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By Laurent Michel

This publication constitutes the court cases of the twelfth overseas convention at the Integration of synthetic Intelligence (AI) and Operations examine (OR) concepts in Constraint Programming, CPAIOR 2015, held in Barcelona, Spain, in might 2015. The 29 papers provided including eight brief papers during this quantity have been rigorously reviewed and chosen from ninety submissions. the aim of the convention sequence is to assemble researchers within the fields of Constraint Programming, synthetic Intelligence and Operations learn to discover methods of fixing demanding and big scale combinatorial optimization difficulties that emerge in a variety of business domain names. Pooling the abilities and strengths of this varied staff of researchers has proved super potent and worthy up to now decade resulting in advancements and cross-fertilization among the 3 fields in addition to step forward for genuine applications.

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We also want to see if the successor relations stored in the precedence graph can be exploited in this context. We plan to evaluate our new constraint on other benchmarks, and compare it with other approaches. Acknowledgments. This work has been done in the context of the Optimod’Lyon project. We would like to give our special thanks to Thomas Baudel for his help in the obtention of traffic data. A. Melgarejo et al. Christine Solnon is supported by the LABEX IMU (ANR-10-LABX-0088) of Universit´e de Lyon, within the program “Investissements d’Avenir” (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR).

Next succ (i, j, ta ) and flatest (i, j, ta ), are the transition times giving the latest 2. flatest departure time from i in order to arrive at j at time ta or earlier. With these functions, the TDNoOverlap constraint propagates the earliest time for j (5) and the latest time for i (6), by using the adequate lower bound function depending on whether we propagate a successor arc (x = succ) or a next arc (x = next): x (i, j, time[i] + D[i]) time[j] ≥ time[i] + D[i] + fearliest (5) x time[i] + D[i] ≤ time[j] − flatest (i, j, time[j]) (6) Now we introduce the formal definitions of the bounding functions and explain how to calculate them.

Let ℘i,j τ,f be the set of all timed-paths from i to j starting after time τ with travel times function f . We have: succ (i, j, td ) = min t(j, p) − td fearliest p∈℘i,j t ,f d where t(j, p) is the start time of j in path p. A Time-Dependent No-Overlap Constraint: Application 13 If there exists a shortest path from i to j, shorter than the direct arc, then the triangular inequality extended to the time-dependent case does not hold. It means that there is at least one vertex k such that passing through k allows to arrive faster at j.

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