## 1 Introduction  
Packing optimization is an important problem class that concerns various disciplines including warehouse management, shipping, and design of engineering products. The broad nature of this problem requires robust and efficient algorithms that are easy to utilize. Various techniques have been developed to solve different packing optimization problems. A large amount of available studies have addressed the problem of packing two-dimensional rectangular objects into rectangular bins while keeping the object edges orthogonal to the domain boundaries. For instance, [PERSON] and [PERSON] [1] computed solutions for two-dimensional rectangle packing problems by introducing a search algorithm that uses a corner occupation strategy to individually place the objects into the container. Later, [PERSON] et al. [2] proposed a hybrid heuristic algorithm that combines greedy strategy and simulated annealing methods to solve the rectangular knapsack packing problem. [PERSON] et al. [3] studied the same problem by proposing a bidirectional heuristic placement algorithm that attempts to fit rectangles around both left and right boundaries of the domain. [PERSON] et al. [4] subsequently developed a deterministic heuristic algorithm for solving the two-dimensional rectangular packing problems that require maximizing the filled portion of the rectangular domain. Recently, [PERSON] et al. [5] proposed an adaptive genetic algorithm for solving two-dimensional packing problems that aim to maximize the filling rate of a rectangular region. Packing problems concerning nonrectangular objects and domains have also been prevalently investigated. For example, [PERSON] et al. [6] developed heuristic approaches for solving two-dimensional cutting/packing problems involving irregular objects. Later, [PERSON] et al. [7] proposed a heuristic algorithm for solving circle packing problems for placing multiple identical circles into the smallest circular container. Lately, [PERSON] and [PERSON] [8] investigated orthogonal packing of rectangular objects into a circular space of fixed radius. The complexity of the packing problems notably increases when the nonorthogonal rotation of the objects is allowed in addition to the translation [9]. These problems received relatively lesser attention compared to the problems involving fixed object orientations or orthogonal rotations. In one study, [PERSON] and [PERSON] [10] introduced a two-dimensional packing optimization technique called the finite-circle method, which approximates polygons with a set of circles and converts the non-overlapping constraints into simple constraints between circles. [PERSON] and [PERSON] [11] used a heuristic approach to minimize the waste space during the rotational placement of two-dimensional polygons into irregular containers. In another study by [PERSON] et al. [12], a strategy was proposed to solve the bin packing problems with irregular pieces that can be freely rotated. The difficulties in the formulations for packing problems involving irregular objects have led to the development of raster point methods, which rely on approximating the objects on a discretized grid. With these methods, packing configurations can be represented by assigning zeroes to the free domain cells and different values to the cells where a single object exists or multiple objects overlap. The key advantage of raster techniques is their applicability to the problems involving objects with complex shapes, where the main drawback is their resolution-dependent precision [13]. In the literature, the research on packing optimization with raster methods is limited compared to the available work based on other techniques. In a particular study, [PERSON] et al. [14] proposed a discrete modeling approach called the Dotted-Board Model, which relies on representing the bin with a two-dimensional grid and using the plausible grid points for the placement of arbitrary polygons. Later, [PERSON] et al.