萤火虫算法

萤火虫算法（Firefly Algorithm）是一种启发式算法，灵感来自于萤火虫闪烁的行为。萤火虫的闪光，其主要目的是作为一个信号系统，以吸引其他的萤火虫。剑桥大学的Xin-She Yang（音译：杨新社）教授提出了萤火虫算法，其假设为： 萤火虫不分性别，这样一个萤火虫将会吸引到所有其他的萤火虫; 吸引力与它们的亮度成正比，对于任何两个萤火虫，不那么明亮的萤火虫被吸引，因此移动到更亮的一个，然而，亮度又随着其距离的增加而减少; 如果没有比一个给定的萤火虫更亮的萤火虫，它会随机移动。 亮度应与目标函数联系起来。萤火虫算法是以自然为灵感的启发式优化算法。 萤火虫算法的伪代码可以概括为： Begin 1）目标函数 f ( x ) x = ( x 1 , x 2 , . . . , x d ) T {\displaystyle f(\mathbf {x} )\quad \mathbf {x} =(x_{1},x_{2},...,x_{d})^{T}} 2）生成一个萤火虫的初始人口 x i , ( i = 1 , 2 , . . . , n ) {\displaystyle \mathbf {x} _{i},\quad (i=1,2,...,n)} 3）制定光照强度 I {\displaystyle I} ，因此，它与 f ( x ) {\displaystyle f(\mathbf {x} )} （例如，对于最大化问题 I ∝ {\displaystyle I\propto } 或 I = f ( x ) {\displaystyle I=f(\mathbf {x} )} ; 4）定义吸收系数 γ {\displaystyle \gamma } while(T < MaxGeneration) for i =1:n(所有n萤火虫) for j =1:n(n萤火虫) if( I j > I i {\displaystyle I_{j}>I_{i}} )， 移动萤火虫i向j; end if 吸引力与距离 r = exp ⁡ [ − γ r 2 ] {\displaystyle r=\exp[-\gamma r^{2}]} ; 评估新的解决方案和更新的光强度; end for j end for i 排名萤火虫和找到当前最佳; end while 处理后的结果和可视化; end 对于任何一两只萤火虫的主要更新公式 x i {\displaystyle \mathbf {x} _{i}} and x j {\displaystyle \mathbf {x} _{j}} 是 x i t + 1 = x i t + β exp ⁡ [ − γ r i j 2 ] ( x j t − x i t ) + α t ϵ t {\displaystyle \mathbf {x} _{i}^{t+1}=\mathbf {x} _{i}^{t}+\beta \exp[-\gamma r_{ij}^{2}](\mathbf {x} _{j}^{t}-\mathbf {x} _{i}^{t})+\alpha _{t}{\boldsymbol {\epsilon }}_{t}} 其中 α t {\displaystyle \alpha _{t}} 是步长参数, e ϵ t {\displaystyle {\boldsymbol {\epsilon }}_{t}} 是一个矢量（服从高斯或其他的分布）。 可以证明在 γ → 0 {\displaystyle \gamma \rightarrow 0} 的情况，FA可以简化为 准粒子群优化(PSO).事实上，，如果内环（j）条被删除，亮度 I j {\displaystyle I_{j}} 替换为当前的全球最佳 g ∗ {\displaystyle g^{*}} ，FA基本上成为标准PSO。 离散形式的萤火虫算法（Discrete Firefly Algorithm，DFA） DFA优于现有算法如蚁群算法。 对于图像分割，基于FA-方法比Otsu的方法更为有效. 同时， 离散萤火虫算法对QAP问题，Durkota已进很好的实现行 针对负荷预测中的特征选择问题，应用FA实现Wrapper特征选择算法. Apostolopoulos and Vlachos对FA进行了一个重要的多目标研究。同时，Yang提出了多目标萤火虫算法（Multiobjective Firefly Algorithm，MOFA），对连续优化问题有很好的效果。 拉格朗日萤火虫算法用来解决电力系统优化单元承诺问题。 混沌萤火虫算法（Chaotic Firefly Algorithm，CFA）也显示了算法的有效性。 萤火虫算法与蚁群优化算法相结合的混合算法，能够解决金融投资组合优化 。 一种基于萤火虫算法（FA）的Memetic算法（FA-MA）被用来优化支持向量机（SVR）预测模型的参数。在该FA-MA中，FA用来搜索全局解空间，而模式搜索（pattern Search） 被用来进行个体学习和局部解空间搜索。 萤火虫算法已被应用到几乎所有领域科学和工程，如数字图像压缩和图像处理,特征值优化,特征提取和故障检测,天线设计,工程结构设计, 调度和旅行商问题,语义组成,化学相平衡， 聚类,动态问题, 刚性图像配准问题,参数选择，蛋白质折叠问题等等。 Yang, X. S. (2008). Nature-Inspired Metaheuristic Algorithms. Frome: Luniver Press, UK 存档副本. [2013-05-18]. （原始内容存档于2013-05-21）.  Sayadi, M. K.; Ramezanian, R.; Ghaffari-Nasab, N. A discrete firefly meta-heuristic with local search for makespan minimization in permutation flow shop scheduling problems (PDF). Int. J. of Industrial Engineering Computations. 2010, 1: 1–10 [2013-05-21]. （原始内容存档 (PDF)于2013-10-13）.  T. Hassanzadeh, H. Vojodi and A. M. E. 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