Small Size Problem Research Articles

Applying quantum approximate optimization to the heterogeneous vehicle routing problem

Quantum computing offers new heuristics for combinatorial problems. With small- and intermediate-scale quantum devices becoming available, it is possible to implement and test these heuristics on small-size problems. A candidate for such combinatorial problems is the heterogeneous vehicle routing problem (HVRP): the problem of finding the optimal set of routes, given a heterogeneous fleet of vehicles with varying loading capacities, to deliver goods to a given set of customers. In this work, we investigate the potential use of a quantum computer to find approximate solutions to the HVRP using the quantum approximate optimization algorithm (QAOA). For this purpose we formulate a mapping of the HVRP to an Ising Hamiltonian and simulate the algorithm on problem instances of up to 21 qubits. We show that the number of qubits needed for this mapping scales quadratically with the number of customers. We compare the performance of different classical optimizers in the QAOA for varying problem size of the HVRP, finding a trade-off between optimizer performance and runtime.

Distributed multi-object tracking under limited field of view heterogeneous sensors with density clustering

We consider the problem of tracking multiple, unknown, and time-varying numbers of objects using a distributed network of heterogeneous sensors. In an effort to derive a formulation for practical settings, we consider limited and unknown sensor field-of-views (FoVs), sensors with limited local computational resources and communication channel capacity. The resulting distributed multi-object tracking algorithm involves solving an NP-hard multidimensional assignment problem either optimally for small-size problems or sub-optimally for general practical problems. For general problems, we propose an efficient distributed multi-object tracking algorithm that performs track-to-track fusion using a clustering-based analysis of the state space transformed into a density space to mitigate the complexity of the assignment problem. The proposed algorithm can more efficiently group local track estimates for fusion than existing approaches. To ensure we achieve globally consistent identities for tracks across a network of nodes as objects move between FoVs, we develop a graph-based algorithm to achieve label consensus and minimise track segmentation. Numerical experiments with synthetic and real-world trajectory datasets demonstrate that our proposed method is significantly more computationally efficient than state-of-the-art solutions, achieving similar tracking accuracy and bandwidth requirements but with improved label consistency.

A new mathematical model and meta-heuristic algorithm for order batching, depot selection, and assignment problem with multiple depots and pickers

The ‘order picking problem’ involves the efficient and organized retrieval of items from shelves to fulfill customer orders. In this study, we consider a new configuration of warehouse system with multiple pickers and depots (m-pickers & n-depots) for manually operated ‘picker-to-parts’ warehouses. The efficiency of the process is measured based on two metrics: i- total order picking distance of each picker ii- total number of pickers assigned to each of depots. The handled problem is called as ‘Order Batching, Depot Selection and Assignment Problem with Multiple Depots and Multiple Pickers (OBDSAPMDMP)11OBDSAPMDMP = Order Batching, Depot Selection, and Assignment Problem with Multiple Depots and Multiple Pickers.’. To solve this complex problem, a new bi-objective Mixed-Integer Linear Programming (MILP) formulation for small-sized problems and a meta-heuristic called ‘Dependent Harmony Search (DHS)22DHS = Dependent Harmony Search.’ for large-sized problems are proposed. The performance of DHS algorithm is evaluated by comparing the optimal results attained by MILP model. For the problem size of 10 orders, the average gap (%) in distance between the solution of DHS and MILP is 4.22%, although in some experiments DHS can find the optimal solution in a very short time. Also, in related analysis, it is seen that constructing multiple depots instead of one left-most located depot decreases total order picking distance by 7.11% on average.

