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 also 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 system's design has to include the spatial and temporal dimensions of these interactions, 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.
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We introduce resource allocation techniques for problems where (i) the agents express requests for obtaining item bundles as compact edge-weighted directed acyclic graphs (each path in such a graph is a bundle whose valuation is the sum of the weights of the traversed edges), and (ii) the agents do not bid on the exact same items but may bid on conflicting items that cannot be both assigned or that require accessing a specific resource with limited capacity. This setting is motivated by real applications such as Earth observation slot allocation, virtual network functions, or multi-agent path finding. We model several directed path allocation problems (vertex-constrained and resource-constrained), investigate several solution methods (qualified as exact or approximate, and utilitarian or fair), and analyze their performances on an orbit slot ownership problem, for realistic requests and constellation configurations.
In the context of Earth observation constellations, we consider the problem of allocating orbit slots to clients requesting some ownership of orbit portions overflying desired regions on Earth. This problem arises prior to operational scheduling of observation tasks, in constellations where users can directly communicate with the satellites using their own ground stations. Observation scheduling in the exclusive slots is then delegated to the clients themselves. To perform the allocation of exclusive slots, we propose a two-level optimization approach, where the optimization process (led by either utilitarian or fair criterion) explores the solution space using a feasibility checker based on a constraint solver. We experimentally evaluate and analyze their performance on randomly generated order books and real constellation configurations.
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