A scalable stochastic programming approach for the design of flexible systems

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.

Measuring and optimizing system reliability: a stochastic programming approach

“…This problem is fully decoupled in the MC samples k ∈ K and, thus, can be trivially parallelized. It has been recently reported that a continuous relaxation of this problem (in combination with an appropriate rounding strategy) provides high-quality approximations of the exact solution (Pulsipher and Zavala 2019). Specifically, we can relax y k ∈ {0, 1} to 0 ≤ y k ≤ 1 and then round the optimized relaxed y k * values to 1 if they are nonzero.…”

“…We observe that 5 out of 6 pairs are exactly recovered and a pair is underestimated. In Pulsipher and Zavala (2019) it is hypothesized that the quality of the approximations is the result of degeneracy associated with the joint chance constraint (i.e., multiple solutions yield the same optimal value). This simple network exhibits little degeneracy at that solution because its solution space is small.…”