On parallel Branch and Bound frameworks for Global Optimization

Abstract

Branch and Bound (B&B) algorithms are known to exhibit an irregularity of the search tree. Therefore, developing a parallel approach for this kind of algorithms is a challenge. The efficiency of a B&B algorithm depends on the chosen Branching, Bounding, Selection, Rejection, and Termination rules. The question we investigate is how the chosen platform consisting of programming language, used libraries, or skeletons influences programming effort and algorithm performance. Selection rule and data management structures are usually hidden to programmers for frameworks with a high level of abstraction, as well as the load balancing strategy, when the algorithm is run in parallel. We investigate the question by implementing a multidimensional Global Optimization B&B algorithm with the help of three frameworks with a different level of abstraction (from more to less): Bobpp, Threading Building Blocks (TBB), and a customized Pthread implementation. The following has been found. The Bobpp implementation is easy to code, but exhibits the poorest scalability. On the contrast, the TBB and Pthread implementations scale almost linearly on the used platform. The TBB approach shows a slightly better productivity.

mplrs: A scalable parallel vertex/facet enumeration code

“…ZRAM is a general-purpose framework that is able to handle a number of other applications, such as branch-and-bound and backtracking, for which there are by now a large number of competing frameworks. Recent papers by Crainic et al [25], McCreesh et al [50] and Herrera et al [38] describe over a dozen such systems. While branch-and-bound may seem similar to reverse search enumeration, there are fundamental differences.…”

“…All of these methods use job stealing for load balancing [16]. In [38] these three approaches are applied to a global optimization algorithm. They are compared on a rather small setup of 16 processors, perhaps due to the shared memory limitation of the last two approaches.…”

Group Connectivity-Based UAV Positioning and Data Slot Allocation for Tactical MANET

“…In order to avoid an n! exhaustive search, the branch and bound method takes O(log 2 n) searches on average [47]. In Problem 2, the gradient descent method is used to solve the maximization problem.…”

mts: a light framework for parallelizing tree search codes

“…Relevant to the heaviness of the wrapper and amount of programming effort required, a comparison of three frameworks is given in [25]. The first, Bob++ [19], is a high level abstract framework, similar in nature to ZRAM, on top of which the application sits.…”

“…All of these methods use job stealing for load balancing [13]. In [25] these three approaches are applied to a global optimization algorithm. They are compared on a rather small setup of 16 processors, perhaps due to the shared memory limitation of the last two approaches.…”