Scheduling Objective Function Research Articles

One-dimensional bin packing with pattern-dependent processing time

In this paper the classical one-dimensional bin packing problem is integrated with scheduling elements: a due date is assigned to each item and the time required to process each bin depends on the pattern being used. The objective is to minimize a convex combination of the material waste and the delay costs, both significant in many real-world contexts. We present a novel pattern-based mixed integer linear formulation suitable for different classical scheduling objective functions, and focus on the specific case where the delay cost corresponds to the maximum tardiness. The formulation is tackled by a branch-and-price algorithm where the pricing of the column generation scheme is a quadratic problem solved by dynamic programming. A sequential value correction heuristic (SVC) is used to feed with warm starting solutions the column generation which, in turn, feeds the SVC with optimal prices so as to compute refined feasible solutions during the enumeration. Computational tests show that both column generation and branch-and-price substantially outperform standard methods in computing dual bounds and exact solutions. Additional tests are presented to analyze the sensitivity to parameters’ changes.

Dynamic scheduling for manufacturing workshops using Digital Twins, Competitive Particle Swarm Optimization, and Siamese Neural Networks

Flexible manufacturing workshops often encounter scheduling challenges due to complex processes and cumbersome procedures. To address these issues, a dynamic scheduling method is proposed. Initially, a discrete manufacturing workshop scheduling problem model is developed, considering the unique characteristics of the workshop. Digital Twin technology and a Competitive Particle Swarm Optimization algorithm are then integrated to create the scheduling model. Finally, Siamese Neural Networks are incorporated to form a dynamic scheduling mechanism that optimizes disturbance scheduling. The research model demonstrated a quick convergence, efficiently searching for the optimal fitness value using both the Sphere and Griewank functions. In the scheduling objective function test, the model achieved a maximum completion time of 244.8 minutes, the shortest time compared to similar technologies. In Siamese Neural Network experiments, the model successfully suppressed the influence of disturbances, maintaining optimal scheduling performance. Without adjustments for disturbances, the maximum completion time was 58.5 minutes. After optimization, it decreased to 54.2 minutes. These results demonstrate the effective application of the proposed technology in workshop scheduling. The findings provide valuable technical insights for the application of intelligent technologies in workshop scheduling optimization.

Research on Parallel Task Scheduling Algorithm of SaaS Platform Based on Dynamic Adaptive Particle Swarm Optimization in Cloud Service Environment

To efficiently realize the parallel task scheduling of SaaS platform in large-scale cloud service environment, this paper studies the parallel task scheduling algorithm of SaaS platform based on dynamic adaptive particle swarm optimization in cloud service environment. Users access the cloud through the user access interface module, and issue task scheduling instructions or send task scheduling requests. After the service management module provides diversified application service support according to the scheduling requirements, the core service module determines the SaaS platform parallel scheduling objective function, and uses dynamic adaptive particle swarm optimization to solve the objective function to obtain the SaaS platform parallel task scheduling results. The test results show that the algorithm has better multi-objective solving ability and can obtain higher quality objective solutions, and the test results of the total execution time of parallel scheduling tasks and the total transmission time of task data on SaaS platform are all within 30 s. The results of virtual machine resource load balancing degree are all below 15%; the utilization rate of virtual machine resources is above 92.2%.

Dynamic Robust Optimization Method Based on Two-Stage Evaluation and Its Application in Optimal Scheduling of Integrated Energy System

As an emerging energy allocation method, shared energy storage devices play an important role in modern power systems. At the same time, with the continuous improvement in renewable energy penetration, modern power systems are facing more uncertainties from the source side. Therefore, a robust optimization algorithm that considers both shared energy storage devices and source-side uncertainty is needed. Responding to the above issues, this paper first establishes an optimal model of a regional integrated energy system with shared energy storage. Secondly, the uncertainty problem is transformed into a dynamic optimization problem with time-varying parameters, and a modified robust optimization over time algorithm combined with scenario analysis is proposed to solve such optimization problems. Finally, an optimal scheduling objective function with the lowest operating cost of the system as the optimization objective is established. In the experimental part, this paper first establishes a dynamic benchmark test function to verify the validity of proposed method. Secondly, the multi-mode actual verification of the proposed algorithm is carried out through a regional integrated energy system. The simulation results show that the modified robust optimization over time (ROOT) algorithm could find solutions with better robustness in the same dynamic environment based on the two-stage evaluation strategy. Compared with the existing algorithms, the average fitness and survival time of the robust solution obtained by the modified ROOT algorithm are increased by 94.41% and 179.78%. At the same time, the operating cost of the system is reduced by 11.65% by using the combined optimization scheduling method proposed in this paper.

