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.
HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Une contrainte de circuit adaptée aux tournées multiples Nicolas Briot, Philippe Vismara, Christian Bessière
HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Une contrainte de circuit adaptée aux tournées multiples Nicolas Briot, Philippe Vismara, Christian Bessière
In this paper, we study the problem of differential harvest in precision viticulture. Some recent prototypes of grape harvesting machines are supplied with two hoppers and are able to sort two types of grape quality. Given estimated qualities and quantities on the different areas of the vineyard, the problem is to optimize the routing of the grape harvester under several constraints. The main constraints are the amount of first quality grapes to harvest and the capacity of the hoppers. We model the differential harvest problem as a constraint optimization problem. We present preliminary results on real data. We also compare our constraint model to an integer linear programming approach and discuss expressiveness and efficiency.
One of the most important applications of precision agriculture to viticulture is the management of the quality of grapes at the field level through selective harvest. The recent developments of prototypes of conventional grape harvesting machines are able to sort two types of harvest quality. In this paper, we propose a formal description of the problem of differential harvesting. The objective is to optimize the routing of the grape harvester under several constraints. Our approach is based on Constraint Programming (CP), which is a powerful paradigm to solve combinatorial problems. We give a formulation of the problem as a Constraint Optimization Problem. The last section of the paper is devoted to preliminary experimental results on real data from a French vineyard.
