Spatial branch-and-bound algorithm for MIQCPs featuring multiparametric disaggregation

Abstract

Spatial branch-and-bound (B&B) is widely used for the global optimization of non-convex problems. It basically works by iteratively reducing the domain of the variables so that tighter relaxations can be achieved that ultimately converge to the global optimal solution. Recent developments for bilinear problems have brought us piecewise relaxation techniques that can prove optimality for a sufficiently large number of partitions and hence avoid spatial B&B altogether. Of these, normalized multiparametric disaggregation (NMDT) exhibits a good performance due to the logarithmic increase in the number of binary variables with the number of partitions. We now propose to integrate NMDT with spatial B&B for solving mixed-integer quadratically constrained minimization problems. Optimality-based bound tightening is also part of the algorithm so as to compute tight lower bounds in every step of the search and reduce the number of nodes to explore. Through the solution of a set of benchmark problems from the literature, it is shown that the new global optimization algorithm can potentially lead to orders of magnitude reduction in optimality gap when compared to commercial solvers BARON and GloMIQO.

Keywords:

• mixed-integer nonlinear programming
• nonlinear programming
• quadratic optimization
• discretization
• bilinear terms

Disclosure statement

No potential conflict of interest was reported by the author.

ORCID

Pedro M. Castro http://orcid.org/0000-0002-4898-8922

Additional information

Funding

Financial support from Fundação para a Ciência e Tecnologia through the Investigador FCT 2013 program and project UID/MAT/04561/2013.