Geodesic
Parallel global optimization algorithm for obtaining uniform convergence when simultaneously solving a set of global optimization problems
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika, Tome 9 (2020) no. 2, pp. 5-18

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In this work building of a parallel version of a method simultaneously solving a set of constrained global optimization problems is considered. This method converges uniformly to solutions of all the problems. That allows the method to arrange computational resources in an optimal way, since uniform convergence guarantees approximately equal precision of numerical solutions at the whole set of problems at the each iteration of optimization. The algorithm assigns a priority to each problem, and then at the each iteration carries out calculation of objective functions and constraints in several problems in parallel. If the method stops at any arbitrary moment, in all the problems numerical sulutions with the similar accuracy will be obtained. Sets of similar global optimization problems appear for an instance after scalarization of multi-objective problems or when a global optimization problem has a discrete parameter which takes a finite number of possible values. The considered method uses Peano-type curves to transform multidimensional problems into univariate ones. Efficiency of the implemented parallel algorithm is evaluated on several sets of synthetically generated constrained global optimization problems and on a scalarized multi-objective problem. Also the uniform convergence was confirmed numerically by validation quality of intermediate solutions during the optimization process.
Keywords: global optimization, parallel computations, derivative-free optimization
Mots-clés : uniform convergence. 
@article{VYURV_2020_9_2_a0,
     author = {V. V. Sovrasov and K. A. Barkalov},
     title = {Parallel global optimization algorithm for obtaining uniform convergence when simultaneously solving a set of global optimization problems},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a Vy\v{c}islitelʹna\^a matematika i informatika},
     pages = {5--18},
     publisher = {mathdoc},
     volume = {9},
     number = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURV_2020_9_2_a0/}
}
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V. V. Sovrasov; K. A. Barkalov. Parallel global optimization algorithm for obtaining uniform convergence when simultaneously solving a set of global optimization problems. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika, Tome 9 (2020) no. 2, pp. 5-18. http://geodesic.mathdoc.fr/item/VYURV_2020_9_2_a0/