Dynamic Flexible Job Shop Scheduling Research Articles

Automatic Design of Energy-Efficient Dispatching Rules for Multi-Objective Dynamic Flexible Job Shop Scheduling Based on Dual Feature Weight Sets

Considering the requirements of the actual production scheduling process, the utilization of the genetic programming hyper-heuristic (GPHH) approach to automatically design dispatching rules (DRs) has recently emerged as a popular optimization approach. However, the decision objects and decision environments for routing and sequencing decisions are different in the dynamic flexible job shop scheduling problem (DFJSSP), leading to different required feature information. Traditional algorithms that allow these two types of scheduling decisions to share one common feature set are not conducive to the further optimization of the evolved DRs, but instead introduce redundant and unnecessary search attempts for algorithm optimization. To address this, some related studies have focused on customizing the feature sets for both routing and sequencing decisions through feature selection when solving single-objective problems. While being effective in reducing the search space, the selected feature sets also diminish the diversity of the obtained DRs, ultimately impacting the optimization performance. Consequently, this paper proposes an improved GPHH with dual feature weight sets for the multi-objective energy-efficient DFJSSP, which includes two novel feature weight measures and one novel hybrid population adjustment strategy. Instead of selecting suitable features, the proposed algorithm assigns appropriate weights to the features based on their multi-objective contribution, which could provide directional guidance to the GPHH while ensuring the search space. Experimental results demonstrate that, compared to existing studies, the proposed algorithm can significantly enhance the optimization performance and interpretability of energy-efficient DRs.

A Double Deep Q-Network framework for a flexible job shop scheduling problem with dynamic job arrivals and urgent job insertions

In the semiconductor manufacturing industry, the Dynamic Flexible Job Shop Scheduling Problem is regarded as one of the most complex and significant scheduling problems. Existing studies consider the dynamic arrival of jobs, however, the insertion of urgent jobs such as testing chips poses a challenge to the production model, and there is an urgent need for new scheduling methods to improve the dynamic response and self-adjustment of the shop floor. In this work, deep reinforcement learning is utilized to address the dynamic flexible job shop scheduling problem and facilitate near-real-time shop floor decision-making. We extracted eight state features, including machine utilization, operation completion rate, etc., to reflect real-time shop floor production data. After examining machine availability time, the machine's earliest available time is redefined and incorporated into the design of compound scheduling rules. Eight compound scheduling rules have been developed for job selection and machine allocation. By using the state features as inputs to the Double Deep Q-Network, it is possible to acquire the state action values (Q-values) of each compound scheduling rule, and the intelligent agent can learn a reasonable optimization strategy through training. Simulation studies show that the proposed Double Deep Q-Network algorithm outperforms other heuristics and well-known scheduling rules by generating excellent solutions quickly. In most scenarios, the Double Deep Q-Network algorithm outperforms the Deep Q-Network, Q-Learning, and State-Action-Reward-State-Action (SARSA) frameworks. Moreover, the intelligent agent has good generalization ability in terms of optimization for similar objectives.

A discrete event simulator to implement deep reinforcement learning for the dynamic flexible job shop scheduling problem

The job shop scheduling problem, which involves the routing and sequencing of jobs in a job shop context, is a relevant subject in industrial engineering. Approaches based on Deep Reinforcement Learning (DRL) are very promising for dealing with the variability of real working conditions due to dynamic events such as the arrival of new jobs and machine failures. Discrete Event Simulation (DES) is essential for training and testing DRL approaches, which are based on the interaction of an intelligent agent and the production system. Nonetheless, there are numerous papers in the literature in which DRL techniques, developed to solve the Dynamic Flexible Job Shop Problem (DFJSP), have been implemented and evaluated in the absence of a simulation environment. In the paper, the limitations of these techniques are highlighted, and a numerical experiment that demonstrates their ineffectiveness is presented. Furthermore, in order to provide the scientific community with a simulation tool designed to be used in conjunction with DRL techniques, an agent-based discrete event simulator is also presented.

