Scheduling Problem Research Articles

Application and Research of Intelligent Algorithms in Scheduling Optimization of Civil Engineering Projects

Efficient scheduling optimization is a critical component of resource management in civil engineering projects, which often involve dynamic and complex environments. Traditional scheduling approaches face challenges in addressing large-scale constraints, real-time adaptability, and the combinatorial nature of tasks, leading to resource underutilization and delays. To address these issues, this study proposes a novel Adaptive Scheduling Framework (ASF) integrated with a Dynamic Task Allocation Strategy (DTAS) tailored specifically for civil engineering applications. The ASF employs graph-based task-resource modeling and multi-objective optimization to manage the scalability and flexibility required in construction projects. By representing scheduling problems as bipartite graphs, the framework captures temporal dynamics, task dependencies, and resource constraints to achieve a balance between priority and feasibility. The DTAS enhances scheduling efficiency by introducing dynamic task prioritization, iterative conflict resolution, and real-time feedback-driven refinement. Experimental results, focused on civil engineering scenarios, demonstrate that the proposed methods significantly reduce project completion time, improve resource utilization, and adapt effectively to changes in construction requirements and resource availability. This study underscores the transformative potential of intelligent algorithms in optimizing scheduling for civil engineering project management and other resource-intensive domains.

Parallel Machine Scheduling Problem with Machine Rental Cost and Shared Service Cost

With the rapid development of industrial internet, blockchain, and other new-generation information technology, the shared manufacturing model provides a new way to address the problems of low resource utilization of the traditional manufacturing industry and serious duplication of construction through the mechanism of collaborative resource sharing. Concurrently, to meet the requirements of sustainable development, manufacturing enterprises need to balance economic efficiency with production efficiency in their production practices. This study investigates an identical parallel machine offline scheduling problem with rental costs and shared service costs of shared machines. In machine renting, manufacturers with a certain number of identical parallel machines will incur fixed rental costs, unit variable rental costs, and shared service costs when renting the shared machines. The objective is to minimize the sum of the makespan and total sharing costs. To address this problem, an integer linear programming model is established, and several properties of the optimal solution are provided. A heuristic algorithm based on the number of rented machines is designed. Finally, numerical simulation experiments are conducted to compare the proposed heuristic algorithm with a genetic algorithm and the longest processing time (LPT) rule. The results demonstrate the effectiveness of the proposed heuristic algorithm in terms of calculation accuracy and efficiency. Additionally, the experimental findings reveal that the renting and scheduling results of the machines are influenced by various factors, such as the manufacturer’s production conditions, the characteristics of the jobs to be processed, production objectives, rental costs, and shared service costs.

Multi skill project scheduling optimization based on quality transmission and rework network reconstruction

Quality deficiencies are widely acknowledged as a primary driver of project rework, with personnel skill levels serving as a critical determinant of activity quality. This study presents a scheduling model that integrates quality transmission mechanisms and dynamic rework subnet reconstruction within the Multi-Skill Resource-Constrained Project Scheduling Problem (MSRCPSP) framework. The proposed model aims to optimize project duration while mitigating rework risks. To address the computational complexity of the model, an Improved Gazelle Optimization Algorithm (GOAIP) was developed, incorporating dynamic operators, shuffle crossover, and Gaussian mutation strategies to balance global and local optimization. Experimental validation across diverse case scales demonstrates that the proposed model and algorithm outperform mainstream optimization techniques in solution accuracy and convergence efficiency, highlighting their robust applicability and practical significance.

