Exact Zoning Optimization Model for Marine Spatial Planning (MSP)

Marine spatial planning (MSP) serves as a crucial decision-making tool for the sustainable management of marine resources, especially given the increasing and often competing demands for ocean space. A significant challenge within MSP is the precise determination of optimal zones for new activities, considering the locations and implications of existing marine uses. Current approaches to spatial zoning predominantly rely on non-linear optimization models, typically solved using stochastic search algorithms, which often result in sub-optimal solutions. This paper introduces a novel approach to model the zoning problem within MSP as a Multi-Objective Integer Linear Program (MOILP). The proposed model is designed to work with raster data, aiming to achieve two primary objectives simultaneously: maximizing the 'interest' of the area allocated for a new activity and maximizing its spatial compactness. The 'interest' refers to the suitability or attractiveness of a particular marine area for the new activity, based on various environmental and operational factors. Spatial compactness, on the other hand, is crucial for minimizing potential conflicts with future marine activities and ensuring efficient use of space. Two distinct resolution methods are explored for solving this MOILP: a weighted-sum approach and an interactive method known as AUGMECON2, which is an enhanced version of the classical ε-constraint method. The weighted-sum method combines the two objectives into a single function using a weighting parameter (λ), allowing for a trade-off between interest maximization and compactness maximization. The AUGMECON2 method, in contrast, generates a set of Pareto-optimal solutions, providing decision-makers with a range of non-dominated options that represent different compromises between the conflicting objectives. A key innovation to address the computational complexity arising from a large number of integer variables and constraints in the MOILP model is a two-step resolution process. First, a buffering technique is applied in a preprocessing phase to significantly reduce the feasible region by eliminating areas that violate predefined minimum and maximum distance constraints to existing marine activities such as shipping lanes, ports, and restricted zones. This pre-processing step effectively prunes the search space, making the subsequent optimization problem more tractable. After this reduction, the simplified mathematical program, devoid of the complex distance constraints, is solved using either the weighted-sum or AUGMECON2 techniques. Experimental validation is conducted using artificially generated datasets with varying characteristics, including different interest maps and configurations of existing marine activities. The study evaluates the models based on three criteria: validity (ability to find optimal solutions), sensitivity of solutions to algorithmic parameters, and computational complexity. The results demonstrate that both resolution methods are capable of identifying optimal solutions. Notably, AUGMECON2 emerges as the more promising approach, offering greater relevance and diversity in solutions, superior compactness, and competitive computation times. It effectively generates a broader range of distinct solutions and allows for better control over the number of generated outcomes, making it more flexible for decision-makers. In contrast, the weighted-sum method tends to produce less balanced solutions concerning interest and compactness and is less sensitive to the buffering technique's impact on the solution space. #MarineSpatialPlanning #MultiObjectiveOptimization #IntegerLinearProgramming #SpatialZoning #AUGMECON2 #RasterData #EnvironmentalManagement #DecisionSupportTool #MarineSpatialPlanning #MultiObjectiveOptimization #IntegerLinearProgramming #SpatialZoning #AUGMECON2 #RasterData #EnvironmentalManagement #DecisionSupportTool