Parallel Branch and Bound — Principles and Personal Experiences

Abstract

The solution of difficult real world optimization problems usually requires far more computational power than offered by todays fastest computer. However, several computers may work in parallel on the solution of one single problem. Hereby, a way of increasing computational power is created, which scales with advances in hardware, i.e. if processors become 10 times faster, so will execution times for systems built by a number of these processors. If the solution algorithms for the problems in question are well designed, also solution times for these will then decrease by a factor 10.

Branch and Bound (B&B) is by far the most widely used tool for solving large scale hard combinatorial optimization problems, and the combination of parallel computing and B&B has now for a number of years been studied in connection with different applications to derive principles for design of efficient parallel B&B algorithms.

In this paper I briefly review the principles of sequential B&B and sketch the main trends in parallel Branch and Bound and the problems experienced. Based on personal experiences with parallel B&B over the last 5 years, I then give my view on the applicability of parallel B&B — where do one find the large advantages, and which are the ideas to be exploited and pitfalls to be avoided when using parallel B&B in practical problem solving.