Dynamic Events in the Flexible Job-Shop Scheduling Problem: Rescheduling with a Hybrid Metaheuristic Algorithm

In the real world of manufacturing systems, production planning is crucial for organizing and optimizing various manufacturing process components. The objective of this paper is to present a methodology for both static scheduling and dynamic scheduling. In the proposed method, a hybrid algorithm is utilized to optimize the static flexible job-shop scheduling problem (FJSP) and dynamic flexible job-shop scheduling problem (DFJSP). This algorithm integrates the genetic algorithm (GA) as a global optimization technique with a simulated annealing (SA) algorithm serving as a local search optimization approach to accelerate convergence and prevent getting stuck in local minima. Additionally, variable neighborhood search (VNS) is utilized for efficient neighborhood search within this hybrid algorithm framework. For the FJSP, the proposed hybrid algorithm is simulated on a 40-benchmark dataset to evaluate its performance. Comparisons among the proposed hybrid algorithm and other algorithms are provided to show the effectiveness of the proposed algorithm, ensuring that the proposed hybrid algorithm can efficiently solve the FJSP, with 38 out of 40 instances demonstrating better results. The primary objective of this study is to perform dynamic scheduling on two datasets, including both single-purpose machine and multi-purpose machine datasets, using the proposed hybrid algorithm with a rescheduling strategy. By observing the results of the DFJSP, dynamic events such as a single machine breakdown, a single job arrival, multiple machine breakdowns, and multiple job arrivals demonstrate that the proposed hybrid algorithm with the rescheduling strategy achieves significant improvement and the proposed method obtains the best new solution, resulting in a significant decrease in makespan.

An improved genetic programming hyper-heuristic for the dynamic flexible job shop scheduling problem with reconfigurable manufacturing cells

The Dynamic Flexible Job Shop Scheduling Problem (DFJSP) is a classical and important research direction. However, current research usually considers the case where each manufacturing cell has a fixed and constant process capability. There are often situations in non-machining shops where each manufacturing cell is capable of capability reconfiguration and performs many different types of process operations, such as assembly shops and test shops. The variability of the manufacturing cell's capabilities increases the complexity of the problem compared to traditional FJSP. In this paper, we study the dynamic flexible job shop scheduling problem considering reconfigurable manufacturing cells (DFJSP-RMCs) with completion time, delay time and reconfiguration time as optimization objectives, and propose an improved Genetic Programming Hyper-Heuristic (GPHH) method to solve it. The method weighs the solution efficiency and the effectiveness of the results. In addition, an individual simplification policy (ISP) is proposed to reduce the evaluation time of the heuristic. Finally, random instances were generated under three production conditions and 10 independent runs were performed for each. Experiments show that the proposed method significantly reduces the time consumption while ensuring the quality of the results.

Dynamic constrained evolutionary optimization based on deep Q-network

Dynamic constrained optimization problems (DCOPs) are common and important optimization problems in real-world, which have great difficulty to solve. Dynamic constrained evolutionary algorithms (DCEAs) are widely used methods for solving DCOPs. However, existing DCEAs often struggle with convergence, particularly for DCOPs with drastic dynamic changes or intricate constraints. To address this issue, this paper proposes a novel DCEA called DCEA-DQN, which leverages the powerful perception and decision-making capabilities of Deep Q-Network (DQN). DCEA-DQN integrates two DQNs to enhance its performance. The first DQN is designed to adaptively respond to dynamic changes, enabling effective handling of DCOPs with various types and degrees of changes. It provides a high-quality re-initialized population for subsequent static optimization, resulting in faster and improved convergence. The second DQN is introduced to guide the mutation direction during offspring generation. It steers the population towards better feasible regions or directs it towards the optimal individual within the current feasible region. Moreover, a penalty mechanism is employed to handle constraints during offspring generation. To evaluate the performance of DCEA-DQN, comprehensive empirical studies are conducted using a new test suite called C-GMPB and a dynamic flexible job-shop scheduling problem. The experimental results, using two commonly used metrics EB and EO in the field of DCOPs, demonstrate that DCEA-DQN outperforms six state-of-the-art DCEAs and achieved optimal performance on 80% and 75% of all 24 test problems, respectively. The source code for DCEA-DQN is available at https://github.com/CIA-SZU/YRT.

Genetic Programming with Lexicase Selection for Large-scale Dynamic Flexible Job Shop Scheduling

Dynamic flexible job shop scheduling is a prominent combinatorial optimisation problem with many real-world applications. Genetic programming has been widely used to automatically evolve effective scheduling heuristics for dynamic flexible job shop scheduling. A limitation of genetic programming is the premature convergence due to the loss of population diversity. To overcome this limitation, this work considers using lexicase selection to improve population diversity, which has achieved success on regression and program synthesis problems. However, it is not trivial to apply lexicase selection to genetic programming for dynamic flexible job shop scheduling, since a fitness case (training scheduling simulation) is often large-scale, making the fitness evaluation very time-consuming. To address this issue, we propose a new multi-case fitness scheme, which creates multiple cases from a single scheduling simulation. Based on the multi-case fitness, we develop a new genetic programming algorithm with lexicase selection, which uses a single simulation for fitness evaluation, thus achieving a better balance between the number of cases for lexicase selection and evaluation efficiency. The experiments on a wide range of dynamic scheduling scenarios show that the proposed algorithm can achieve better population diversity and final performance than the current genetic programming parent selection methods and a state-of-the-art deep reinforcement learning method.

