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An extension of an RLT-based solver to MINLP polynomial problems

Julio González-Díaz, Brais González-Rodríguez, Iria Rodríguez-Acevedo

Abstract

In this paper we extend the core branch-and-bound algorithm of an RLT-based solver for continuous polynomial optimization, RAPOSa, to handle mixed-integer problems. We do so by a direct adaptation, in which LP relaxations are replaced with MILP ones and, therefore, the additional burden caused by the discrete variables is taken care of by the auxiliary MILP solver. The analysis then focuses on the impact of a number of choices that must be made for the resulting algorithm to be effective at providing good lower and upper bounds upon termination.

An extension of an RLT-based solver to MINLP polynomial problems

Abstract

In this paper we extend the core branch-and-bound algorithm of an RLT-based solver for continuous polynomial optimization, RAPOSa, to handle mixed-integer problems. We do so by a direct adaptation, in which LP relaxations are replaced with MILP ones and, therefore, the additional burden caused by the discrete variables is taken care of by the auxiliary MILP solver. The analysis then focuses on the impact of a number of choices that must be made for the resulting algorithm to be effective at providing good lower and upper bounds upon termination.

Paper Structure

This paper contains 23 sections, 5 equations, 3 figures, 10 tables.

Table of Contents

  1. Introduction
  2. Preliminaries: RLT and computational setup
  3. RLT for continuous polynomial optimization
  4. Computational setup
  5. The RLT-based solver: RAPOSa
  6. Baseline solver.
  7. Branching point selection.
  8. Moving to mixed-integer problems.
  9. Testing environment
  10. Reporting of numerical results
  11. RLT in mixed-integer polynomial optimization
  12. Prioritization of branching decisions
  13. Controlling integer branching depth
  14. Comparison with other state-of-the-art solvers
  15. Getting bounds consistently
  16. ...and 8 more sections

Figures (3)

  • Figure 1: Scheme of the baseline (continuous) RLT-based algorithm.
  • Figure 2: Performance profiles comparing RAPOSa with other BARON and Couenne.
  • Figure 3: Performance profiles comparing two configurations of RAPOSa with BARON.