Conception de systèmes de verger-maraîcher à l’aide de la programmation mathématique
Revue Ouverte d'Intelligence Artificielle, Volume 2 (2021) no. 1, pp. 157-188.

Dans le cadre du développement durable et des innovations dans les systèmes agroalimentaires, les systèmes mixtes horticoles (vergers et maraîchage) visent à répondre aux enjeux actuels auxquels l’agriculture est confrontée, à savoir une diminution de la pollution des sols, une meilleure gestion des ressources (eau, énergies) et un enrichissement de la biodiversité, tout en continuant d’assurer des fonctions alimentaires. Ils combinent des productions à la fois diversifiées et relativement intensifiées, leur permettant de s’insérer en périphérie urbaine. Ces systèmes agroforestiers reposent sur un ensemble complexe d’interactions modifiant l’utilisation de la lumière, de l’eau et des nutriments. La conception d’un tel système doit donc optimiser l’utilisation de ces ressources en maximisant les interactions positives (facilitations) et en minimisant celles négatives (compétitions). Nous définissons le problème de verger-maraîcher comme un problème d’allocation des arbres et des cultures dans les dimensions spatio-temporelles. Nous proposons deux formulations mathématiques  : un modèle quadratique en variables binaires (BQP) et un modèle linéaire en variables mixtes (MILP), obtenant des premiers résultats sur des instances de taille réaliste. Les modèles de l’article sont disponibles ici  : https://miat.inrae.fr/degivry/ROIA21.zip.

Mixed fruit-vegetable cropping systems are a promising way of ensuring environmentally sustainable agricultural production systems in response to the challenge of being able to fulfill local market requirements. They combine productions and make a better use of biodiversity. These agroforestry systems are based on a complex set of interactions modifying the utilization of light, water and nutrients. Thus, designing such systems requires to optimize the use of these resources : by maximizing positive interactions (facilitations) and minimizing negative ones (competitions). To reach these objectives, the system’s design has to include the spatial and temporal dimensions, taking into account the evolution of above- and belowground interactions over a time horizon. For that, we define the mixed fruit-vegetable cropping allocation problem using a discrete representation of the land and the interactions between vegetable crops and fruit trees. We propose two formulations of the problem, using Binary Quadratic Programming (BQP) and Mixed Integer Linear Programming (MILP), obtaining first results on realistic problem sizes. Models are available at https://miat.inrae.fr/degivry/ROIA21.zip.

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DOI : 10.5802/roia.13
Mots clés : Systèmes d’aide à la décision, agroécologie, problème d’allocation spatio-temporelle de cultures, optimisation combinatoire, programmation mathématique
Sara Maqrot 1 ; Simon de Givry 1 ; Marc Tchamitchian 2 ; Gauthier Quesnel 1

1 UR 875 MIAT, Université de Toulouse, INRAE, Castanet-Tolosan, France
2 UR 767 Ecodéveloppement, INRAE, Avignon, France
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Sara Maqrot; Simon de Givry; Marc Tchamitchian; Gauthier Quesnel. Conception de systèmes de verger-maraîcher à l’aide de la programmation mathématique. Revue Ouverte d'Intelligence Artificielle, Volume 2 (2021) no. 1, pp. 157-188. doi : 10.5802/roia.13. https://roia.centre-mersenne.org/articles/10.5802/roia.13/

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