Study on the Development Path of Rural Cultural Industry under the Perspective of Rural Revitalization

Abstract Based on the theory of systematics and synergy, this paper measures the degree of coordination within the system by measuring the system order parameters that determine the phase transition characteristics and laws of the system and establishes a model of the coordination degree of the composite system that can be realistically calculated. This paper sorts out the main constraints on the coordinated development of rural cultural industries, constructs an index system to evaluate the level of coordinated development of regional cultural industries, and introduces it into the composite system coordination model to measure the synergy degree of rural cultural industries. Starting from the interaction effect between the digital cultural industry and rural revitalization, this paper designs the research on the digital cultural industry from the perspective of rural revitalization and uses data analysis software to analyze the development path of the rural cultural industry. The results show that the iterative scheduling strategy achieves the best scheduling objective function in each test set, with values of 154.62, 287.074, 360.262 and 348.408, respectively. That is, the iterative scheduling strategy can better complete the passenger flow scheduling. In 2012 and 2019, the ‘ Moran sI values of rural cultural industry efficiency were 0.1752 and 0.3094, respectively. That is, the technical efficiency of rural cultural industries from the perspective of rural revitalization has a significant spatial dependence on geographical space and has a positive autocorrelation relationship. This study analyzes the dilemmas faced by the development of rural cultural industries and proposes practical ways to solve these issues.

Information Extraction and Data Planning of Smart City Based on Internet of Things

In order to solve the problem of slow resource scheduling in the process of smart city management, the author proposes a smart city information extraction and data planning system based on the Internet of Things. IoT requires different technologies for analysis for different data types. Managers use different IoT applications to analyze data from different devices and integrate relevant data for possible machine failure or emergency in smart home applications. Situation is predicted. The system includes a cloud platform intelligence center, uses the cloud management module to monitor various hardware devices, constructs the cloud computing resource scheduling objective function, uses the cultural particle swarm algorithm to solve the objective function, and obtains the cloud computing resource scheduling scheme. The experimental results show that the overall utilization rate of the system is the best, close to 100%. Conclusion. The system can realize the effective management of the smart city and monitor the city situation in real time. When implementing resource scheduling, the task completion time is short, the system utilization rate is high, and the resources can be maximized.

Scheduling of Multisensor for UAV Cluster Based on Harris Hawks Optimization With an Adaptive Golden Sine Search Mechanism

Multisensor scheduling, a multi-objective optimization problem, simultaneously aims to find the optimal matching between sensors and targets in a certain period, that is, to generate the optimal multisensor scheduling scheme. Several sensor scheduling literatures proposed multisensor scheduling schemes incorporating various algorithms, but the majority of them dealt with sensors to targets in two dimensions. First, the visual relationship between sensors and UAV cluster targets is investigated, and a three-dimensional correspondence between sensors, targets, and time is designed while dividing the scheduling time. Secondly, the detection advantage of sensors to UAV cluster, sensor load, and sensor handover numbers in the scheduling time interval are summed to create multisensor scheduling objective functions for UAV cluster. Furthermore, for the UAV cluster optimization problem, a hybrid optimization algorithm is proposed, which integrates the golden sine mechanism and adaptive weight factor in Harris hawks optimization algorithm. Finally, extensive experimental and statistical analyses show that the models and algorithms proposed in this paper outperform the existing ones. It has better convergence, does not need additional computational cost, and generates better multisensor scheduling schemes.

Multiobjective Optimal Dispatching Method of Generalized Power Active Distribution Network Based on Game Theory

To improve the operating dependability of a generalized power active distribution network, a multiobjective optimal scheduling approach based on game theory is proposed. The active distribution network's multistakeholder coordinated and optimal dispatching mode is then established, and the game interaction between various stakeholders in the generalized power active distribution network is evaluated. Using the multistakeholder game coordinated and optimal dispatching strategy, manage and regulate the distribution firms, distributed generation operators, and users engaging in demand response in the active distribution network, to guarantee that the distribution system runs smoothly and fairly. The rate of renewable energy usage, network loss, and user satisfaction are all factored into the multiobjective optimum scheduling objective function of a generalized power active distribution network. Using the multistakeholder game coordinated and optimal dispatching strategy, manage and regulate the distribution firms, distributed generation operators, and demand response participants in the active distribution network, to make sure the distribution system runs smoothly and equitably. Taking into account the rate of renewable energy usage, network loss, and user satisfaction, a multiobjective optimum scheduling objective function for a generalized power active distribution network is thus created.

