A technology for path determination using robust optimization is provided. In accordance with one aspect, a network graph of a network is generated. The network graph comprises nodes corresponding to points in the network, and edges which connect the nodes. Costs for each edge of the network are determined and modeled using reference point, upper bound and lower bound parameters. A user input which includes a source node, destination node, and cost target may be received from a client device. A resultant path connecting the source node and destination node are determined by solving a target-oriented robust optimization problem, which optimizes a cost of the resultant path based on the modeled costs of the edges. The resultant path is displayed on a user interface of the client device.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A computer-implemented method for determining a path in a network, comprising: generating a network graph of the network, wherein the network graph comprises nodes corresponding to points in the network, and edges connecting the nodes; determining costs for each edge of the network, wherein determining the costs comprises modeling the costs of the edges using reference point, upper bound and lower bound parameters; receiving user input from a client device, wherein the user input includes a source node, destination node, and cost target; determining a resultant path connecting the source node and destination node by solving a target-oriented robust optimization problem, wherein solving the target-oriented robust optimization problem comprises optimizing a cost of the resultant path based on the modeled costs of the edges; and displaying the resultant path on a user interface of the client device. 2. The computer-implemented method of claim 1 wherein the network is a traffic network, the nodes represent locations in the traffic network and the cost target is a travel time target. 3. The computer-implemented method of claim 2 wherein the value of the reference point parameter for an edge (i,j) is the mean of a sample set of travel times between node i and node j. 4. The computer-implemented method of claim 3 wherein the values of the upper bound and lower bound parameters for an edge (i, j) is the reference point plus and minus triple the standard deviation of the sample set of the travel times between the node i and node j. 5. The computer-implemented method of claim 1 wherein solving the target-oriented robust optimization problem comprises solving a deterministic equivalence problem of the target-oriented robust optimization problem, wherein a total cost of the resultant path does not exceed a user specified maximum value in the cost target. 6. The computer-implemented method of claim 5 wherein solving the deterministic equivalence problem of the target-oriented robust optimization problem further comprises solving a mixed integer linear programming equivalence problem of the target-oriented robust optimization problem. 7. The computer-implemented method of claim 1 wherein solving the target-oriented robust optimization problem comprises defining an adjustable uncertainty set Cij(γ) for each cost {tilde over (c)}ij associated to an edge (i, j) of the network using: Cij(γ):={{tilde over (c)}ij|γ(cij−ĉij)≦{tilde over (c)}ij−ĉij≦γ(cij−ĉij)} where γε[0, 1], γ denotes a decision variable taking a value between 0 and 1, and represents the size of the uncertainty set, ĉij denotes the reference point parameter, cij denotes the lower bound parameter and cij denotes the upper bound parameter. 8. The computer-implemented method of claim 7 wherein solving the target-oriented robust optimization problem comprises performing a binary search over γ and solving a deterministic problem repeatedly. 9. The computer-implemented method of claim 8 wherein solving the deterministic problem comprises using Dijkstra's algorithm. 10. The computer-implemented method of claim 8 wherein solving the deterministic problem comprises providing the cost target and maximal number of iteration as input parameters to a binary search procedure. 11. The computer-implemented method of claim 1 wherein optimizing the cost of the resultant path comprises determining that the cost of the resultant path is less than the cost target. 12. The computer-implemented method of claim 1 further comprising defining a binary decision variable for each edge of the network graph and solving the target-oriented robust optimization problem to determine the values of the binary decision variables. 13. A path determination system, comprising: a non-transitory memory device for storing computer-readable program code; and a processor in communication with the memory device, the processor being operative with the computer-readable program code to generate a network graph of a traffic network, wherein the network graph comprises nodes corresponding to locations in the traffic network, and edges connecting the nodes; determine travel time costs for each edge of the network, wherein determining the travel time costs comprises modeling the travel time costs of the edges using reference point, upper bound and lower bound parameters; receive user input from a client device, wherein the user input includes a source node, destination node, and travel time target; determine a resultant path connecting the source node and destination node by solving a target-oriented robust optimization problem, wherein solving the target-oriented robust optimization problem comprises optimizing a travel time cost of the resultant path based on the modeled costs of the edges; and display a route defined by the resultant path on a user interface of the client device. 14. The system of claim 13 wherein solving the target-oriented robust optimization problem comprises solving a mixed integer linear programming equivalence of the target-oriented robust optimization problem. 15. The system of claim 13 wherein solving the target-oriented robust optimization problem comprises defining an adjustable uncertainty set Cij(γ) for each travel time cost {tilde over (c)}ij associated to an edge (i, j) of the network using: Cij(γ):={{tilde over (c)}ij|γ(cij−ĉij)≦{tilde over (c)}ij−ĉij≦γ(cij−ĉij)} where γε[0, 1], γ denotes a decision variable taking a value between 0 and 1, and represents the size of the uncertainty set, ĉij denotes the reference point parameter, cij denotes the lower bound parameter and cij denotes the upper bound parameter. 16. The system of claim 15 comprising determining the solution of the robust optimization problem by performing a binary search over γ and solving a deterministic problem repeatedly. 17. A non-transitory computer-readable medium having stored thereon a program code, the program code executable by a computer for determining a route in traffic network, comprising: generating a network graph of the traffic network, wherein the network graph comprises nodes corresponding to locations in the traffic network, and edges connecting the nodes; determining travel time costs for each edge of the network, wherein determining the travel time costs comprises modeling the travel time costs of the edges using reference point, upper bound and lower bound parameters; receiving user input from a client device, wherein the user input includes a source node, destination node, and travel time target; determining a resultant path connecting the source node and destination node by solving a target-oriented robust optimization problem, wherein solving the target-oriented robust optimization problem comprises optimizing a travel time cost of the resultant path based on the modeled costs of the edges; and displaying a route defined by the resultant path on a user interface of the client device. 18. The non-transitory computer readable medium of claim 17 wherein solving the target-oriented robust optimization problem comprises solving a mixed integer linear programming equivalence problem of the target-oriented robust optimization problem. 19. The non-transitory computer readable medium of claim 17 wherein solving the target-oriented robust optimization problem comprises defining an adjustable uncertainty set Cij(γ) for each travel time cost {tilde over (c)}ij associated to an edge (i, j) of the network using: Cij(γ):={{tilde over (c)}ij|γ(cij−ĉij)≦{tilde over (c)}ij−ĉij≦γ(cij−ĉij)} where γε[0, 1], γ denotes a decision variable taking a value between 0 and 1, and represents the size of the uncertainty set, ĉij denotes the reference point parameter, cij denotes the lower bound parameter and cij denotes the upper bound parameter. 20. The non-transitory computer readable medium of claim 19 comprising determining the solution of the robust optimization problem by performing a binary search over γ and solving a deterministic problem repeatedly.