MAB-Based Online Client Scheduling for Decentralized Federated Learning in the IoT

Different from conventional federated learning (FL), which relies on a central server for model aggregation, decentralized FL (DFL) exchanges models among edge servers, thus improving the robustness and scalability. When deploying DFL into the Internet of Things (IoT), limited wireless resources cannot provide simultaneous access to massive devices. One must perform client scheduling to balance the convergence rate and model accuracy. However, the heterogeneity of computing and communication resources across client devices, combined with the time-varying nature of wireless channels, makes it challenging to estimate accurately the delay associated with client participation during the scheduling process. To address this issue, we investigate the client scheduling and resource optimization problem in DFL without prior client information. Specifically, the considered problem is reformulated as a multi-armed bandit (MAB) program, and an online learning algorithm that utilizes contextual multi-arm slot machines for client delay estimation and scheduling is proposed. Through theoretical analysis, this algorithm can achieve asymptotic optimal performance in theory. The experimental results show that the algorithm can make asymptotic optimal client selection decisions, and this method is superior to existing algorithms in reducing the cumulative delay of the system.

Quantum Computing as a Catalyst for Microgrid Management: Enhancing Decentralized Energy Systems Through Innovative Computational Techniques

This paper introduces a groundbreaking framework for optimizing microgrid operations using the Quantum Approximate Optimization Algorithm (QAOA). The increasing integration of decentralized energy systems, characterized by their reliance on renewable energy sources, presents unique challenges, including the stochastic nature of energy supply-and-demand management. Our study leverages quantum computing to enhance the operational efficiency and resilience of microgrids, transcending the limitations of traditional computational methods. The proposed QAOA-based model formulates the microgrid scheduling problem as a Quadratic Unconstrained Binary Optimization (QUBO) problem, suitable for quantum computation. This approach not only accommodates complex operational constraints—such as energy conservation, peak load management, and cost efficiency—but also dynamically adapts to the variability inherent in renewable energy sources. By encoding these constraints into a quantum-friendly Hamiltonian, QAOA facilitates a parallel exploration of multiple potential solutions, enhancing the probability of reaching an optimal solution within a feasible time frame. We validate our model through a comprehensive simulation using real-world data from a microgrid equipped with photovoltaic systems, wind turbines, and energy storage units. The results demonstrate that QAOA outperforms conventional optimization techniques in terms of cost reduction, energy efficiency, and system reliability. Furthermore, our study explores the scalability of quantum algorithms in energy systems, providing insights into their potential to handle larger, more complex grid architectures as quantum technology advances. This research not only underscores the viability of quantum algorithms in real-world applications but also sets a precedent for future studies on the integration of quantum computing into energy management systems, paving the way for more sustainable, efficient, and resilient energy infrastructures.

An efficient enhanced exponential distribution optimizer: applications in global, engineering, and combinatorial optimization problems

This paper introduces an enhanced exponential distribution optimizer (EDO), termed the exponential distribution optimizer with Levy flight orthogonal learning (EDO-LFOL). EDO-LFOL enhances EDO by integrating the Levy flight (LF) strategy during the intensification phase and utilizing the orthogonal learning (OL) approach after the end of the optimization cycle. This adjustment aims to mitigate the risk of local optima entrapment and improve the quality of the solutions obtained. This paper presents EDO-LFOL as a viable global and practical optimization problem solution. To evaluate the effectiveness of EDO-LFOL, we compare it against seven robust optimizers across 12 unconstrained test functions associated with the IEEE Congress on Evolutionary Computation 2022 (CEC 2022). The optimizers include the improved multi-operator differential evolution algorithm (IMODE), adaptive guided differential evolution algorithm (AGDE), whale optimization algorithm (WOA), grey wolf optimizer (GWO), sinh cosh optimizer (SCHO), RIME optimization algorithm (RIME), and the original EDO. Additionally, EDO-LFOL is tested on three combinatorial optimization challenges: the job shop scheduling problem (JSSP), quadratic assignment problem (QAP), and bin packing problem (BPP), to evaluate its applicability. Furthermore, EDO-LFOL addresses four distinct design engineering challenges: the pressure vessel design, three-bar truss, welded beam, and speed reducer. The results, supported by significance tests, demonstrate that EDO-LFOL significantly outperforms the standard EDO and its competitors.

