Search Results (16)

This paper addresses the maximum coverage location problem in a generalized setting, where both facilities (service areas) and regional demand are modeled as continuous entities. Unlike traditional formulations, our approach allows for arbitrary shapes for both service areas and demand regions, with additional constraints on facility placement. The key novelty of this work is its ability to handle complex, irregularly shaped service areas, including approximating them as unions of centrally symmetric shapes. This enables the use of an analytical approach based on spatial symmetry, which allows for efficient estimation of the covered area. The problem is formulated as a nonlinear optimization task. We analyze the properties of the objective function and leverage the Shapely library in Python 3.13.3 for efficient geometric computations. To improve computational efficiency, we develop an extended elastic model that significantly reduces processing time. This model generalizes the well-known quasi-physical, quasi-human algorithm for circle packing, extending its applicability to more complex spatial configurations. The effectiveness of the proposed approach is validated through test cases in which service areas take the form of circles, ellipses, and irregular polygons. Our method provides a robust and adaptable solution for various settings of practically interesting continuous maximum coverage location problems involving irregular regional demand and service areas. Full article

We review and present several challenging model classes arising in the context of finding optimized object packings (OP). Except for the smallest and/or simplest general OP model instances, it is not possible to find their exact (closed-form) solution. Most OP problem instances become increasingly difficult to handle even numerically, as the number of packed objects increases. Specifically, here we consider classes of general OP problems that can be formulated in the framework of nonlinear optimization. Research experience demonstrates that—in addition to utilizing general-purpose nonlinear optimization solver engines—the insightful exploitation of problem-specific heuristics can improve the quality of numerical solutions. We discuss scalable OP problem classes aimed at packing general circles, spheres, ellipses, and ovals, with numerical (conjectured) solutions of non-trivial model instances. In addition to their practical relevance, these models and their various extensions can also serve as constrained global optimization test challenges. Full article

Background: The Irregular Strip Packing Problem (ISPP) involves packing a set of irregularly shaped items within a strip while minimizing its length. Methods: This study introduces the Normalized Direct Trigonometry Model (NDTM), an innovative enhancement of the Direct Trigonometry Model (DTM). The NDTM incorporates a distance function that supports the integration of the separation constraint, which mandates a minimum separation distance between items. Additionally, the paper proposes a new set of constraints based on the bounding boxes of the pieces aimed at improving the non-overlapping condition. Results: Comparative computational experiments were performed using a comprehensive set of 90 instances. Results show that the NDTM finds more feasible and optimal solutions than the DTM. While the NDTM allows for the implementation of the separation constraint, the number of feasible and optimal solutions tends to decrease as more separation among the items is considered, despite not increasing the number of variables or constraints. Conclusions: The NDTM outperforms the DTM. Moreover, the results indicate that the new set of non-overlapping constraints facilitates the exploration of feasible solutions at the expense of optimality in some cases. Full article

Packing irregular objects composed by generalized spheres is considered. A generalized sphere is defined by an arbitrary norm. For three classes of packing problems, balance, homothetic and sparse packing, the corresponding new (generalized) models are formulated. Non-overlapping and containment conditions for irregular objects composed by generalized spheres are presented. It is demonstrated that these formulations can be stated for any norm. Different geometrical shapes can be treated in the same way by simply selecting a suitable norm. The approach is applied to generalized spheres defined by Lp norms and their compositions. Numerical solutions of small problem instances obtained by the global solver BARON are provided for two-dimensional objects composed by spheres defined in Lp norms to demonstrate the potential of the approach for a wide range of engineering optimization problems. Full article

The problem of two-dimensional irregular packing involves the arrangement of objects with diverse shapes and sizes within a given area. This challenge arises across various industrial sectors, where effective packing optimization can yield cost savings, enhanced productivity, and reduced material waste. Existing methods for addressing the two-dimensional irregular packing problem encounter several challenges, such as limited computing resources, a prolonged solving time, and the propensity to converge to local optima. To address this issue, this study proposes a hybrid algorithm called the GA-LP algorithm to optimize the two-dimensional irregular packing problem in the manufacturing industry. The algorithm combines the global search capability of a genetic algorithm with the precise solving characteristics of linear programming. Matheuristics merges the advantages of metaheuristics, such as genetic algorithms, and mathematical programming, such as linear programming. The algorithm employs the no-fit-polygon technique along with the bottom-left and lowest-gravity center mixing placement strategies to acquire an initial solution via the utilization of a genetic algorithm. The algorithm then optimizes the solution obtained by the genetic algorithm using linear programming to obtain the final packing result. Experimental results, drawn from a real case involving the European Special Interest Group on Cutting and Packing (ESICUP) demonstrate that the GA-LP algorithm outperforms two hybrid algorithms from the relevant literature. Compared with recent methods, this algorithm can increase the best and average utilization rates by up to 5.89% and 4.02%, respectively, with important implications for improving work quality in areas such as packing and cutting. Full article

