In the manufacturing of printed circuit boards, holes need to be drilled on the boards through...
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In the manufacturing of printed circuit boards, holes need to be drilled on the boards through which chips and other components are later wired. It is required that these holes be drilled as quickly as possible; hence, the problem of the most efficient order to drill the holes is a traveling salesman problem. Given the table below are the distances (in millimeters) between any pair of hole locations. Hence, minimum time equals finding the minimum total distance traveled between the hole locations. Hole locations 1 2 3 4 8 1 13 15 16 19 21 2 13 5 14 22 11 14 9. 9. 3 8 15 17 13 12 4 15 7 15 8 7 10 7 14 17 8 12 18 11 16 22 12 8 14 7 19 11 13 18 8 15 21 14 12 10 11 14 15 (a) Use the nearest neighbor heuristic to find an efficient ordering of the holes. Start your algorithm once at hole 1 and once at hole 3 (producing two different efficient orderings). (b) Use the cheapest insertion heuristic to find an efficient ordering of the holes. Start your algorithm once at hole 2 and once at hole 4 (producing two different efficient orderings). BONUS Produce an efficient ordering using the nearest neighbor heuristic for ev- ery starting hole. Also, produce an efficient ordering using the cheapest insertion heuristic for every starting hole. +1 pts if completed. BONUS 2 Use a 2-interchange method to improve the best path you have yet found. +2 pt if completed, but you must complete the first bonus question as well as well. In the manufacturing of printed circuit boards, holes need to be drilled on the boards through which chips and other components are later wired. It is required that these holes be drilled as quickly as possible; hence, the problem of the most efficient order to drill the holes is a traveling salesman problem. Given the table below are the distances (in millimeters) between any pair of hole locations. Hence, minimum time equals finding the minimum total distance traveled between the hole locations. Hole locations 1 2 3 4 8 1 13 15 16 19 21 2 13 5 14 22 11 14 9. 9. 3 8 15 17 13 12 4 15 7 15 8 7 10 7 14 17 8 12 18 11 16 22 12 8 14 7 19 11 13 18 8 15 21 14 12 10 11 14 15 (a) Use the nearest neighbor heuristic to find an efficient ordering of the holes. Start your algorithm once at hole 1 and once at hole 3 (producing two different efficient orderings). (b) Use the cheapest insertion heuristic to find an efficient ordering of the holes. Start your algorithm once at hole 2 and once at hole 4 (producing two different efficient orderings). BONUS Produce an efficient ordering using the nearest neighbor heuristic for ev- ery starting hole. Also, produce an efficient ordering using the cheapest insertion heuristic for every starting hole. +1 pts if completed. BONUS 2 Use a 2-interchange method to improve the best path you have yet found. +2 pt if completed, but you must complete the first bonus question as well as well.
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