A mixed-integer linear programming model and a metaheuristic approach for the selection and allocation of land parcels problem

This article is about the current agricultural scenario, where large-scale production causes large amounts of food to be transported to various points of consumption, causing substantial emissions of so-called greenhouse gases and increasing the carbon footprint. Land use optimization and land parcel allocation are essential areas of agriculture research that currently represent relevant challenges and are classified as combinatorial optimization problems. In this context, the Selection and Allocation of Land Parcels Problem (SA-LPP) is proposed; its goal is to optimize the selection and allocation of land parcels with rectangular shapes in small areas available for food production. We propose a reformulation of the SA-LPP as a variant of the two-dimensional orthogonal packing problem (2OPP), called Group-2OPP. This problem was solved through a Mixed-Integer Linear Programming (MILP) model, but due to the model complexity, we also propose a Greedy Randomized Adaptive Search Procedure metaheuristic approach. Some sensitivity analyses were performed as well to evaluate the impact of parameters on the solutions. Computational results show that the proposed metaheuristic outperforms the MILP model in terms of solution quality and computational times.