, Volume 56, Issue 3, pp 1101-1121,
Open Access This content is freely available online to anyone, anywhere at any time.

On interval branch-and-bound for additively separable functions with common variables

Abstract

Interval branch-and-bound (B&B) algorithms are powerful methods which look for guaranteed solutions of global optimisation problems. The computational effort needed to reach this aim, increases exponentially with the problem dimension in the worst case. For separable functions this effort is less, as lower dimensional sub-problems can be solved individually. The question is how to design specific methods for cases where the objective function can be considered separable, but common variables occur in the sub-problems. This paper is devoted to establish the bases of B&B algorithms for separable problems. New B&B rules are presented based on derived properties to compute bounds. A numerical illustration is elaborated with a test-bed of problems mostly generated by combining traditional box constrained global optimisation problems, to show the potential of using the derived theoretical basis.

This work has been funded by grants from the Spanish Ministry of Science and Innovation (TIN2008-01117), Junta de Andalucía (P08-TIC3518 and P11-TIC7176), in part financed by the European Regional Development Fund (ERDF) and Seneca Foundation (Murcia Region nr 15254/PI/10). Eligius Hendrix is a fellow of the Spanish “Ramon y Cajal” contract program, co-financed by the European Social Fund.