Abstract：
Water pollution escalates with rising waste discharge in river systems, as the rivers\' limited pollution tolerance and constrained self-cleaning capacity compel the release of treated pollutants. Although several studies have shown that the non-dominated sorting genetic algorithm-II (NSGA-II) is an effective algorithm regarding the management of river water quality to reach water quality standards, to our knowledge, the literature lacks using a new optimization model, namely, the multi-objective cuckoo optimization algorithm (MOCOA). Therefore, this research introduces a new optimization framework, including non-dominated sorting and ranking selection using the comparison operator densely populated towards the best Pareto front and a trade-off estimation between the goals of discharges and environmental protection authorities. The suggested algorithm is implemented for a waste load allocation issue in Jajrood River, located in the North of Iran. The limitation of this research is that discharges are point sources. To analyze the performance of the new optimization algorithm, the simulation model is linked with a hybrid optimization model using a cuckoo optimization algorithm and non-dominated sorting genetic algorithms to convert a single-objective algorithm to a multi-objective algorithm. The findings indicate that, in terms of violation index and inequity values, MOCOA\'s Pareto front is superior to NSGA-II, which highlights the MOCOA\'s effectiveness in waste load allocation. For instance, with identical population sizes and violation indexes for both algorithms, the optimal Pareto front ranges from 1.31 to 2.36 for NSGA-II and 0.379 to 2.28 for MOCOA. This suggests that MOCOA achieves a superior Pareto front in a more efficient timeframe. Additionally, MOCOA can attain optimal equity in the smaller population size.
摘要：
水污染随着河流系统中废物排放的增加而升级，由于河流有限的污染耐受性和有限的自清洁能力迫使处理后的污染物释放。尽管一些研究表明，非支配排序遗传算法-II（NSGA-II）是关于河流水质管理以达到水质标准的有效算法，根据我们的知识，文献缺乏使用新的优化模型，即,多目标布谷鸟优化算法(MOCOA)。因此,本研究引入了一个新的优化框架，包括非主导排序和排名选择，使用比较运算符密集地朝向最佳帕累托前沿，以及排放目标和环境保护当局之间的权衡估计。建议的算法是针对JajroodRiver中的废物负荷分配问题实现的，位于伊朗北部。这项研究的局限性在于放电是点源。为了分析新优化算法的性能,仿真模型与使用布谷鸟优化算法和非支配排序遗传算法的混合优化模型链接，将单目标算法转换为多目标算法。研究结果表明,在违规指数和不公平值方面，MOCOA的帕累托战线优于NSGA-II，这突出了MOCOA在废物负荷分配中的有效性。例如,两种算法的种群大小和违规指数相同，NSGA-II的最佳帕累托前沿范围为1.31至2.36，MOCOA的最佳帕累托前沿范围为0.379至2.28。这表明MOCOA在更有效的时间范围内实现了卓越的帕累托前沿。此外,MOCOA可以在较小的人口规模中获得最佳公平性。