Turret-index optimisation with mathematical programming and metaheuristic approaches

This paper addresses the turret-index optimisation problem by proposing two mathematical programming approaches based on quadratic programming (QP) and constraint programming (CP). In addition, a metaheuristic algorithm based on weighted superposition attraction (WSA) is developed due to the combinatorial complexity of the problem. Despite attempting to linearise the QP formulation for problem resolution, both the QP and Linearized QP models prove ineffective for medium and larger-sized instances, providing solutions only for small-sized problems. In the second mathematical programming approach, a novel CP model is introduced in the literature. While CP can rapidly offer optimal solutions for small-sized problems, it only provides satisfactory solutions for medium and larger-sized problems within the predetermined computational time limits and does not guarantee optimal results. On the other hand, through computational analysis and relevant statistical tests, the proposed WSA algorithm provides the best solutions for all test problems within a reasonable computational time.

QUBO Models for the FIFO Stack-Up Problem and Experimental Evaluation on a Quantum Annealer

Quantum annealing has been applied to combinatorial optimization problems in recent years. In this paper we study the possibility to use quantum annealing for solving the combinatorial FIFO Stack-Up problem, where bins have to be stacked-up from a conveyor belt onto pallets. The problem is NP-hard and can be solved using linear programming approaches. We developed two QUBO (quadratic unconstrained binary optimization) objective functions based on a bin stack-up solution and a pallet stack-up solution for this problem suitable for a quantum annealer. The number of variables was minimized to increase the performance and their dependence on the number of bins and pallets was discussed. The performances of both methods were studied for various small problem sizes on a D-Wave quantum annealer. We found that only tiny instances could be solved and looked at the terms of the QUBO-formulations, which cause the quantum annealer to fail for larger problem sizes. Furthermore we compare the results to the performance of a classic computer using the same QUBO-formulations.

26‐5: Feasibility Analysis of Image Sensors Scanner on Glass

Image sensors on silicon have the problems of small size and high cost. Therefore, we propose a method for making image sensors on glass substrates and analyzes the feasibility of replacing Image Sensors on Silicon from the performance and cost. Through calculation and measurement, the scanning resolution, conversion gain, signal‐to‐noise ratio, and scanning time of image sensors on glass substrates can all meet the requirements of the document scanner and barcode scanner; In addition, the image sensors on glass can be formed in large size and does not require splicing, resulting in lower costs compared to image sensors on silicon of the document scanner. Therefore, image sensors on glass can replace image sensors on silicon of the document scanner. The cost and the module size of the barcode scanner is higher than the existing product, So image sensors on glass used for barcode scanners is lack of advantages in application.

Qigong Master: A Qigong-Based Attention Training Game Using Action Recognition and Balance Analysis

Baduanjin is a type of martial art that is aimed at the development and health of the physical, emotional and spiritual aspects. It emphasizes on gentle movements, relaxed yet disciplined, and training of mental concentration through relaxation. In order to make Baduanjin attention training more effective and easier, we proposed a novel Baduanjin-based attention training game that instructs the subject to practice Baduanjin using virtual reality (VR) and motion analysis. Through a virtual instructor who demonstrates a series of Baduanjin actions, the subject is asked to follow the instructor's movement at any time. Meanwhile, the 3D position of the subject's body joints is collected by a motion capture device for further analysis using a deep learning model to evaluate the order correctness and precision of the Baduanjin actions. In addition, transfer learning technique is used to solve the problem of small size of Baduanjin data. Preliminary tests with 20 normal individuals showed that the recognition accuracy of the Baduanjin actions reached nearly 97%, and the balance analysis reflected the position change of the body center of mass to a certain extent. We also compared the performance of the model with and without pre-training to demonstrate the importance of transfer learning. The result of these explorations shows the feasibility of this prototype system as an attention training system and its potential as an assistive treatment option. In conclusion, we not only created the virtual instructor that could provide accurate movement demonstration, but also collected objective action data for more accurate balance analysis to provide appropriate feedback.

