(190n) Scalable Modeling and Solution of Stochastic Multiobjective Optimization Problems

Authors: 
Zavala, V. M., University of Wisconsin-Madison
Cao, Y., University of Wisconsin-Madison
Fuentes-Cortes, L. F., Instituto Tecnológico de Celaya
We present a scalable computing framework for the solution stochastic multiobjective optimization problems. The proposed framework uses a nested conditional value-at-risk (nCVaR) metric to find compromise solutions among conflicting random objectives. We prove that the associated nCVaR minimization problem can be cast as a standard stochastic programming problem with expected value (linking) constraints.We also show that the solutions satisfy stochastic dominance of second order. Finally, we demonstrate that these problems can be implemented in a modular and compact manner using PLASMO (a Julia-based structured modeling framework) and can be solved efficiently using PIPS-NLP (a parallel nonlinear solver). We apply the framework to a combined heat and power design study in which we seek to find compromise solutions that trade-off cost, water, and emissions in the face of uncertainty in electricity and water demands.