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.

解决多目标混合整数非线性规划 (MO-MINLP) 问题是许多研究人员的兴趣点，因为它们出现在多个实际应用中，尤其是在机械工程领域。许多研究人员提出使用具有单目标分支定界的元启发式混合算法。其他人建议使用具有多标准分支定界 (MCBB) 的启发式方法。基于MCBB和非支配排序遗传算法2（NSGAII）提出了一种通用混合方法来增强MO-MINLP问题的近似Pareto前沿。提出了一个基于统计评估的计算实验，以使用文献中众所周知的指标来比较所提出算法 (BnB-NSGAII) 与 NSGAII 的性能。为了评估计算效率，一个新的指标，投资比率（IR），建议将解决方案的质量与所消耗的努力联系起来。五个现实世界机械工程问题和两个数学问题的实验结果表明，BnB-NSGAII 可以成为解决 MO-MINLP 问题的竞争选择。