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The traveling salesperson problem (TSP)

can be solved with the minimum- spanning-tree (MST) heuristic, which estimates the

cost of completing a tour, given that a partial tour has already been constructed. The MST

cost of a set of cities is the smallest sum of the link costs of any tree that connects all the

cities.

1 Model this problem as a search problem, including, how to define the state space,

start states, operators, path cost and goal state. Show that how the MST heuristic can

be derived from a relaxed version of the TSP, and it is admissible.

2 Write a problem generator for instances of the TSP where cities are represented by

random points in the unit square.

3 Find an efficient algorithm for constructing the MST, and use it with the A * graph

search to solve instances of the TSP.

4 Implement an A* search algorithm to solve the problem. How far can you go with the

A* approach, as the problem size (#cities increases) increases, record the time

(measured by the number of nodes explored) and space (measured by the maximum

number of nodes stored in the open list during the program execution) needed for a

certain size of problem.

5 When the problem size increase, A* runs out of memory. So implement the SMA* to

solve the memory limit problem. Put a fixed limit on the number of nodes that you

can store in open list, show that with the same amount of memory available, SMA* is

able to solve larger size of problem while A* cannot solve. What is the solution found

by SMA*, is it optimal?

6 Sometimes you need find a solution within limited amount of time, you need trade off

the computation time with the solution quality. Modify the A* to an anytime A* and

try it with different w values, record the results you get. Show the multiple different

solutions found by the anytime A* as search time increases.

7 Implement a GUI that allows the choices of #cities, memory size (#nodes) and the

algorithm to run, and demonstrate the solution both graphically and numerically.

Skills: Java

See more: tree algorithm, sum tree, sum solutions, solution algorithm, smallest amount time, search graph, problem points solution, problem graph, problem approach, path graph, path algorithm, number nodes tree, minimum unit cost, minimum cost path, minimum cost algorithm, memory graph, maximum path, maximum minimum algorithm, list graph, link graph, write search algorithm, use algorithm, find optimal solution, find solutions, find minimum cost

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