中文摘要：

考虑到智能算法对各类饲料配方优化模型的广泛适用性，首次将人工鱼群算法（AFSA）应用于饲料配方优化。为满足饲料配方优化对收敛精度的要求，采用了一种基于共生系统的人工鱼群算法运行框架，显著提高了原算法的收敛精度与速度。在优化过程中，人工鱼在解空间的位置直接以饲料配比进行编码，采取基于罚函数的评价函数计算其适应度；人工鱼以预定的行为策略执行各行为算子对解空间进行搜索。最后三个实际算例验证了所提算法的有效性。验证结果表明，所提算法设计出的饲料配比方案的吨成本显著降低，各项营养达标，提出算法的优化性能明显优于其他已有算法。

英文摘要：

In consideration of intelligence algorithms＇ extensive applicability to various types of feed formulation optimization models, the Artificial Fish Swarm Algorithm （AFSA） was firstly applied in feed formulation optimization. For meeting the required precision of feed formulation optimization, a symbiotic system-based AFSA was employed, which significantly improved the convergence accuracy and speed compared with the original AFSA. In the process of optimization, the positions of Artificial Fish （AF） individuals in solution space were directly coded as the form of solution vector to the problem via the feed ratio, a penalty-based objective function was employed to evaluate AF individuals＇ fitness. AF individuals performed several behavior operators to explore the solution space according to a predefined behavioral strategy. The validity of the proposed algorithm was verified on three practical instances. The verification results show that, the proposed algorithm has worked out the optimal feed formulation, which can not only remarkably reduce the fodder cost, but also satisfy various nutrition constraints. The optimal performance of the proposed algorithm is superior to the other existing algorithms.