Assessing the Effectiveness of (Parallel) Branch-and-bound Algorithms

Empirical studies are fundamental in assessing the effectiveness of implementations of branch-and-bound algorithms. The complexity of such implementations makes empirical study difficult for a wide variety of reasons. Various attempts have been made to develop and codify a set of standard techniques for the assessment of optimization algorithms and their software implementations; however, most previous work has been focused on classical sequential algorithms. Since parallel computation has become increasingly mainstream, it is necessary to re-examine and modernize these practices. In this paper, we propose a framework for assessment based on the notion that \emph{resource consumption} is at the heart of what we generally refer to as the "effectiveness" of an implementation. The proposed framework carefully distinguishes between an implementation's baseline efficiency, the efficacy with which it utilizes a fixed allocation of resources, and its scalability, a measure of how the efficiency changes as resources (typically additional computing cores) are added or removed. Efficiency is typically applied to sequential implementations, whereas scalability is applied to parallel implementations. Efficiency and scalability are both important contributors in determining the overall effectiveness of a given parallel implementation, but the goal of improved efficiency is often at odds with the goal of improved scalability. Within the proposed framework, we review the challenges to effective evaluation and discuss the strengths and weaknesses of existing methods of assessment.