From Adaptive Population based Simplex
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APS has been inspired by some previous works, in particular the ones of Luo et al. [1] [2] on Low dimensional simplex evolution (LDSE).

Each phase is explained on its own page (just click on the corresponding area of the figure). After the initialisation of $N$ individuals, all the other phases are in a loop on them. In the explanation, the current individual is called $x_i$. This loop is repeated as long as a stop criterion is not met. As usually, the stop criterion is either a maximum number of fitness evaluations, or an error value found smaller than a predefined threshold.

  1. Luo, C. & Yu, B. Low dimensional simplex evolution: a new heuristic for global optimization Journal of Global Optimization, 2012, 52, 45-55
  2. Luo, C.; Zhang, S.-L. & Yu, B. Some modifications of low-dimensional simplex evolution and their convergence Optimization Methods and Software, 2013, 28, 54-81