Resilience-based network design under uncertainty

- A flexible nonlinear function is developed to characterize the component restoration behavior after the disruption.
- We formulate the resilience-based network design optimization problem for both deterministic and stochastic cases of a network system.
- We develop a probabilistic solution discovery algorithm and integrate it with a stochastic ranking to approach the problem.

This paper introduces an approach to quantify resilience for the design of systems that can be described as a network. A key characteristic of resilience is the ability of restoring functionality and performance in response to a disruptive event. Therefore, the restoration behavior is encapsulated via a non-linear function that provides the ability to model at the component level more refined attributes of restoration. In particular, it considers the remaining capacity (absorptive ability), the degree to which capability can be recovered (restoration ability) and the recovery speed. The component restoration functions can then be used to impose a resilience target at a given time as a design constraint.The resilience-based design optimization is then formulated for both deterministic and stochastic cases of a network system. The objective is to have as the design solution a network that incurs the least cost while meeting system resilience constraints. Maximum flow through the network is used as a measure of system performance. Several possible links are examined with regards to flow performance from origin node to a destination node. A probabilistic solution discovery algorithm is combined with stochastic ranking to approach this problem. Two numerical examples are used to illustrate the procedure and the effectiveness of the proposed method.