Optimal Completion Time Research Articles

Multi-objective scheduling for an energy-efficient flexible job shop problem with peak power constraint

Controlling electricity costs, which are closely related to the peak power reached, while simultaneously reducing completion time and energy consumption, is crucial for achieving sustainability in the manufacturing industry. However, most existing research on energy-efficient flexible job shop scheduling problems primarily focuses on optimizing completion time and energy consumption, often neglecting the critical aspect of controlling electricity costs. With decreasing resources and increasing energy prices, it is necessary to control electricity costs by limiting the peak power reached during production. To address this gap, this paper investigates an energy-efficient flexible job shop scheduling problem with peak power constraint considering setup and transportation time (EEFJSSP-PPST). We establish a mathematical model for EEFJSSP-PPST and propose an improved non-dominated sorting genetic algorithm II (INSGA-II) incorporating several key improvements. We first introduce three scheduling rules in decoding to optimize objectives and employ heuristic rules to generate a high-quality initial population. Then, we propose an innovative cluster crossover method to accelerate convergence and design an adaptive-based local optimization strategy to further enhance performance. Finally, our experiments explore the impacts of different degrees of the peak power constraint on objectives and evaluate the effectiveness of the three scheduling rules. Additionally, the performance of INSGA-II is tested using 135 benchmark instances. The results indicate that INSGA-II outperformed its variations without improvements, achieving the best hypervolume (HV) indicator in 80% of the instances and the best inverted generational distance (IGD) indicator in 68.89% of the instances. Compared to other state-of-the-art algorithms, INSGA-II achieves the best HV and IGD indicators in 82.2% and 81.5% of the instances, respectively, and demonstrates better convergence and a superior Pareto front. Therefore, we conclude that the improvements in INSGA-II are effective and enhance the algorithm’s performance, making it outstanding in solving EEFJSSP-PPST.

A Decomposition Method for the Group-Based Quay Crane Scheduling Problem

This study addresses the quay crane scheduling problem (QCSP), which involves scheduling a fixed number of quay cranes to load and unload containers from ships in a maritime container terminal. The objective is to minimize the completion time while adhering to precedence, safety margin, and noncrossing constraints. Efficient scheduling of quay cranes plays a crucial role in reducing the time vessels spend at terminals. To solve the QCSP, we explore different schedule directions for the quay cranes. Specifically, we consider three directions: unidirectional, where the quay cranes maintain a consistent movement direction from upper to lower bays or vice versa after initial repositioning; bidirectional, allowing the cranes to change direction once during operations; and multidirectional, permitting freely changing movement direction during operations. For the bidirectional QCSP, we propose a new compact mathematical formulation. To obtain valid lower bounds on the optimal completion time, we derive various relaxations of this new formulation based on the different schedule directions. Our solution framework employs logic-based Benders decomposition, decomposing the problem into an assignment master problem and operation-sequence slave subproblems. Extensive computational experiments using benchmark instances from existing literature and newly generated instances validate the efficiency and effectiveness of the lower bounds and the exact solution approach. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms–Discrete. Funding: This work was supported by the Major Program of the National Natural Science Foundation of China [Grants 72192830 and 72192831], the National Natural Science Foundation of China [Grant 72102034], and the 111 Project [Grant B16009]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoc.2022.0298

Pengembangan Algoritma Tabu Search Berbasis Bilangan Grey Untuk Optimalisasi Flexible Job Shop Dengan Ketidakpastian

This research aims to make a step-by-step process to determine the most optimal completion time for the Flexible Job Shop Scheduling case. Flexible Job Shop Scheduling which not only aims to sequence operations on jobs but also chooses the machine to be used in processing an operation makes this scheduling more complicated than ordinary Job Shop Scheduling. This scheduling involves interval-shaped gray numbers to accommodate uncertainty in job ordering time. This further extends the complexity of scheduling. To solve this case a metaheuristic algorithm namely Tabu Search will be used. This algorithm uses mutation on the solution a number of iterations until it produces the best solution. The use of a tabu list in the Tabu Search algorithm to ensure the search is not trapped in the local minimum.

An optimal control problem for resource utilisation by microorganisms

Decomposition of organic matter controls the flow of carbon and nutrients in terrestrial and aquatic ecosystems. Several kinetic laws have been proposed to describe decomposition rates, but they neglect adaptation of the microbial decomposer to environmental conditions. Here we formalise decomposition as an optimal control problem by assuming that microorganisms regulate the uptake rate of a substrate to maximise their growth over the period of decomposition. The result is an optimal control problem consisting of two differential equations and auxiliary conditions that determine the optimal value of the control variable (the uptake rate), the remaining substrate at any given time, and the optimal completion time. This problem serves as a case study to illustrate the solution of differential equations and optimal control problems for students in undergraduate courses. The mathematical analysis of the problem requires rewriting the differential equations in reverse time along with the solution of a nonhomogeneous linear first order differential equation. We then return to modelling with some biologically motivated questions about how the parameters of the model representing environmental conditions and microbial functional traits affect the outcome. Finally, we discuss alternative ways to use the material with students.

