Journal of Global Optimization

, Volume 56, Issue 3, pp 1101-1121

First online:

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

  • J. L. BerenguelAffiliated withTIC 146: “Supercomputing-Algorithms” Research Group, University of Almería
  • , L. G. CasadoAffiliated withDepartment of Computer Architecture and Electronics, University of Almería Email author 
  • , I. GarcíaAffiliated withDepartment of Computer Architecture, University of Málaga
  • , E. M. T. HendrixAffiliated withDepartment of Computer Architecture, University of MálagaOperations Research and Logistics, Wageningen University
  • , F. MessineAffiliated withENSEEIHT-IRIT UMR-CNRS-5505, University of Toulouse


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.


Branch-and-bound Interval arithmetic Separable functions