Non-Linear Marine Spatial Zoning Through Particle Filtering

Non-Linear Marine Spatial Zoning Through Particle Filtering 1st Leonidas Ioannou Maritime Digitalisation Centre Cyprus Marine and Maritime Institute Larnaca, Cyprus [email protected] 2nd Neofytos Dimitriou Maritime Digitalisation Centre Cyprus Marine and Maritime Institute Larnaca, Cyprus [email protected] 3rd Ioannis Kyriakides Marine Technology Division Cyprus Marine and Maritime Institute Larnaca, Cyprus [email protected] Abstract—Marine Spatial Planning (MSP) is a critical approach for allocating marine areas to various activities and competing sectors – such as fisheries, renewable energy, conservation, and tourism – while managing their operations to balance ecological, economic, and regulatory considerations. This work explores the application of Sequential Monte Carlo (SMC) and Particle Filtering methods to MSP, and in particular marine zoning. We evaluate the method using synthetic data sets that were generated for zones with ground truth of varying spatial compactness and connectivity. Further, we conduct a sensitivity analysis on the parameters of the method and identify that decreasing particle noise injection during optimization improves time to convergence and the F1-score. The results highlight the potential of SMCbased optimization for efficient and adaptive marine zoning decisions, providing a scalable approach to support sustainable ocean management. Index Terms—Marine Spatial Planning, Zoning Optimization, Sequential Monte Carlo, Non-Linear Optimization I. INTRODUCTION MSP aims to minimize conflicts among marine users, promote synergies, and ensure environmental sustainability through spatial allocation and temporal scheduling of ocean activities [1]. Historically, marine and maritime activities were largely unregulated, in part due to the common misbelief that the ocean was an inexhaustible resource [2]. However, rising pressures from overfishing, pollution, and habitat degradation have underscored the urgent need for structured spatial planning frameworks and sophisticated algorithmic solutions, herein termed Intelligent Marine Spatial Planning (iMSP) [3] [4]. A key application for iMSP is marine zoning, i.e. designating areas for economic activities, such as ones related to aquaculture or the maritime sector, conservation efforts, e.g. designating new Marine Protected Areas (MPAs), and sustainability, e.g. offshore wind farms. Effective zoning requires a coordinated decision-making approach that integrates multiple factors, including ecological constraints, proximity to existing infrastructure, and spatial dependencies between This work was co-financed by the European Union – NextGenerationEU, through the Research and Innovation Foundation under the project MSP4GROWTH (Grant Number: ENTERPRISES/0223/Sub-Call1/0131), the SeaTecHub project, funded by the European Union under Grant Agreement No. 101087162, and the EU H2020 Research and Innovation Programme under Grant Agreement No. 857586 (CMMI-MaRITeC-X). maritime activities. The primary challenges in marine zoning are twofold: data-related challenges, encompassing issues such as data availability, quality, dimensionality, and asynchronicity across diverse sources; and methodology-related challenges, including limited current research and inadequacies of existing methods in addressing the complexity of marine spatial optimization problems both effectively and efficiently at-scale [5]. Multi-Criteria Decision Analysis (MCDA) techniques have been previously used to evaluate site suitability based on multiple factors [3]. Under the umbrella of MCDA techniques, Multi-Objective Integer Programming (MOIP) provides a structured framework for maximizing spatial efficiency by optimizing multiple conflicting objectives such as proximity to ports, the coastline, wind farms, Marine Protected Areas (MPAs), and shipping lanes, ensuring sustainable and conflictfree zoning. [5]. However, MOIP cannot be adopted for large areas under consideration as its computational complexity grows polynomially with the number of cells, posing challenges for large-scale real-world applications. Alternatively, non-linear methods, such as Sequential Monte Carlo (SMC) methods, provide an efficient approach for MSP by iteratively refining solutions via resampling and spatial exploration [3]. The computational complexity of these methods typically scales linearly with the number of particles and can therefore enable large-scale MSP. This work explores the application of Sequential Monte Carlo (SMC) and Particle Filtering methods to MSP and, in particular, marine zoning. We