Large-sized Problems Research Articles

Solution approaches for the bi-objective Skiving Stock Problem

The Skiving Stock Problem (SSP) aims to determine an optimal plan for producing as many large objects as possible by combining small items. The skiving process may need different considerations depending on the production environment and the product characteristics. In this study, we address bi-objective 1D-SSP with two conflicting objectives. One common objective is to minimize the trim loss remaining after skiving, as removing the excess width is an extra procedure. When welding is an element of the skiving process, increasing the number of items for each product indicates compromised quality. Therefore, minimizing the number of small items for each product becomes a primary objective in such cases. To solve this bi-objective version of the NP-hard problem, we implement a Lexicographic Method (LM) in which the importance of the objectives imposes their preference orders. We propose two methodologies within the LM framework. The first methodology integrates Column Generation (CG) and Branch & Bound (B&B) to search for an exact solution. Given the excessive computational time an exact solver may require for tight or large-sized problems, we propose a heuristic method integrating the Dragonfly Algorithm (DA) and a Constructive Heuristic (CH). Real-world application results validate the exact solver and demonstrate comparable results for the heuristic solver in terms of solution quality and computational time. The efficiency of the solution methodologies for a preemptive multi-objective SSP aims to support decision-makers with make-or-buy decisions.

Integrated mixed-model assembly line balancing and parts feeding with supermarkets

In the automotive industry, decentralized in-house logistic areas called supermarkets are used for parts feeding to mixed-model assembly lines. In the literature, generally, the number of supermarkets and their locations are determined according to a previously balanced assembly line. As a result, supermarket locations have to be completely dependent on the line balance. There may be more than one solution that gives the same performance criterion value in the line balancing. Among these alternative solutions, it is more reasonable to use a solution that provides lower logistics costs than others. For this purpose, in this study, the mixed-model assembly line balancing problem and the supermarket location problem are considered simultaneously. Accordingly, in order to minimize the total costs of the assembly line and supermarkets, a mixed-integer mathematical model is developed, and the developed model is solved by using constraint programming (CP). In addition, a new approach based on Ant Colony Optimization (ACO) and Simulated Annealing (SA) is presented for large-sized problems. An illustrative example problem is solved using both the developed model and the proposed algorithm. The effectiveness of the proposed approach is tested through a new data set of test problems presented to the literature for a computational experiment. The experimental results show that the total costs are reduced meaningfully and a more realistic and applicable structure is achieved by the proposed approach.

Urban 5G MmWave Networks: Line-of-Sight Probabilities and Optimal Site Locations

In this work, we implemented line-of-sight (LoS) ray tracing functionality to investigate problems in millimetre-wave propagation modelling and network planning in 3D city model environments. First, we validated an existing LoS propagation probability model expressed as an exponential rule with the link distance. By fitting ray tracing simulation results under different scenarios to the model, the relationships between key parameters in the model and factors including the building density and the transmitter height were qualitatively analysed. Next, we developed a network planning framework for a multi-hop outdoor urban network by formulating a mixed-integer linear programming problem which minimises the overall deployment cost through optimal site selection. Taking the sets of potential site locations and potential links as inputs, we selected a subset of the sites that comprise a tree-structured network that satisfies all the user demands at a minimum deployment cost. We also analysed the time required for solving this optimisation problem in order to provide a prediction of the execution time for larger-sized problems.

A knowledge-inherited learning for intelligent metasurface design and assembly

Recent breakthroughs in deep learning have ushered in an essential tool for optics and photonics, recurring in various applications of material design, system optimization, and automation control. Deep learning-enabled on-demand metasurface design has been the subject of extensive expansion, as it can alleviate the time-consuming, low-efficiency, and experience-orientated shortcomings in conventional numerical simulations and physics-based methods. However, collecting samples and training neural networks are fundamentally confined to predefined individual metamaterials and tend to fail for large problem sizes. Inspired by object-oriented C++ programming, we propose a knowledge-inherited paradigm for multi-object and shape-unbound metasurface inverse design. Each inherited neural network carries knowledge from the “parent” metasurface and then is freely assembled to construct the “offspring” metasurface; such a process is as simple as building a container-type house. We benchmark the paradigm by the free design of aperiodic and periodic metasurfaces, with accuracies that reach 86.7%. Furthermore, we present an intelligent origami metasurface to facilitate compatible and lightweight satellite communication facilities. Our work opens up a new avenue for automatic metasurface design and leverages the assemblability to broaden the adaptability of intelligent metadevices.