Genetic Programming for Dynamic Flexible Job Shop Scheduling: Evolution With Single Individuals and Ensembles

Genetic Programming for Dynamic Flexible Job Shop Scheduling: Evolution With Single Individuals and Ensembles

Large-Scale Dynamic Scheduling for Flexible Job-Shop With Random Arrivals of New Jobs by Hierarchical Reinforcement Learning

As the intelligent manufacturing paradigm evolves, it is urgent to design a near real-time decision-making framework for handling the uncertainty and complexity of production line control. The dynamic flexible job shop scheduling problem (DFJSP) is frequently encountered in the manufacturing industry. However, it is still challenging to obtain high-quality schedules for DFJSP with dynamic job arrivals in real-time, especially facing thousands of operations from a large-scale scene with complex contexts in an assembly plant. This paper aims to propose a novel end-to-end hierarchical reinforcement learning framework for solving the large-scale DFJSP in near real-time. In the DFJSP, the processing information of newly arrived jobs is unknown in advance. Besides, two optimization tasks, including job operation selection and job-to-machine assignment, have to be handled, which means multiple actions must be controlled simultaneously. In our framework, a higher-level layer is designed to automatically divide the DFJSP into sub-problems, i.e., static FJSPs with different scales. And two lower-level layers are constructed to solve the sub-problems. In particular, one layer based on a graph neural network is in charge of sequencing job operations, and another layer based on a multi-layer perceptron is used to assign a machine to process the job operations. Numerical experiments, including offline training and online testing, are conducted on several instances with different scales. The results verify the superior performance of the proposed framework compared with existing dynamic scheduling methods, such as well-known dispatching rules and meta-heuristics.

A DRL-Based Reactive Scheduling Policy for Flexible Job Shops With Random Job Arrivals

In real-life production systems, arrivals of jobs are usually unpredictable, which makes it necessary to develop solid reactive scheduling policies to meet delivery requirements. Deep reinforcement learning (DRL) based scheduling methods are capable of quickly responding to dynamic events by learning from the training data. However, most of policy networks in DRL algorithms are trained to choose priority dispatching rules (PDR), thus, to some extent, the efficiency of obtained scheduling plans is limited by the performance of PDRs. This paper investigates a dynamic flexible job shop scheduling problem with random job arrivals for the total tardiness minimization. A DRL-based reactive scheduling method, proximal policy optimization with attention-based policy network (PPO-APN), is proposed to make real-time decisions for the dynamic scheduling environment, where the attention-based policy network (APN) is able to directly select pending jobs distinguished from the action space that consists of PDRs. Additionally, a global/local reward function (GLRF) is designed to address the reward sparsity issue during training processes. The proposed PPO-APN is tested on randomly generated instances with different production configurations, and is compared with frequently-used PDRs and DRL-based methods. Numerical experimental results indicate that APN and GLRF components significantly improve the training efficiency, and the PPO-APN shows better overall performance compared with other methods. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This work is motivated by a typical production scenario in discrete manufacturing systems, where orders randomly arrive at the shop floor and require to be scheduled in a short time to ensure the on-time delivery. Previous research work tends to apply DRL algorithms to choose suitable dispatching rules for the ease of implementation. Nevertheless, the jobs that can be selected by dispatching rules are rather limited, thus many possible high-quality scheduling plans are ignored. This work first sorts all the unscheduled jobs by a heuristic algorithm, and puts some of top-ranked jobs to a pool. When a machine becomes available, it will directly choose a job from the pool as the next processing task. The job selection policy is represented by a novel attention-based network, and is trained by a powerful DRL algorithm. The aforementioned process is repeatedly executed in a simulation environment to collect the training data. Therefore, after being trained for a certain period of time, the policy will become smarter and can be applied to make right decisions in real-time. The proposed reactive scheduling method has been proved to be more efficient than dispatching rules and DRL-based approaches, and is effective in the production scheduling for a wide variety of discrete manufacturing scenarios, such as automobile and electronics industries. Moreover, the proposed method can be further extended to address dynamic scheduling problems with some production characteristics via adding constraints for the job selection or re-defining calculations for the completion time of operations accordingly.

