On estimating workload in interval branch-and-bound global optimization algorithms

• Published in: Journal of global optimization Vol. 56; no. 3; pp. 821 - 844
• Main Authors: Berenguel, José L., Casado, L. G., García, I., Hendrix, Eligius M. T.
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01-07-2013; Springer; Springer Nature B.V
• Subjects: Algorithms; Branch & bound algorithms; Computation; Computational efficiency; Computer Science; Integer programming; Intervals; Linear programming; Mathematical models; Mathematical optimization; Mathematics; Mathematics and Statistics; Methods; Operations Research/Decision Theory; Optimization; Optimization algorithms; Processors; Real Functions; Running; Statistical analysis; Studies; Workload; Workloads; Interval Arithmetic; Global optimization; Parallel algorithms; Branch-and-Bound; Workload prediction
• ISSN: 0925-5001; 1573-2916
• DOI: 10.1007/s10898-011-9771-5

In general, solving Global Optimization (GO) problems by Branch-and-Bound (B&B) requires a huge computational capacity. Parallel execution is used to speed up the computing time. As in this type of algorithms, the foreseen computational workload (number of nodes in the B&B tree) changes dynamically during the execution, the load balancing and the decision on additional processors is complicated. We use the term
left-over
to represent the number of nodes that still have to be evaluated at a certain moment during execution. In this work, we study new methods to estimate the
left-over
value based on the observed amount of pruning. This provides information about the remaining running time of the algorithm and the required computational resources. We focus on their use for interval B&B GO algorithms.