Scalable modeling and solution of stochastic multiobjective optimization problems

Abstract

We present a scalable computing framework for the solution stochastic multiobjective optimization problems. The proposed framework uses a nested conditional value-at-risk (nCVaR) objective 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.

A Graph-Based Modeling Abstraction for Optimization: Concepts and Implementation in Plasmo.jl

“…Subsequent development provided data management capabilities to facilitate model reduction and re-use (for real-time optimization applications) [39] and provided an interface to communicate graph structures to the parallel interior-point solver PIPS-NLP [10]. The abstraction was later used to create a computational graph abstraction wherein nodes are computational tasks and edges communicate data between tasks.…”

Optimal PID controller tuning using stochastic programming techniques

“…Plasmo is a Julia‐based algebraic modeling framework that facilitates the construction and analysis of large‐scale structured optimization models. To do this, it leverages a hierarchical graph abstraction wherein nodes and edges can be associated with individual JuMP scenario problems that are linked together (e.g., by using non‐anticipativity constraints) . Given a graph structure with models and connections, Plasmo can produce either a pure (flattened) optimization model to be solved using off‐the‐shelf optimization solvers such as IPOPT or it can communicate graph structures to structure‐exploiting solvers such as PIPS‐NLP and SNGO .…”

Perspectives for Implementing Distributed Generation in Developing Countries through Modeling Techniques

“…121 On the other hand, the nonlinear approach is used for considering the detailed behavior of the equipment for evaluating the performance and effects of different operative policies. 24,28,29,40,50,51,53,56,57,60,62,80,84,100,119,140,163 It leads to the solution method for nonlinear models. The use of heuristic tools, 24,50,53,60,62,81,82,140,143 despite the polemic around these methodologies, 165−167 is the predominant trend for solving nonlinear problems over the analytical approaches.…”

“…The second one is to define the interest and priorities of the decision makers or the particular solution area for defining a set of specific solutions for the problem. 40,57,97,100,120,163 In this way, it is possible to show how the priorities of the decision makers affect the performance of the system and to avoid computing multiple Pareto solutions which are out of the interest area. 40,57,168,169 Finally, the main approaches for considering the uncertainty use the multiscenario approach 81,83,84,162,163 for analyzing the behavior and sensitivity of the system to the variations on specific variables or fuzzy logic 49 for controlling the effects of uncertainties on the objective functions.…”

“…40,57,97,100,120,163 In this way, it is possible to show how the priorities of the decision makers affect the performance of the system and to avoid computing multiple Pareto solutions which are out of the interest area. 40,57,168,169 Finally, the main approaches for considering the uncertainty use the multiscenario approach 81,83,84,162,163 for analyzing the behavior and sensitivity of the system to the variations on specific variables or fuzzy logic 49 for controlling the effects of uncertainties on the objective functions. The stochastic approaches have focused on economic, ambient, social, and demographic phenomena as well as the resource availability that affect the energy projects.…”