目录
- 1.背景
- 2.算法原理
- 2.1算法思想
- 2.2算法过程
- 3.结果展示
- 4.参考文献
- 5.代码获取
1.背景
2024年，A Bouaouda受到自然界中花斑翠鸟社会行为启发，提出了花斑翠鸟优化算法（Pied Kingfisher Optimizer, PKO）。
2.算法原理
2.1算法思想
PKO的灵感来自于自然界中斑翠鸟的狩猎行为和共生关系，其包括三个阶段：栖息和悬停，潜水策略，共生阶段。
2.2算法过程
栖息和悬停策略
PKO的探索阶段灵感来自于花斑翠鸟的栖息和悬停行为，位置更新：
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(1)
X_i(\mathfrak{t}+\mathfrak{l})=X_i(\mathfrak{t})+\alpha*T\times(X_j(\mathfrak{t})-X_i(\mathfrak{t}))\tag{1}
Xi(t+l)=Xi(t)+α∗T×(Xj(t)−Xi(t))(1)
栖息时参数T表述为:
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T=\left(\exp(1)-\exp\biggl(\frac{t-1}{\textit{Max\_Iter}}\biggr)^{\frac{1}{\text{BF}}}\biggr)*\cos(\textit{Crest\_angles})\right. \tag{2}
T=(exp(1)−exp(Max_Itert−1)BF1)∗cos(Crest_angles)(2)
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Crest \_angles = 2*pi* rand\tag{3}
Crest_angles=2∗pi∗rand(3)
悬停时参数T表述为:
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T=beating\_rate*\left(\frac{t^{\frac{1}{BF}}}{Max\_Iter^{\frac{1}{BF}}}\right)\tag{4}
T=beating_rate∗(Max_IterBF1tBF1)(4)
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beating\_rate=rand*\left(\frac{PKO\_Fitness(j)}{PKO\_Fitness(i)}\right)\tag{5}
beating_rate=rand∗(PKO_Fitness(i)PKO_Fitness(j))(5)
潜水策略
斑翠鸟以其潜水行为而闻名，它用这种行为来捕鱼:
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(6)
\begin{gathered}X_i(\mathfrak{t}+1)=X_i(\mathfrak{t})+HA*o*\alpha*(b-X_{best}(\mathfrak{t})),\quad i=1,2,\ldots,N\end{gathered}\tag{6}
Xi(t+1)=Xi(t)+HA∗o∗α∗(b−Xbest(t)),i=1,2,…,N(6)
参数表述为:
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\begin{aligned} &HA=rand*\left(\frac{PKO\_Fitness(i)}{Best\_Fitness}\right) \\ &o=\exp\left(\frac{-t}{Max\_Iter}\right)^{2} \\ &b=X_{i}(\mathrm{t})+o^{2}*randn*X_{best}(\mathrm{t}) \end{aligned}\tag{7}
HA=rand∗(Best_FitnessPKO_Fitness(i))o=exp(Max_Iter−t)2b=Xi(t)+o2∗randn∗Xbest(t)(7)
共生阶段
斑翠鸟的捕食效率会受到多种因素的影响，比如猎物的可用性、单个鸟的捕猎技巧以及该地区竞争对手或捕食者的存在。
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(8)
\left.X_i(\mathbf{t}+1)=\left\{\begin{matrix}X_m(\mathbf{t})+o*\alpha*abs(X_i(\mathbf{t})-X_n(\mathbf{t}))&if\quad rand>(1-PE)\\X_i(\mathbf{t})&otherwise\end{matrix}\right.\right.\tag{8}
Xi(t+1)={Xm(t)+o∗α∗abs(Xi(t)−Xn(t))Xi(t)ifrand>(1−PE)otherwise(8)
伪代码
3.结果展示
4.参考文献
[1] Bouaouda A, Hashim F A, Sayouti Y, et al. Pied kingfisher optimizer: a new bio-inspired algorithm for solving numerical optimization and industrial engineering problems[J]. Neural Computing and Applications, 2024: 1-59.
5.代码获取
免费获取花斑翠鸟优化算法（PKO）
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资源清单：https://docs.qq.com/sheet/DU1V0QWtSeHJnY0JU?u=989d90f9b14449ec9419aa7b51473c1b&tab=BB08J2
