Adaptive Covariance Pattern Search

Neri, Ferrante

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.

Citation

Neri, F. (2021). Adaptive Covariance Pattern Search. In P. A. Castillo, & J. L. Jiménez Laredo (Eds.), Applications of Evolutionary Computation – 24th International Conference, EvoApplications 2021 (178-193). Springer. https://doi.org/10.1007/978-3-030-72699-7_12

• Online Publication Date: Apr 1, 2021
• Publication Date: 2021
• Deposit Date: Jan 22, 2021
• Publicly Available Date: Apr 2, 2022
• Publisher: Springer
• Pages: 178-193
• Series Title: Lecture Notes in Computer Science
• Series Number: 12694
• Series ISSN: 0302-9743
• Book Title: Applications of Evolutionary Computation – 24th International Conference, EvoApplications 2021
• ISBN: 9783030726980
• DOI: https://doi.org/10.1007/978-3-030-72699-7_12
• Public URL: https://nottingham-repository.worktribe.com/output/5250277
• Publisher URL: https://www.springer.com/gb/book/9783030726980
• Contract Date: Jan 20, 2021