Optimal distribution of perishable foods with storage temperature control and quality requirements: An integrated vehicle routing problem

The quality of food products deteriorates continuously over time at a speed depending on the storage temperature. Therefore, they must be stored at low temperatures to prolong their shelf life, which increases storage costs significantly. In this paper, we study a distribution problem in which a temperature-controlled warehouse is responsible for supplying a perishable food product, using a homogenous fleet of capacitated vehicles, to multiple customers with minimum quality requirements and delivery time windows. The objective is to minimize the sum of the energy cost at the warehouse and the transportation cost to deliver the customer demand. Decisions include the storage temperature at the warehouse and delivery routes. The distribution problem is formulated as a Mixed-Integer Linear Programming (MILP) model. After presenting an analytical study of the problem, a heuristic based on General Variable Neighborhood Search (GVNS) is designed to solve the large-size problem instances. Using the case of a dairy product, the model is solved under various scenarios. It is observed that the distribution and temperature decisions are dependent. Moreover, the optimal distribution plan and storage temperature are significantly impacted by changes in factors related to food quality, such as truck and environmental temperatures and energy price.

Tridigpu: A GPU Library for Block Tridiagonal and Banded Linear Equation Systems

In this article, we present a CUDA library with a C API for solving block cyclic tridiagonal and banded systems on one GPU. The library can process block tridiagonal systems with block sizes from 1 × 1 (scalar) to 4 × 4 and banded systems with up to four sub- and superdiagonals. For the compute-intensive block size cases and cases with many right-hand sides, we write out an explicit factorization to memory; however, for the scalar case, the fastest approach is to only output the coarse system and recompute the factorization. Prominent features of the library are (scaled) partial pivoting for improved numeric stability; highest-performance kernels, which completely utilize GPU memory bandwidth; and support for multiple sparse or dense right-hand side and solution vectors. The additional memory consumption is only 5% of the original tridiagonal system, which enables the solution of systems up to GPU memory size. The performance of the state-of-the-art scalar tridiagonal solver of cuSPARSE is outperformed by factor 5 for large problem sizes of 2 25 unknowns, on a GeForce RTX 2080 Ti.

A MIP model and a hybrid genetic algorithm for flexible job-shop scheduling problem with job-splitting

In the scheduling literature, it is generally assumed that jobs are not split into sub-lots, or that the number and size of sub-lots are limited or predetermined. These assumptions make the problem more manageable. However, they may prevent more successful schedules. For many businesses, considering the splitting of jobs while scheduling them can create significant improvement opportunities. This study addresses the Flexible Job-Shop Scheduling Problem (FJSP) with job-splitting, determining how many sub-lots each job should be split into and the size of each sub-lot. A MIP model is proposed for the considered problem. In the model, the size and number of sub-lots of a job are not predefined or bounded. The objective function of the model is to minimize the makespan. Feasible solutions could not be found for large-sized problems by the mathematical model. So, a Hybrid Genetic Algorithm (HGA) is also proposed. In the proposed HGA, a Local Search Algorithm (LSA) that determines the size of sub-lots has been included in the GA to improve the efficiency. To show the success of the proposed HGA, its performance is compared with the classical GA.