Dynamic resource matching in manufacturing using deep reinforcement learning

Matching plays an important role in the logical allocation of resources across a wide range of industries. The benefits of matching have been increasingly recognized in manufacturing industries. In particular, capacity sharing has received much attention recently. In this paper, we consider the problem of dynamically matching demand-capacity types of manufacturing resources. We formulate the multi-period, many-to-many manufacturing resource-matching problem as a sequential decision process. The formulated manufacturing resource-matching problem involves large state and action spaces, and it is not practical to accurately model the joint distribution of various types of demands. To address the curse of dimensionality and the difficulty of explicitly modeling the transition dynamics, we use a model-free deep reinforcement learning approach to find optimal matching policies. Moreover, to tackle the issue of infeasible actions and slow convergence due to initial biased estimates caused by the maximum operator in Q-learning, we introduce two penalties to the traditional Q-learning algorithm: a domain knowledge-based penalty based on a prior policy and an infeasibility penalty that conforms to the demand–supply constraints. We establish theoretical results on the convergence of our domain knowledge-informed Q-learning providing performance guarantee for small-size problems. For large-size problems, we further inject our modified approach into the deep deterministic policy gradient (DDPG) algorithm, which we refer to as domain knowledge-informed DDPG (DKDDPG). In our computational study, including small- and large-scale experiments, DKDDPG consistently outperformed traditional DDPG and other RL algorithms, yielding higher rewards and demonstrating greater efficiency in time and episodes.

A bi-objective model for location, dispatch and relocation of ambulances with a revision of dispatch policies

PurposeUntimely responses to emergency situations in urban areas contribute to a rising mortality rate and impact society's primary capital. The efficient dispatch and relocation of ambulances pose operational and momentary challenges, necessitating an optimal policy based on the system's real-time status. While previous studies have addressed these concerns, limited attention has been given to the optimal allocation of technicians to respond to emergency situation and minimize overall system costs.Design/methodology/approachIn this paper, a bi-objective mathematical model is proposed to maximize system coverage and enable flexible movement across bases for location, dispatch and relocation of ambulances. Ambulances relocation involves two key decisions: (1) allocating ambulances to bases after completing services and (2) deciding to change the current ambulance location among existing bases to potentially improve response times to future emergencies. The model also considers the varying capabilities of technicians for proper allocation in emergency situations.FindingsThe Augmented Epsilon-Constrained (AEC) method is employed to solve the proposed model for small-sized problem. Due to the NP-Hardness of the model, the NSGA-II and MOPSO metaheuristic algorithms are utilized to obtain efficient solutions for large-sized problems. The findings demonstrate the superiority of the MOPSO algorithm.Practical implicationsThis study can be useful for emergency medical centers and healthcare companies in providing more effective responses to emergency situations by sending technicians and ambulances.Originality/valueIn this study, a two-objective mathematical model is developed for ambulance location and dispatch and solved by using the AEC method as well as the NSGA-II and MOPSO metaheuristic algorithms. The mathematical model encompasses three primary types of decision-making: (1) Allocating ambulances to bases after completing their service, (2) deciding to relocate the current ambulance among existing bases to potentially enhance response times to future emergencies and (3) considering the diverse abilities of technicians for accurate allocation to emergency situations.

A Sustainable Multi-Objective Model for Capacitated-Electric-Vehicle-Routing-Problem Considering Hard and Soft Time Windows as Well as Partial Recharging.

Due to the high pollution of the transportation sector, nowadays the role of electric vehicles has been noticed more and more by governments, organizations, and environmentally friendly people. On the other hand, the problem of electric vehicle routing (EVRP) has been widely studied in recent years. This paper deals with an extended version of EVRP, in which electric vehicles (EVs) deliver goods to customers. The limited battery capacity of EVs causes their operational domains to be less than those of gasoline vehicles. For this purpose, several charging stations are considered in this study for EVs. In addition, depending on the operational domain, a full charge may not be needed, which reduces the operation time. Therefore, partial recharging is also taken into account in the present research. This problem is formulated as a multi-objective integer linear programming model, whose objective functions include economic, environmental, and social aspects. Then, the preemptive fuzzy goal programming method (PFGP) is exploited as an exact method to solve small-sized problems. Also, two hybrid meta-heuristic algorithms inspired by nature, including MOSA, MOGWO, MOPSO, and NSGAII_TLBO, are utilized to solve large-sized problems. The results obtained from solving the numerous test problems demonstrate that the hybrid meta-heuristic algorithm can provide efficient solutions in terms of quality and non-dominated solutions in all test problems. In addition, the performance of the algorithms was compared in terms of four indexes: time, MID, MOCV, and HV. Moreover, statistical analysis is performed to investigate whether there is a significant difference between the performance of the algorithms. The results indicate that the MOSA algorithm performs better in terms of the time index. On the other hand, the NSGA-II-TLBO algorithm outperforms in terms of the MID, MOCV, and HV indexes.

