Parallel versions of the mesh adaptive direct search algorithm
2026-07-09 • Mathematical Software
Mathematical Software
AI summaryⓘ
The authors review different ways of running the mesh adaptive direct search (MADS) algorithm in parallel to solve hard optimization problems where the rules are unknown and expensive to check. These problems can take a long time to solve because they have many variables and tricky solution spaces. To make things faster, the authors explore using modern computers with multiple cores to run parts of the algorithm at the same time. They explain how these parallel versions work, show results from using them, and discuss what makes each method good or bad.
mesh adaptive direct searchblackbox optimizationparallel computingconstrained optimizationmulti-core architecturemulti-modalitycomputational costalgorithm implementationoptimization algorithmssearch space
Authors
Sébastien Le Digabel, Antoine Lesage-Landry, Samuel Mendoza, Christophe Tribes
Abstract
This work surveys the different parallel variants of the mesh adaptive direct search (MADS) algorithm for constrained blackbox optimization. These problems can inherently imply high computational costs due to the possible large number of variables and multi-modality of the search space. In addition, the potential time-intensive nature and time heterogeneity of the blackboxes defining the problem prompts the need for efficient implementations. Parallelism emerges as an actionable solution to mitigate computation time, as modern computer systems rely on multi-core architecture. The reviewed methods employ diverse levels of parallelism and distinct parallel strategies to effectively tackle each aspect outlined above. The manuscript details the practical implementations, provides computational results, and offers insights into the advantages and limitations of each MADS parallel method.