Improved filtering for weighted circuit constraints

Benchimol, Pascal; Hoeve, Willem‐Jan van; Régin, Jean‐Charles; Rousseau, Louis-Martin; Rueher, Michel

doi:10.1007/s10601-012-9119-x

Cited by 33 publications

(72 citation statements)

References 43 publications

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“…We note that Lagrangian relaxations have been applied before in the context of CP, see for example [16,17,18,19,20,21,22,23]. Our results further strengthen the idea that Lagrangian relaxations are a particularly useful method from operations research for enhancing the inference process of constraint programming.…”

Section: Introductionsupporting

confidence: 76%

A Lagrangian Relaxation for Golomb Rulers

Slusky

Hoeve

2013

Lecture Notes in Computer Science

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Abstract. 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.

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Section: Introductionsupporting

confidence: 76%

A Lagrangian Relaxation for Golomb Rulers

Slusky

Hoeve

2013

Lecture Notes in Computer Science

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“…Reasoning on successors is in fact complementary with reasoning on a prev/ next graph. In future work we plan to improve our constraint propagation by calculating tighter bounds for the TDTSP by using Minimum Spanning Trees or Assignment Problem relaxations on the prev/next graph, extending the approaches described in [15,6,12]. We also want to see if the successor relations stored in the precedence graph can be exploited in this context.…”

Section: Discussionmentioning

confidence: 99%

“…We present here a TDTSP model adapted from the classic CP model used to solve the TSP (see [6]). We added variables time[i], which give the arrival time at each vertex i, and modified constraints to take into account the fact that a duration D i is associated with every vertex i, and that travel durations are time-dependent.…”

Section: Cp Modelmentioning

confidence: 99%

A Time-Dependent No-Overlap Constraint: Application to Urban Delivery Problems

Melgarejo

Laborie

Solnon

2015

Integration of AI and OR Techniques in Constraint Programming

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International audienceThe 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

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“…Moreover, according to the upper bound of Z, some edges can be discarded because they cannot be part of a solution. This filtering is based on computing a reduced cost for each arc (i, j) not in the solution of AP (G * ), i.e., the minimum increase of the overall cost for setting N ext i to j (see [2,7]). For instance, with ub(Z) = 40, edges (8,10) and (9, 11) could be eliminated.…”

Section: Weightedsubcircuitsmentioning

confidence: 99%

A Circuit Constraint for Multiple Tours Problems

Vismara

Briot

2018

Lecture Notes in Computer Science

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Routing problems appear in many practical applications. In the context of Constraint Programming, circuit constraints have been successfully developed to handle problems like the well-known Traveling Salesman Problem or the Vehicle Routing Problem. These kind of constraints are linked to the search for a Hamiltonian circuit in a graph. In this paper we consider a more general multiple tour problem that consists in covering a part of the graph with a set of minimal cost circuits. We define a new global constraint WeightedSubCircuits that generalizes the WeightedCircuit constraint by releasing the need to obtain a Hamiltonian circuit. It enforces multiple disjoint circuits of bounded total cost to partially cover a weighted graph, the subsets of vertices to be covered being induced by external constraints. We show that enforcing Bounds Consistency for WeightedSubCircuits is NP-hard. We propose an incomplete but polynomial filtering method based on the search for a lower bound of a weighted Steiner circuit.

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Improved filtering for weighted circuit constraints

Cited by 33 publications

References 43 publications

A Lagrangian Relaxation for Golomb Rulers

A Lagrangian Relaxation for Golomb Rulers

A Time-Dependent No-Overlap Constraint: Application to Urban Delivery Problems

A Circuit Constraint for Multiple Tours Problems

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