2019/10/27 by Pooriya Beyhaghi, Beyhaghi, Pooriya, Ryan Alimo +3
Computer Science · Decision Sciences · Mathematics · #Advanced Multi-Objective Optimization Algorithms #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Probabilistic and Robust Engineering Design
paper · pdf · doi:10.48550/arxiv.1910.12393
openalex publication_date 2019/10/27 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
This paper considers the efficient minimization of the infinite time average\nof a stationary ergodic process in the space of a handful of design parameters\nwhich affect it. Problems of this class, derived from physical or numerical\nexperiments which are sometimes expensive to perform, are ubiquitous in\nengineering applications. In such problems, any given function evaluation,\ndetermined with finite sampling, is associated with a quantifiable amount of\nuncertainty, which may be reduced via additional sampling. The present paper\nproposes a new optimization algorithm to adjust the amount of sampling\nassociated with each function evaluation, making function evaluations more\naccurate (and, thus, more expensive), as required, as convergence is\napproached. The work builds on our algorithm for Delaunay-based Derivative-free\nOptimization via Global Surrogates (\Δ-DOGS). The new algorithm, dubbed\n\α-DOGS, substantially reduces the overall cost of the optimization\nprocess for problems of this important class. Further, under certain\nwell-defined conditions, rigorous proof of convergence to the global minimum of\nthe problem considered is established.\n