Most research on flexible job shop scheduling assumes constant processing speeds. However, in real production, machines need to operate at variable speeds to achieve energy-efficient scheduling, which requires balancing multiobjective between production efficiency and green development. Such tradeoffs thus trigger the phenomenon in which massive solutions converge to identical objective values (i.e., the multimodal property), which is often neglected in scheduling problems. To address the above challenges, this work introduces a knowledge-enhanced evolutionary multitasking memetic algorithm (KEMMA) to solve the multimodal multiobjective flexible job shop scheduling problem considering speed (MMFJSP-S). First, self-paced learning motivated us to construct a simple auxiliary task and employ an evolutionary multitasking (EMT) framework to tackle the complex MMFJSP-S. Moreover, a knowledge enhancement and explicit transfer strategy is designed to reduce the effects of negative transfer by reinforcing and sharing beneficial knowledge across tasks. Finally, a mapping transformation mechanism is proposed to handle the multimodal property of the MMFJSP-S in the decision space. By comparing with ten advanced algorithms, the experimental results verify the remarkable superiority of the proposed KEMMA in solving MMFJSP-S and reveal the significance of studying the multimodal property.

Dynamic and multi-resource flexible job shop scheduling in pharmaceutical manufacturing: A MILP-based decision support tool

An adaptive large neighborhood search algorithm with customized search operators for solving home healthcare scheduling and routing problems with skill matching and periodic visits

Collaborative deep reinforcement learning algorithm for solving multi-AGV dynamic scheduling problem

An improved genetic algorithm based on game theory for multi-objective flexible job shop scheduling problem with batch processing machines

Multi-strategy collaborative hybrid optimization algorithm for the hybrid flowshop scheduling problems with the learning and forgetting effects

A neural-driven constructive heuristic for the flexible job shop scheduling problem: An efficient alternative to complex deep learning methods

Constraint programming approaches for stochastic Resource-Constrained Project Scheduling Problem subject to disruptions

The Agile Earth Observation Satellite Scheduling Problem is a multi-objective optimization task involving conflicting goals. These objectives include task priority, imaging quality, and energy consumption, which are highly correlated and often in conflict. Pareto optimisation is a key measure for evaluating the quality of complex multi objective solutions. However, conventional linear weighting methods neglect interactions among sub-objectives, generating suboptimal Pareto fronts with uneven trade-off distributions. This study proposes a multi-objective scheduling method for agile satellites based on Nonlinear Utility and Deep Reinforcement Learning. Within this framework, a Unified Scheduling Model (USM) was developed to provide a unified representation of constrained multi-objective observation tasks. Building on the USM, a contrastive learning–based nonlinear utility network was designed to capture inter-objective relationships via cosine similarity, thereby providing adaptive and diversified guidance for multi-objective trade-offs. Subsequently, a distributed training strategy combined with the Proximal Policy Optimization algorithm was employed to improve learning efficiency and policy stability under complex operational constraints. Results show that, compared with multi-objective deep reinforcement learning and multi-objective heuristic baseline algorithms, the proposed method achieved significant improvements in the Pareto volume and outperformed existing baseline methods in multiple performance indicators.

ABSTRACT Efficient resource allocation and leveling are critical to successful construction project scheduling, yet conventional methods often fail to balance project duration with stable resource utilization. This study introduces a modified mountain gazelle optimizer (mMGO), which extends the original single-objective MGO into a multi-objective optimization approach to address the complex trade-offs inherent in construction scheduling. In addition, the algorithm integrates opposition-based learning and dynamically controlled chaotic mapping to enhance global search capability and avoid premature convergence. The mMGO is embedded within a two-phase scheduling framework, in which the first phase generates resource-feasible baseline schedules, while the second phase redistributes activities to minimize fluctuations in multi-resource demand. To validate its performance, mMGO was verified through two case studies. Case study 1 consisted of five projects, each containing six activities, whereas case study 2 included three projects, each involving 60 activities. The results show that mMGO consistently achieved the highest hypervolume values, indicating closer convergence to the true Pareto front and greater diversity of non-dominated solutions. Moreover, mMGO produced schedules that simultaneously reduced project makespan, resource intensity, and resource utilization instability metrics. These findings indicate that mMGO has potential as a computational decision-support approach for multi-objective resource scheduling in benchmark multi-project environments.

