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

Abstract

Solving Multi-Objective Mixed Integer NonLinear Programming (MO-MINLP) problems is a point of interest for many researchers as they appear in several real-world applications, especially in the mechanical engineering field. Many researchers have proposed using hybrids of metaheuristics with mono-objective branch and bound. Others have suggested using heuristics with Multi-Criteria Branch and Bound (MCBB). A general hybrid approach is proposed based on MCBB and Non-dominated Sorting Genetic Algorithm 2 (NSGAII) to enhance the approximated Pareto front of MO-MINLP problems. A computational experiment based on statistical assessment is presented to compare the performance of the proposed algorithm (BnB-NSGAII) with NSGAII using well-known metrics from the literature. To evaluate the computational efficiency, a new metric, the Investment Ratio (IR), is proposed that relates the quality of solution to the consumed effort. Experimental results on five real-world mechanical engineering problems and two mathematical ones indicate that BnB-NSGAII could be a competitive alternative for solving MO-MINLP problems.

Keywords:

• Multi-criteria
• branch-and-bound algorithm
• NSGAII
• MINLP problems
• mixed variables

Acknowledgements

The majority of the numerical experiments were performed on resources provided by the University of Technology of Troyes (UTT).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Lebanese University (LU) (Université Libanaise); the regional council of the ‘Grand Est’ (Conseil régional du Grand Est) region, France; and the European Regional Development Fund (ERDF).