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

TL;DR

This paper introduces a hybrid algorithm combining branch-and-bound and NSGAII to effectively approximate Pareto fronts for complex multi-objective mixed-integer nonlinear problems, demonstrating competitive performance on real-world and mathematical benchmarks.

Contribution

The paper presents a novel hybrid approach integrating MCBB and NSGAII, along with a new metric IR, for better solving MO-MINLPs.

Findings

BnB-NSGAII outperforms standard NSGAII in experiments.

The new IR metric effectively measures solution quality relative to effort.

Algorithm shows promise on real-world mechanical engineering problems.

Abstract

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.