Time-constrained and network-aware containers scheduling in GPU era

The recent advances on data center management and applications development are reflected by lightweight containers technology and critical Quality-of-Service (QoS) requirements. Tenants encapsulate applications in containers abstracting away details on the infrastructure, and entrust its management framework with the provisioning of network and time QOS requirements. In this paper, we addressed this NP-hard scheduling problem proposing a GPU Accelerated Containers Scheduler (GPUACS). We model the joint allocation of network and containers with QoS requirements as a graph embedding problem. GPUACS innovates by refactoring two Multicriteria Decision Makings (MCDMs) to GPU model, as well as by defining an efficient data structure to speed up the comparison of time-evolving QoS requirements. GPUACS follows a modular and configurable architecture, and the scheduling objective function can be adjusted by selecting the MCDM method and setting the appropriated weights to guide the comparisons. An experimental analysis demonstrated the sensitivity that GPU-tailored MCDM methods have to schedule container requests considering critical time, network, and processing criteria, as well as multiple queueing policies.

Risk decision based sensor scheduling in target tracking

PurposeThis paper aims to introduce a new target tracking method based on risk theory in a 2-D discrete environment. After that, the related sensor scheduling method is proposed. This can make up the blank of target tracking and sensor management in the 2-D discrete environment.Design/methodology/approachThe definition of risk is proposed based on risk decision theory firstly. Then the target tracking model in a two-dimensional discrete environment is built. The motion state updating and estimation method of target’s motion state based on Bayes theory is given. Thirdly, the method of computing sensor emission interception risk is provided. Afterwards, the optimization rule of obtaining the minimum risk is followed to model the sensor scheduling objective function. The lion algorithm is adjusted and improved combined with Chaos theory to generate the optimal sensor management projects.FindingsThe risk-based sensor target tracking method and sensor management method are both effective in a 2-D discrete environment.Originality/valueTo the best of the authors’ knowledge, this paper is the first to study the target tracking method and sensor scheduling method in a 2-D environment. Furthermore, the lion algorithm is improved combined with Chaos theory to show a better optimization performance.

Granular-Causality-Based Byproduct Energy Scheduling for Energy-Intensive Enterprise

The energy-intensive enterprises (EIEs), such as iron and steel enterprises, account for a significant part of the total energy consumption in society. The Linz–Donawitz converter gas (LDG) is a kind of crucial byproduct energy resource recycled during the steelmaking process, and its reasonable scheduling can effectively reduce the LDG emission and increase its efficiency. In this study, a granular-causality-based scheduling approach for the LDG system in steel industry is proposed. A granular causality technique is modeled to confirm the casual relationship of the LDG system based on the discontinuous production characteristic, in which a causality diagram is established and the phase space of the training sample is reconstructed to improve the prediction accuracy. Then, a multioutput least-square support vector machine model is constructed for the prediction of the gas tank levels. In order to consider the impact of multiple solutions on the scheduling result in a period of time, a scheduling objective function that combines the economy criterion and the safety one is designed and optimized by a modified particle swarm optimization (PSO) algorithm. The validation experiments using real-world data coming from the energy data center of a steel plant are carried out, and the results indicate that the proposed method exhibits reliable performance. Moreover, an application software system based on the proposed method is developed and implemented, which demonstrates the applicability of the proposed approach. Note to Practitioners —Given that the steelmaking process is a discontinuous one and the LDG system can hardly be described by a physical or mechanism-based model, its energy scheduling works is usually operated by the manual method currently, which leads to low accuracy and a waste of energy. Since a large number of real-time data had been accumulated by the existing SCADA system implemented in most steel plants, a data-driven long-term scheduling approach is proposed in this study. The proposed method aims at the long-term scheduling of the LDG system in steel industry, and the acquisition frequency of the real-time data is 1 min. The application system designed on the basis of the proposed method can provide effective scheduling solutions. Furthermore, it is necessary to ensure the data integrity and reliability via data imputation and filtering methods since there may exist some missing data or outliners in the acquired data from the SCADA system onsite. This study avoids the redundant introduction of such preliminary preprocessing methods for the sample data.