Optimal Innovation-Based Deception Attacks on Multi-Channel Cyber–Physical Systems

This article addresses the optimal scheduling problem for linear deception attacks in multi-channel cyber–physical systems. The scenario where the attacker can only attack part of the channels due to energy constraints is considered. The effectiveness and stealthiness of attacks are quantified using state estimation error and Kullback–Leibler divergence, respectively. Unlike existing strategies relying on zero-mean Gaussian distributions, we propose a generalized attack model with Gaussian distributions characterized by time-varying means. Based on this model, an optimal stealthy attack strategy is designed to maximize remote estimation error while ensuring stealthiness. By analyzing correlations among variables in the objective function, the solution is decomposed into a semi-definite programming problem and a 0–1 programming problem. This approach yields the modified innovation and an attack scheduling matrix. Finally, numerical simulations validate the theoretical results.

Privacy-and-Utility-Aware Publishing of Schedules

Scheduling is adopted in various domains to assign jobs to resources, such that an objective is optimized. While schedules enable the analysis of the underlying system, publishing them also incurs a privacy risk. Recently, privacy attacks on schedules have been proposed, which may reveal sensitive information on the jobs by solving an inverse scheduling problem. In this work, we study the protection against such attacks. We formulate the problem of privacy-and-utility preservation of schedules, which bounds both, the privacy leakage and the loss in the utility of the schedule due to obfuscation. We address the problem based on a set of perturbation functions for schedules, study their instantiations for standard scheduling problems, and implement privacy-and-utility-aware publishing of a schedule using constraint programming. Experiments with synthetic and real-world schedules demonstrate the feasibility, robustness, and effectiveness of our mechanism.

Clean Energy Self-Consistent Systems for Automated Guided Vehicle (AGV) Logistics Scheduling in Automated Ports

To enhance the logistics scheduling efficiency of automated guided vehicles (AGVs) in automated ports and achieve the orderly charging and battery swapping of AGVs as well as self-sufficient clean energy, this paper proposes an integrated optimization method. The method first utilizes graph theory to construct a theoretical model that includes AGVs, the port road network, and charging and battery-swapping stations, in order to analyze the optimal logistics scheduling and charging and swapping strategies. Subsequently, for the multi-objective optimization problems in AGV logistics scheduling and charging and swapping, a fast solution method based on the immune optimization algorithm is proposed, with scheduling time and the self-sufficiency rate of clean energy for port AGVs as the constraint conditions. Finally, the effectiveness of the proposed model and algorithm is verified through a simulation scenario. The results show that in the simulated port logistics scenario, after optimization, the total operation time of AGVs is significantly reduced. Compared with the cases that only consider scheduling time, the charging strategy, or wind and solar output, the average clean energy self-sufficiency rate under the proposed strategy increased by 82.7%, 27.5%, and 53.9%, respectively. In addition, as the weight of the self-sufficiency rate increases, both the total driving time and the total clean energy self-sufficiency rate of AGVs show an upward trend and are approximately linearly related. Within the specified maximum scheduling time, the actual scheduling time and self-sufficiency rate can be flexibly coordinated, with significant carbon reduction benefits.

Balanced Adaptive Subspace Collaboration for Mixed Pareto-Lexicographic Multi-Objective Problems with Priority Levels

Multi-objective Optimization Problems (MOPs) where objectives have different levels of importance in decision-making, known as Mixed Pareto-Lexicographic MOPs with Priority Levels (PL-MPL-MOPs), are increasingly prevalent in real-world applications. General-purpose Multi-Objective Evolutionary Algorithms (MOEAs) that treat all objectives equally not only increase the workload of decision-making but also suffer from computational inefficiencies due to the necessity of generating many additional solutions. Conversely, strictly adhering to Priority Levels (PLs) during optimization can easily result in premature convergence within some PLs. To address this issue, we suggest an effective Balanced Adaptive Subspace Collaboration (BASC) method in this paper. Specifically, this method decomposes the search space into sub-fronts based on PLs and utilizes a sampling mechanism that operates exclusively within subspaces formed by sub-fronts at the same PL to generate new solutions, thereby emphasizing the exploitation of individual PLs. Furthermore, a set of parameters is employed to control the strictness of adherence to each PL, with these parameters adaptively adjusted to balance exploration across different PLs. The two mechanisms are then collaboratively integrated into MOEAs. Comprehensive experimental studies on benchmark problems and a set of complex job-shop scheduling problems in semiconductor manufacturing demonstrate the competitiveness of the proposed method over existing methods.