evaluate SMC methods using a newly introduced evaluation framework [5] to assess their effectiveness in optimizing marine spatial planning synthetic scenarios. In particular, we develop probabilistic models that utilize particle filtering-based spatial exploration to identify optimal marine zones. We conduct experiments on synthetic datasets, as introduced by Basirati et al. [5], to assess the method’s performance across different spatial scenarios, categorized as “Very Compact”, “Compact”, and “Not Compact”. Our experimental results corroborate to the effectiveness of the particle filtering-based spatial exploration method. II. PROBLEM DEFINITION Marine zoning in MSP involves identifying an optimal area for a new activity within a busy marine environment. Existing applications requiring marine zoning, such as shipping lanes, ports, and marine protected areas, impose constraints that must be respected. To ensure compatibility with existing activities, the zoning problem must satisfy several key criteria, including distance constraints, spatial compactness, and environmental suitability. Distance constraints are crucial for maintaining spatial separation between marine activities, preventing conflicts, and ensuring operational feasibility. The placement of new zones must account for e.g. their proximity to shipping lanes and ports to avoid interference with vessel traffic and ensure safe navigation. Similarly, marine protected areas (MPAs) require strict separation to prevent disruption to sensitive ecosystems and ensure compliance with environmental regulations. Additionally, conflict zones such as pipelines, energy infrastructure, and restricted areas must be avoided to minimize risks and operational challenges. Beyond spatial separation, spatial compactness is essential for effective marine zoning. The designated zone should be as contiguous as possible to minimize fragmentation, ensuring that the new activity is efficiently contained within a welldefined area. A compact zoning layout also supports longterm spatial planning by reducing spatial conflicts and making future expansions or modifications more manageable. At the same time, environmental suitability constraints ensure that site selection aligns with ecological and regulatory guidelines. For example, the bathymetry and substrate type influence the feasibility of specific activities, such as aquaculture, where stable seabed conditions are necessary for infrastructure placement. Wind speed is another critical factor, as high wind exposure can impact offshore structures and operational stability. By incorporating spatial constraints into the optimization process, the proposed framework ensures that marine zoning provides an efficient approach to spatial planning in complex marine environments. III. METHODOLOGY A. Data Generation To evaluate the optimization model, synthetic marine spatial datasets are generated, following an approach to ensure realistic zoning scenarios [5]. The marine space is modeled as a raster grid, where each cell is assigned a randomly generated interest value. While random in the data generation process, these interest values conceptually represent the fusion of multiple real-world factors, such as environmental suitability, economic viability, and regulatory constraints. Key spatial elements, including shipping lanes, ports, and restricted zones, are randomly placed within the grid to create diverse marine zoning scenarios. This approach ensures a comprehensive evaluation of the proposed optimization model under different spatial configurations. B. Buffering Technique To reduce the computational burden of the optimization process, a a buffering technique, as introduced by Basirati et al. (2021) [5] is applied. This preprocessing step identifies the feasible zoning area by systematically eliminating regions that fail to meet certain conditions (e.g. less than 30 meters) for specific criteria (e.g. marine protected area). Minimum distance constraints ensure that areas too close to existing activities are excluded from the feasible region. Maximum distance constraints maintain accessibility by preventing the selection of zones that are too far from essential infrastructure. By eliminating infeasible areas, the search space is significantly reduced, allowing the optimization algorithm to focus on high-potential locations and improving computational efficiency. C. Sequential Monte Carlo The optimization model employs a Sequential Monte Carlo (SMC) approach to iteratively refine marine zoning decisions. This non-linear optimization method is capable of navigating through the possibly multimodal