Machine learning assisted delay minimization in full duplex energy constrained cooperative communication network

Cooperative communication is key in attaining high network throughput and better coverage area for a wireless powered communication network. The conventional solution methodologies proposed in the literature for these networks suffer from high run-time complexity. This paper presents an efficient polynomial-time machine learning approach for solving the total transmission time minimization problem through relay selection and scheduling of the users in a full duplex wireless powered cooperative communication network. Exploiting the simplicity offered by the tree ensemble models, a distributed gradient-boosted decision tree based model (XGBoost) is incorporated. The inputs of the model are the uplink channel coefficients and energy harvesting rates of the relays and the users, and outputs are the optimal completion time of the relays and users, relay selection and schedule of the users. Simulation results indicate that the proposed model very well approximates the true outputs, i.e., performs very close to the optimal solution of the optimization problem, while maintaining a very low run-time computational complexity. Specifically, for a network of 9 users, the run-time of the proposed model is just 25% of the optimal solution, and this ratio grows as the number of users increases in the network.

An Integrated Scheduling Algorithm for the Same Equipment Process Sequencing Based on the Root-Subtree Vertical and Horizontal Pre-Scheduling

Given the existing integrated scheduling algorithms, all processes are ordered and scheduled overall, and these algorithms ignore the influence of the vertical and horizontal characteristics of the product process tree on the product scheduling effect. This paper presents an integrated scheduling algorithm for the same equipment process sequencing based on the Root-Subtree horizontal and vertical pre-scheduling to solve the above problem. Firstly, the tree decomposition method is used to extract the root node to split the process tree into several Root-Subtrees, and the Root-Subtree priority is set from large to small through the optimal completion time of vertical and horizontal pre-scheduling. All Root-Subtree processes on the same equipment are sorted into the stack according to the equipment process pre-start time, and the stack-top processes are combined with the schedulable process set to schedule and dispatch the stack. The start processing time of each process is determined according to the dynamic start processing time strategy of the equipment process, to complete the fusion operation of the Root-Subtree processes under the constraints of the vertical process tree and the horizontal equipment. Then, the root node is retrieved to form a substantial scheduling scheme, which realizes scheduling optimization by mining the vertical and horizontal characteristics of the process tree. Verification by examples shows that, compared with the traditional integrated scheduling algorithms that sort the scheduling processes as an overall, the integrated scheduling algorithm in this paper is better. The proposed algorithm enhances the process scheduling compactness, reduces the length of the idle time of the processing equipment, and optimizes the production scheduling target, which is of universal significance to solve the integrated scheduling problem.

Cloneable Jellyfish Search Optimizer Based Task Scheduling in Cloud Environments

For cloud environments, task scheduling focusing on the optimal completion time (makespan) is vital. Metaheuristic approaches can be used to produce efficient solutions that will provide important cost savings to both the cloud service provider and the clients. On the other hand, since there is a high probability of getting stuck in local minima in metaheuristic solutions due to the type of problem, it may not always be possible to quickly reach the optimal solution. This study, using a metaheuristic approach, proposes a solution based on the Cloneable Jellyfish Algorithm for optimal task distribution in cloud environments. The unique feature of the proposed algorithm is that it allows dynamic population growth to be carried out in a controlled manner in order not to get stuck in local minima during the exploration phase. In addition, this algorithm, which uses a different cloning mechanism so that similar candidates are not generated in the population growth, has made it possible to achieve the optimal solution in a shorter time. To observe the solution performance, cloud environment simulations created in the Cloudsim simulator have been used. In experiments, the success of the proposed solution compared to classical scheduling algorithms has been proven.

