Optimisation with simulated annealing through regularisation of the target function

Abstract

A method is presented for function optimisation that generalises the Simulated Annealing algorithm by applying convolutions of the target function with smooth, infinitely differentiable kernels. Hence the search for a global optimum is performed over a sequence of functions that preserve the structure of the original one and converge to it pointwise. From an experimental point of view, the purpose of this paper was to compare the efficiency of this approach with that of the conventional Simulated Annealing. To do this, the proposed technique was tested both on complex combinatorial (discrete) problems (e.g. the Travelling Salesman Problem) and on the search of global minima for continuous functions. In some cases, performance was improved in terms of final results, while in other ones, even if no improvements were attained over the usual Simulated Annealing algorithm, the proposed method shows interesting abilities to provide fairly good approximations in relatively few iterations, i.e. at early stages of the search process