Geometric Generalisation of Surrogate Model-Based Optimisation to Combinatorial and Program Spaces

Algorithm 1

Surrogate model-based optimisation (SMBO).

(1) Sample uniformly at random a small set of candidate solutions and evaluate them using the

 expensive objective function (initial set of data-points)

(2) while a limit on the number of expensive function evaluations has not been reached do

(3) Construct a new surrogate model (SM) using all data-points available

(4) Determine the optimum value of the SM by search, for example, using an evolutionary algorithm

  (this is feasible as the model is cheap to evaluate)

(5) Evaluate the solution which optimises the SM using the expensive objective function

  (making an additional data-point available)

(6) end while

(7) Return the best solution found