thoroughly investigated to
determine if there exists any significant difference in their search
performance. The sensitivity of all these MOEAs to various qualitative and
quantitative parameters, such as the choice of recombination mechanism,
crossover and mutation probabilities, is also studied. These issues are
critically analyzed considering seven discrete-time and a continuous-time
benchmark nonlinear system as well as a practical case study of non-linear
wave-force modeling. The results of this investigation demonstrate that MOEAs
can be tailored to determine the correct structure of nonlinear systems.
Further, it has been established through frequency domain analysis that it is
possible to identify multiple valid discrete-time models for continuous-time
systems. A rigorous statistical analysis of MOEAs via performance sweet spots
in the parameter space convincingly demonstrates that these algorithms are
robust over a wide range of control parameters.
