Approximation algorithm case study

Approximation algorithm case study

Approximation algorithm (15%)
Implement a simple heuristic for solving the TSP approximately. Include your program code in your submission.
Your program should:
1. Parse a .tsp file from TSPLib, preprocess it and store the graph in memory;
2. Generate a TSP solution using the simple heuristic;
3. Output the solution in the form of node sequence as well as its total weight.
Test the simple heuristic on at least 10 instances from the TSPLib, and discuss the results compared to the
best-known results provided on the website. You should include the necessary screenshots in your final
report in order for the marker to verify the correct functioning of your program. You should also
include a short description of your simple heuristic.
Hint: One simple heuristic to consider is to choose to start the TSP tour from the city with the lowest average
distance to all other cities and then always visit the next city with the shortest distance from the current city (make
sure that the next city has never been visited previously until the tour goes back to the start city).
2.3 Local search (20%)
Develop a simulated annealing algorithm for solving the TSP. Include your program code in your submission.
Clearly describe your algorithm (including solution representation, initialisation method, neighbourhood definition, cooling schedule, and stopping criteria) in the report.
Test your algorithm on a280.tsp, and draw a convergence curve, where the x-axis is the number of iterations,
and the y-axis is the total weight (or distance) of the current solution. Include and discuss the convergence
curve in the final report. Compare your simulated annealing algorithm to the best-known solution and the
approximation algorithm developed in Subsection 2.2 in terms of their performances. You should include
the necessary screenshots in your final report in order for the marker to verify the correct
functioning of your program.
2.4 Evolutionary computation (20%)
Develop a genetic algorithm for solving the TSP. Include your program code in your submission.
Clearly describe your algorithm (including solution representation, initialisation method, evolution process,
selection operator, crossover and mutation operators) in the report.
Clearly describe the algorithm parameters (including population size, crossover and mutation rates, and stopping criteria).
Test your algorithm on a280.tsp, and draw a convergence curve, where the x-axis is the number of generations,
and the y-axis is the best individual (solution) in the current population. Include and discuss the convergence
curve in the final report. Compare your genetic algorithm to the best-known solution and your simulated
annealing algorithm in terms of their performances. You should include the necessary screenshots in
your final report in order for the marker to verify the correct functioning of your program.

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