NSGA-Ⅱ和NSGA-Ⅲ应用于换热网络多目标优化的对比

针对换热网络多目标优化问题，采用目前应用较广泛的两种多目标遗传算法，即NSGA-Ⅱ和NSGA-Ⅲ，对两种算法的性能进行对比研究。案例研究结果表明，NSGA-Ⅱ算法比NSGA-Ⅲ算法运行效率更高，NSGA-Ⅲ的运行时间是NSGA-Ⅱ的2倍以上；NSGA-Ⅱ算法的应用并不严格地受限于3个目标的最大目标数量，NSGA-Ⅱ在求解大于3个目标的多目标优化问题时也可能具有良好的性能，目标数量并非选择NSGA-Ⅱ和NSGA-Ⅲ算法的严格标准。对10×5换热网络案例进行4个相关目标改造优化时，从换热网络的单一性能指标来看，NSGA-Ⅱ算法更容易获得各目标的极值。从最小年度总费用的评价指标来看，两种算法的最优方案效果相近。对7×3换热网络案例进行6个目标的优化时，NSGA-Ⅲ算法得到各目标的极值较优。从最小年度总费用的评价指标来看，NSGA-Ⅲ算法获得的投资费用和年度总费用更小。对于目标函数数量不超过3个，或者3个以上具有一定相关性的多目标优化问题，推荐优先使用NSGA-Ⅱ算法实现快速寻优；而NSGA-Ⅲ算法由于其基于参考点的选择机制，运行效率较慢，更适合用于收敛困难的高维多目标优化问题。

Comparative study of NSGA-Ⅱ and NSGA-Ⅲ on multi-objective optimization of heat exchanger network

For the widely used multi-objective genetic algorithms, NSGA-Ⅱ and NSGA-Ⅲ, this paper combines the specific heat exchanger network retrofit problems to compare the performance of the two algorithms. The case study results showed that the NSGA-Ⅱ is more efficient than the NSGA-Ⅲ, especially under the condition of large population, and the running time of NSGA-Ⅲ is above 2 times that of NSGA-Ⅱ. The application of NSGA-Ⅱ algorithm is not strictly limited by the maximum target number of three. NSGA-Ⅱ may also have good performance when solving multi-objective optimization problems with more than 3 targets. The number of targets is not the strict standard of selecting NSGA-Ⅱ or NSGA-Ⅲ algorithm. The NSGA-Ⅱ algorithm is more likely to obtain the extreme value of each target from the single performance index of the heat exchanger network in the 10H×5C heat exchanger network case including four related targets. From the index of the minimum total annual cost, the optimal schemes of the two algorithms are similar. In the 7H×3C heat exchanger network optimization including six targets, the NSGA-Ⅲ algorithm obtains better target extreme values. From the index of the minimum annual cost， the capital cost and annual total cost by the NSGA-Ⅲ algorithm are smaller. Therefore, for multi-objective optimization problems with no more than 3 objective functions or more than 3 related objective functions, it is recommended to use the NSGA-Ⅱ algorithm to achieve fast optimization. The NSGA-Ⅲ algorithm is based on the reference point-based selection mechanism, so its calculation efficiency is slower, and it is more suitable for high-dimensional multi-objective optimization problems with difficulty in convergence.