Abstract
Pattern search is a family of single solution deterministic optimisation algorithms for numerical optimisation. Pattern search algorithms generate a new candidate solution by means of an archive of potential moves, named pattern. This pattern is generated by a basis of vectors that span the domain where the function to optimise is defined.
The present article proposes an adaptive implementation of pattern search that performs, at run-time, a fitness landscape analysis of the problem to determine the pattern and adapt it to the geometry of the problem. The proposed algorithm, called Adaptive Covariance Pattern Search (ACPS) uses at the beginning the fundamental orthonormal basis (directions of the variables) to build the pattern. Subsequently, ACPS saves the successful visited solutions, calculates the covariance matrix associated with these samples, and then uses the eigenvectors of this covariance matrix to build the pattern. ACPS is a restarting algorithm that at each restart recalculates the pattern that progressively adapts to the problem to optimise. Numerical results show that the proposed ACPS appears to be a promising approach on various problems and dimensions.