System and method for determining optimal path arrangements for an infrastructure link with terrain slope consideration

A computer-implemented method for determining optimal path arrangements for a sub-marine cable between two geographic locations, comprising:

• modelling, using one or more processors, a geographic terrain containing the two geographic locations,
• the modelling including modelling the geographic terrain into a grid with multiple grid points such that each point on the model is denoted by a 3D coordinate including altitude of the geographic terrain;
• optimizing, using the one or more processors, an arrangement cost and a repair rate for two or more potential paths for the sub-marine cable based on the modelled geographic terrain, an arrangement cost model, and a repair rate model, taking into account at least one design level, wherein the arrangement cost model incorporates direction-dependent arrangement cost factors and direction-independent arrangement cost factors associated with path arrangements of the two or more potential paths, the direction-dependent arrangement cost factors being associated with a capsize risk of a remotely operated vehicle arranged to lay the sub-marine cable;
• determining, using the one or more processors, and based on the optimization, the optimal path arrangements each including multiple path portions and the at least one design level associated with the path portions;
• and displaying, at a display operably connected with the one or more processors, at least one of the optimized path arrangements on a map of the geographic terrain;
• wherein the optimization comprises:
• calculating a minimum weighted cost value over the at least one design level for each point on the modelled geographic terrain;
• transforming the optimization to a Hamilton-Jacobi-Bellman equation based on the calculated minimum weighted cost value;
• and applying Ordered Upwind Method to solve the Hamilton-Jacobi-Bellman equation for determining the optimal path arrangements;
• and wherein determining the optimal path arrangements comprises:
• determining a set of Pareto optimal solutions representing the optimal path arrangements, wherein the optimal path arrangements are optimal laying paths,
• wherein the arrangement cost model models the direction-dependent arrangement cost factors as
• h1(x,a)=eq1(x,a)−θ1+eq2(x,a)−θ2,
• where wherein h1 is the direction dependent arrangement cost, x is the 3D coordinate of the grid point, a is a direction of the path, e is an exponential function, q1(x, a) is a slope parallel to the direction of the path as a function of x and a, q2(x, a) is a slope perpendicular to the direction of the path as a function of x and a, θ1 is a threshold representing an allowable maximum slope parallel to the direction of the path, and θ2 is a threshold representing an allowable maximum slope perpendicular to the direction of the path.