surface of a cost function that considers various spatial and environmental factors. [3] The process begins with an initialization step, in which hypotheses representing candidate zones are uniformly distributed within the feasible search space. Each hypothesis undergoes an iterative state update process during which its position is adjusted using a stochastic movement model. The movement of each hypothesis is governed by a controlled step size and a Gaussian noise term. The position update equation for each particle at iteration jis given by: xl,j =xl,j−1+V ηl,j (1) where: xl,j is the position of the l-th particle at iteration j,Vis a diagonal matrix controlling the step size and ηl,j ∼ N(0, σ2) is a zero-mean Gaussian noise vector, allowing particles to explore the search space. Each particle is assigned a suitability score based on its location within the spatial interest map. The suitability value of each cell, wi, is originally defined on a discrete domain: wi∈ {1,2,3,4,5,6}(2) To enhance the selection pressure towards optimal locations, the suitability values of each cell are provided by the following, where γcontrols the contrast between high and lowinterest areas: w′ i=wγ i, γ > 1(3) where: wiis the original suitability value of cell iand γ is a scaling exponent that amplifies the differences between optimal and suboptimal locations. Particles are weighted based on their transformed suitability scores, ensuring that higher-weighted particles—those in more suitable areas—have a greater probability of survival. Lowerweighted particles, representing suboptimal zones, are replaced with new candidates in more promising areas, following the resampling process: P(xl,j) = w′ l,j Plw′ l,j (4) where P(xl,j)represents the probability that a given point in marine space is suitable for this activity. This ensures that particles in highly suitable zones are more likely to be propagated while maintaining diversity in the search process. To refine the search, a resampling process is applied at each iteration. This iterative process allows the particle set to converge toward high-suitability zones, ensuring that the final zoning solution maximizes spatial efficiency. IV. RESULTS We conducted a sensitivity analysis to assess how variations in key parameters influence the effectiveness of our methodology. Specifically, we tested different values for the number of generated particles, the initial noise level, and the rate at which noise changes throughout the optimization process. The noise variation was examined under three scenarios: increasing, decreasing, and fixed. Additionally, we analyzed the impact of the step at which noise adjustments begin, as well as the rate of these changes. By systematically altering these parameters, we aimed to identify their effects on the stability and efficiency of the optimization model. A. Evaluation Following the methodology applied by Basirati et al. [5], we evaluate our model’s performance using three different types of control areas that represent optimal locations in our generated maps: •Very Compact: A highly contiguous zone with minimal gaps. •Compact: A somewhat contiguous zone with a few small gaps. •Not Compact: A fragmented zone with multiple disjointed sections. Furthermore, to assess the performance of our model, we compute the F1score at each iteration. The F1score is a widely used metric that balances precision and recall, providing a comprehensive measure of accuracy. In our context, precision reflects the proportion of generated particles that fall within the control area, while recall measures the extent to which the control area’s optimal location is covered by these particles. By tracking the F1score across iterations, we not only evaluate the model’s accuracy but also determine the number of iterations required to reach a satisfactory performance level. This approach helps us understand how efficiently the optimization process converges to an optimal solution and provides insights into parameter tuning for improved results. B. Sensitivity Analysis Results First, we analyzed how different noise variation scenarios—increasing, decreasing, or fixed—affect the F1score for the three types of control areas (Very Compact, Compact, and Not Compact). The results are summarized in Table I, showing the maximum F1score achieved under each scenario. From these results, we observe that the decreasing noise scenario consistently leads to the highest F1score (1.00) across all types of control areas. This suggests that linearly reducing noise at each iteration allows the model to better TABLE I MAXIMUM F1SCORE ACHIEVED FOR EACH NOISE