On a parallelised diffusion induced stochastic algorithm with pure random search steps for global optimisation

Funding Information: Funding: For the second author, this work was undertaken with partial financial support of RFBR (Grant n. 19-01-00451). For the first and third author, this work was partially supported through the project of the Centro de Matemática e Aplicações, UID/MAT/00297/2020, financed by the Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology). The APC was by supported the New University of Lisbon through the PhD program in Statistics and Risk Management of the FCT Nova Faculty.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.publishersversionpublishe