I have an inverse problem in which the optimal positions for a variable number of injections needs to be determined. If the number of injections was fixed, I could easily imagine implementing Simplex or Genetic Algorithm (or really any optimisation algorithm). With a changing number of variables, however, it seems that reflection in Simplex and crossover in GA become impossible.I could use a meta-optimiser to find the optimal positions for a given number of injections and repeat this process for every number of injections, but this is computationally expensive.Are there any thoughts on what I could do? Or any sources you can point me to (searching optimising a variable number of variables unsurprisingly isn't very fruitful)?
Inverse problem with changing number of variables
inverse problem