CONFIGURATION AND ACROSS THE DIFFERENT CONTROL AREA SCENARIOS. Noise Scenarios Types of control areas Increasing Decreasing Fixed Very Compact 0.82 1.00 0.94 Compact 0.80 1.00 0.9 Not Compact 0.79 1.00 0.97 converge towards the control area, improving accuracy. In contrast, the fixed noise scenario performs slightly worse, and the increasing noise scenario results in the lowest F1scores, indicating that excessive noise can disrupt convergence. Since decreasing noise was the most effective strategy, we conducted a sensitivity analysis to evaluate how different initial noise values and decay timings influence the convergence rate, measured as the number of iterations required to achieve F1score = 1. The initial noise values were defined as the standard deviation of a zero-mean Gaussian distribution, which influences the degree of randomness in the search process. We tested three levels of initial noise. The first, N1(0.1), introduces low noise, leading to minimal exploration and more localized movements. The second, N2(0.5), provides a moderate level of noise that balances exploration and convergence. The third, N3(1.0), introduces high noise, enabling larger exploratory movements across the map in the early iterations. In addition to varying noise levels, we examined different decay timings, which determine when the noise begins to linearly decrease. The first setting, D1(1st iteration), initiates noise reduction immediately. The second, D2(5th iteration), represents an early decay strategy, while D3(10th iteration) introduces a moderate decay timing. Lastly, D4(20th iteration) delays the reduction of noise for a longer period before decreasing. For each combination of initial noise level and decay timing, we measured the number of iterations required to reach an F1score of 1 across three different control area types: Very Compact, Compact, and Not Compact. This analysis helps determine the optimal noise configuration that minimizes convergence time while ensuring effective exploration and accuracy. The results reveal variations in convergence behavior across different control area types, initial noise values, and decay schedules. Instances where the model failed to achieve F1= 1within the 50 observed iterations are marked with ”–” to indicate non-convergence. A key observation is that earlier noise decay (D1-D2) accelerates convergence, particularly for lower noise levels (N1= 0.1). In contrast, delayed decay (D3-D4) increases the number of required iterations, with a pronounced effect in Very Compact and Not Compact control areas. For N3= 1.0 at D3and D4, the model often fails to reach F1= 1, suggesting that high noise levels combined with late decay impede convergence. TABLE II NUMBER OF ITERATIONS REQUIRED TO REACH F1= 1 FOR DIFFERENT INITIAL NOISE VALUES AND DECAY TIMINGS Decay Timing Control Area Type N1(0.1) N2(0.5) N3(1.0) D1(1st Iteration) Very Compact 24 26 26 Compact 24 27 22 Not Compact 22 23 23 D2(5th Iteration) Very Compact 24 27 26 Compact 20 27 33 Not Compact 23 30 35 D3(10th Iteration) Very Compact 21 26 – Compact 24 37 – Not Compact 26 40 – D4(20th Iteration) Very Compact 30 – – Compact 30 48 – Not Compact 32 – – For Very Compact areas, moderate noise levels (N2= 0.5) with intermediate decay timing (D2-D3) provide a balanced trade-off between exploration and convergence speed. However, Compact and Not Compact areas exhibit higher sensitivity to noise and decay timing, where delayed decay frequently results in extended convergence times or failure to converge. Overall, earlier decay (D1, D2) and lower noise values (N1= 0.1) promote faster convergence, whereas higher noise (N3= 1.0) and late decay (D3, D4) often lead to instability, particularly in Compact and Not Compact areas. Building on these findings, we analyze the sensitivity of the decreasing noise rate for an initial noise value of N1= 0.1, which demonstrated the most consistent and rapid convergence. This analysis examines whether adjusting the noise reduction rate can further optimize convergence time or introduce stability variations across control area types. By systematically varying the decay rate, we assess whether the previously observed trend—where earlier decay (D1, D2) led to faster convergence—remains valid under different noise reduction rates. The goal is to identify the optimal strategy for N1= 0.1, ensuring an effective balance between exploration and convergence efficiency. TABLE III SENSITIVITY ANALYSIS OF DECREASING NOISE RATE FOR INITIAL NOISE VALUE N1= 0.1 Decreasing Noise Rate Control Area Type D1 (1st Iter.) D2 (5th Iter.) D3 (10th Iter.) Slow Decay Very Compact 24 29 25 