High School Course Scheduling: Student Preferences and Fairness Constraints (Student Abstract)

Increasing student populations and diverse course offerings have led to perceived inequities in U.S. high school course scheduling. Traditional integer programming (IP) methods for the High School Scheduling Problem (HSSP) fail to address these fairness concerns. This research introduces the Fair High School Scheduling Problem (FHSSP), an extension of the HSSP that incorporates student preferences and fairness principles from market design. We develop an IP model to generate course schedules that are both feasible and equitable. Tested on real course request data from a California high school, our model successfully produces schedules that ensure fairness without compromising feasibility. These results demonstrate the potential of our approach to enhance fairness in high school scheduling and its applicability to various real-world scheduling challenges. Additionally, this study highlights the feasibility of integrating human preferences and emotions into mathematical models, promoting more inclusive and balanced allocation systems.

Neural Combinatorial Optimization for Stochastic Flexible Job Shop Scheduling Problems

Neural combinatorial optimization (NCO) has gained significant attention due to the potential of deep learning to efficiently solve combinatorial optimization problems. NCO has been widely applied to job shop scheduling problems (JSPs) with the current focus predominantly on deterministic problems. In this paper, we propose a novel attention-based scenario processing module (SPM) to extend NCO methods for solving stochastic JSPs. Our approach explicitly incorporates stochastic information by an attention mechanism that captures the embedding of sampled scenarios (i.e., an approximation of stochasticity). Fed with the embedding, the base neural network is intervened by the attended scenarios, which accordingly learns an effective policy under stochasticity. We also propose a training paradigm that works harmoniously with either the expected makespan or Value-at-Risk objective. Results demonstrate that our approach outperforms existing learning and non-learning methods for the flexible JSP problem with stochastic processing times on a variety of instances. In addition, our approach holds significant generalizability to varied numbers of scenarios and disparate distributions.

Learning Valid Dual Bounds in Constraint Programming: Boosted Lagrangian Decomposition with Self-Supervised Learning

Lagrangian decomposition (LD) is a relaxation method that provides a dual bound for constrained optimization problems by decomposing them into more manageable sub-problems. This bound can be used in branch-and-bound algorithms to prune the search space effectively.In brief, a vector of Lagrangian multipliers is associated with each sub-problem, and an iterative procedure (e.g., a sub-gradient optimization) adjusts these multipliers to find the tightest bound. Initially applied to integer programming, Lagrangian decomposition also had success in constraint programming due to its versatility and the fact that global constraints provide natural sub-problems. However, the non-linear and combinatorial nature of sub-problems in constraint programming makes it computationally intensive to optimize the Lagrangian multipliers with sub-gradient methods at each node of the tree search. This currently limits the practicality of LD as a general bounding mechanism for constraint programming. To address this challenge, we propose a self-supervised learning approach that leverages neural networks to generate multipliers directly, yielding tight bounds. This approach significantly reduces the number of sub-gradient optimization steps required, enhancing the pruning efficiency and reducing the execution time of constraint programming solvers. This contribution is one of the few that leverage learning to enhance bounding mechanisms on the dual side, a critical element in the design of combinatorial solvers. This work presents a generic method for learning valid dual bounds in constraint programming. We validate our approach on two challenging combinatorial problems: The multi-dimensional knapsack problem and the shift scheduling problem. The results show that our approach can solve more instances than the standard application of LD to constraint programming, reduce execution time by more than half, and has promising generalization ability through fine-tuning.