Crowdsourcing offers on-demand access to large numbers of human workers to implement new forms of human–computer collaborative functionalities that can be seamlessly integrated into advanced software and algorithms. However, crowdsourcing tasks are primarily undertaken by urban rather than rural workers. To enable the development of skilled rural employment, this research aims to assess rural crowdsourcing workers’ spatial reasoning and creative abilities and their abilities to solve irregular strip packing problems associated with the manufacture of sheet materials. The study conducted experiments and data collection with 140 rural Business Processing Outsourcing (BPO) workers located in six states of India. The statistical analyses of the data collected from seven rural BPO firms (140 rural workers) reveal that rural workers can achieve a 2D packing efficiency that is up to 8% higher than that of commercial algorithm outcomes. The results suggest that rural crowdsourcing can lead to effective job creation, skill development, and, for a modest cost, it can support industries that employ CAD/CAM systems to generate geometric data for common manufacturing processes. Full article

The key research question in this study is how to cut pieces in irregular plate remainders, because there are many irregular plate leftovers created during the CNC (Computer Numerical Control) process. This will increase material utilization and allow plate leftovers to be reused. One of the issues being researched is how to arrange plate remainders on the surface of the CNC machine; this issue is known as combination layout optimization. The other issue being researched is combination cutting-path optimization of plate remainders, which aims to determine the cutting path of parts of plate remainders. A genetic algorithm based on the gravity-center NFP (No-Fit Polygon) method was applied to optimize the layout pattern, and then the geometric coordinates of a part included in one plate remainder after packing were obtained by geometric transformation with the help of a three-layer graphic data correlation model, which quickly identified the inside and outside contours of parts. A colony algorithm based on the mathematical model of cutting-path optimization was used to optimize the cutting path of the parts in the plate remainders. Finally, some simulation tests were performed to illustrate the feasibility and effectiveness of the proposed method. The results of the algorithm for packing irregular shapes for some instances show that our algorithm outperforms the other algorithms. On most instances, the average plate utilization ratio using our algorithm, after running 20 times, is improved by 1% to 9% in comparison to the best plate utilization ratio using the tree search algorithm. The best idle travel of an example achieved by the algorithm in this paper is 7632 mm after running the cutting-path optimization algorithm 20 times, while that of the traditional equivalent TSP (Traveling Salesman Problem) algorithm is 11,625 mm, which significantly demonstrates the efficiency of the algorithm. Full article

Packing problems, also known as nesting problems or bin packing problems, are classic and popular NP-hard problems with high computational complexity. Inspired by classic reinforcement learning (RL), we established a mathematical model for two-dimensional (2D) irregular-piece packing combined with characteristics of 2D irregular pieces. An RL algorithm based on Monte Carlo learning (MC), Q-learning, and Sarsa-learning is proposed in this paper to solve a 2D irregular-piece packing problem. Additionally, mechanisms of reward–return and strategy-update based on piece packing were designed. Finally, the standard test case of irregular pieces was used for experimental testing to analyze the optimization effect of the algorithm. The experimental results show that the proposed algorithm can successfully realize packing of 2D irregular pieces. A similar or better optimization effect can be obtained compared to some classical heuristic algorithms. The proposed algorithm is an early attempt to use machine learning to solve 2D irregular packing problems. On the one hand, our hybrid RL algorithm can provide a basis for subsequent deep reinforcement learning (DRL) to solve packing problems, which has far-reaching theoretical significance. On the other hand, it has practical significance for improving the utilization rate of raw materials and broadening the application field of machine learning. Full article

This paper introduces an efficient and robust sliding algorithm for the creation of no-fit polygons. The improved algorithm can cope with complex cases and is given an implementation in detail. The proposed concept of a touching group can simplify the judging process when recognizing the potential translation vector for an orbital polygon. In addition, the generation of the no-fit polygon only involves three main steps based on the proposed concept. The proposed algorithm has a mechanism that searches other start positions to generate a complete no-fit polygon for handling complex cases. To improve the efficiency, many acceleration strategies have been proposed, such as point exclusion strategy and point inclusion test. The robust and efficient performance of the algorithm is tested by well-known benchmark instances and degenerate and complex cases, such as holes, interlocking concavities and jigsaw-type pieces. Experimental results show that the proposed algorithm can produce complete no-fit polygons for complex cases, and acceleration strategies can reduce the creation time of no-fit polygon on benchmark instances by more than sixteen percent on average. Full article

Despite their versatility in treating irregular geometries, the raster methods have received limited attention in solving packing problems involving rotatable objects. In addition, raster approximation allows the use of unique performance metrics and indirect consideration of constraints, which have not been exploited in the literature. This study presents the Concurrent or Ordered Matrix-based Packing Arrangement Computation Technique (COMPACT). The method allows the objects to be rotated by arbitrary angles, unlike the right-angled rotation restrictions imposed in many existing packing optimization studies based on raster methods. The raster approximations are obtained through loop-free operations that improve efficiency. Additionally, a novel performance metric is introduced, which favors efficient filling of the available space by maximizing the overall contact within the domain. Moreover, the objective functions are exploited to discard the overlap and overflow constraints and enable the use of unconstrained optimization methods. The results of the case studies demonstrate the effectiveness of the proposed technique. Full article

