Population Simplex Evolution method

The Population Simplex Evolution (PSE) method is a global optimisation algorithm that is especially suited for parallel execution using the simultane­ous simulation option in AutoCal. The method evolves a population of points using the reflection and contraction operators included in the simplex method. In addition a mutation component is added to minimise the risk of premature convergence.

The PSE algorithm can be summarised as follows:

1.       Initialisation. An initial sample of size s 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.

2.       Evolution. From the population s simplexes of size q are formed. A trian­gular probability distribution is used for assigning the probability of a point to be included in the simplex (i.e. larger probability for points with smaller objective function value). The simplex is evolved according to the simplex operators and a mutation operator. Thus, a simplex can be evolved by reflection (with probability p_r), contraction (with probability p_c) or mutation (with probability 1-p_c-p_r). For each simplex a random value e between 0 and 1 is generated and this value then determines which operator should be applied for the evolution, i.e. reflection if e < p_r, con­traction if e is in the interval [p_r, p_r + p_c], and mutation if e > p_c + p_r.

3.       Selection of new population. The algorithm applies the principle of elitism to select the new population. The old population and the evolved popula­tion of points are sorted with respect to their objective function value. The best (i.e. smallest objective function value) s points defines the new pop­ulation.

4.       Steps 2-3 are repeated until a stopping criterion is met.

Algorithmic parameters
Initial sample
Stopping criteria