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Collaborating Authors

Cambazard, Hadrien


A global constraint for the capacitated single-item lot-sizing problem

arXiv.org Artificial Intelligence

The goal of this paper is to set a constraint programming framework to solve lot-sizing problems. More specifically, we consider a single-item lot-sizing problem with time-varying lower and upper bounds for production and inventory. The cost structure includes time-varying holding costs, unitary production costs and setup costs. We establish a new lower bound for this problem by using a subtle time decomposition. We formulate this NP-hard problem as a global constraint and show that bound consistency can be achieved in pseudo-polynomial time and when not including the costs, in polynomial time. We develop filtering rules based on existing dynamic programming algorithms, exploiting the above mentioned time decomposition for difficult instances. In a numerical study, we compare several formulations of the problem: mixed integer linear programming, constraint programming and dynamic programming. We show that our global constraint is able to find solutions, unlike the decomposed constraint programming model and that constraint programming can be competitive, in particular when adding combinatorial side constraints.


Alternative Filtering for the Weighted Circuit Constraint: Comparing Lower Bounds for the TSP and Solving TSPTW

AAAI Conferences

Many problems, and in particular routing problems, require to find one or many circuits in a weighted graph. The weights often express the distance or the travel time between vertices. We propose in this paper various filtering algorithms for the weighted circuit constraint which maintain a circuit in a weighted graph. The filtering algorithms are typical cost based filtering algorithms relying on relaxations of the Traveling Salesman Problem. We investigate three bounds and show that they are incomparable. In particular we design a filtering algorithm based on a lower bound introduced in 1981 by Christophides et al.. This bound can provide stronger filtering than the classical Held and Karp’s approach when additional information, such as the possible positions of the clients in the tour, is available. This is particularly suited for problems with side constraints such as time windows.


A Constraint-Based Dental School Timetabling System

AI Magazine

We describe a constraint-based timetabling system that was developed for the dental school based at Cork University Hospital in Ireland. Dental school timetabling differs from other university course scheduling in that certain clinic sessions can be used by multiple courses at the same time, provided a limit on room capacity is satisfied. Solutions for the years 2010, 2011 and 2012 have been used in the dental school, replacing a manual timetabling process, which could no longer cope with increasing student numbers and resulting resource bottlenecks. The use of the automated system allowed the dental school to increase the number of students enrolled to the maximum possible given the available resources.


A Constraint-Based Dental School Timetabling System

AI Magazine

We describe a constraint-based timetabling system that was developed for the dental school based at Cork University Hospital in Ireland. This sy stem has been deployed since 2010. Dental school timetabling differs from other university course scheduling in that certain clinic sessions can be used by multiple courses at the same time, provided a limit on room capacity is satisfied. Starting from a constraint programming solution using a web interface, we have moved to a mixed integer programming-based solver to deal with multiple objective functions, along with a dedicated Java application, which provides a rich user interface. Solutions for the years 2010, 2011 and 2012 have been used in the dental school, replacing a manual timetabling process, which could no longer cope with increasing student numbers and resulting resource bottlenecks. The use of the automated system allowed the dental school to increase the number of students enrolled to the maximum possible given the available resources. It also provides the school with a valuable “what-if” analysis tool.


A Combinatorial Optimisation Approach to Designing Dual-Parented Long-Reach Passive Optical Networks

arXiv.org Artificial Intelligence

We present an application focused on the design of resilient long-reach passive optical networks. We specifically consider dual-parented networks whereby each customer must be connected to two metro sites via local exchange sites. An important property of such a placement is resilience to single metro node failure. The objective of the application is to determine the optimal position of a set of metro nodes such that the total optical fibre length is minimized. We prove that this problem is NP-Complete. We present two alternative combinatorial optimisation approaches to finding an optimal metro node placement using: a mixed integer linear programming (MIP) formulation of the problem; and, a hybrid approach that uses clustering as a preprocessing step. We consider a detailed case-study based on a network for Ireland. The hybrid approach scales well and finds solutions that are close to optimal, with a runtime that is two orders-of-magnitude better than the MIP model.