Centralized multi-visitor trip planning with activity reservations in crowded destinations

We study the problem of centralized planning of leisure trips in congested areas for visitor groups with reservations for activities. We develop an algorithm that through a combination of customization and coordination can improve average happiness considerably. Extensive numerical experimentation with both synthetic and real-life data show that our algorithm strongly outperforms the classical First-Come-First-Served reservation policy, both in terms of visitor happiness and in terms of fairness among visitors. Moreover, our results show that our algorithm leads to good solutions for small-sized problem instances (with errors typically within 5%–10% from an optimal solution obtained via Integer Linear Programming). Finally, the computational effort with regard to number of visitors is bounded by the capacity and the number of activities, while the increase in computation time for the number of attractions is bounded by the average number of activities that fit into a trip. As a result, our approach leads to good solutions within minutes in realistic settings with more than 10 thousand visitors a day.

The Allen–Cahn model with a time-dependent parameter for motion by mean curvature up to the singularity

In this article, we investigate the temporal evolution of arbitrary, simple, closed two-dimensional (2D) and three-dimensional (3D) interfaces under motion driven by mean curvature up to a singularity. To facilitate this investigation, we propose a novel Allen–Cahn (AC) model with a time-dependent interfacial thickness parameter. The original AC equation was developed to model the phase separation of a binary mixture. It is well known that a level set or interface of the solution of the AC equation obeys the dynamics of motion by curvature as the interfacial thickness parameter approaches zero. Generally, it is difficult to find a closed-form analytic solution of the AC equation with any initial condition. Therefore, we need to estimate the solution of the AC equation through computational approaches such as finite difference method (FDM), finite element method (FEM), Fourier-spectral method (FSM), and finite volume method (FVM). Any simple, closed curves and convex surfaces eventually shrink to a point due to motion by mean curvature. Therefore, it becomes necessary to use adaptive mesh techniques to resolve this small size problem. However, even though we use adaptive mesh techniques, we still confront the relatively thick interfacial transition layer when the curves or interfaces become very small. To avoid this problem, we can start with a very small mesh size for a small value of the interfacial parameter, which results in an extremely high computational cost even when using adaptive mesh techniques. To resolve these issues, we present the AC equation with a time-dependent interfacial parameter and develop an adaptive mesh refinement system. To show the superior performance of the proposed mathematical equation and its computational algorithm, we present various numerical experiments and investigate the motion by mean curvature up to the singularity of curves in 2D space and interfaces in 3D space.

FVCNet: Detection obstacle method based on feature visual clustering network in power line inspection

AbstractPower line inspection is an important means to eliminate hidden dangers of power lines. It is a difficult research problem how to solve the low accuracy of power line inspection based on deep neural network (DNN) due to the problems of multi‐view‐shape, small‐size object. In this paper, an automatic detection model based on Feature visual clustering network (FVCNet) for power line inspection is established. First, an unsupervised clustering method for power line inspection is proposed, and applied to construct a detection model which can recognize multi‐view‐shape objects and enhanced object features. Then, the bilinear interpolation method is used to Feature enhancement method, and the enhanced high‐level semantics and low‐level semantics are fused to solve the problems of small object size and single sample. In this paper, FVCNet is applied to the MS‐COCO 2017 data set and self‐made power line inspection data set, and the test accuracy is increased to 61.2% and 82.0%, respectively. Compared with other models, especially for the categories that are greatly affected by multi‐view‐shape, the test accuracy has been improved significantly.