Hybridizing local searching with genetic algorithms for the job sequencing and tool switching problem with non-identical parallel machines

The job sequencing and tool switching problem (SSP) is an old and highly studied problem. However, the SSP with non-identical parallel machines (SSP-NPM) is a new generalization of this problem. Since the SSP-NPM has been very recently introduced, the number of solution methods for this problem is low. Additionally, exact solution methods are mostly insufficient to find a good solution within a reasonable computational time since this problem is NP-hard. Therefore, heuristic approaches are more appropriate, especially when solving large-size problems. Thus, this study presents a new hybrid algorithm that is a combination of a genetic algorithm (GA) and a local search (LS) technique. Both of these methods are greatly preferred by authors for solving job scheduling problems. Thereby, this study combines their strengths to solve the SSP-NPM. Two versions of the proposed method are tested with benchmark instances. These versions differ in terms of their tool optimization policies: the first uses the well-known “keep tool needed soonest” (KTNS) policy, while the second uses the “randomly remove tool” (RRT) policy. Computational experiments showed that combining some of the features of GA and LS methods for the SSP-NPM contributed greatly to the quality of the solution. Two versions of the proposed hybrid method were compared to a mixed-integer programming model and several schemes of an iterated local search algorithm. Our computational results show that both versions of the proposed hybrid method were significantly better than the other methods, and were able to find the solutions within a reasonable computational time.

A two-echelon location routing problem considering sustainability and hybrid open and closed routes under uncertainty

Location-routing is an extremely important problem in supply chain management. In the location-routing problem, decisions are made about the location of facilities such as distribution centers as well as the set of vehicle routes. Today, organizations seek to reduce the transportation cost by outsourcing leading to a particular kind of transportation problems known as open routing. However, the increasing attention to environment have led to paying more attention to environmental issues and reducing the environmental impacts of logistics activities. To this end, in this paper, both open and closed routes were simultaneously addressed by developing a multi-objective mixed integer linear programming model that included three economic, environmental, and social responsibility aspects. The three objective functions of the proposed model encompass the minimization of total costs and greenhouse gas emissions, and the maximization of employment rate and economic development. Also, in this study, a different type of routing was considered in each echelon. A small-sized problem instance was solved using the Augmented Epsilon Constraint (AEC) method with the CPLEX Optimizer Solver for the validation of the proposed model. Moreover, the sensitivity analysis was performed to investigate the effect of changing main parameters on the values of the objective function. Due to the NP-Hardness of the problem, two efficient metaheuristic algorithms of Non-dominated Sorting Genetic Algorithm (NSGA-II) and Multi-Objective Stochastic Fractal Search (MOSFS) were exploited to solve the medium and large size problems. The performance of the algorithms was compared on the basis of six different well-known indexes of Time, MID, RAS, Diversity, Spacing, and SNS. According to the obtained results, the performance of the MOSFS algorithm was %20, %9, %11.22, %10.03, and %19.06 higher than the performance of the NSGA-II on the basis of SNS, RAS, MID, Diversity, and Time indexes, respectively. On the other hand, the NSGA-II performance was %6.3 higher than the MOSFS performance in terms of Spacing index.

Synthesis of Large-Scale Instant IoT Networks

While most networks have long lifetimes, temporary network infrastructure is often useful for special events, pop-up retail, or disaster response. An <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">instant IoT</i> network is one that is rapidly constructed, used for a few days, then dismantled. We consider the synthesis of instant IoT networks in urban settings. This synthesis problem must satisfy complex and competing constraints: sensor coverage, line-of-sight visibility, and network connectivity. The central challenge in our synthesis problem is quickly <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">scaling</i> to large regions while producing cost-effective solutions. We explore two qualitatively different representations of the synthesis problems using satisfiability modulo convex optimization (SMC), and mixed-integer linear programming (MILP). The former is more expressive, for our problem, than the latter, but is less well-suited for solving optimization problems like ours. We show how to express our network synthesis in these frameworks. To scale to problem sizes beyond what these frameworks are capable of, we develop a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">hierarchical synthesis</i> technique that independently synthesizes networks in sub-regions of the deployment area, then combines these. We find that, while MILP outperforms SMC in some settings for smaller problem sizes, the fact that SMC's expressivity matches our problem ensures that it uniformly generates better quality solutions at larger problem sizes.

