(288a) Antigone: Algorithms for Continuous / Integer Global Optimization of Nonlinear Equations

Authors: 
Misener, R., Imperial College
Floudas, C. A., Princeton University



Deterministic global optimization of mixed-integer nonlinear programs (MINLP) is broadly applicable in diverse domains ranging from molecular biology to refinery operations to computational chemistry to synthesizing sustainable processes. Our recent work developed solution strategies for two classes of deterministic global optimization problems: mixed-integer quadratically constrained quadratic programs (MIQCQP) and mixed-integer signomial optimization problems (MISO) [4, 5, 6, 7]. A software implementation illustrated and validated the proposed MIQCQP and MISO computational frameworks; we further collaborated with the GAMS Development Corporation to publicly release the MIQCQP framework as the Global Mixed-Integer Quadratic Optimizer (GloMIQO; first available in GAMS 23.8).  GloMIQO has been subsequently used for applications including multiperiod blend scheduling [2, 3] and water-using network design [1].

This presentation introduces ANTIGONE (Algorithms for coNTinuous / Integer Global Optimization of Nonlinear Expressions), a computational framework and associated software implementation for globally optimizing nonconvex MINLP. ANTIGONE integrates our previous MIQCQP [4, 5, 7] and MISO [6] work into a cohesive whole; ANTIGONE further generalizes the computational framework to include exponential and logarithmic functions.

The structure of the ANTIGONE framework includes: reformulating input; finding special mathematical structure; branch-and-cut global optimization. The types of special structure that ANTIGONE considers are: reformulation-linearization technique (RLT) equations; convexity/concavity; edge-convexity/edge-concavity; αBB relaxations; term-specific underestimators.

The purpose of this presentation is to show how the extensible structure of ANTIGONE realizes the MIQCQP and MISO computational frameworks [4, 5, 6, 7]; We develop ANTIGONE as a global optimization framework exploiting an array of special mathematical structure components. After defining a test suite of 1705 optimization problems from standard libraries and the open literature, we present extensive computational results demonstrating the capacity of ANTIGONE.

References

[1] P. M. Castro and J. P. Teles. Comparison of global optimization algorithms for the design of water-using networks. Comput. Chem. Eng., 52(0):249 – 261, 2013.

[2] S. P. Kolodziej, P. M. Castro, and I. E. Grossmann. Global optimization of bilinear programs with a multiparametric disaggregation technique. J. Glob. Optim., 2013. In Press.

[3] S. P. Kolodziej, I. E. Grossmann, K. C. Furman, and N. W. Sawaya. A discretization-based approach for the optimization of the multiperiod blend scheduling problem. Comput. Chem. Eng., 2013. In Press.

[4] R. Misener and C. A. Floudas. Global optimization of mixed-integer quadratically-constrained quadratic programs (MIQCQP) through piecewise-linear and edge-concave relaxations. Math. Program. B, 136:155–182, 2012.

[5] R. Misener and C. A. Floudas. GloMIQO: Global Mixed-Integer Quadratic Optimizer. J. Glob. Optim., 2012. In Press; DOI: 10.1007/s10898-012-9874-7.

[6] R. Misener and C. A. Floudas. A framework for globally optimizing mixed-integer signomial programs. 2013. Submitted for Publication.

[7] R. Misener, J. B. Smadbeck, and C. A. Floudas. Dynamically-generated cutting planes for mixed-integer quadratically-constrained quadratic programs and their incorporation into GloMIQO 2.0. 2012. Submitted for Publication.