Performance Modeling and Analysis of a Massively Parallel Direct—Part 2

Abstract

Modeling and analysis techniques are used to investigate the performance of a massively parallel version of DIRECT, a global search algorithm widely used in multidisciplinary design optimization applications. Several high-dimensional benchmark functions and real world problems are used to test the design effectiveness under various problem structures. Theoretical and experimental results are compared for two parallel clusters with different system scale and network connectivity. The present work aims at studying the performance sensitivity to important parameters for problem configurations, parallel schemes, and system settings.The performance metrics include the memory usage, load balancing, parallel efficiency, and scalability. An analytical bounding model is constructed to measure the load balancing performance under different schemes. Additionally, linear regression models are used to characterize two major overhead sources-interprocessor communication and processor idleness, and also applied to the isoefficiency functions in scalability analysis. For a variety of high-dimensional problems and large scale systems, the massively parallel design has achieved reasonable performance. The results of the performance study provide guidance for efficient problem and scheme configuration. More importantly, the generalized design considerations and analysis techniques are beneficial for transforming many global search algorithms to become effective large scale parallel optimization tools.

Derivative-free optimization methods

“…DIRECT generates centres that are dense in Ω and will therefore identify the global minimizers of f over Ω, even when f is non-smooth [Jones et al, 1993, Finkel and Kelley, 2004. Several versions of DIRECT that perform concurrent function evaluations take significant care to ensure the sequence of points generated is the same as that produced by DIRECT [He et al, 2009a[He et al, , 2007[He et al, , 2009b. Similar hyper-rectangle partitioning strategies are used by the methods of Munos [2011].…”

Review and Computational Study on Practicality of Derivative-Free DIRECT-Type Methods

“…Through the analysis of Table 1, noticeable patterns and trends have emerged in terms of implementation, programming language, and availability of source code. The iterative nature of partitioning-based DIRECT-type algorithms often limits the potential for efficient parallelism (Griffin and Kolda, 2010;He et al, 2008He et al, , 2009aHe et al, , 2009bHe et al, , 2009cPaulavičius et al, 2013;Watson and Baker, 2001). Consequently, most of the implementations listed in the table are sequential.…”

Optimized drag reduction and wake dynamics associated with rotational oscillations of a circular cylinder

“…For the global optimization, the parallel CFD code ( [1]) that computes the flow past a circular cylinder undergoing rotational oscillation is coupled with the parallel deterministic global optimization algorithm VTDIRECT95 ( [11,10,12]) through an interface function that computes the drag coefficient. VTDIRECT95 is a Fortran 95 package for deterministic global optimization that contains the subroutine VTdirect (serial) and pVTdirect(parallel) implementing a version of the algorithm known as DIRECT ( [15]).…”

“…A detailed description and both serial and parallel implementations of the code are provided in [11,10,12]. A distinctive characteristic of deterministic algorithms like VTDIRECT95 is their frugal use of function evaluations, compared to population based evolutionary algorithms.…”