标题： 基于NSGAII算法的多目标混合整数非线性优化问题的分支定界方法 显示英文标题

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

摘要： 多目标混合整数非线性规划问题（MO-MINLPs）出现在多个现实世界的应用中，特别是在机械工程领域。 为了确定此类问题的良好近似帕累托前沿，我们提出了一种基于多准则分支定界（MCBB）和非支配排序遗传算法2（NSGAII）的通用混合方法。 我们基于统计评估进行计算实验，使用文献中的已知度量来比较所提出的算法（BnB-NSGAII）与NSGAII的性能。 我们提出了一种新的度量标准，投资比率（IR），它将解决方案的质量与消耗的努力联系起来。 我们考虑了五个现实世界的机械工程问题和两个数学问题作为该实验中的测试问题。 实验结果表明，BnB-NSGAII可能是解决MO-MINLPs的一种有竞争力的替代方法。 显示英文摘要

摘要： 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.