Shuffled Complex Evolution method

The Shuffled Complex Evolution (SCE) method is a global optimisation algo­rithm that combines various search strategies, including (i) competitive evolu­tion, (ii) controlled random search, (iii) the simplex method, and (iv) complex shuffling.

The SCE algorithm includes the following steps:

1.       Initialisation. An initial sample of parameter sets q_i are randomly gener­ated from the feasible parameter space defined by the lower and upper limits of each parameter on the Model Parameters page. For each parameter set the objective function value F_i = F(q_i) is calculated. The ini­tial sample has the size s = pm where p is the number of complexes and m is the number of points in each complex.

2.       Partitioning into complexes. The s points are ranked in order of increas­ing objective function value (F(1) < F(2) <... < F(s)). The s points are par­titioned into p complexes, such that points corresponding to function values {F(1), F(p+1), .., F((s-1)p+1)} form the 1^st complex, points corre­sponding to function values {F(2), F(p+2), .., F((s-1)p+2)} form the 2^nd complex, etc.

3.       Evolution. A sub-complex of size q is formed from the complex by ran­domly choosing q points from the p points in the complex. A triangular probability distribution is used for assigning the probability of a point to be included in the sub-complex (i.e. larger probability for points with smaller objective function value). The sub-complex is evolved (offspring generation) according to the simplex algorithm. Each complex is evolved b times.

4.       Complex shuffling. The new sample of s points is shuffled, cf. step 2.

5.       Steps 2-4 are repeated until a stopping criterion is met.

Algorithmic parameters
Initial sample
Stopping criteria