A novel competitive exact approach to solve assembly line balancing problems based on lexicographic order of vectors

The assembly line balancing problem (ALBP) is an eminent NP-hard topic that is discussed in mass production systems with low diversity. Primarily, two types of ALBPs are discussed in the literature as type I, which aims to find the minimum number of workstations for a given cycle time, and type II, which assigns some tasks to a given number of workstations such that the maximum workstation load is minimized. To solve ALBPs, various exact, heuristic, and metaheuristic methods have been proposed. However, these methods lose their efficiency when handling large-size problems. Therefore, researchers have focused on proposing heuristic and metaheuristic algorithms to solve large-size problems, especially when they deal with real-life case problems in the industry. This study aims to present a novel and competitive exact method for solving ALBP type II based on the lexicographic order of vectors for feasible solutions. To evaluate the performance of the developed method, a group of highly used standard test problems in the literature is utilized, and the results are compared and discussed in detail. The computational results in this study specify that the developed solution approach performs efficiently and yields the best global solution of all the ALB test problems, which proves the proposed method's potential and its competitive advantage.

A Two-Step Approach to Scheduling a Class of Two-Stage Flow Shops in Automotive Glass Manufacturing

Driven from real-life applications, this work aims to cope with the scheduling problem of automotive glass manufacturing systems, that is characterized as a two-stage flow-shop with small batches, inevitable setup time for different product changeover at the first stage, and un-interruption requirement at the second stage. To the best knowledge of the authors, there is no report on this topic from other research groups. Our previous study presents a method to assign all batches to each machine at the first stage only without sequencing the assigned batches, resulting in an incomplete schedule. To cope with this problem, if a mathematical programming method is directly applied to minimize the makespan of the production process, binary variables should be introduced to describe the processing sequence of all the products, not only the batches, resulting in huge number of binary variables for the model. Thus, it is necessary and challenging to search for a method to solve the problem efficiently. Due to the mandatory requirement that the second stage should keep working continuously without interruption, solution feasibility is essential. Therefore, the key to solve the addressed problem is how to guarantee the solution feasibility. To do so, we present a method to determine the minimal size of each batch such that the second stage can continuously work without interruption if the sizes of all batches are same. Then, the conditions under which a feasible schedule exists are derived. Based on the conditions, we are able to develop a two-step solution method. At the first step, an integer linear program (ILP) is formulated for handling the batch allocation problem at the first stage. By the ILP, we need then to distinguish the batches only, greatly reducing the number of variables and constraints. Then, the batches assigned to each machine at the first stage are optimally sequenced at the second step by an algorithm with polynomial complexity. In this way, by the proposed method, the computational complexity is greatly reduced in comparison with the problem formulation without the established feasibility conditions. To validate the proposed approach, we carry out extensive experiments on a real case from an automotive glass manufacturer. We run ILP on CPLEX for testing. For large-size problems, we set 3600 s as the longest time for getting a solution and a gap of 1% for the lower bound of solutions. The results show that CPLEX can solve 96.83% cases. Moreover, we can obtain good solutions with the maximum gap of 4.9416% for the unsolved cases.

Optimizing task reassignments for reconfigurable multi-model assembly lines with unknown order of product arrival

This paper deals with the multi-model assembly line balancing problem (MuMALBP) in a reconfigurable environment. The considered line is composed of a fixed number of workstations and can produce different products in batches. Each product requires an appropriate line configuration. Thus, when the product changes, the line has to be reconfigured to satisfy new requirements related to task precedence and cycle time constraints. Reconfiguring the line consists in reassigning certain tasks between the existing workstations. The objective of this paper is to design a line configuration for each product while minimizing the maximum number of task reassignments whatever the sequence of product arrival. To solve this NP-hard problem, a mixed-integer linear program (MILP) is first formulated. Subsequently, a constructive heuristic and a MILP-based heuristic, named Halt-and-Fix, are developed to solve large-size problem instances. All the approaches are tested and approved on a dataset derived from the well-known instances of the assembly line balancing literature. The numerical results show that the Halt-and-Fix heuristic provides a better trade-off between solution quality and CPU time, compared to the constructive heuristic and the MILP formulation.

