Optimizing Vehicle Placement in the Residual Spaces of Unmarked Parking Areas: A Comparative Study of Heuristic Methods  
[PERSON] 1  
1 Department of Geomatics Engineering, Faculty of Engineering, Nigde Omer Hallsdemir University, Nigde 51240, Turkiye; [EMAIL_ADDRESS] (M.H. ); [EMAIL_ADDRESS] (A.E.K. )1  
[PERSON] 2  
2 Institute of Geodesy and Construction, University of Warmia and Mazury in Olsztyn, 10-720 Olsztyn, Poland 2  
[PERSON] 1  
1 Department of Geomatics Engineering, Faculty of Engineering, Nigde Omer Hallsdemir University, Nigde 51240, Turkiye; [EMAIL_ADDRESS] (M.H. ); [EMAIL_ADDRESS] (A.E.K. )1  
Footnote 1: email: {[[https://www.sciencedirect.com/science/article/pii/article/pii/](https://www.sciencedirect.com/science/article/pii/article/pii/)]([https://www.sciencedirect.com/science/article/pii/article/pii/](https://www.sciencedirect.com/science/article/pii/article/pii/))  
guidance to ensure the most efficient use of available spaces. [PERSON] et al. [1] examined parking areas in Lviv's historic city center and highlighted that simple IoT (Internet of Things) solutions were insufficient for unmarked parking spaces, necessitating more advanced systems. Similarly, [PERSON] and [PERSON] [2] compared the efficiency of marked and unmarked parking areas, demonstrating that unmarked spaces suffer from significant capacity losses due to randomly positioned vehicles. Mathematical modeling and simulation studies have indicated that, while fixed-length constraints in marked parking areas can lead to inefficiencies, random parking behavior in unmarked spaces can reduce capacity utilization [3]. [PERSON] et al. [4] found that parking accessibility for different vehicle types directly affects traffic flow and environmental costs, with limited parking availability increasing search times and exacerbating congestion. [PERSON] and [PERSON] [5] and [PERSON] [6] suggested that unmarked parking areas offer more flexible solutions than fixed-size parking lines. However, they emphasized that without an appropriate optimization strategy, this advantage cannot be fully utilized. These findings indicate the need for novel approaches, particularly in cities like Kayseri, where a significant portion of roadside parking areas are unmarked. Although the optimization problem addressed in this study is inherently nonconvex due to vehicle rotation, buffer zones, spatial overlap constraints, and irregular parking boundaries, it is conceptually valuable to acknowledge the role of convex optimization techniques under idealized conditions. For instance, equality-constrained quadratic programming has been successfully applied in structured spatial estimation problems [7]. While originally developed for direction-of-arrival estimation, its mathematical formulation illustrates how convex approaches can yield global optima in environments with well-defined and continuous constraints. In the presented context, one can imagine hypothetical scenarios where all vehicles are identical, parking areas are rectangular and symmetric, and no rotation is permitted. In such simplified cases, multiple vehicle configurations (e.g., symmetric placements in mirrored subspaces) could produce equivalent or optimal results. If the objective were limited to minimizing maneuver time or maximizing vehicle count with continuous variables and smooth constraints, a convex relaxation might, in theory, offer a tractable formulation. However, real-world parking scenarios involve multiple vehicle types, variable rotation angles, and discontinuous feasibility conditions. These features result in a multimodal and fragmented solution space, which makes heuristic and swarm-based methods far more suitable in practice. Optimization methods have been employed for various purposes in parking management. Advanced algorithms have been developed for dynamic parking allocation [8], and the integration of electric vehicle parking areas with power grids has been optimized [9; 10].