A Scalable Stochastic Programming Approach for the Design of Flexible Systems

TL;DR

This paper introduces a scalable continuous relaxation method for designing flexible systems that minimizes cost while satisfying joint chance constraints, offering a practical alternative to traditional mixed-integer programming approaches.

Contribution

It presents a novel continuous relaxation approach for joint chance-constrained system design, improving scalability and solution quality compared to MIP reformulations.

Findings

The relaxation closely approximates the Pareto set of the original problem.

The method significantly outperforms MIP techniques in scalability.

Solutions effectively balance cost and flexibility.

Abstract

We study the problem of designing systems in order to minimize cost while meeting a given flexibility target. Flexibility is attained by enforcing a joint chance constraint, which ensures that the system will exhibit feasible operation with a given target probability level. Unfortunately, joint chance constraints are complicated mathematical objects that often need to be reformulated using mixed-integer programming (MIP) techniques. In this work, we cast the design problem as a conflict resolution problem that seeks to minimize cost while maximizing flexibility. We propose a purely continuous relaxation of this problem that provides a significantly more scalable approach relative to MIP methods and show that the formulation delivers solutions that closely approximate the Pareto set of the original joint chance-constrained problem.