Abstract
The probabilistic traveling salesman problem is a paradigmatic example of a stochastic combinatorial optimization problem. For this problem, recently an estimation-based local search algorithm using delta evaluation has been proposed. In this paper, we adopt two well-known variance reduction procedures in the estimation-based local search algorithm: the first is an adaptive sampling procedure that selects the appropriate size of the sample to be used in Monte Carlo evaluation; the second is a procedure that adopts importance sampling to reduce the variance involved in the cost estimation. We investigate several possible strategies for applying these procedures to the given problem and we identify the most effective one. Experimental results show that a particular heuristic customization of the two procedures increases significantly the effectiveness of the estimation-based local search.
| Original language | English |
|---|---|
| Pages (from-to) | 98-110 |
| Number of pages | 13 |
| Journal | European Journal of Operational Research |
| Volume | 199 |
| Issue number | 1 |
| DOIs | |
| State | Published - Nov 16 2009 |
| Externally published | Yes |
Funding
The authors thank Leonora Bianchi for providing the source code of 2-p-opt and 1-shift . This research has been supported by COMP 2 SYS , an Early Stage Trainig project funded by the European Commission within the Marie Curie Actions program (MEST-CT-2004-505079), and by ANTS and META-X, which are ARC projects funded by the French Community of Belgium. The authors acknowledge support from the fund for scientific research F.R.S.-FNRS of the French Community of Belgium.
| Funders | Funder number |
|---|---|
| Australian Nurse Teachers' Society | |
| European Commission | MEST-CT-2004-505079 |
| Fédération Wallonie-Bruxelles |
Keywords
- Combinatorial optimization
- Heuristics
- Importance sampling
- Iterative improvement algorithm
- Metaheuristics
- Probabilistic traveling salesman problem