Automated search of an optimal configuration of FETI-based algorithms with the swarm and evolutionary algorithms

• Published in: Applied soft computing Vol. 167; p. 112437
• Main Authors: Panoc, Tomáš, Meca, Ondřej, Tomaszek, Lukas, Brzobohatý, Tomáš, Říha, Lubomír, Zelinka, Ivan, Kozubek, Tomáš
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.12.2024
• Subjects: Autotuning; Evolutionary algorithms; FETI method; High-performance computing; Linear solver; Numerical simulations; Parameter selection; Swarm intelligence; Numerical simulations; 68T20; High-performance computing; FETI method; Linear solver; 90C59; Evolutionary algorithms; 65F10; Swarm intelligence; Autotuning; Parameter selection; 65N55; 65N30
• ISSN: 1568-4946
• DOI: 10.1016/j.asoc.2024.112437

Finite Element Tearing and Interconnecting (FETI) methods are used in the engineering community to solve extremely large engineering simulations on clusters and supercomputers with thousands of computational nodes. This paper focuses on minimizing the execution time of these methods by searching for an optimal configuration with swarm and evolutionary algorithms (SEAs). It incorporates optimization of an expensive cost function (taking tens to hundreds of seconds) of discrete search space with up to hundreds of thousands of combinations constrained by its boundaries and incompatible individuals (invalid combination of FETI solver parameters). In addition, the optimization occurs in real time, i.e., during a simulation. Hence, the number of objective function evaluations must remain low (tens to lower hundreds). The paper compares the performance of 3 basic SEAs with a reduced population size (Differential Evolution, Particle Swarm Optimization, and Self-Organizing Migrating Algorithm), 4 micro SEAs (Micro Differential Evolution Ray, Improved Micro-Particle Swarm Optimization, Micro-Particle Swarm Optimization, and Micro-Genetic Algorithm), and a random search on 4 distinct time-dependent simulations of a heat transfer. The experiments show that basic SEAs with a small population (about 5 individuals) and a penalty system as protection against incompatible configurations represent the most effective solution. One can use them to find the optimal configuration of FETI-based methods in approximately 130 evaluations. It can improve the utilization of expensive hardware resources of modern computational clusters. [Display omitted] •Real-time optimization of an expensive cost function (tens to hundreds of seconds).•Limited budget for evaluations (tens to lower hundreds of trials).•Constrained search space due to incompatible individuals.•Basic swarm and evolutionary algorithms with a small population work well.•Penalty system is an effective protection against incompatible configurations.