Problem 1. [70 points) Consider the following list of node locations, where node 0 represents a depot and all other locations represent customers Node x-coordinate y-coordinate 50 11 56 50 22 * SUSAN Suppose the cost to travel between any pair of locations is given by the Manhattan metric, that is, the rectilinear distance between them. (This is the sum of the horizontal and vertical distances between the points, and is used in urban logistics to model travel time between locations in a city.) (a) (20 points) Run the Nearest Neighbor heuristics using the depot as a starting point; report the heuristics' partial solution after every iteration, and the final solutions. (b) (30 points) Run the Cheapest Insertion heuristics using the depot as a starting point; report the heuristics' partial solution after every iteration, the final solutions, and compare its cost to the one obtained in part (a) using the Nearest Neighbor heuristic. (c) (20 points) For the Cheapest Insertion solutions you obtained in (b), identify a 2-opt im- provement step, or verify that none exists. Problem 1. [70 points) Consider the following list of node locations, where node 0 represents a depot and all other locations represent customers Node x-coordinate y-coordinate 50 11 56 50 22 * SUSAN Suppose the cost to travel between any pair of locations is given by the Manhattan metric, that is, the rectilinear distance between them. (This is the sum of the horizontal and vertical distances between the points, and is used in urban logistics to model travel time between locations in a city.) (a) (20 points) Run the Nearest Neighbor heuristics using the depot as a starting point; report the heuristics' partial solution after every iteration, and the final solutions. (b) (30 points) Run the Cheapest Insertion heuristics using the depot as a starting point; report the heuristics' partial solution after every iteration, the final solutions, and compare its cost to the one obtained in part (a) using the Nearest Neighbor heuristic. (c) (20 points) For the Cheapest Insertion solutions you obtained in (b), identify a 2-opt im- provement step, or verify that none exists