SCE

Concepts：

1）combination of random and deterministic approaches 随机和确定性方法的组合

2）the concept of clustering 聚类的概念

3）the concept of a systematic evolution of a complex of points spanning the space, in the direction of global improvement 在全局优化的方向，

跨空间点的复杂系统演化的概念

4） the concept of competitive evolution 竞争进化的概念

 

SCE=CRS with the concept of competitive evolution + complex shuffling

 

The philosophy:  The ampled points(s in number) constitute a population. The population is partitioned into several communities(complexes), each of which is permitted to evolve independently. After a certain number of generations, the communities are forced to mix, and new communities are formed though a process of shuffling. This procedure enhances survivability by a sharing of the information gained independently by each community.

 

Step 0. Initialize. p>=1 : number of complexes m>=n+1 : number of points in each complex. the sample size s=p*m.

 

Step 1. Generate Sample. Sample s points x₁,...,x_s in the feasible space omega. Compute the function value fi at each point x_i.

 

Step 2. Rank Points. Sort the s points in order of increasing function value. Store them in an arry D={x_i,f_i, i=1,...,s}, so that i=1 represents the point with the smallest function value.

Step 3. Partition into Complexes. Partition D into p complexes A¹,...,A^P, each containing m points, such that:

　　　　　　A^k={x^k_j,f^k_j| x^k_j=x_k+p(j-1), f^k_j=f_k+p(j-1), j=1,...,m)} .

Step 4. Evolve Each Complex. Evolve each complex A^k, k=1,...,p according to the competitive complex evolution(CCE) algorithm outlined separately.

 

Step 5. Shuffle Complexes. Replace A¹,...,A^P into D, such that D={A^k, k=1,...,p}. Sort D in order of increasing function value.

 

Step 6. Check Convergence. If the convergence criteria are satisfied, stop; otherwise, return to Step 3.

 

　　The competitive complex evolution(CCE) algorithm required for the evolution of each complex in Step 4 of the SCE method is presented below

　　Step 0. Initialize. Select q, α, and β， where 2<=q<=m, α>=1, and β>=1.

　　Step 1. Assign Weights. Assign a triangular probability distribution to A^k;

　　　　　　　　p_i=2(m+1-i)/m(m+1), i=1,...,m.

　　The point x^k₁ has the highest probability, ρ₁=2/m+1. The point x^k_m has the lowest probability, ρ_m=2/m(m+1).

　　Step 2. Select Parents. Randomly choose q distinct points 随机选择q个不同点 u1,...,uq from A^k according to the probability distribution specified above(根据上面指定的概率分布) the q points define a subcomplex. Store them in array B={ui,vi, i=1,...,q}, where vj is the function value associated with point uj. Store in L the locations of A^k which are used to construct B.

　　Step 3. Generate Offspring.

　　Step 4. Replace Parents by Offspring. Replace B into A^k using the original locatios stored in L. Sort A^k in order of increasing function value.

　　Step 5. Iterate. Repeat Steps 1 though 4 β times, where β>=1 is a user-specified parameter which determines how many offspring should be generated.