1. Consider the following 5-city traveling salesman problem (TSP). The distance

1. Consider the following 5-city traveling salesman problem (TSP). The distance between each city (in miles) is shown in the following table: City 1 City 2 City 3 City 4 City 5 City 1 ?? 8 4 8 11 City 2 8 ?? 5 6 3 City 3 4 5 ?? 4 7 City 4 8 6 4 ?? 6 City 5 11 3 7 6 ?? (a) Formulate an IP whose solution will solve this TSP (2 points). (b) Use an optimization solver package such as LINDO LINGO and Xpress to find the optimal solution (2 points). (c) Use the branch-and-bound algorithm to find the optimal solution (Show me detailed procedure) (3 points).
1. Consider the following 5-city traveling salesman problem (TSP). The distance between each city (in miles) is shown in the following table: City 1 City 2 City 3 City 4 City 5 City 1 ?? 8 4 8 11 City 2 8 ?? 5 6 3 City 3 4 5 ?? 4 7 City 4 8 6 4 ?? 6 City 5 11 3 7 6 ?? (a) Formulate an IP whose solution will solve this TSP (2 points). (b) Use an optimization solver package such as LINDO LINGO and Xpress to find the optimal solution (2 points). (c) Use the branch-and-bound algorithm to find the optimal solution (Show me detailed procedure) (3 points). (d) What order of visiting each city will minimize the total distance traveled? Starting with 1-2-4-3-5-1 as the initial trial solution apply the basic tabu search algorithm by hand to this problem (Show me detailed procedure) (3 points). Hint: ?? List the links such that a particular sub-tour reversal would be tabu if both links to be deleted in the reversal are on the list. ?? Set maximum size of tabu list equals 4 i.e. 2 from each of the two most recent iterations. Thus whenever a pair of links is added to a full list delete the two oldest links on the list. ?? Stop the algorithm if there is no improvement in the objective function value within 3 consecutive iterations.
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