基于遗传算法的土地利用优化：NSGA-Ⅱ和NSGA-Ⅲ的对比研究

土地利用优化通常要兼顾不同群体的多种要求，理论上是复杂的超多目标(4个及以上)优化问题。但实际操作中却往往被简化为多目标(2—3个)优化问题，通过一种流行的多目标优化算法第Ⅱ代非支配排序遗传算法(NSGA-Ⅱ)求解。究其原因是对超多目标优化算法认知的缺失和与多目标优化算法理论对比的匮乏。对NSGA系列中应用最广泛的多目标优化算法NSGA-Ⅱ和最新提出、面向超多目标优化的算法NSGA-Ⅲ进行探究，从理论和实验两方面对Ⅲ和Ⅱ进行对比，从而探究二者进行土地利用优化时的优劣。在理论上，对比两种算法原理的异同。在实验中，分别设计多目标(3个目标)和超多目标(13个目标)土地利用优化问题，利用两种算法进行求解。对实验结果采用四层架构、六大指标进行全面评价，以对比两种算法的可用性。理论对比发现，两个算法只有种群多样性保护的方法不同，其中NSGA-Ⅲ是基于与固定的参考点的距离，而NSGA-Ⅱ则是基于相邻解间的距离。通过实验对比发现，NSGA-Ⅲ在超多目标优化时运算速度快，且产生的最优方案实用价值更高，NSGA-Ⅱ在算法的有效性方面更有优势。

Land-use optimization based on genetic algorithm: A comparison between NSGA-II and NSGA-III

Land use optimization usually considers the various requirements of different groups, and is a complex many-objective (more than 3 objectives) problem in theory. However, it is usually simplified as a multi-objective (2-3 objectives) problem in practice and solved using a popular multi-objective optimization algorithm, nondominated sorting genetic algorithm-II (NSGA-II). The reasons behind this fact include the lack of cognition of many-objective optimization algorithms and the lack of effectiveness comparison between many- and multi-objective optimization algorithms. This paper explored NSGA-II, which is one of the most widespread multi-objective optimizations, and a many-objective optimization algorithm, namely NSGA-III, which is the latest version of NSGA series. We made an effectiveness comparison between NSGA-III and NSGA-II theoretically and experimentally, to explore the advantages and disadvantages of these two algorithms in land-use optimization. In theory, the principles of the two algorithms were compared. The experimental comparison includes two experiments, a three-objective land use optimization and a thirteen-objective land use optimization taking Lhasa as the research area. After the experiments, a four-layer framework with six indicators was used to evaluate algorithms comprehensively. The theoretical comparison results showed that the only difference between the two algorithms lied in the determination of population diversity. Specifically, NSGA-III employed the distances between solutions and reference points, while NSGA-II utilized the distances between adjacent solutions. The determination of population diversity in NSGA-III was easier to achieve global diversity and avoided the situation of local diversity but global compactness. The determination of population diversity in NSGA-II was greatly affected by the dimension. When the dimension increased, the calculation was cumbersome, time-consuming, and slows down the search process. The experimental comparison showed that the two algorithms had their own advantages in different indicators. Compared with NSGA-II, in multi-objective optimization, NSGA-III had advantages in terms of the quality of the results and the degree of optimization, and with the increase of the objective function, NSGA-III will occupy less computational time than NSGA-II, and the effect of population diversity protection was also improving. According to the comparison of the optimal individuals obtained from two algorithms, the optimal individuals generated by NSGA-III were higher than NSGA-II in terms of practical value. Therefore, the NSGA-III algorithm had great potential in the field of land use optimization and could provide more valuable references for planners. The results of this paper can assist empirical research and provide a reference for designing a more comprehensive and more realistic land use optimization model.