Scalable modeling and solution of stochastic multiobjective optimization problems

• Present a computing framework for stochastic multiobjective optimization.
• Use a nested CVaR metric to trade-off multiple random objectives.
• Show that nested CVaR can be formulated as a standard NLP.
• Present a combined heat and power study to demonstrate developments.

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 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 CHP 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.