Subproblem Selection in Branch-and-Bound Algorithms

Mirjam Dür, Technische Universität Darmstadt

We investigate the Branch-and-Bound method which is frequently used both for discrete and for continuous nonconvex optimization problems. Traditionally, much effort has been invested in improving the quality of the bounds and in the development of branching strategies, whereas little is known about good selection rules. After summarizing several known selection methods, we propose to introduce a probabilistic element into the selection process. We describe conditions which guarantee that a Branch-and-Bound algorithm using our randomized selection rule converges with probability one. This new method is a generalization of the well known best-bound selection rule. Numerical experiments on the Maximum Clique Problem show that probabilistic selection can speed up an algorithm in many cases.

This is joint work with Volker Stix, Wirtschaftsuniversität Wien.


Chemnitz Workshop

Last modified: Thu Oct 7 16:01:51 CEST 2004