Les textes publiés dans la série des rapports de recherche Les Cahiers du GERAD n’engagent que ... more Les textes publiés dans la série des rapports de recherche Les Cahiers du GERAD n’engagent que la responsabilite ́ de leurs auteurs. La publication de ces rapports de recherche est rendue possible grâce au soutien de HEC Montréal, Polytechnique Montréal, Universite ́ McGill, Universite ́ du Québec a ̀ Montréal, ainsi que du Fonds de recherche du Québec – Nature et technologies.
Abstract. It is well known that each tree metric M has a unique realization as a tree, and that t... more Abstract. It is well known that each tree metric M has a unique realization as a tree, and that this realization minimizes the total length of the edges among all other realizations of M. We extend this result to the class of symmetric matrices M with zero diagonal, positive entries, and such that mij + mkl ≤ max{mik + mjl, mil + mjk} for all distinct i, j, k, l.
We describe a tabu search algorithm for the vehicle routing problem with split deliveries. At eac... more We describe a tabu search algorithm for the vehicle routing problem with split deliveries. At each iteration, a neighbor solution is obtained by removing a customer from a set of routes where it is currently visited and inserting it either into a new route or into an existing route that has enough residual capacity. The algorithm also considers the possibility of inserting a customer into a route without removing it from another route. The insertion of a customer into a route is done by means of the cheapest insertion method. Computational experiments are reported for a set of benchmark problems, and the results are compared with those obtained by the algorithm proposed by Dror and Trudeau.
... [10] A. Hertz and D. de Werra, "Using tabu search techniques for graph coloring", C... more ... [10] A. Hertz and D. de Werra, "Using tabu search techniques for graph coloring", Computing 39 (1987) 345351. ... [14] DW Matula, G. Marble, JD Isaacson, "Graph coloring algorithms", in: RC Read (ed.), Graph Theo' and Com puting Academic Press, New York, 1972, 108122. ...
We consider the problem of assigning clients to nurses for home care services. The aim is to bala... more We consider the problem of assigning clients to nurses for home care services. The aim is to balance the work load of the nurses while avoiding long travels to visit the clients. We analyze the case of the CSSS Côte-des-Neiges, Métro and Parc Extension for which a previous analysis has shown that demand fluctuations may create work overload for the nursing staff. We present two models, one with linear constraints and a quadratic objective function which we optimize using CPLEX, and a more complex model with non linear constraints that we optimize using a tabu search algorithm.
The following is a chapter of the book entitled Fourmis artificielles, des bases algorithmiques a... more The following is a chapter of the book entitled Fourmis artificielles, des bases algorithmiques aux concepts et réalisations avancés, Nicolas Monmarché, Frédéric Guinand and Patrick Siarry, editors, which will be published by Hermès Science Publishing Ltd in 2008. Les Cahiers du GERAD G–2008–29 1
A profit and a demand are associated with each arc of a set of profitable arcs of a given graph. ... more A profit and a demand are associated with each arc of a set of profitable arcs of a given graph. A travel time is associated with each arc of the graph. A fleet of capacitated vehicles is given to serve the profitable arcs. A maximum duration of the route of each vehicle is also given. The profit of an arc can be collected by one vehicle only that also serves the demand of the arc. The objective of this problem, that is called the Capacitated Arc Routing Problem with Profits (CARPP), is to find a set of routes that satisfy the constraints on the duration of the route and on the capacity of the vehicle and maximize the total collected profit. We propose a branch-and-price algorithm and several heuristics. We can solve exactly instances with up to 97 profitable arcs. The best heuristics find the optimal solution on most of instances where it is available.
Distance metric learning algorithms aim to appropriately measure similarities and distances betwe... more Distance metric learning algorithms aim to appropriately measure similarities and distances between data points. In the context of clustering, metric learning is typically applied with the assist of side-information provided by experts, most commonly expressed in the form of cannot-link and must-link constraints. In this setting, distance metric learning algorithms move closer pairs of data points involved in must-link constraints, while pairs of points involved in cannot-link constraints are moved away from each other. For these algorithms to be effective, it is important to use a distance metric that matches the expert knowledge, beliefs, and expectations, and the transformations made to stick to the side-information should preserve geometrical properties of the dataset. Also, it is interesting to filter the constraints provided by the experts to keep only the most useful and reject those that can harm the clustering process. To address these issues, we propose to exploit the dual...
