Geometric Surrogate-Based Optimisation for Permutation-Based Problems

In continuous optimisation, surrogate models (SMs) are used when tackling real-world problems whose candidate solutions are expensive to evaluate. In previous work, we showed that a type of SMs - radial basis function networks (RBFNs) - can be rigorously generalised to encompass combinatorial spaces based in principle on any arbitrarily complex underlying solution representation by extending their natural geometric interpretation from continuous to general metric spaces. This direct approach to representations does not require a vector encoding of solutions, and allows us to use SMs with the most natural representation for the problem at hand. In this work, we apply this framework to combinatorial problems using the permutation representation and report experimental results on the quadratic assignment problem.