A branch-and-bound algorithm based on NSGAII for multi-objective mixed integer nonlinear optimization problems

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