Les textes publiés dans la série des rapports de recherche Les Cahiers du GERAD n’engagent que ... more Les textes publiés dans la série des rapports de recherche Les Cahiers du GERAD n’engagent que la responsabilite ́ de leurs auteurs. La publication de ces rapports de recherche est rendue possible grâce au soutien de HEC Montréal, Polytechnique Montréal, Universite ́ McGill, Universite ́ du Québec a ̀ Montréal, ainsi que du Fonds de recherche du Québec – Nature et technologies.
Abstract. It is well known that each tree metric M has a unique realization as a tree, and that t... more Abstract. It is well known that each tree metric M has a unique realization as a tree, and that this realization minimizes the total length of the edges among all other realizations of M. We extend this result to the class of symmetric matrices M with zero diagonal, positive entries, and such that mij + mkl ≤ max{mik + mjl, mil + mjk} for all distinct i, j, k, l.
We describe a tabu search algorithm for the vehicle routing problem with split deliveries. At eac... more We describe a tabu search algorithm for the vehicle routing problem with split deliveries. At each iteration, a neighbor solution is obtained by removing a customer from a set of routes where it is currently visited and inserting it either into a new route or into an existing route that has enough residual capacity. The algorithm also considers the possibility of inserting a customer into a route without removing it from another route. The insertion of a customer into a route is done by means of the cheapest insertion method. Computational experiments are reported for a set of benchmark problems, and the results are compared with those obtained by the algorithm proposed by Dror and Trudeau.
... [10] A. Hertz and D. de Werra, "Using tabu search techniques for graph coloring", C... more ... [10] A. Hertz and D. de Werra, "Using tabu search techniques for graph coloring", Computing 39 (1987) 345351. ... [14] DW Matula, G. Marble, JD Isaacson, "Graph coloring algorithms", in: RC Read (ed.), Graph Theo' and Com puting Academic Press, New York, 1972, 108122. ...
We consider the problem of assigning clients to nurses for home care services. The aim is to bala... more We consider the problem of assigning clients to nurses for home care services. The aim is to balance the work load of the nurses while avoiding long travels to visit the clients. We analyze the case of the CSSS Côte-des-Neiges, Métro and Parc Extension for which a previous analysis has shown that demand fluctuations may create work overload for the nursing staff. We present two models, one with linear constraints and a quadratic objective function which we optimize using CPLEX, and a more complex model with non linear constraints that we optimize using a tabu search algorithm.
The following is a chapter of the book entitled Fourmis artificielles, des bases algorithmiques a... more The following is a chapter of the book entitled Fourmis artificielles, des bases algorithmiques aux concepts et réalisations avancés, Nicolas Monmarché, Frédéric Guinand and Patrick Siarry, editors, which will be published by Hermès Science Publishing Ltd in 2008. Les Cahiers du GERAD G–2008–29 1
A profit and a demand are associated with each arc of a set of profitable arcs of a given graph. ... more A profit and a demand are associated with each arc of a set of profitable arcs of a given graph. A travel time is associated with each arc of the graph. A fleet of capacitated vehicles is given to serve the profitable arcs. A maximum duration of the route of each vehicle is also given. The profit of an arc can be collected by one vehicle only that also serves the demand of the arc. The objective of this problem, that is called the Capacitated Arc Routing Problem with Profits (CARPP), is to find a set of routes that satisfy the constraints on the duration of the route and on the capacity of the vehicle and maximize the total collected profit. We propose a branch-and-price algorithm and several heuristics. We can solve exactly instances with up to 97 profitable arcs. The best heuristics find the optimal solution on most of instances where it is available.
Distance metric learning algorithms aim to appropriately measure similarities and distances betwe... more Distance metric learning algorithms aim to appropriately measure similarities and distances between data points. In the context of clustering, metric learning is typically applied with the assist of side-information provided by experts, most commonly expressed in the form of cannot-link and must-link constraints. In this setting, distance metric learning algorithms move closer pairs of data points involved in must-link constraints, while pairs of points involved in cannot-link constraints are moved away from each other. For these algorithms to be effective, it is important to use a distance metric that matches the expert knowledge, beliefs, and expectations, and the transformations made to stick to the side-information should preserve geometrical properties of the dataset. Also, it is interesting to filter the constraints provided by the experts to keep only the most useful and reject those that can harm the clustering process. To address these issues, we propose to exploit the dual...
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Papers by Alain Hertz