基于三维空间关于海豚围捕沙丁鱼群的运动规律

Movement Law of Sardines around the Dolphins Based on Three-Dimensional Space

摘要:

生物学家Craig Reynolds在1987年提出了一个非常有影响的鸟群聚集模型并由此我们可以总结出离散集群的四个运动原则：避免碰撞，速度匹配，中心聚集，惯性因素。在这个研究中粒子群优化(pos)初始化为一群随机粒子，然后通过迭代找到最优解，在每一次迭代中，粒子通过跟踪两个极值来更新自己。所以在本题目中，根据集群的四个运动原则对各个方向求取加权，建立个体运动方向的数据模型由此可对运动状态进行迭代更新。V_t+1=λ₁V_1t+λ₂V_2t+λ₃V_3t+λ₄V_4t+λ₅V_5t λ₁+λ₂+λ₃+λ₄+λ₅=1其中V_5t=arctan y₀-y_5t/x₀-x_5t， 通过迭代，我们可以分析得出个体鱼游动的特点，再由个体鱼推广到海豚对个体鱼运动的影响。后根据粒子群优化算法，建立海豚个体与沙丁鱼群的初始化模型，模拟出海豚个体与沙丁鱼群的运动关系。同样的，我们查阅资料制定了海豚围捕沙丁鱼的策略：简要说就是十分讲究排兵布阵，兵分几路，一部分摆出一个口袋型的包围圈，一部分海豚充当“轰赶者”，将猎物向包围圈中驱赶，防止沙丁鱼扩散逃跑。下面结合粒子群算法和群体运动模型来实现相互配合的海豚觅食行为。设海豚在3维的目标空间搜索食物，群体规模为n，设领导者在空间中的位置x_k，运动速度v_k，领导者在空间中所搜索到的最佳食物位置记为p_k，设整个粒子群迄今为止搜索到的最优位置记为p_g，则以搜索食物的最优位置为目标，调整信息拥有者在t+1时刻的位置x_k^(t+1)和运动方向v_k^(t+1)为：

v_k^t+1=w*v_k^t+c₁r₁(p_t-x_k^t)+c₂r₂(p_g-x_k^t)

X_k^t+1=X_k^t+v_k^t+1

据此可以用粒子群优化算法对海豚间的相互配合进行分析，最后用MATLAB进行模拟，即可以进行仿真。

Abstract:

Biologists Craig Reynolds was proposed in 1987 by a very influential birds gather model and thus we can come to the conclusion of the four movement principles of discrete cluster: collision avoid-ance, speed matching, center gather, and inertia factors. In the study, the particle swarm optimization is initialized to a group of random particles, and then we find the optimal solution through iteration; in each iteration, the particles update themselves by tracking two extreme values. There-fore, according to the four movement principles of the cluster, the weights of each direction are obtained, and the data model of the individual motion direction can be set up to update the motion state. Among them, through iteration, we can analyze the characteristics of individual fish swimming, and then promote the influence of individual fish on individual fish movement. Based on the particle swarm optimization algorithm, the initializing model of individual dolphin and sardine group was established to simulate the movement relationship between individual dolphin and sardine group. In the same way, we have consulted the data to develop a strategy for dolphins to round up sardines: in brief, it is very particular about the formation of soldiers. The soldiers are divided into several ways, some of which have a pocket-shaped encirclement. Some of the dolphins act as “catch-ups”, and the prey is Drive away from the circle to prevent the sardines from spreading and fleeing. In this paper, we combine the particle swarm algorithm and the swarm motion model to realize the mating behavior of dolphins. Set up dolphins to search for food in a three-dimensional tar-get space; group size is n; suppose the leader’s position in space is x_k ; movement speed is v_k. The best food location that the leader found in space is recorded as p_g targeting the optimal location for searching for food. Adjust the position X_k^(t+1) of the information owner at t + 1 and the direction of motion v_k^(t+1):

v_k^t+1=w*v_k^t+c₁r₁(p_t-x_k^t)+c₂r₂(p_g-x_k^t)

X_k^t+1=X_k^t+v_k^t+1 According to this, the interaction between dolphins can be analyzed with particle swarm optimization algorithm, and the simulation can be carried out with MATL