Sensor Scheduling Based on Risk for Target Tracking

A sensor scheduling approach focusing on managing the operational risk in target tracking is proposed. The scheme selects sensor actions so that the operational risks are the minimum. First, given the definition, existence of risk in sensor scheduling is analyzed. Second, the target missing risk and the sensor radiation interception risk are summed to create the sensor scheduling objective functions, including myopic sensor scheduling and non-myopic sensor scheduling. Furthermore, to obtain sensor management schemes according to the objective functions, the improved bee colony algorithm based on double-roulette and in combination with the particle swarm optimization algorithm is proposed. Finally, simulations are carried out to illustrate the models and algorithms in the paper possess some advantages over existing ones, including being more practical, keeping nearly the same or even better tracking performance with lower risk values, and owing better sensor scheduling solutions.

Scheduling with release dates and preemption to minimize multiple max-form objective functions

In this paper, we study multi-agent scheduling with release dates and preemption on a single machine, where the scheduling objective function of each agent to be minimized is regular and of the maximum form (max-form). The multi-agent aspect has three versions, namely ND-agent (multiple agents with non-disjoint job sets), ID-agent (multiple agents with an identical job set), and CO-agent (multiple competing agents with mutually disjoint job sets). We consider three types of problems: The first type (type-1) is the constrained scheduling problem, in which one objective function is to be minimized, subject to the restriction that the values of the other objective functions are upper bounded. The second type (type-2) is the weighted-sum scheduling problem, in which a positive combination of the objective functions is to be minimized. The third type (type-3) is the Pareto scheduling problem, for which we aim to find all the Pareto-optimal points and their corresponding Pareto-optimal schedules. We show that the type-1 problems are polynomially solvable, and the type-2 and type-3 problems are strongly NP-hard even when all jobs’ release dates are zero and processing times are one. When the number of the scheduling criteria is fixed and they are all lateness-like, such as minimizing Cmax, Fmax, Lmax, Tmax, and WCmax, where WCmax is the maximum weighted completion time of the jobs, the type-2 and type-3 problems are polynomially solvable. To address the type-3 problems, we develop a new solution technique that guesses the Pareto-optimal points through some elaborately constructed schedule-configurations.

A Risk-Based Multisensor Optimization Scheduling Method for Target Threat Assessment

The reasonable scheduling of multisensor systems to maximize combat benefits has become a research hotspot in the field of sensor management. To minimize the uncertainty in the threat level of targets and improve the survivability of sensors, a risk-based multisensor scheduling method is proposed in this paper. In this scheduling problem, the best sensors are systematically selected to observe targets for the trade-off between the threat assessment risk and the emission risk. First, the scheduling problem is modelled as a partially observable Markov decision process (POMDP) for target threat assessment. Second, the calculation methods of the threat assessment risk and the emission risk are proposed to quantify the potential loss caused by the uncertainty in the threat level of targets and the emission of sensors. Then, a nonmyopic sensor scheduling objective function is built to minimize the total risk which is the weighted sum of the threat assessment risk and the emission risk. Furthermore, to solve the high complexity computational problem in optimization, a decision tree search algorithm based on branch pruning is designed. Finally, simulations are conducted, and the results show that the proposed algorithm can significantly reduce the searching time and memory consumption in optimization compared with those of traditional algorithms, and the proposed method has a better risk control effect than the existing sensor scheduling methods.

Research on Communication Scheduling Algorithm for Smart Home in Internet of Things Under Cloud Computing

The current communication scheduling algorithm for smart home cannot realize low latency in scheduling effect with unreasonable control of communication throughput and large energy consumption. In this paper, a communication scheduling algorithm for smart home in Internet of Things under cloud computing based on particle swarm is proposed. According to the fact that the transmission bandwidth of any data flow is limited by the bandwidth of network card of sending end and receiving end, the bandwidth limits of network card of smart home communication server are used to predict the maximum practicable bandwidth of data flow. Firstly, the initial value of communication scheduling objective function of smart home and particle swarm is set, and the objective function is taken as the fitness function of particle. Then the current optimal solution of objective function is calculated through predicted value and objective function, current position and flight speed of particle should be updated until the iteration conditions are met. Finally, the optimal solution is output, the communication scheduling of smart home is thus realized. Experiments show that this algorithm can realize low latency with small energy consumption, and the throughput is relatively reasonable.