COMPARISON OF THREE CLASSICAL LOWER BOUNDS FOR THE PARALLEL MACHINES SCHEDULING PROBLEM

This paper compares three classical lower bounds for the Parallel Machines Scheduling Problem (PMSP). The first lower bound considered is the makespan of Jackson's Pseudo Preemptive Schedule (JPPS). The second is the preemptive bound, which is obtained by relaxing the non-preemption constraint, and the third is based on Energetic Reasoning (ER). To compare these three bounds, we first provide a rigorous mathematical characterization. Specifically, we introduce a mathematical definition of the ER-derived lower bound as the smallest value of the trial makespan that results in a successful ER feasibility test. This definition relies on the fundamental concepts of critical intervals and specific operations that we called crossing operations, for which we give some theoretical properties. We establish an Energy theorm, which provides an analytical formulation of the energetic lower bound. In an extension of the JPPS and ER lower bounds, we give an analytical formulation of the preemptive bound. From the analytical characterization of these three bounds, we attempt to analyze their relative performances. In particular, we find that the ER lower bound differs from JPPS because on some machines at least two operations must be scheduled for ER. The preemptive bound differs from JPPS because idle periods may be required in an optimal preemptive schedule. Interestingly, these three characterizations are quite similar, and so can provide insight into the ways in which the bounds differ. Our results can be directly extended to the cumulative scheduling problem, and we report some experimental experiments that compare these bounds and confirm the theoretical results stated above.

An improved scatter search algorithm for solving job shop scheduling problems with parallel batch processing machine

This paper addresses a hybrid processing system in automotive mold casting, which involves single processing machines and parallel batch processing machines. A job shop scheduling problem with parallel batch processing machines (JSP-PBPM) is developed, with the objective of minimizing the maximum completion time. First, a solution decoding strategy combined with the JSP-PBPM problem and a batch job addition algorithm is proposed. This approach addresses the impact of operation precedence relationships on conventional decoding strategies and aims to maximize the utilization of parallel batch processing machines for batch operations. Next, an Improved Scatter Search (ISS) algorithm is introduced to solve the problem. The ISS algorithm finds the optimal solution through several steps, including the construction of the initial population, improvement of the initial solution, creation of a reference set, generation of subsets, and refinement of the final solution. Finally, simulation experiments are conducted to verify the feasibility and effectiveness of the proposed algorithm and decoding strategy in solving such problems.

A hybrid evolution strategies algorithm for non-permutation flow shop scheduling problems

Flow shop scheduling has garnered significant attention from researchers over the past ten years, establishing itself as a prominent area of study within the field of scheduling. Nevertheless, there exists a paucity of research dedicated to addressing Non-Permutation Flow Shop Scheduling Problems. In this study, a Hybrid Evolution Strategies (HES) is suggested by combining the exploitation ability of Nawaz, Enscore, and Ham (NEH) Heuristic, the exploration ability of Improved Evolution Strategies (IES), and a Local Search Technique to minimize the makespan of NPFSSP. The primary solution is produced through the NEH Heuristic, serving as a foundational solution for the IES. The IES is applied in two stages, in the first stage it improves the permutation sequence found from the NEH heuristic. In the second stage of the IES, the permutation sequence on the first 40% of machines is fixed as found in the first stage. The sequence on the last 60% of machines is altered only so that the makespan is minimized and a good non-permutation sequence is found. Recombination and mutation are the main genetic operators in IES. For recombination in IES, 16 offspring are generated randomly from a single parent. The Quad swap mutation operator is employed in the IES to optimize the utilization of the solution space while minimizing computational time. To prevent trapping in local minima, a Local Search Technique is integrated into the IES algorithm, which guides solutions to less explored areas. Computational analyses indicate that HES exhibits superior performance regarding solution quality, computational efficiency, and robustness.

Energy-Efficient Partitioned-RM Scheduling for Shared Resources Imprecise Mixed-Criticality Tasks

Shared resources and energy consumption are important factors to consider in the design of mixed-criticality systems. Existing works have studied these two factors separately. In this article, we simultaneously focus on shared resources and energy consumption on multiprocessor platforms. Firstly, we address the problem of energy-aware scheduling for the fixed-priority imprecise mixed-criticality tasks with shared resources and propose a schedulability test based on the Multiprocessor Priority Ceiling Protocol for a given task-to-processor mapping. Secondly, we calculate the energy-efficient speed of each processor based on the schedulability test and propose the corresponding task-to-processor mapping algorithm, called IMCPA. Finally, we conduct experiments on a real-world case and synthetic tasksets. The experimental results show that IMCPA can improve the schedulability ratio by about 13.76% and save energy consumption by about 34.89% compared to the existing algorithms.

