Sharifi Mohammad Reza, Akbarifard Saeid, Qaderi Kourosh, Madadi Mohamad Reza
Department of Hydrology and Water Resources, Faculty of Water and Environmental Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran.
Department of Water Engineering, Faculty of Agriculture, Shahid Bahonar University of Kerman, Kerman, Iran.
Sci Rep. 2021 Oct 13;11(1):20326. doi: 10.1038/s41598-021-99617-x.
Simultaneous optimization of several competing objectives requires increasing the capability of optimization algorithms. This paper proposes the multi-objective moth swarm algorithm, for the first time, to solve various multi-objective problems. In the proposed algorithm, a new definition for pathfinder moths and moonlight was proposed to enhance the synchronization capability as well as to maintain a good spread of non-dominated solutions. In addition, the crowding-distance mechanism was employed to select the most efficient solutions within the population. This mechanism indicates the distribution of non-dominated solutions around a particular non-dominated solution. Accordingly, a set of non-dominated solutions obtained by the proposed multi-objective algorithm is kept in an archive to be used later for improving its exploratory capability. The capability of the proposed MOMSA was investigated by a set of multi-objective benchmark problems having 7 to 30 dimensions. The results were compared with three well-known meta-heuristics of multi-objective evolutionary algorithm based on decomposition (MOEA/D), Pareto envelope-based selection algorithm II (PESA-II), and multi-objective ant lion optimizer (MOALO). Four metrics of generational distance (GD), spacing (S), spread (Δ), and maximum spread (MS) were employed for comparison purposes. The qualitative and quantitative results indicated the superior performance and the higher capability of the proposed MOMSA algorithm over the other algorithms. The MOMSA algorithm with the average values of CPU time = 2771 s, GD = 0.138, S = 0.063, Δ = 1.053, and MS = 0.878 proved to be a robust and reliable model for multi-objective optimization.
同时优化多个相互竞争的目标需要提高优化算法的能力。本文首次提出了多目标蛾群算法来解决各种多目标问题。在所提出的算法中，对探路蛾和月光提出了新的定义，以增强同步能力并保持非支配解的良好分布。此外，采用拥挤距离机制在种群中选择最有效的解。该机制表明了非支配解围绕特定非支配解的分布情况。因此，通过所提出的多目标算法获得的一组非支配解被保存在一个存档中，以便稍后用于提高其探索能力。通过一组具有7到30维的多目标基准问题研究了所提出的多目标蛾群算法（MOMSA）的能力。将结果与基于分解的多目标进化算法（MOEA/D）、基于帕累托包络的选择算法II（PESA-II）和多目标蚁狮优化器（MOALO）这三种著名的元启发式算法进行了比较。使用了世代距离（GD）、间距（S）、散布（Δ）和最大散布（MS）这四个指标进行比较。定性和定量结果表明，所提出的MOMSA算法比其他算法具有更优越的性能和更高的能力。平均CPU时间为2771秒、GD为0.138、S为0.063、Δ为1.053且MS为0.878的MOMSA算法被证明是一种用于多目标优化的强大且可靠的模型。
