  Multi-Objective Mixed-Integer Non-Linear Programming problems (MO-MINLPs)
appear in several real-world applications, especially in the mechanical
engineering field. To determine a good approximated Pareto front for this type
of problems, we propose a general hybrid approach based on a Multi-Criteria
Branch-and-Bound (MCBB) and Non-dominated Sorting Genetic Algorithm 2 (NSGAII).
We present a computational experiment based on a statistical assessment to
compare the performance of the proposed algorithm (BnB-NSGAII) with NSGAII
using well-known metrics from literature. We propose a new metric, Investment
Ratio (IR), that relate the quality of the solution to the consumed effort. We
consider five real-world mechanical engineering problems and two mathematical
ones to be used as test problems in this experiment. Experimental results
indicate that BnB-NSGAII could be a competitive alternative for solving
MO-MINLPs.