Network Planning Analysis on Road Construction Projects by CV. X Using Evaluation Review Technique (PERT)-Critical Path Method (CPM) and Crashing Method

Indonesia is currently actively developing infrastructure to improve the economy and welfare of itspeople. One of the infrastructure developments undertaken by the government is road pavement. CV.X is the company that won the asphalt project tender with a contract value of IDR 4.046.873.346 and must complete it within 114 days. During the process of working on the project, there were indications of possible delays in project completion. So this study aims to perform optimal planning, scheduling, and control in CV. X in carrying out road construction project. This study usedthe PERT–CPMmethodto determine the optimal completion time using critical pathways and the concept of probability. The result of thePERT–CPMmethodis an activity in critical flow with an optimal durationof 115 days, where the duration exceeds thecontract period so itneeds to becrashing.Thecrashingmethod is an attempt to speed up the duration of the project and streamline thecosts incurred.In this study, 2scenarioswere obtainedto help reduce the duration and cost savingsthat can be usedby projectimplementers. The first scenario is to reduce the duration based on the optimal duration from 115 daysto 108 days with a saving of IDR690,354or 0,02%. The value of the savings is classified as very small because crashing can only be done with additional laborandlimited working hours. If the crashingmethod is notdone, then the secondscenario is to pay a penalty of IDR40,468,733.

Research on Job-shop Scheduling Problem Based on Bee Colony Algorithm

The job-shop scheduling problem (JSP) is currently a problem that affects processing efficiency and economic benefits in large-scale processing workshops. JSP aims at the optimal completion time, which is a difficult process arrangement and machine allocation problem. Artificial bee colony (ABC) algorithm is a common algorithm to solve JSP. Firstly, this article introduces the problem of job-shop scheduling, secondly analyzes the principle of the ABC algorithm, and finally verifies the effectiveness of the ABC algorithm in solving JSP through experiments.

A hybrid artificial bee colony algorithm for scheduling of digital microfluidic biochip operations

SummaryDigital microfluidic biochips (DMFBs) are designed to efficiently carry out biochemical and biomedical analysis in a miniaturized way. DMFBs offer various advantages over traditional laboratory techniques and reduces cost, and increases automation and software programmability. Scheduling of microfluidic operations is the first and essential step in the fluidic‐level synthesis of DMFBs, while the other two are the module placement and droplet routing. Scheduling DMFB operations is a multiconstrained optimization problem, and the particular decision problem is NP‐complete. We propose a hybrid artificial bee colony (ABC) algorithm using generalized N‐point crossover (GNX) based scheduling of DMFB operations. Proposed ABC‐GNX perturbs through search space, evaluates various schedules possible, and returns the best schedule among the evaluated schedules. Simple list scheduling based heuristic algorithms can explore a single schedule based on the sequence generated by the priority function. Iterative improvement based search algorithms explore the search space and evaluate more schedules, but the proposed ABC‐GNX algorithm produces optimal solutions in shorter execution times. Simulation results show that the proposed ABC‐GNX produces a higher number of optimal completion times and faster execution times than existing algorithms.

Selection and Optimization of Software Development Life Cycles Using a Genetic Algorithm

In the software field, a large number of projects fail, and billions of dollars are spent on these failed projects. Many software projects are also produced with poor quality or they do not exactly meet customers’ expectations. Moreover, these projects may exceed project budget and/or time. The complexity of managing software development projects and the poor selection of software development life cycle (SDLC) models are among the top reasons for such failure. Various SDLC models are available, but no model is considered the best or worst. In this work, we propose a new methodology that solves the SDLC optimization problem using a genetic algorithm. The methodology selects the best SDLC and optimizes the completion time of the selected model. This study aims to help project managers in a software development organization select the proper SDLC model for their projects and optimize the selected model by minimizing the project completion time. The proposed SDLC model selection approach is based on a selection matrix that consists of a set of selection criteria and information related to the project’s nature given by the project managers. Our methodology optimizes the selected SDLC model by reducing the project completion time and assigning duration for each phase. Several experiments were conducted to obtain the optimal completion time for the selected SDLC models. These experiments showed that our algorithm can optimally minimize the completion time of a given project and assign a duration for each phase. Experimental results showed that our methodology can reduce the completion time of a given project and produce realistic and optimal completion times for different SDLC models.

A supervised method for scheduling multi-objective job shop systems in the presence of market uncertainties

