(51g) Recent Advances in the E­a­G­O Platform: Global and Robust Optimization in Julia

Parametric uncertainty in process systems modeling and simulation is ever present. Robust optimization has significant applications in design for process safety, control of water-treatment facilities, and the economic assessments of novel projects [1,2]. However, the currently available software tools (ROME, YAMLP), address only narrowly structured robust optimization problems and efforts to develop generalized solvers for parametric uncertainty remain in a nascent state [3,4,5]. For general problems, highly-specialized bounding routines may be necessary [6]. While numerous options exist for constructing meta-optimization algorithms (e.g. Pyomo [7]) easy manipulation of low-level solution routines and propagation of information from these low-level routines to meta-algorithms is still quite difficult.

In 2018, the EAGO optimization platform was introduced to address this gap [8 By introducing, a low-level global/robust optimization platform in Julia, we’re able to reduce the overhead to develop and implement algorithms addressing these novel applications [9]. Our hope is that this will act as a development platform to complementing existing commercial optimization packages. Prior work on EAGO focused on the development of McCormick relaxation libraries [10,11,12], a global optimizer for explicit & implicit functions [6,13], and meta-algorithms for solving semi-infinite programs [5,6]. New features updated this year include:

Additional relaxation schemes for nonconvex NLP problems such as alpha-BB and interval methods [14].

• New library of domain reduction subroutines [15].
• Improved handling for sparse systems including GPGPU-based enhancements to existing global and robust solution routines.
• Incorporation of mixed-integer programming routines into existing robust solvers [16]
• Improved benchmarking framework for use with standard libraries [17].

Other advances in manipulation techniques for directed-acyclic graphs will be discussed. Demonstrations of the above improvements will be given with comparisons to prior techniques as appropriate. Multiple examples will illustrate EAGO’s utility for solving systems that commonly arise in model-based system engineering applications. Additionally, a series of industrially-relevant examples in process systems engineering will be given to illustrate use cases and performance aspects of the new EAGO features.

[1] Ben-Tal A.; El Ghaoui L.; Nemirovski A. Robust optimization. Princeton University Press, 2009.

[2] Li, P., and Geletu, A. Recent Developments in Computational Approaches to Optimization under Uncertainty and Application in Process Systems Engineering. ChemBioEng Reviews, 1(4): 170-190 2014.

[3] Joel Goh. Distributionally Robust Optimization and its Tractable Approximations with ROME. ISMP, Aug 2009, Chicago.

[4] Lofberg, Johan. "YALMIP: A toolbox for modeling and optimization in MATLAB." Computer Aided Control Systems Design, 2004 IEEE International Symposium on. IEEE, 2004.

[5] Mitsos, A. Global Optimization of Semi-Infinite Programs via Restriction of the Right-Hand Side. Optimization. 60:10-1,1291-1308.

[6] Stuber, M.D., and Barton, P.I. Semi-Infinite Optimization with Implicit Functions. Ind. Eng. Chem. Res., 54:307-317, 2015.

[7] Hart WE, Laird C, Watson J-P, Woodruff DL. 2012. Pyomo - Optimization Modeling in Python, Springer US, Boston, MA. doi:10.1007/978-1-4614-3226-5.

[8] Wilhelm, M. and Stuber, M. Easy Advanced Global Optimization (EAGO): An Open-Source Platform for Robust and Global Optimization in Julia. AIChE Annual Meeting 2017.

[9] Bezanson, J. et al. Julia: A fresh approach to numerical computing. SIAM Review. 59, 65-98, 2017.

[10] Scott, J.K., Stuber, M.D., and Barton, P.I. Generalized McCormick Relaxations. J Global Optim, 51:569-606, 2011.

[11] Mitsos, A., Chachuat, B., and Barton, P.I. McCormick-Based Relaxations of Algorithms. SIAM J. Optim. 20(2): 573-601.

[12] Khan, K.A., Watson, H.A., and Barton, P.I. Differentiable McCormick Relaxations. J Global Optim, 67(4):687-729, 2017.

[13] Stuber, M.D., Scott, J.K., and P.I. Barton. Convex and Concave Relaxations of Implicit Functions. Optimization Methods and Software. 30(3), 424-460, 2014.

[14] Adjiman, Claire S., et al. A global optimization method, αBB, for general twice-differentiable constrained NLPs—I. Theoretical advances. Computers & Chemical Engineering 22.9 (1998): 1137-1158. [15] Puranik, Y. and N. V. Sahinidis. Domain reduction techniques for global NLP and MINLP optimization. Constraints, 22: 338-376 (2017).

[16] Floudas, Christodoulos A. Nonlinear and mixed-integer optimization: fundamentals and applications. Oxford University Press, 1995.

[17] O. Shcherbina, et al. Benchmarking Global Optimization and Constraint Satisfaction Codes, In Global Optimization and Constraint Satisfaction, Bliek, Ch., Jermann, Ch. and Neumaier, A. Springer, Berlin 2003, 212-222.