Fundamental energy cost of finite-time parallelizable computing

The fundamental energy cost of irreversible computing is given by the Landauer bound of kTln 2/bit, where k is the Boltzmann constant and T is the temperature in Kelvin. However, this limit is only achievable for infinite-time processes. We here determine the fundamental energy cost of finite-time parallelizable computing within the framework of nonequilibrium thermodynamics. We apply these results to quantify the energetic advantage of parallel computing over serial computing. We find that the energy cost per operation of a parallel computer can be kept close to the Landauer limit even for large problem sizes, whereas that of a serial computer fundamentally diverges. We analyze, in particular, the effects of different degrees of parallelization and amounts of overhead, as well as the influence of non-ideal electronic hardware. We further discuss their implications in the context of current technology. Our findings provide a physical basis for the design of energy-efficient computers.

A lightweight tea bud detection model based on Yolov5

Tea bud detection technology is highly significant in realizing the automation and intelligence of tea bud picking. However, there are still some challenges with tea bud detection technology. For example, the problems of low detection accuracy, heavy computing, and large detection model size make the technology inconducive to the deployment of mobile terminals. Thus, a lightweight tea bud detection model based on the Yolov5 model was proposed in this study. Improvements were made in the following aspects: the Ghost_conv module was introduced to replace the original convolution, considerably reducing the computing and model size; the bottleneck attention module (BAM) was added to the backbone network to suppress invalid information and improve the model detection accuracy; the weighted feature fusion was used in the neck network to efficiently fuse the low-level and high-level features, helping the network to extract effective information for recognition and improve detection accuracy; and CIoU was used as the bounding box loss function to accelerate regression prediction and improve the positioning accuracy of the bounding box of the model. A test was conducted on the collected dataset to verify whether the modified model improved the detection performance of tea buds. The results showed that compared with that of the original Yolov5 model, the mean average precision of the modified model increased by 9.66%, and the floating-point operations and params reduced by 52.402 G and 22.71 M, respectively. An ablation study proved that the proposed method improves the detection performance of the Yolov5 model for tea buds. Compared with other detection algorithm models, the superiority of the proposed algorithm in tea bud detection can be seen. The proposed improved Yolov5 can effectively detect tea buds, which provides theoretical research and technical support for intelligent picking of tea buds in actual scenes.

A Novel Hybrid Simulated Annealing for No-Wait Open-Shop Surgical Case Scheduling Problems

In this paper, the problem of finding an assignment of “n” surgeries to be presented in one of “m” identical operating rooms (ORs) or machines as the surgical case scheduling problem (SCSP) is proposed. Since ORs are among NP-hard optimization problems, mathematical and metaheuristic methods to address OR optimization problems are used. The job or surgical operation ordering in any OR is a permanent part of all sequencing and scheduling problems. The transportation times between ORs are defined based on the type of surgical operations and do not depend on distance, so there is no surgical operation waiting time for transferring. These problems are called no-wait open-shop scheduling problems (NWOSP) with transportation times. The transportation system for the problems is considered a multi-transportation system with no limitation on the number of transportation devices. Accordingly, this study modeled a novel combined no-wait open-shop surgical case scheduling problem (NWOSP-SCSP) with multi-transportation times for the first time to minimize the maximum percentile of makespan for OR as a single objective model. A mixed-integer linear program (MILP) with small-sized instances is solved. In addition to the small-sized model, a novel metaheuristic based on a hybrid simulated annealing (SA) algorithm to solve large-sized problems in an acceptable computational time is suggested, considering the comparison of the SA algorithm and a new recommended heuristic algorithm. Then, the proposed hybrid SA and SA algorithms are compared based on their performance measurement. After reaching the results with a numerical analysis in Nova Scotia health authority hospitals and health centers, the hybrid SA algorithm has generated significantly higher performance than the SA algorithm.

Large Class Size: Its Implications on Students and Teachers of Higher Institutions in Nigeria