In real industries, managers usually consider more than one objective in scheduling process. Minimizing completion time, operational costs and average of machine loads are amongst the main concerns of managers during production scheduling in practice. The purpose of this research is to develop a new scheduling method for job-shop systems in the presence of uncertain demands while optimizing completion time, operational costs and machine load average are taken into account simultaneously. In this research a new multi-objective nonlinear mixed integer programming method is developed for job-shop scheduling in the presence of product demand uncertainty. The objectives of the proposed method are minimizing cost, production time and average of machine loads index. To solve the model, a hybrid NSGA-II and Simulated Annealing algorithms is proposed where the core of the solving algorithm is set based on weighting method. In continue a Taguchi method is set for design of experiments and also estimate the best initial parameters for small, medium and large scale case studies. Then comprehensive computational experiments have been carried out to verify the effectiveness of the proposed solution approaches in terms of the quality of the solutions and the solving times. The outcomes are then compared with a classic Genetic Algorithm. The outcomes indicated that the proposed algorithm could successfully solve large-scale experiments less than 2 min (123 s) that is noticeable. While performance of the solving algorithm are taken into consideration, the proposed algorithm could improve the outcomes in a range between 9.07% and 64.96% depending on the input data. The results also showed that considering multi-objective simultaneously more reasonable results would be reached in practice. The results showed that the market demand uncertainty can significantly affect to the process of job shop scheduling and impose harms in manufacturing systems both in terms of completion time and machine load variation. Operational costs, however, did not reflect significantly to market demand changes. The algorithm is then applied for a manufacturing firm. The outcomes showed that the proposed algorithm is flexible enough to be used easily in real industries.

Research on Multi-Agent Task Optimization and Scheduling Based on Improved Ant Colony Algorithm

As a key problem of cloud computing, the performance of task scheduling strategy may seriously affect the efficiency and service quality of the system. With the purpose of achieving balanced task scheduling with optimal completion time, ant colony optimization (ACO) algorithm is adopted as task scheduling strategy in this paper. Considering the problem of premature convergence to local optimal solution of ACO, an improved Max-Min Ant System (MMAS) is introduced to find the global optimal solution. Based on the study of pheromone’s updating mechanism of MMAS, MMAS is applied as task scheduling strategy with reasonable mapping from the objective of shortest path to shortest completion time. The task scheduling strategy based on MMAS has been simulated from views of tasks’ number, size and load balance, and the results shows that MMAS task scheduling strategy is with a better performance on completion time and load balance than ACO based strategy.?

Improved Whale Optimization with Buffer Setup Time

The job shop problem is widespread in industrial applications due to lateness in getting a better solution. Buffer plays an important role in the completion of jobs. Proper utilization of buffer by fixing optimal buffer setup time can lead to optimal completion time so that lateness is minimized. This work introduced Improved Whale Optimization with Buffer Setup time Technique (IWOBS) for setting optimal buffer setup time. Using tabu movements, an optimum solution for the nearest buffer setup time is derived and the genetic algorithm is equipped to find fitness score to gather the best buffer setup time with respect to problem consideration. The proposed IWOBS algorithm is proved to be highly effective compared to other existing algorithms.

A genetic algorithm‐based flow update scheduler for software‐defined networks

SummarySoftware‐defined networking (SDN) facilitates network programmability through a central controller. It dynamically modifies the network configuration to adapt to the changes in the network. In SDN, the controller updates the network configuration through flow updates, ie, installing the flow rules in network devices. However, during the network update, improper scheduling of flow updates can lead to a number of problems including overflowing of the switch flow table memory and the link bandwidth. Another challenge is minimizing the network update completion time during large‐network updates triggered by events such as traffic engineering path updates. The existing centralized approaches do not search the solution space for flow update schedules with optimal completion time. We proposed a hybrid genetic algorithm‐based flow update scheduling method (the GA‐Flow Scheduler). By searching the solution space, the GA‐Flow Scheduler attempts to minimize the completion time of the network update without overflowing the flow table memory of the switches and the link bandwidth. It can be used in combination with other existing flow scheduling methods to improve the network performance and reduce the flow update completion time. In this paper, the GA‐Flow Scheduler is combined with a stand‐alone method called the three‐step method. Through large‐scale experiments, we show that the proposed hybrid approach could reduce the network update time and packet loss. It is concluded that the proposed GA‐Flow Scheduler provides improved performance over the stand‐alone three‐step method. Also, it handles the above‐mentioned network update problems in SDN.

Collaborative Optimization of Dock Door Assignment and Vehicle Scheduling in Cross-Docking

Cross-docking is a logistic strategy that can transport goods directly from suppliers or manufacturers to retailers or customers. In daily life, the requirements for timeliness of goods distribution have been continuously improved. Cross-docking can realize the rapid transshipment of goods and improve the process efficiency of distribution greatly. Meanwhile, during the cross-docking process, goods are deposited in the temporary storage area, which reduces the storage cost. This paper focuses on the analysis of reasonable vehicle scheduling and dock door allocation problems in cross-docking. The goal is to minimize the working time of cross-docks by the research on this combinatorial optimization problem. This paper proposes the genetic algorithm (GA) and the hybrid particle swarm optimization to solve the three-scale (small, medium and large) cross-docks. Optimal completion time, average completion time and average solution time are considered as factors to evaluate the efficiency of two algorithms on three scales. And then the concept of mixed-mode dock door is introduced. GA is used to conduct numerical experiments with mixed dock doors on different scales. Finally, by comparing the utilization rate of mixed dock doors, we can analyze the influence of mixed dock door on vehicles’ waiting time.