Compact 33 28 40 Not Compact 22 40 26 Moderate Decay Very Compact 25 24 30 Compact 35 26 33 Not Compact 35 25 25 Fast Decay Very Compact 27 24 21 Compact 24 20 24 Not Compact 25 23 28 The results indicate that faster noise decay generally improves convergence, particularly at D2(5th iteration), where the lowest iteration counts are observed for Compact and Not Compact areas. Very Compact areas benefit most from fast decay at D3, where the lowest iteration count (21) is recorded. Conversely, slow decay requires more iterations, especially in Compact and Not Compact areas, where gradual noise reduction often delays convergence or leads to instability in reaching F1= 1. These findings reinforce the importance of an appropriately tuned decay rate, particularly in non-compact areas where delayed noise reduction can significantly hinder convergence efficiency. C. Implementation This work was implemented in Python 3.10 on a Linux/Ubuntu system. NumPy, Pandas, Matplotlib, and Seaborn were used for data processing and visualization. Experiments were conducted on an AMD Ryzen 9 5900X 12-core processor with 64 GB of RAM, ensuring efficient computation. V. DISCUSSION Herein, we have explored a particle-filtering based optimization method to marine spatial planning, conducting a sensitivity analysis to evaluate how different noise settings impact convergence efficiency and solution accuracy. Unlike prior applications of optimization models in spatial zoning, this work systematically examines the role of noise variation, decay timing, and initial noise levels, providing empirical insights into their influence on zoning effectiveness and efficiency. The results emphasize that decreasing noise over time leads to the highest F1scores, striking the right balance between space exploration and exploitation. In contrast, fixed and increasing noise settings resulted in lower F1score, suggesting that excessive randomness disrupts convergence. It is important to highlight that previous works in MSP [3] [4] assumed a constant noise scenario, which contrasts with the significantly improved convergence and performance observed when noise is gradually reduced. One of the most significant findings is the effect of noise decay timing on convergence speed. The analysis shows that early decay (D1, D2) consistently accelerates convergence, particularly when paired with low initial noise (N1). On the other hand, delayed decay (D3, D4) extended convergence times or led to non-convergence, highlighting the importance of adapting noise levels dynamically. Additionally, the study found that spatial compactness influences optimization performance, as Very Compact control areas achieved faster convergence than Not Compact areas, where fragmentation introduced additional complexity. These insights can guide researchers in making informed methodological decisions tailored to their specific use cases. ACKNOWLEDGMENT The authors would like to express their gratitude to Andreas Hadjipieris for his valuable assistance in optimizing the code. REFERENCES [1] T. S. Agardy, “Marine protected areas and ocean planning,” in Routledge Handbook of Ocean Resources and Management, H. D. Smith and J. Luis, Eds. London: Routledge; Springer, 2015, pp. 476–492. [Online]. Available: https://www.taylorfrancis.com/chapters/edit/10.4324/978020311539832/marineprotectedareas-ocean-planning-tundiagardy [2] A. T. Lombard, R. A. Dorrington, J. R. Reed, K. Ortega-Cisneros, G. S. Penry, L. Pichegru, K. P. Smit, E. A. Vermeulen, M. Witteveen, K. J. Sink, A. M. McInnes, and T. Ginsburg, “Key challenges in advancing an ecosystem-based approach to marine spatial planning under economic growth imperatives,” Frontiers in Marine Science, vol. 6, 2019. [Online]. Available: https://www.frontiersin.org/journals/marinescience/articles/10.3389/fmars.2019.00146 [3] M. Polykarpou, F. Karathanasi, T. Soukissian, V. Loukaidi, and I. Kyriakides, “A novel data-driven tool based on non-linear optimization for offshore wind farm siting,” Energies, vol. 16, no. 5, 2023. [Online]. Available: https://www.mdpi.com/1996-1073/16/5/2235 [4] M. Polykarpou, F. Karathanasi, I. Kyriakides, and S. Charalambous, “A tool for the dynamic allocation of multiple marine activities,” in 2022 IEEE 13th Annual Information Technology, Electronics and Mobile Communication Conference (IEMCON), 2022, pp. 0082–0087. [5] M. Basirati, R. Billot, P. Meyer, and E. Bocher, “Exact zoning optimization model for marine spatial planning (msp),” Frontiers in Marine Science, vol. 8, 2021. [Online]. Available: https://www.frontiersin.org/journals/marinescience/articles/10.3389/fmars.2021.726187