SIT399: Asymmetric Travelling Salesman Problem in Integer Programming - IT Assessment Answer

IT Assessment Task

Problem description You have learned the Asymmetric Travelling Salesman Problem in Integer Programming, where you were taught an exponential-size formulation. What you may or may not know is that there is actually a polynomial-size formulation. What is cool about the polynomial-size formulation is that it uses a continuous variable for each vertex on the graph as a time-stamp. Now, if we visit City j immediately after City i, then the timestamp of City j, uj should be at least ui + 1, for ui the time-stamp of City i. With the u-variables, and the original x-variables, we are able to model the Asymmetric Travelling Salesman Problem with polynomially many variables and constraints. Now, for this task, you are to find out what the polynomial-size formulation is, understand how it works, model it using CPLEX, and solve the data instance provided for this assignment (see Excel file: data.xlsx). In specific, you are required to perform the following tasks and to produce a report that is no longer than 8 pages. 1. Research the web for references of the polynomial-size formulation for ATSP, it can be lecture notes, papers, or videos.

2. Write down the entire polynomial-size formulation for ATSP

3. Explain the constraints and the variables, and how the polynomially many constraints work in eliminating subtours

4. Code up the model in CPLEX OPL modelling language.

5. Solve the data instance provided in the assignment folder and write down the solution.

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