Scheduling for a processor sharing system with linear slowdown

We consider the problem of scheduling arrivals to a congestion system with a finite number of users having identical deterministic demand sizes. The congestion is of the processor sharing type in the sense that all users in the system at any given time are served simultaneously. However, in contrast to classical processor sharing congestion models, the processing slowdown is proportional to the number of users in the system at any time. That is, the rate of service experienced by all users is linearly decreasing with the number of users. For each user there is an ideal departure time (due date). A centralized scheduling goal is then to select arrival times so as to minimize the total penalty due to deviations from ideal times weighted with sojourn times. Each deviation is assumed quadratic, or more generally convex. But due to the dynamics of the system, the scheduling objective function is non-convex. Specifically, the system objective function is a non-smooth piecewise convex function. Nevertheless, we are able to leverage the structure of the problem to derive an algorithm that finds the global optimum in a (large but) finite number of steps, each involving the solution of a constrained convex program. Further, we put forward several heuristics. The first is the traversal of neighbouring constrained convex programming problems, that is guaranteed to reach a local minimum of the centralized problem. This is a form of a "local search", where we use the problem structure in a novel manner. The second is a one-coordinate "global search", used in coordinate pivot iteration. We then merge these two heuristics into a unified "local-global" heuristic, and numerically illustrate the effectiveness of this heuristic.

Reducing the Impact of Bounded Parametric Uncertainty on Hodgson's Scheduling Algorithm Using Interval Programming

Input uncertainty is a major challenge to the decision-making process as it leads to output inaccuracy, which increases the cost and the risk. Bounded uncertainty is usually formulated as mathematical intervals as it provides the upper bound and the lower bound without any information between them such as probability distribution or membership function. The lack of descriptive function between the upper and lower bounds makes the probabilistic and fuzzy techniques not effective. This research aims to reduce the impact of bounded uncertainty on the final result of the scheduling objective function and algorithm. The premise of this research is that performing the calculations using uncertain values and then approximating the final result produces more accurate results than approximating the uncertain input values before performing the calculations. The proposed methodology was to extend the scheduling algorithm to be interval based through extending numerical arithmetic to interval arithmetic and extending Boolean logic to interval logic. The methodology is applied to Hodgson's scheduling algorithm, which is used to minimize the number of delayed tasks. The solution is implemented using a MATLAB toolbox named TORSCHE by slicing its code and extending it. The experiments used the aircraft landing data with bounded uncertainty, and it enhanced the accuracy of the results by 12% than using the averaging or midpoint approximation.

Scheduling two job families on a single machine with two competitive agents

We consider the scheduling problems arising when two agents, each with a family of jobs, compete to perform their respective jobs on a single machine. A setup time is needed for a job if it is the first job to be processed on the machine or its processing on the machine follows a job that belongs to another family. Each agent wants to minimize a certain cost function, which depends on the completion times of its jobs only. The aim is to find a schedule for all the jobs of the two agents that minimizes the objective of one agent while keeping the objective of the other agent being bounded by a fixed value $$Q$$Q. Polynomial-time and pseudo-polynomial-time algorithms are designed to solve the problem involving various combinations of regular scheduling objective functions.

Two-agent single machine scheduling with forbidden intervals

We consider the resumable version of the two-agent single machine scheduling problems with forbidden intervals in which the jobs cannot be processed. The goal is to minimize the sum of the objective functions of the two agents. Polynomial and pseudo-polynomial time algorithms are presented for various combinations of regular scheduling objective functions.

A note: Minimizing maximum earliness on a proportionate flowshop

Most classical scheduling objective functions have been studied in the context of a proportionate flowshop. In most cases, the solution was shown to be identical to that of the single machine version. In this note we introduce a rare case where the extension to a proportionate flowshop leads to a different solution. Specifically, we study the problem of minimizing maximum earliness. We show that the problem remains polynomially solvable, but the running time of our proposed greedy-type algorithm is larger than that of the single machine case.