Aiming at the flexible job shop scheduling problem with limited AGV transportation, this paper presents an AGV and machine-integrated scheduling model with the optimisation objectives of minimising the maximum completion time and total energy consumption. It proposes an Improved SPEA2 Algorithm Combining DQN Algorithm (DQN-ISPEA2). The algorithm adopts a three-stage coding scheme for the workpiece, machine, and AGV. In the population initialisation stage, a hybrid initialisation strategy is employed to enhance the quality of the initial solution. DQN is used to adaptively select appropriate mutation operations, thereby enhancing the local search capability of the SPEA2 algorithm. Finally, it is compared with NSGA-III, NSGA-II, and SPEA2 algorithms on the MK and Kacem datasets. The experimental results demonstrate that the DQN-ISPEA2 algorithm yields satisfactory outcomes in most arithmetic cases, thereby verifying the feasibility and effectiveness of the proposed method in addressing the flexible job shop scheduling problem with limited AGV transportation. At the same time, the analysis of the impact of different AGV numbers on the optimisation objective reveals that the number of AGVs in the flexible workshop conforms to the law of diminishing marginal returns, providing a reference for actual manufacturing workshops when configuring AGVs.

This article addresses a two-stage flow-shop scheduling problem (FSSP) considering uncertain job processing and release time. To minimize the worst-case expected makespan, a distributionally robust optimization (DRO) approach is designed. By introducing effective bounds and valid inequalities, the problem is transformed into a mixed integer linear program (MlLP), which is solvable via off-the-shelf commercial solvers. To verify the performance of the model, the DRO model is compared with the stochastic linear program (SLP) and its deterministic counterpart under various parameter settings, where the DRO model exhibits greater robustness and computational efficiency in handling almost all the scenarios. Besides, the DRO model demonstrates a prominent advantage when the uncertain interval of the mean is larger, the release time is less scattered and more jobs are scheduled. It is discovered that the proposed DRO model is capable of providing robust schedules in a highly volatile environment, thereby enhancing the resilience and robustness of manufacturing operations.

ABSTRACT This study addresses two critical and interrelated problems in public transit operations: the Transit Network Timetabling Problem (TNTP) and the Bus Driver Scheduling Problem (BDSP). While integrated approaches exist theoretically, they often suffer from computational intractability when applied to large-scale real-world networks. To bridge the gap between theoretical optimization and practical implementation, we propose a robust sequential optimization framework. First, passenger demand is analyzed using ticket transaction data to formulate the TNTP model, minimizing passenger waiting times. Subsequently, the output constitutes the input for the BDSP model, which aims to optimize driver workload fairness by minimizing the deviation between the actual and ideal driving hours (8 hours) and reducing idle times. To solve the NP-hard BDSP effectively, we develop and compare two hybrid metaheuristics: Genetic Algorithm combined with Simulated Annealing (GA-SA) and Genetic Algorithm with Tabu Search (GA-TS). Empirical results based on real-world transit data demonstrate that the proposed GA-SA hybrid algorithm outperforms standard approaches in terms of solution quality with short calculation time. The study provides transit operators with a decision-support tool that balances passenger satisfaction and driver resource utilization efficiently.

Integrated community energy systems (ICES) provide an efficient and sustainable approach to local energy management through multiple energy carriers including electricity, heating, and cooling while enhancing end-use energy management. Electrical and thermal connections between ICESs can further improve energy utilization and economic efficiency. However, energy sharing among ICESs still faces challenges, including complex centralized scheduling constraints, privacy protection concerns, and slow convergence and reduced efficiency of distributed algorithm convergence. To address these challenges, this paper develops a stochastic optimization model for day-ahead energy sharing scheduling, accounting for uncertainties in renewable energy sources and losses in inter-community heat networks. The key idea is to establish a multi-community energy management framework in which the ICES operator provides dynamic electricity and heat trading prices based on the initial supply-demand information. Each ICES optimizes power output and energy interactions to minimize operational costs, carbon emissions, and renewable curtailment, thereby improving overall system efficiency. A distributed linearized surrogate augmented Lagrangian relaxation (LSALR) algorithm is developed to solve the optimal scheduling problem for interconnected ICESs in a privacy-preserving and computationally efficient manner. Testing results demonstrate the model significantly improves operational efficiency and promotes renewable energy utilization within ICESs. Compared with benchmark distributed algorithms, the proposed method achieves superior performance in terms of convergence rate and solution quality.

