A fully‐distributed parallel global search algorithm

Abstract

The n-dimensional direct search algorithm DIRECT of Jones, Perttunen, and Stuckman has attracted recent attention from the multidisciplinary design optimization community. Since DIRECT only requires function values (or ranking) and balances global exploration with local refinement better than n-dimensional bisection, it is well suited to the noisy function values typical of realistic simulations. While not efficient for high accuracy optimization, DIRECT is appropriate for the sort of global design space exploration done in large scale engineering design. Direct and pattern search schemes have the potential to exploit massive parallelism, but efficient use of massively parallel machines is nontrivial to achieve. This paper presents a fully distributed control version of DIRECT that is designed for massively parallel (distributed memory) architectures. Parallel results are presented for a multidisciplinary design optimization problem-configuration design of a high speed civil transport.

Global Search Based on Efficient Diagonal Partitions and a Set of Lipschitz Constants

“…Due to its simplicity and efficiency, DIRECT has been widely adopted in practical applications (see, e.g., [1,2,3,4,10,13,22,35]). In fact, DIRECT is a derivativefree deterministic algorithm which does not require multiply runs.…”

Design and implementation of a massively parallel version of DIRECT

“…The multiple function evaluation tasks at each iteration give rise to a natural functional parallelism used in [5] and [19]. This is especially beneficial for expensive objective functions, since the communication cost of distributing evaluation tasks to multiple processors is negligible compared to the computational cost.…”

“…The global search algorithm DIRECT (Dividing RECTangle) by Jones et al (1993) [13] is one such algorithm. Several research projects ( [19], [10], and [11]) address its parallel design issues on large systems. Baker et al ([19]) discuss the performance of several load balancing strategies for a fully distributed version of DIRECT, which solved a 28-dimensional problem on a 256 processor supercomputer.…”

“…However, the nature of the DIRECT algorithm presents both potential benefits and difficulties for a sophisticated and efficient parallel implementation. Gablonsky [5] and Baker et al [19] are among the few parallel DIRECT implementations known in the public domain. In [5], Gablonsky adopts a master-slave paradigm to parallelize the function evaluations, but little discussion is given to the issue of parallel performance and potential problems, such as load balancing and interprocessor communication, both of which raise many challenging design issues.…”

“…In [5], Gablonsky adopts a master-slave paradigm to parallelize the function evaluations, but little discussion is given to the issue of parallel performance and potential problems, such as load balancing and interprocessor communication, both of which raise many challenging design issues. A major contribution in [19] is a distributed control version equipped with dynamic load balancing strategies. Nevertheless, that work did not fully address other design issues such as a single starting point and a strong data dependency.…”