Multiobjective path optimization for critical infrastructure links with consideration to seismic resilience

We study the generic problem of path optimization for a critical infrastructure link between two locations on the surface of the Earth in the vicinity of earthquake-prone areas. The problem has two (conflicting) objective functions, one for minimizing the construction cost of the link and the other for minimizing the number of potential repairs along the link in the wake of earthquakes. In our model, the Earth's surface is approximated by a triangulated manifold, and ground motion intensity data are used to provide a measure of repair rate. We approach the multiobjective variational problem by first converting it into a single objective variational problem using the weighted sum method. Then, we show that the problem can be further transformed into an Eikonal equation and solved by a computationally efficient algorithm based on the fast marching method. Extensive simulations are performed on real-world three-dimensional geographical data, from which we obtain Pareto optimal solutions that provide insight and guidance to design trade-offs between cost effectiveness and seismic resilience.