Heuristic Load Balancing Based Zero Imbalance Mechanism in Cloud Computing

Cloud computing using virtualization technology has emerged as a new paradigm of large-scale distributed computing. One of its fundamental challenges is to schedule a vast amount of heterogeneous tasks while maintaining load balancing amongst different heterogeneous virtual machines (VMs) to meet both cloud users and providers’ requirements, such as minimum makespan low monetary costs, and high resource utilization. This problem is often classified as, NP-hard optimization, and while many heuristic algorithms have attempted to solve the NP-problem. However, they fail in load balancing and lower running times when the number of tasks grows exponentially, while that of VMs with set of resources, such as CPU, memory RAM and bandwidth remains stagnant. To solve the NP-problem effectively, we propose a fast heuristic algorithm based on the zero imbalance approach, as a new concept in the heterogeneous environment. Specifically, this approach focuses on minimizing the completion time difference among heterogeneous VMs without priority methods and complex scheduling decision which often subject the heuristic algorithms to the particular cloud configuration. The proposed approach defines two constraints, optimal completion time and earliest finish time which take account the task transfer time onto network bandwidth of VM to achieve load balancing and task scheduling effectively. The experimental results below show that the proposed algorithm effectively solves the NP-hard optimization problem better than existing heuristic algorithms by satisfying cloud users and providers’ requirements.

Heuristics and lower bound for minimizing maximum lateness on a batch processing machine with incompatible job families

Production efficiency can be greatly improved by using batch processing machines which can process several jobs in parallel. When job processing characteristics are different, job family should be further considered to group jobs properly in a batch. The problem of scheduling non-identical jobs from incompatible job families on a batch processing machine is investigated in this paper. Job sizes are non-identical and the objective is to minimize the maximum lateness Lmax. Batch processing time is determined by the job with the longest processing time and batch due date equals to the earliest job due date in the batch. Only jobs from the same job family can be grouped together in the same batch. A mathematical model of the problem under study is formulated and validated by using CPLEX. A lower bound is proposed based on the lower bound and the upper bound of the batch number. Because of the NP-hardness of the problem, heuristics are designed to solve the problem under study. These heuristics are then improved by optimizing completion time or due date of the critical batch. Experimental studies show that heuristics could be effectively improved by CTD (Completion Time Decreasing) rules.

Rumor Spreading and Conductance

In this article, we study the completion time of the PUSH-PULL variant of rumor spreading, also known as randomized broadcast. We show that if a network has n nodes and conductance ϕ then, with high probability, PUSH-PULL will deliver the message to all nodes in the graph within O (log n /ϕ) many communication rounds. This bound is best possible. We also give an alternative proof that the completion time of PUSH-PULL is bounded by a polynomial in log n /ϕ, based on graph sparsification. Although the resulting asymptotic bound is not optimal, this proof shows an interesting and, at the outset, unexpected connection between rumor spreading and graph sparsification. Finally, we show that if the degrees of the two endpoints of each edge in the network differ by at most a constant factor, then both PUSH and PULL alone attain the optimal completion time of O (log n /ϕ), with high probability.

Heuristic Cloudlet Allocation Approach Based on Optimal Completion Time and Earliest Finish Time

Cloud computing is an information technology paradigm that enables ubiquitous access to shared pools of configurable system resources and higher level services required by modern technology. Task scheduling is an important part in cloud computing for limited number of heterogeneous resources and increasing number of user tasks. Task scheduling is to allocate tasks (cloudlets) to the best suitable resources to increase performance in terms of some parameters, such as makespan and resource utilization. Allocating cloudlets with good load balancing and minimum makespan is an NP-hard optimization problem. Many meta-heuristic and heuristic algorithms have been proposed to solve the said problem, but they lack in considering the completion time of virtual machine and total length of its allocated cloudlets instead of only considering completion time of a cloudlet. This lack leads to decrease the performance of a cloud system in some cases, such as large cloudlets. To address the said problem, in this paper, we propose an optimal heuristic cloudlet allocation algorithm for resource allocation and task scheduling, referred as HCA, to cope with the increasing large number of user cloudlets under minimum resource capacity. So, we devise a new mechanism to combine optimal completion time and earliest finish time to minimize both degree of imbalance and overall completion time. The experimental results show that the proposed HCA can achieve effectively and efficiently good performance, best load balancing, and improve the resource utilization in comparison with the other existing cloudlet allocation methods.