Submarine telecommunication cables, as a critical component of critical infrastructures, play a crucial role in transmitting Internet data from one location to another. Constructing a long-haul submarine cable requires an investment of hundred millions of US dollars with a need to keep costs to a minimum. At the same time, cable survivability is also important because cable breaks can result in Internet shutdowns that have harmful financial and social consequences. In practice, the path planning of submarine cables is done manually, based on the knowledge and experience of experts. Under this time-consuming approach, even the most experienced and skilled designers cannot guarantee an optimal path (given the data). This thesis provides methodologies based on real data for cable path planning on the Earth's surface by an automated procedure to minimize both construction costs and risks.

As a first step, we start with a fundamental path planning problem of how to lay a link of critical infrastructures, such as a submarine cable, connecting two nodes on the Earth's surface taking into account seismic hazards. We approximate the Earth's surface as a triangulated manifold. The problem is formulated as a multi-objective optimization problem, where the laying cost and resilience of the link are the two objectives. The multi-objective optimization problem is first converted into a single-objective problem by weighting the two objectives. Then, this single-objective problem can be converted into an Eikonal equation, which can be solved by the well-established fast marching method (FMM). Extensive simulations are performed on real-world three-dimensional geographical data, from which we generate Pareto optimal solutions that provide insights and guidance to design trade-offs between cost-effectiveness and seismic resilience.

Next, we extend the methodology described above to address the more challenging problem of submarine cable network extension, taking into account a wide range of design considerations. The problem is formulated as a variational optimization problem to minimize the overall life-cycle cost of submarine cables taking into account multiple design considerations; this problem is expressible in terms of an Eikonal equation and solved by leveraging FMM. A specific example is given to demonstrate the benefits of FMM in terms of path planning solutions over Dijkstra's algorithm.

Then, we consider the situation where the cable or cable segments are allowed to be protected by various methods to improve its survivability, though at additional cost. We provide methods for optimal shielding design and path planning of a long-haul optical fiber cable between two locations on the Earth’s surface. The problem is formulated as a multi-objective optimization problem to minimize the laying cost and the total number of repairs of the cable under multiple design levels. We solve this problem by a variant of the label setting algorithm and obtain all the Pareto optimal solutions, including the solutions at non-convex portions of the Pareto front. However, the running time of the label setting method is too long to be applicable to a large region with high-resolution data. To this end, we provide an FMM-based method with low computational complexity to solve this problem. Numerical results show that the FMM-based method outperforms the discrete methods in terms of cable path planning solutions.

Finally, we consider the overturn risk of a remotely operated vehicle as it buries the cable in an uneven seabed. The overturn risk depends on the terrain slope and direction of the cable path. Minimizing the cable laying cost and the total number of repairs are the two objectives used to formulate the corresponding multi-objective optimal control problem. We solve the problem via dynamic programming and propose a computationally efficient algorithm which is based on the Ordered Upwind Method (OUM). Numerical results demonstrate the high quality of the cable path solutions produced by the OUM-based method and its effectiveness.