Emergence of COVID-19 across the world is more than enough for us to start pondering on how to address the issue of large class size in Nigerian tertiary institutions. Large class size is a common phenomenon in our higher institutions especially for core courses which every student in the department or faculty must offers. Over 1,000 students usually converge in a small lecture hall with capacity of 300 students and this inadequacy has been giving lecturers tough time during their lectures. Lecturers who are not that audible find it very much difficult to pass messages effectively to the students and this has been contributing to falling standard of education in Nigeria. More so, students who are supposed to get the best out of brilliant lecturers are denied of this opportunity, why? Because the classroom size is not bigger enough to accommodate students, therefore, discouraging them from attending classes on a regular basis and also making lecturers inactive in the lectures’ halls. The researchers who have been working assiduously to ensure that the problems encountered by students as a result of class size have not done enough to provide lasting solutions to these problems, making the problems persist. Paradigm shift is one of the ways suggested by the researcher to tackle the problems of large class size in our tertiary institutions. The transnational ways of team teaching, group discussion are no longer effective for large class size as the population of Nigeria keeps increasing and the researcher believes it has become paramount importance to devise ways of overcoming difficulties encountered by the students and lecturers in a large class size. Division of large class size into half to encourage group work among the students and introduction of a blend of learning instructional methods are inevitable at this junction. Introduction of these two things in our tertiary institutions will go a very long way in addressing the issues of large class size. The researcher recommends that, government should employ more lecturers to increase performance of lecturers teaching core courses in our tertiary institutions after the division of large class size into small groups, government should build more lectures’ halls to encourage blend of learning methods for overcrowded classes.

A bi-objective home care routing and scheduling problem considering patient preference and soft temporal dependency constraints

A Home Health Care Routing and Scheduling Problem (HHCRSP) is one of the most practical branches in Home Health Care (HHC) optimization. The main focus of this study is to investigate an HHCRSP with both soft and Hard Time Windows (HTWs) associated with caregivers and patients, respectively. Furthermore, five different types of soft temporal dependency constraints are considered, which specify different relations amongst the starting time of dependent visits. Accordingly, a bi-objective Mixed-Integer Programming (MIP) model is devised to incorporate staff rostering, vehicle routing, and scheduling simultaneously. This model aims at minimizing the system’s total cost while maximizing the total satisfaction of patient preference. Since the problem is NP-hard, Iterated Local Search (ILS) is applied to solve large-sized problems in high frequencies and within reasonable computational time. Computational results on some real-world-inspired benchmark instances highlight the overall efficiency of the employed algorithm compared to the Non-dominated Sorting Genetic Algorithm (NSGA-II).

Problem-size-independent angles for a Grover-driven quantum approximate optimization algorithm

The quantum approximate optimization algorithm (QAOA) requires that circuit parameters are determined that allow one to sample from high-quality solutions to combinatorial optimization problems. Such parameters can be obtained using either costly outer-loop optimization procedures and repeated calls to a quantum computer or, alternatively, via analytical means. In this work, we consider a context in which one knows a probability density function describing how the objective function of a combinatorial optimization problem is distributed. We show that, if one knows this distribution, then the expected value of strings, sampled by measuring a Grover-driven, QAOA-prepared state, can be calculated independently of the size of the problem in question. By optimizing this quantity, optimal circuit parameters for average-case problems can be obtained on a classical computer. Such calculations can help deliver insights into the performance of and predictability of angles in QAOA in the limit of large problem sizes, in particular, for the number partitioning problem.

A Location Routing Problem with Time Windows Consideration: A Metaheuristics Approach

A substantial distribution system is achievable to attain through the simultaneous design of the location facility and route generation. This problem is generally called a location routing problem (LRP), where both strategic decision and operational decisions are considered during the decision initial phase. Nevertheless, for some real applications, a consideration of time restriction due to several reasons should be included in the model. Some examples include the distribution system of perishable goods, a company’s objective towards a high level of customer service, or emergency/disaster situations. Consequently, this research incorporates the location routing problem (LRP) with time window constraints, including the working hour and also time restriction in each customer. The location routing problem with time windows (LRPTW) could not be solved easily, especially for a large-sized problem and or one which is considered an NP-hard problem. In consideration with its large solution pools, this paper suggests an integration of variable neighborhood search (VNS) with path relinking (PR) to solve LRPTW. The method is first applied in the LRP benchmark to validate the effectiveness and the robustness of the proposed method. Computational results clarify that VNSPR can achieve some of the best and most competitive solutions for the LRP when compared to existing approaches. Further, we developed LRPTW instances from the best solution found in LRP datasets. The proposed VNSPR method is also able to yield nearly optimal solutions for LRPTW instances.