Noah’s Ark Phenomenon in Medicine: A Novel Description of Clustering of Clinical Conditions, the Surgical Perspective

Abstract Patients with similar diagnoses often arrive in clusters, followed by periods lacking such cases. I observed this pattern during internship and continued to do so throughout my training and years as a surgeon. During specific call hours, clusters of ectopic gestations would occur, while obstructed labour dominated another day. Similar phenomena were noted across various clinical rotations, including paediatric surgery, where multiple intussusception cases would present in quick successions. I have termed this pattern the “Noah’s ark phenomenon in medicine (NAPM).” Collaborating with a colleague, we researched to understand the scientific basis for this observation. Seasonal variations, infectious diseases, behavioural and cultural factors, genetics, healthcare policies, geographical factors, and referral systems have been documented to influence the clustering of surgical cases. This phenomenon highlights the importance of recognizing patterns in clinical case presentations. Understanding NAPM can aid timely resource management, improve targeted training opportunities, engender peer support among patients, and inspire further research to uncover underlying causes and optimize clinical practice. It can also solve master surgery scheduling problems. The clustering of surgical conditions implies more volume, and this translates into better outcomes for surgeons and institutions.

Hybridizing biogeography-based optimization and integer programming for solving the travelling tournament problem in sport scheduling

Combining metaheuristics with exact methods improves solution quality by efficiently exploring promising regions and refining the obtained solutions. This paper introduces a novel hybrid approach that combines exact methods and metaheuristics to address the Traveling Tournament Problem (TTP) in sports scheduling. The TTP, a critical aspect of sports management, aims to create a tournament schedule that minimizes the total travel distance of participating teams, which is essential for controlling league management costs and maximizing revenue. However, its complex optimization requirements and tournament structure make it highly challenging to solve efficiently. Our hybrid approach combines exact methods with the Biogeography-Based Optimization (BBO) metaheuristic to tackle both the TTP and its variant, the Unconstrained Traveling Tournament Problem (UTTP). We introduce a novel relaxation technique to enhance the efficiency of the Integer Linear Programming (ILP) formulation for the TTP. This technique involves fixing the schedule for a subset of teams and employing an ILP solver to optimize the schedule for the remaining teams. This relaxation technique is seamlessly integrated into the BBO operators. We evaluate the effectiveness of our method using publicly available benchmark instances and compare it with existing techniques for both TTP and UTTP. Our experimental results demonstrate that the proposed approach achieves competitive solution quality. It outperforms prior methods on UTTP for the US National Baseball League NL16 instances and some prominent methods when applied to TTP.

Multi-Satellite Task Parallelism via Priority-Aware Decomposition and Dynamic Resource Mapping

Multi-satellite collaborative computing has achieved task decomposition and collaborative execution through inter-satellite links (ISLs), which has significantly improved the efficiency of task execution and system responsiveness. However, existing methods focus on single-task execution and lack multi-task parallel processing capability. Most methods ignore task priorities and dependencies, leading to excessive waiting times and poor scheduling results. To address these problems, this paper proposes a task decomposition and resource mapping method based on task priorities and resource constraints. First, we introduce a graph theoretic model to represent the task dependency and priority relationships explicitly, combined with a novel algorithm for task decomposition. Meanwhile, we construct a resource allocation model based on game theory and combine it with deep reinforcement learning to achieve resource mapping in a dynamic environment. Finally, we adopt the theory of temporal logic to formalize the execution order and time constraints of tasks and solve the dynamic scheduling problem through mixed-integer nonlinear programming to ensure the optimality and real-time updating of the scheduling scheme. The experimental results demonstrate that the proposed method improves resource utilization by up to about 24% and reduces overall execution time by up to about 42.6% in large-scale scenarios.