System and method for determining optimal path arrangements for an infrastructure link with two or more design levels

1. A computer-implemented method for determining optimal laying paths for a 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 of the grid points on the modelled geographic terrain is denoted by a respective 3D coordinate including an altitude of a corresponding geographic location of the geographic terrain;

jointly optimizing, using the one or more processors, two or more potential paths for the cable between the two geographic locations and at least two levels of shielding for each of the two or more potential paths of the cable, based on the modelled geographic terrain, an arrangement cost model that takes into account the at least two levels of shielding, and a repair rate model that takes into account the at least two levels of shielding, so as to optimize an arrangement cost and a repair rate for each of the two or more potential paths of the cable, the at least two levels of shielding provide different levels of protection for the cable; and

determining, using the one or more processors and based on the jointly optimizing, the optimal laying paths for the cable, each of the optimal laying paths respectively including multiple path portions, the multiple path portions of a corresponding optimal path arrangement defining a shape of the corresponding optimal path arrangement and having the at least two levels of shielding such that the corresponding optimal path arrangement is a non-homogenous path arrangement with different levels of shielding for at least some of the path portions; and

displaying, at a display operably connected with the one or more processors, at least one of the determined optimal laying paths on a map of the geographic terrain;

wherein the arrangement cost model incorporates a factor associated with location and level of shielding of the path, and can be represented as H(γ,u(·))=∫ l(γ) h(γ(s),u(s))ds, where H(γ,u(·)) is a laying cost of the cable, h(γ(s),u(s)) is a unit laying cost at location γ(s) of the geographic terrain with a design level u(s), and l(γ) represents a total length of the cable;

wherein the repair rate model is represented as G(γ,u(·))=∫ l(γ) g(γ(s),u(s))ds, where G(γ,u(·) is a total number of potential required repairs of the cable, g (γ(s),u(s)) is a potential required repair rate at the location γ(s) of the geographic terrain with the design level u(s), and 1 (γ) represents the total length of the cable;

wherein the jointly optimizing comprises solving a single-objective optimization problem defined as

min Φ′(γ,u(·))=∫ 0 l(γ) (h(γ(s),u(s))+c·g(γ(s),u(s))ds, s,t,γ(0)=A and γ(l(γ))=B, where A and B are the two geographic locations, c is a weighing factor and c ∈ R 4 1 ∪{o};

wherein the single-objective optimization problem can be transformed to an Eikonal equation and the solving comprises:

calculating a minimum weighted cost value over all of the levels of shielding for each of the grid points on the modelled geographic terrain; and

applying fast marching method to solve the Eikonal equation for determining the optimal laying paths;

wherein determining the optimal laying paths comprises determining a set of Pareto optimal solutions representing the optimal laying paths.

2. The computer-implemented method of claim 1 , includes: local geographic attributes, labor, and licenses.

3. The computer-implemented method of claim 2 , further comprising receiving input associated with the factors.

4. The computer-implemented method of claim 1 , wherein the repair rate model is based on spatially distributed ground motion intensity associated with the geographic terrain in which the path is arranged.

5. The computer-implemented method of claim 4 , wherein the spatially distributed ground motion intensity comprises peak ground velocity.

6. The computer-implemented method of claim 1 , further comprising receiving input associated with dimensions of the grid points for modelling the geographic terrain.

7. The computer-implemented method of claim 1 , further comprising receiving input associated with the two geographic locations.

8. The computer-implemented method of claim 1 , wherein the repair rate model is based on spatially distributed ground motion intensity associated with the geographic terrain of each portion of a path and sums the repair rate per unit length of a path to determine a repair rate of the path.

9. The computer-implemented method of claim 1 , wherein the at least two levels of shielding are provided by at least two of the following types of cable: single armoured cable, double armoured cable, and rock armoured cable.

10. The computer-implemented method of claim 1 , wherein the cable is an optical cable.

11. An information handling system for determining optimal laying paths for a cable between two geographic locations, comprising:

one or more processors arranged to:

model a geographic terrain containing the two geographic locations, including modelling the geographic terrain into a grid with multiple grid points such that each of the grid points on the modelled geographic terrain is denoted by a respective 3D coordinate including an altitude of a corresponding geographic location of the geographic terrain;

jointly optimize two or more potential paths for the cable between the two geographic locations and at least two levels of shielding for the cable of each of the two or more potential paths of the cable, based on the modelled geographic terrain, an arrangement cost model that takes into account the at least two levels of shielding, and a repair rate model that takes into account the at least two levels of shielding, so as to optimize an arrangement cost and a repair rate for the cable of each of the two or more potential paths, the at least two levels of shielding for the cable provide different levels of protection for the cable; and

determine, based on the joint optimization, the optimal laying paths for the cable, each of the optimal laying paths respectively including multiple path portions, the multiple path portions of a corresponding optimal path arrangement defining a shape of the corresponding optimal path arrangement and having the at least two levels of shielding such that the corresponding optimal path arrangement is a non-homogenous path arrangement with different levels of shielding for at least some of the path portions; and

a display operably connected with the one or more processors and arranged to display at least one of the determined optimal laying paths on a map of the geographic terrain;

wherein the arrangement cost model incorporates a factor associated with location and level of shielding of the path for the cable, and can be represented as H(γ,u(·))=∫ l(γ) h(γ(s),u(s))ds, where H(γ,u(·)) is a laying cost of the cable, h(γ(s),u(s)) is a unit laying cost at location y(s) of the geographic terrain with a design level u(s), and l(γ) represents a total length of the cable;

wherein the repair rate model is represented as G(γ,u(·))=∫ l(γ) g(γ) (s),u(s))ds, where G(γ,u(·)) is a total number of potential required repairs of the cable, g(γ(s),u(s)) is a potential required repair rate at the location y(s) of the geographic terrain with the design level u(s), and 1 (γ) represents the total length of the cable

wherein the one or more processors are arranged to perform the joint optimization by solving a single-objective optimization problem defined as

min Φ′(γ,u(·))=∫ 0 l(γ) (h(γ(s),u(s))+c·g(γ(s),u(s)))ds, s,t, γ(0)=A and γ(l(γ))=B, where A and B are the two geographic locations, c is a weighing factor and c ∈R 4 1 ∪{o};

wherein the single-objective optimization problem can be transformed to an Eikonal equation, and the solving comprises, at least:

calculating a minimum weighted cost value over all of the levels of shielding for each of the grid points on the modelled geographic terrain; and

applying fast marching method to solve the Eikonal equation for determining the optimal laying paths; and

wherein the one or more processors are arranged to determine the optimal laying paths by, at least:

determining a set of Pareto optimal solutions representing the optimal laying paths.

12. The information handling system of claim 11 , wherein the at least two levels of shielding are provided by at least two of the following types of cable: single armoured cable, double armoured cable, and rock armoured cable.

13. The information handling system of claim 11 , wherein the cable is an optical cable.