Real-Time Multi-Robot Mission Planning in Cluttered Environment

Addressing a collision-aware multi-robot mission planning problem, which involves task allocation and path-finding, poses a significant difficulty due to the necessity for real-time computational efficiency, scalability, and the ability to manage both static and dynamic obstacles and tasks within a complex environment. This paper introduces a parallel real-time algorithm aimed at overcoming these challenges. The proposed algorithm employs an approximation-based partitioning mechanism to partition the entire unassigned task set into several subsets. This approach decomposes the original problem into a series of single-robot mission planning problems. To validate the effectiveness of the proposed method, both numerical and hardware experiments are conducted, involving dynamic obstacles and tasks. Additionally, comparisons in terms of optimality and scalability against an existing method are provided, showcasing its superior performance across both metrics. Furthermore, a computational burden analysis is conducted to demonstrate the consistency of our method with the observations derived from these comparisons. Finally, the optimality gap between the proposed method and the global optima in small-size problems is demonstrated.

Scheduling for the Flexible Job-Shop Problem with a Dynamic Number of Machines Using Deep Reinforcement Learning

The dynamic flexible job-shop problem (DFJSP) is a realistic and challenging problem that many production plants face. As the product line becomes more complex, the machines may suddenly break down or resume service, so we need a dynamic scheduling framework to cope with the changing number of machines over time. This issue has been rarely addressed in the literature. In this paper, we propose an improved learning-to-dispatch (L2D) model to generate a reasonable and good schedule to minimize the makespan. We formulate a DFJSP as a disjunctive graph and use graph neural networks (GINs) to embed the disjunctive graph into states for the agent to learn. The use of GINs enables the model to handle the dynamic number of machines and to effectively generalize to large-scale instances. The learning agent is a multi-layer feedforward network trained with a reinforcement learning algorithm, called proximal policy optimization. We trained the model on small-sized problems and tested it on various-sized problems. The experimental results show that our model outperforms the existing best priority dispatching rule algorithms, such as shortest processing time, most work remaining, flow due date per most work remaining, and most operations remaining. The results verify that the model has a good generalization capability and, thus, demonstrate its effectiveness.

An adaptive differential evolution algorithm to solve the multi-compartment vehicle routing problem: A case of cold chain transportation problem

This research paper introduces an adaptive differential evolution algorithm (ADE algorithm) designed to address the multi-compartment vehicle routing problem (MCVRP) for cold chain transportation of a case study of twentyeight customers in northeastern Thailand. The ADE algorithm aims to minimize the total cost, which includes both the expenses for traveling and using the vehicles. In general, this algorithm consists of four steps: (1) The first step is to generate the initial solution. (2) The second step is the mutation process. (3) The third step is the recombination process, and the final step is the selection process. To improve the original DE algorithm, the proposed algorithm increases the number of mutation equations from one to four. Comparing the outcomes of the proposed ADE algorithm with those of LINGO software and the original DE based on the numerical examples In the case of small-sized problems, both the proposed ADE algorithm and other methods produce identical results that align with the global optimal solution. Conversely, for larger-sized problems, it is demonstrated that the proposed ADE algorithm effectively solves the MCVRP in this case. The proposed ADE algorithm is more efficient than Lingo software and the original DE, respectively, in terms of total cost. The proposed ADE algorithm, adapted from the original, proves advantageous for solving MCVRPs with large datasets due to its simplicity and effectiveness. This research contributes to advancing cold chain logistics with a practical solution for optimizing routing in multi-compartment vehicles.

