Designing mixed fruit-vegetable cropping systems by integer quadratic programming
Mixed fruit-vegetable cropping systems (MFVCS) are a promising way of ensuring environmentally sustainable agricultural production systems in response to the challenge of being able to fulfill local market requirements. Indeed, they combine productions and they 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 a system must optimize the use of these resources, by maximizing positive interactions (facilitation) and minimizing negative ones (competition). To attain these objectives, the systemRSQUOs design has to include the spatial and temporal dimensions, taking into account the evolution of above- and belowground interactions over a time horizon. However, a considerable amount of research has been conducted, on the one hand, to prove the interest of agroforestry, and on the other hand to propose models supporting cropping plan and crop rotation decisions, but to our knowledge, no model supports the spatial and temporal allocation of both vegetable crops and trees in agroforestry systems. Therefore, we initially built a first MFVCS prototype using the weighted constraint satisfaction framework but the resolution was limited to small-scale systems. In this paper, we explore larger MFVCS models using a solver based on integer quadratic programming. The limits of exact methods in solving the MFVCS problem are presented showing the need for approximation methods able to solve a large-scale system with solutions of good quality in reasonable time, which could be used in interactive design with farmers and advisers.
Maqrot, S., de Givry, S., Quesnel, G. and Tchamitchian, M. (2017). Designing mixed fruit-vegetable cropping systems by integer quadratic programming. Acta Hortic. 1182, 265-274
agroforestry, agro-ecology, ecological interactions, spatial and temporal crop allocation problem, exact methods