Paper waste in the mockups design with regular, irregular, and amorphous patterns is a critical problem in digital printing presses. Paper waste reduction directly impacts production costs, generating business and environmental benefits. This problem can be mapped to the two-dimensional irregular bin-packing problem. In this paper, an iterated local search algorithm using a novel neighborhood structure to detect overlaps between amorphous shapes is introduced. This algorithm is used to solve the paper waste problem, modeled as one 2D irregular bin-packing problem. The experimental results show that this approach works efficiently and effectively to detect and correct the overlaps between regular, irregular, and amorphous figures. Full article

Erosion at either dam or spillway foundations, destabilization in riverbanks, and damage in the natural environment located downstream of either dams or spillways represent crucial elements to be taken into account in the risk assessment of hydraulic structures. One of the main problems is related to the scouring that water flow may induce at the downstream boundary of spillways. This issue is exacerbated in the case of undersized stilling basins, i.e., when a significant level of energy migrates downstream by acting on unprotected natural riverbed. If the scour depths are large enough, the structural stability of the infrastructure will be threatened. This paper aims to illustrate an innovative technical solution suitable to protect the riverbed located just downstream of stilling basins by means of artificial Antifer blocks. These kinds of artificial blocks are widely used in the field of maritime construction, but in the literature, there are no theoretical formulations for their design within the frame of river engineering. In order to demonstrate the efficacy of the proposed technical solution, it is applied to a real case investigated by means of physical modeling. The riverbed located just downstream of the stilling basin of Liscione Dam (Campobasso, Italy) experienced scour due to high discharges during and after extreme rain events. Different protection strategies have been tested to assess the influence of different placement methods and packing densities on the stability of Antifer block armor layers. Experimental findings reveal that regular placements behave more stable than irregular placements with a similar packing density. Full article

Research on the rectangle packing problems has mainly focused on rectangular raw material sheets without defects, while natural slate has irregular and defective characteristics, and the existing packing method adopts manual packing, which wastes material and is inefficient. In this work, we propose an effective packing optimization method for nature slate; to the best of our knowledge, this is the first attempt to solve the guillotine packing problem of rectangular items in a single irregular and defective slate. This method is modeled by the permutation model, uses the horizontal level (HL) heuristic proposed in this paper to obtain feasible solutions, and then applies the genetic algorithm to optimize the quality of solutions further. The HL heuristic is constructed on the basis of computational geometry and level packing. This heuristic aims to divide the irregular plate into multiple subplates horizontally, calculates the movable positions of the rectangle in the subplates, determines whether or not the rectangle can be packed in the movable positions through computational geometry, and fills the scraps appropriately. Theoretical analysis confirms that the rectangles obtained through the HL heuristic are inside the plate and do not overlap with the defects. In addition, the packed rectangles do not overlap each other and satisfy the guillotine constraint. Accordingly, the packing problem can be solved. Experiments on irregular slates with defects show that the slate utilization through our method is between 89% and 95%. This result is better than manual packing and can satisfy actual production requirements. Full article

Packing irregular 3D objects in a cuboid of minimum volume is considered. Each object is composed of a number of convex shapes, such as oblique and right circular cylinders, cones and truncated cones. New analytical tools are introduced to state placement constraints for oblique shapes. Using the phi-function technique, optimized packing is reduced to a nonlinear programming problem. Novel solution approach is provided and illustrated by numerical examples. Full article

The areas planted with avocado in Colombia have increased to position this fruit in international markets. To achieve this goal, the offered fruits need to meet optimal production standards. The aim of this study was to identify the main physiopathologies and damages that may cause the rejection of avocado cv. Hass fruits for export purposes during pre-harvest, harvest, and processing in packinghouses, and quantify the economic impact of said exclusion criteria. Typological characterization and quantification of damages that may cause fruit rejection were performed at the laboratory, field, and packinghouses. Data were obtained from 136 Colombian productive plots with monitoring and data collection records for a minimum of five years. At the packinghouse level, data associated with factors that affect quality (both, those identified at packing plants and those detected in simulated shipments) were considered. The main causes of fruit rejection during pre-harvest and harvest were: low calibers, damage to the epidermis by insect pests from the subfamily Melolonthidae, thrips, mites, the bug Monalonion, overripe fruits, and sunburn damage. In addition, pathologies such as anthracnose and stem end rot, and problems associated with browning of vascular bundles, irregular ripening, chilling injury, and lenticel damage were highly limiting at packinghouses. The economic analysis identified losses of 5.78 and 5.68% in farms and packinghouses, respectively, which are equivalent to US dollar (USD) 80.29 per produced ton. This work generated information that allows prioritizing strategies to improve fruit quality and reduce economic impact. Full article