# A Branch and Bound Based on NSGAII Algorithm for Multi-Objective Mixed Integer Non Linear Optimization Problems

arXiv: https://arxiv.org/abs/2012.00115 · HTML: https://mlsanity.com/paper/2012.00115/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Nov 2020.

## Built on by (most cited first, 1 of 1)

- [Data-Driven Differential Evolution in Tire Industry Extrusion: Leveraging Surrogate Models](https://mlsanity.com/paper/2507.11191/) (2025)

## Abstract (arXiv)

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.