# Project 2 Presentation --- ## Enhanced Elephant Herding Optimization 機械所 劉政勳 Note: ###### tags: `最佳設計` I'm going to tlak Enhanced Elephant Herding Optimization. Herding is to make animals move together as a group. --- ## Elephant Herding Optimization Note: But first, we need to know what is the origin Elephant Herding Optimization. ---- ### Behavior of elephants * An elephant group is composed of several clans under the leadership of a matriarch. * Male elephants will leave their family group when growing up. Note: there are two elephant's behavior that the algorithm use. ---- ### Algorithm #### CLAN UPDATING OPERATOR $$ x_{new,ci,j}=x_{ci,j}+\alpha\times(x_{best,ci}-x_{ci,j})\times r $$ $$ x_{center,ci,d}=\frac{1}{n_{ci}}\times\sum_{j=1}^{n_{ci}} x_{ci,j,d} $$ Note: the first function update each elephant's position in every generation. and the second one is the clan center function. * $x_{new,ci,j}$ and $x_{ci,j}$ are newly updated and old position for elephant j in clan ci. * $\alpha\in[0,1]$ the influence of the clan matriarch on the elephant new position. ---- <font color="#B6B6B6">**if** $x_{ci,j}=x_{besst,,ci}$</font> $$ x_{new,ci,j}=\beta\times(x_{center,ci}) $$ Note: * $\beta\in[0,1]$ determines the influence of the $x_{center,ci}$ on $x_{new,ci,j}$. * **d** indicates the d-th dimension, ---- ### Algorithm #### SEPARATING OPERATOR $$ x_{worst,ci}=x_{min}+(x_{max}-x_{min}+1)\times rand $$ Note: $x_{min}$ and $x_{max}$ are upper and lower bound of the position of elephant. ---- ### Pseudo Code * Step 1: Initialization. Set generation counter t=1; initialize the population; the maximum generation $MaxGen$. ---- ### Pseudo Code * Step 2: **While** $t<MaxGen$ do Sort all the elephants according to their fitness. Implement *clan updating operator*. Implement *separating operator*. Evaluate population by the newly updated positions. $t=t+1$ * Step 3: end while ---- ### Result Mean function value  Note: EHO get better result is most the benchmark function. --- ## Enhanced Elephant Herding Optimization ---- ### Why **EHO** have the problems of the **fast unjustified convergence towards the <font color="#E70A0A">origin</font>** Note: EHO is lack of ability to control exploration-exploitation tradeoff. ----  Note: BBO: Biogeography-based optimization DE: Differential evolution GA: Genetic Algorithms ---- ### Improvement ##### CLAN UPDATING OPERATOR $$ x_{i,j}^{t+1}=x_{i,j}^t+\alpha\times(m_{i}^t-x_{i,j}^t)+\beta\times(c_{i}^t-x_{i,j}^t)+\gamma\times r $$ $$ c_i^t=\frac{1}{n_i}\times\sum_{i}x_{i,j}^t $$ Note: * $\gamma\in[0,1]$ determining the tendency of elephant to walk randomly * $\beta\in[0,1]$ the tendency of elephant to move towards the clan center * $\gamma\in[0,1]$ determining the tendency of elephant to walk randomly * $n_i$ the number of elephants in clan i ---- <font color="#EFF4B2">$$ x_{new,ci,j}=x_{ci,j}+\alpha\times(x_{best,ci}-x_{ci,j})\times r $$</font> $$ x_{i,j}^{t+1}=x_{i,j}^t+\alpha\times(m_{i}^t-x_{i,j}^t)+\beta\times(c_{i}^t-x_{i,j}^t)+\gamma\times r $$ Note: EEHO introduce beta and gamma. these two parameter let the previous generation have influence to next generation. Also, the clan center and the matriarch can influence next generation. ----  ----  ---- ### Improvement ##### CLAN UPDATING OPERATOR $$ m^{t+1}=m^{t}+\beta(c^{t}-m^{t}) $$ Note: In EHO, the matriarch is random in each generation. EEHO has improved this problem. The old position of the matriarch had been considered. ----  ----  ---- ### Improvement ##### SEPARATING OPERATOR $$ x_{i,worst}^t=x_{min}+(x_{max}-x_{min})\times rand $$ Note: $x_{min}$ and $x_{max}$ same as before. ---- ### Result #### Benchmark function CEC'17 benchmark function have total 2 functions. Contain with 4 kinds of problems. **Unimodal, Simple multimodal, Hybrid and Composition type.** ----  ----  ----  ---- Enhanced elephant herding algorithm(EEHO) have solved the problem such as unjustified convergence towards the origin and the lack of ability to control exploration-exploitation tradeoff. --- ## Conclusion In general,EEHO have better results than traditional EHO, PSO, BSA and ALO in most benchmark functions. --- ## Q&A