NEURAL-DRIVEN HYBRID METHOD FOR OPTIMAL AREA COVERAGE WITH PLACEMENT CONSTRAINTS

Abstract

The article proposes a novel methodology for addressing the Maximum Coverage Location Problem (MCLP) in continuous spaces, incorporating arbitrarily shaped objects, their rotation, and restricted zones for object centers. The problem is formulated as a nonlinear optimization task, where constraints are enforced through a dynamically tuned penalty function driven by a neural network. To enhance computational efficiency, a surrogate neural network approximates the computationally intensive objective function, significantly reducing processing time. The proposed hybrid evaluation strategy integrates precise geometric computations using the Shapely library with Monte Carlo approximations, achieving an optimal balance between accuracy and computational speed. Swarm intelligence algorithms, such as Particle Swarm Optimization (PSO), and memetic algorithms, which combine global exploration with local refinement, are employed to navigate the high-dimensional, multi-extremal solution space effectively. The adaptive penalty mechanism, powered by a neural network, enables automatic adjustment of constraint parameters, eliminating the need for manual tuning and enhancing the robustness of the method across varying problem conditions. This approach proves highly effective for complex geometric configurations, where traditional optimization techniques struggle due to the multi-extremal nature of the objective function and placement constraints. The method is scalable and adaptable to diverse object shapes and restricted zone configurations, making it suitable for practical applications in multiple domains, including telecommunications (e.g., optimal placement of base stations), healthcare (e.g., deployment of mobile medical units in crisis scenarios), ecology (e.g., sensor placement for environmental monitoring), and urban planning (e.g., infrastructure design with restricted access zones). The integration of neural network-based adaptive penalties with geometric optimization provides a robust and efficient framework for solving real-world coverage problems. Future prospects include real-time optimization integration with geographic information systems, further refinement through deep neural networks with active learning, and expansion to dynamic environments with time-varying constraints. This approach advances the state-of-the-art in AI-driven optimization, offering a versatile and reliable solution for complex spatial planning challenges.