The Kunming-Montreal Global Biodiversity Framework aims to protect 30% of terrestrial, inland water, marine, and coastal ecosystems worldwide, and ensuring that at least 30% of these areas are under effective restoration by 2030. Maintaining and restoring ecological connectivity between natural habitats and protected areas is a key feature of this target. Achieving it will require effective and inclusive spatial planning supported by appropriate decision-support tools. Most spatial planning models address budget as an objective and connectivity as a constraint, formulating problems with Steiner trees. In many real-world cases, such as landscape-scale restoration planning, this formulation is inappropriate when environmental managers seek to optimise connectivity under a budget constraint. This problem was previously addressed with Constraint Programming (CP) and graph variables, but the current approach is severely limited in terms of spatial resolution. In this article, we formalise this problem as the budget-constrained graph connectivity optimisation problem. Based on a real case study: the restoration of forest connectivity in New Caledonia, we illustrate why ``naive'' CP approaches are inefficient. In response, we provide a preprocessing method based on Hanan grids which preserves the existence of at least one optimal solution. Finally, we assess the efficiency of our approach in the New Caledonian case study.

Meeting the UN's objective of developing sustainable agriculture requires, in particular, accompanying small farms in their agroecological transition. This transition often requires making the agrosystem more complex and increasing the number of crops to increase biodiversity and ecosystem services. This paper introduces a flexible model based on Constraint Programming (CP) to address the crop allocation problem. This problem takes a cropping calendar as input and aims at allocating crops to respect several constraints. We have shown that it is possible to model both agroecological and operational constraints at the level of a small farm. Experiments on an organic micro-farm have shown that it is possible to combine these constraints to design very different cropping scenarios and that our approach can apply to real situations. Our promising results in this case study also demonstrate the potential of AI-based tools to address small farmers' challenges in the context of the sustainable agriculture transition.

Faced with natural habitat degradation, fragmentation, and destruction, it is a major challenge for environmental managers to implement sustainable land use policies promoting socioeconomic development and natural habitat conservation in a balanced way. Relying on artificial intelligence and operational research, reserve selection and design models can be of assistance. This paper introduces a partitioning approach based on Constraint Programming (CP) for the reserve selection and design problem, dealing with both coverage and complex spatial constraints. Moreover, it introduces the first CP formulation of the buffer zone constraint, which can be reused to compose more complex spatial constraints. This approach has been evaluated in a real-world dataset addressing the problem of forest fragmentation in New Caledonia, a biodiversity hotspot where managers are gaining interest in integrating these methods into their decisional processes. Through several scenarios, it showed expressiveness, flexibility, and ability to quickly find solutions to complex questions.

Given a set of axis-parallel n-dimensional boxes, the q-intersection is defined as the smallest box encompassing all the points that belong to at least q boxes. Computing the q-intersection is a combinatorial problem that allows us to handle robust parameter estimation with a numerical constraint programming approach. The q-intersection can be viewed as a filtering operator for soft constraints that model measurements subject to outliers. This paper highlights the equivalence of this operator with the search of q-cliques in a graph whose boxicity is bounded by the number of variables in the constraint network. We present a computational study of the q-intersection. We also propose a fast heuristic and a sophisticated exact q-intersection algorithm. First experiments show that our exact algorithm outperforms the existing one while our heuristic performs an efficient filtering on hard problems.