On a Parallelised Diffusion Induced Stochastic Algorithm with Pure Random Search Steps for Global Optimisation

Manuel L. Esquível, Nadezhda P. Krasii, Pedro P. Mota and Nélio Machado
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Manuel L. Esquível: Department of Mathematics, Centre for Mathematics and Applications, NOVA School of Science and Technology, New University of Lisbon, 2829-516 Caparica, Portugal
Nadezhda P. Krasii: Department of Higher Mathematics, Faculty of Informatics and Computer Engineering, Don State Technical University, 344003 Rostov-on-Don, Russia
Pedro P. Mota: Department of Mathematics, Centre for Mathematics and Applications, NOVA School of Science and Technology, New University of Lisbon, 2829-516 Caparica, Portugal
Nélio Machado: Department of Mathematics, Faculty of Science and Technology, New University of Lisbon, 2829-516 Caparica, Portugal

Mathematics, 2021, vol. 9, issue 23, 1-30

Abstract: We propose a stochastic algorithm for global optimisation of a regular function, possibly unbounded, defined on a bounded set with regular boundary; a function that attains its extremum in the boundary of its domain of definition. The algorithm is determined by a diffusion process that is associated with the function by means of a strictly elliptic operator that ensures an adequate maximum principle. In order to preclude the algorithm to be trapped in a local extremum, we add a pure random search step to the algorithm. We show that an adequate procedure of parallelisation of the algorithm can increase the rate of convergence, thus superseding the main drawback of the addition of the pure random search step.

Keywords: global optimisation; stochastic algorithms; pure random search; rate of convergence; parallelisation of algorithms (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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