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Improving the asymmetric TSP by considering graph structure. arXiv preprint arXiv:1206.3437
, 2012
"... Abstract. Recent works on cost based relaxations have improved Constraint Programming (CP) models for the Traveling Salesman Problem (TSP). We provide a short survey over solving asymmetric TSP with CP. Then, we suggest new implied propagators based on general graph properties. We experimentally sho ..."
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Abstract. Recent works on cost based relaxations have improved Constraint Programming (CP) models for the Traveling Salesman Problem (TSP). We provide a short survey over solving asymmetric TSP with CP. Then, we suggest new implied propagators based on general graph properties. We experimentally show that such implied propagators bring robustness to pathological instances and highlight the fact that graph structure can significantly improve search heuristics behavior. Finally, we show that our approach outperforms current state of the art results. 1
C.: Global and reactive routing in urban context: first experiments and difficulty assessment
- In: CP-2012 Workshop on Optimization and Smart Cities
, 2012
"... experiments / first difficulty assessment ..."
A Time-Dependent No-Overlap Constraint: Application to Urban Delivery Problems
"... Abstract. The Time-Dependent Traveling Salesman Problem (TDTSP) is the extended version of the TSP where arc costs depend on the time when the arc is traveled. When we consider urban deliveries, travel times vary considerably during the day and optimizing a delivery tour comes down to solving an ins ..."
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Abstract. The Time-Dependent Traveling Salesman Problem (TDTSP) is the extended version of the TSP where arc costs depend on the time when the arc is traveled. When we consider urban deliveries, travel times vary considerably during the day and optimizing a delivery tour comes down to solving an instance of the TDTSP. In this paper we propose a set of benchmarks for the TDTSP based on real traffic data and show the interest of handling time dependency in the problem. We then present a new global constraint (an extension of no-overlap) that integrates time-dependent transition times and show that this new constraint outper-forms the classical CP approach. 1
A Lagrangian Relaxation for Golomb Rulers
, 2013
"... The Golomb Ruler Problem asks to position n integer marks on a ruler such that all pairwise distances between the marks are distinct and the ruler has minimum total length. It is a very challenging combinatorial problem, and provably optimal rulers are only known for n up to 26. Lower bounds can be ..."
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The Golomb Ruler Problem asks to position n integer marks on a ruler such that all pairwise distances between the marks are distinct and the ruler has minimum total length. It is a very challenging combinatorial problem, and provably optimal rulers are only known for n up to 26. Lower bounds can be obtained using Linear Programming formulations, but these are computationally expensive for large n. In this paper, we propose a new method for finding lower bounds based on a Lagrangian relaxation. We present a combinatorial algorithm that finds good bounds quickly without the use of a Linear Programming solver. This allows us to embed our algorithm into a constraint programming search procedure. We compare our relaxation with other lower bounds from the literature, both formally and experimentally. We also show that our relaxation can reduce the constraint programming search tree considerably.
