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Tabu Search on Travelling Salesperson Problems with Profits

In this project, we tried to solve Travelling Salesperson Problems with Profits (TSPs with profits) with Tabu Search (TS). Before I start doing anything on the problem, I made a literature survey. There are lots of papers in the literature about TSPs with profits but those papers are generally tries to solve it with some constraints. So actually I couldn't find a good paper to pointing out our problem which has no constraint. But the following paper has some good ideas about the general structer of the problem even it has a constraint on the tour length:

• Gendreau, Michel, Gilbert Laporte, and Frédéric Semet. "A tabu search heuristic for the undirected selective travelling salesman problem." European Journal of Operational Research 106.2-3 (1998): 539-545.

Travelling Salesperson Problems with Profits

Traveling Salesperson problems with profits (TSPs with profits) are a generalization of the traveling salesman problem (TSP), where it is not necessary to visit all vertices. A profit is associated with each vertex. The overall goal is the simultaneous optimization of the collected profit and the travel costs. (http://pubsonline.informs.org/doi/abs/10.1287/trsc.1030.0079?journalCode=trsc)

Solution Representation

I used a simple permutation representation. The list [1, 2, 3, 4, 5, 1] represents the route of the salesperson. All the routes should start with "1" and end with "1" which is the depot.

Tabu Search

In this part I will explain the steps of tabu search for the travelling salesperson problems with profits.

Pseudocode

1. (Initialization) Construct an initial tour by means of a construction heuristic.
2. (Insertion Partitions) Determine all insertion partitions according to proximity measure and retain 10 of them. Repeat Step 3-8 for $10000$ iterations:
3. (Insertion Candidate) Randomly choose one insertion partition and determine the best insertion candidate from this partition
4. (Deletion Chains) Determine the deletion chains.
5. (Deletion Candidate) Determine the best deletion candidate from deletion chains
6. (Insertion or Deletion) Compare the results of the insertion and deletion then apply the best one. If the best move is deletion then declare all vertices of deletion tabu for $\theta$ iteration
7. (Tour Improvement) If the iteration count is multiple of 5, apply 2-opt
8. (Best Solution Update) If newly generated solution has a better objective then the incumbent solution then apply 3-opt to the newly generated solution to improve the tour quality and make it the incumbent solution.
9. (Shuffle to Reset) If there hasn't been an improvement in $\gamma$ iteration, then assign incumbent solution to the current solution and shuffle the route. Also clear the tabu list.