Classical scheduling problems such as Unrelated Parallel Machine Scheduling (UPMSP), Flexible Job Shop Scheduling (FJSP), and Resource-Constrained Project Scheduling (RCPSP) each capture important aspects of industrial scheduling, but real-world applications often require a combination of constraints from several of these formulations and additional requirements that are typically not supported in standard models. We propose a Generalized Parallel Machine Scheduling (GPMS) framework that, to the best of our knowledge, is the most general machine scheduling formulation to date and unifies machine eligibility with machine-dependent processing times, sequence- and machine-dependent setup times, rich temporal constraints, and secondary-resource constraints in a single formulation. Temporal constraints include machine calendars and precedence relations with min/max time lags and conditional machine eligibilities. Secondary resources are modeled with capacity calendars and pulse or step demands. To model and solve this generalized problem, we investigate a constraint programming approach and propose two CP models: a solver-agnostic high-level model and an interval-variable model. We also develop a randomized construction heuristic that finds feasible, high-quality schedules even for large and highly constrained instances; these schedules serve as warm starts for the interval-variable model. We evaluate 216 generated and 91 real-world instances, comparing the interval-variable model to the solver-agnostic model and to the construction heuristic. The warm-start interval-variable model attains the best objective on the majority of both generated and real-world instances, proves optimality for many small-to-medium instances, and finds near-optimal schedules for most industrial instances within a one-hour time limit. We release all models, code, and instances to support reproducible research.

This study proposes a novel hybrid hyper-heuristic approach based on the memetic algorithm and artificial rabbits optimization (ARO) algorithm for the no-wait flowshop group scheduling problem with sequence-dependent setup times. The ARO algorithm is used to generate the initial population, which is then evolved implementing a memetic-algorithm-based hyper-heuristic framework incorporating multiple crossover, mutation and hill climbing operators. Each operator and its parameters are regarded as low-level heuristics and are dynamically selected based on scores derived from a reinforcement learning mechanism. The performance of the proposed algorithm is rigorously evaluated on 270 benchmark instances widely used in the literature. Comparative analyses against two state-of-the-art simulated annealing approaches demonstrate the clear superiority of the proposed method, which achieves better results in 73% and 57% of the instances. These results not only highlight the robustness and effectiveness of the developed approach but also establish a strong foundation for its potential in solving complex scheduling problems. Notably, this study represents the first successful application of the ARO algorithm in the domain of discrete optimization, and its integration with a hyper-heuristic framework further amplifies its performance, setting a new benchmark for future research.

A population diffusion algorithm for energy-efficient distributed flexible job shop scheduling problem

Mixed-integer linear programming and constraint programming formulations for solving the three-stage no-wait surgery scheduling problem

This paper presents a planning and control strategy to manage the provision of ancillary services with aggregates of electric vehicles (EVs). The study is inspired by recent directives from the Italian Regulatory Authority for Energy, Networks and Environment (ARERA), which opens the way for the participation of new actors in the ancillary services market, including EV aggregates. On a day-ahead basis, the charging point operator computes its total EV power baseline and upward/downward bids for the next day, by solving a dynamic scheduling problem, based on a vehicle-by-vehicle assessment of the next day’s charging demand. Then, in real time, a model predictive controller manages the EV charging sessions to track the baseline and to respond to possible upward/downward regulation signals from the TSO. This two-level approach allows to fulfill the day-ahead obligations (the agreed baseline and regulation bids) and to provide efficient charging service to the EV users, also in presence of deviations of the actual demand from the day ahead forecast. Simulation results validate the approach on realistic scenarios in line with the ARERA resolution 300/17, and show that demand-based ancillary services paradigm is feasible, if supported by a flexible recharging planning and control system. • Electric vehicles aggregates participation in the ancillary services market. • Joint day-ahead planning and real time control of binding services. • Assessment of service technical feasibility in relation to electric vehicles flexibility margins. • A bidding strategy based on a vehicle-by-vehicle representation of charging demand. • A multi-player model predictive control application.

Cooperative multi-agent dual attention framework for flexible job shop scheduling problem considering complex worker heterogeneity under multi-worker collaboration