Solving the cumulative capacitated vehicle routing problem with drones

ABSTRACT In this paper, we consider the Cumulative Capacitated Vehicle Routing Problem (CCVRP), which is used to model many real-world applications, especially in the area of supplying humanitarian aid after a natural disaster. Interestingly, in this study, Unmanned Aerial Vehicles (UAVs) so-called drones are used to assist the trucks in delivering parcels to customers. Each of them travels to different locations to perform specified tasks and meet periodically with the vehicle from which it takes off to swap its battery. In this paper, a mathematical model is formulated which is then tested with small-sized problems using CPLEX software. Due to the difficulty of solving large instances to optimality, we propose a heuristic algorithm based on a well-established type of cluster-first, route-second approach. Then, it is enhanced by some proposed properties. Hereafter, we develop a minimum spanning tree based-lower bound. Finally, extensive computational experiments are carried out by using instances from the literature. They show the good performance of the proposed heuristic algorithm to solve large instances in a very competitive running time.

A stable diffusion enhanced YOLOV5 model for metal stamped part defect detection based on improved network structure

Machine-vision-based defect detection for large metal stamping is a fundamental requirement for improving product quality and inspection speed. However, the performance of machine vision in detecting defects is limited by the large variety of stamped products, significant dimensional differences, and long data-acquisition cycles. To overcome these problems, metal stamping detection has been achieved using the improved YOLOV5 model, which features a slim neck and a multiheaded self-attentive mechanism for detecting wrinkles, holes, and cracks in metal stamping. An image-processing module was used to reduce the impact of metal reflections and improve image quality. Stable diffusion improvement was used to augment the dataset to overcome the small dataset size problem and enhance its generalisation capability. In addition, a BotNet structure with a self-attentive mechanism was introduced into the YOLOV5 model backbone to improve the image feature extraction capability. We then optimised the prediction head structure of YOLOV5 to improve the detection speed and accuracy. Ablation experiments were performed to analyse and verify the effectiveness of each module. The results of the ablation experiments show that the mAP of our proposed stable diffusion improvement data enhancement method, and the YOLO-Bot-VOV algorithm, for metal stamped part defect detection reached 98.2 %, and the parameters were reduced by 0.432 million.

A Multi-Objective Mathematical Programming Model for Project-Scheduling Optimization Considering Customer Satisfaction in Construction Projects

The aim of this study was to develop a multi-objective mathematical programming model for the trade-off of time, cost, and quality in the project-scheduling problem (PSP) by taking priorities and resource constraints as well as activity preemption into account. First, a small-sized problem instance that was a sub-project of an oil and gas construction project was used for te validation of the proposed model and algorithm. Subsequently, considering the sensitivity, complexity, and importance of oil and gas projects, the proposed model was implemented in a large-sized oil and gas construction project. Considering the NP-hardness of this problem, the NSGA-II metaheuristic algorithm was used to deal with the time, cost, and quality trade-off problem. Finally, a sensitivity analysis was implemented on the three main parameters of time, cost, and quality to investigate the effects of changes on the results. The findings show that the proposed model is more sensitive to cost changes, so an increase in project costs leads to a drastic change in the values of other objective functions.

An algorithm for stochastic convex-concave fractional programs with applications to production efficiency and equitable resource allocation

We propose an algorithm to solve convex and concave fractional programs and their stochastic counterparts in a common framework. Our approach is based on a novel reformulation that involves differences of square terms in the constraints, and subsequent employment of piecewise-linear approximations of the concave terms. Using the branch-and-bound (B&B) framework, our algorithm adaptively refines the piecewise-linear approximations and iteratively solves convex approximation problems. The convergence analysis provides a bound on the optimality gap as a function of approximation errors. Based on this bound, we prove that the proposed B&B algorithm terminates in a finite number of iterations and the worst-case bound to obtain an ϵ-optimal solution reciprocally depends on the square root of ϵ. Numerical experiments on Cobb–Douglas production efficiency and equitable resource allocation problems support that the algorithm efficiently finds a highly accurate solution while significantly outperforming the benchmark algorithms for all the small size problem instances solved. A modified branching strategy that takes the advantage of non-linearity in convex functions further improves the performance. Results are also discussed when solving a dual reformulation and using a cutting surface algorithm to solve distributionally robust counterpart of the Cobb–Douglas example models.