Task Relatedness-Based Multitask Genetic Programming for Dynamic Flexible Job Shop Scheduling

Multitasking learning has been successfully used in handling multiple related tasks simultaneously. In reality, there are often many tasks to be solved together, and the relatedness between them is unknown in advance. In this paper, we focus on multitask genetic programming for the dynamic flexible job shop scheduling problems, and address two challenges. The first is how to measure the relatedness between tasks accurately. The second is how to select task pairs to transfer knowledge during the multitask learning process. To measure the relatedness between dynamic flexible job shop scheduling tasks, we propose a new relatedness metric based on the behaviour distributions of the variable-length genetic programming individuals. In addition, for more effective knowledge transfer, we develop an adaptive strategy to choose the most suitable assisted task for the target task based on the relatedness information between tasks. The findings show that in all of the multitask scenarios studied, the proposed algorithm can substantially increase the effectiveness of the learned scheduling heuristics for all the desired tasks. The effectiveness of the proposed algorithm has also been verified by the analyses of task relatedness and structures of the evolved scheduling heuristics, and the discussions of population diversity and knowledge transfer.

Dynamic scheduling for flexible job shop with insufficient transportation resources via graph neural network and deep reinforcement learning

The smart workshop is a powerful tool for manufacturing companies to reduce waste and improve production efficiency through real-time data analysis for self-organized production. Automated Guided Vehicles (AGVs) have been widely used for material handling in smart workshop due to their high degree of autonomy, flexibility and powerful end-to-end capability to cope with logistics tasks in production modes such as multiple species and small batch, and mass customization. However, the highly dynamic, complex and uncertain nature of the smart job shop environment makes production scheduling with insufficient transportation resources in mind a challenge. To this end, this paper addresses the dynamic flexible job shop scheduling problem with insufficient transportation resources (DFJSP-ITR), and learn high-quality priority dispatching rule (PDR) end-to-end to minimize makespan by the proposed deep reinforcement learning (DRL) method. To achieve integrated decision making for operation, machine and AGV, an architecture based on heterogeneous graph neural network (GNN) and DRL is proposed. Considering the impact of different AGV distribution methods on the scheduling objective, this paper compares two different AGV distribution methods. Experiments show that the proposed method has superiority and good generalization ability compared with the current PDRs-based methods regardless of the AGV distribution strategy used.

A multi-objective migrating birds optimization algorithm based on game theory for dynamic flexible job shop scheduling problem

A multi-objective migrating birds optimization algorithm based on game theory for dynamic flexible job shop scheduling problem

Deep reinforcement learning for dynamic flexible job shop scheduling problem considering variable processing times

In recent years, the uncertainties and complexity in the production process, due to the boosted customized requirements, has dramatically increased the difficulties of Dynamic Flexible Job Shop Scheduling (DFJSP). This paper investigates a new DFJSP model taking into account the minimum completion time under the condition of machine processing time uncertainty, e.t. VPT-FJSP problem. In the formulated VPT-FJSP process, each workpiece needs to be processed by required machine at a certain time slot where Markov decision process (MDP) and reinforcement learning methods are adopted to solve VPT-FJSP. The agent designed in this paper employs the Proximal Policy Optimization(PPO) algorithm in deep reinforcement learning, which includes the Actor-Critic network. The input of the network is to extract the processing information matrix and to embed some advanced states in the workshop by graph neural network, which enables the agent to learn the complete state of the environment. Finally, we train and test the proposed framework on the canonical FJSP benchmark, and the experimental results show that our framework can make agent better than genetic algorithm and ant colony optimization in most cases, 94.29% of static scheduling. It is also shown superiority compared to the scheduling rules in dynamic environment and has demonstrated strong robustness in solving VPT-FJSP. Furthermore, this study conducted tests to assess the generalization capability of the agent on VPT-FJSP at different scales. In terms of exploring Makespan minimization, the agent outperformed four priority scheduling rules. These results indicate that the proposed dynamic scheduling framework and PPO algorithm are more effective in achieving superior solutions.

Agent-based hybrid tabu-search heuristic for dynamic scheduling

Dynamic scheduling has received widespread attention from academia and industry due to the increasing complexity in manufacturing systems. Highly dynamic and adaptable behaviours are necessary for an improved production efficiency in unstable and constantly changing environments. This paper proposes an agent-based hybrid tabu-search heuristic (AB-TSH) to solve dynamic flexible job-shop scheduling problems. The solution is fully implemented and tested in an industrial environment for seven distinct dynamic scenarios derived from a static scenario using the benchmark of AIP-PRIMECA Flexible Manufacturing System. The scheduling plan is obtained by exploitation using a greedy heuristic on tabu search solution points. The hybrid tabu-search heuristic is supported by a multi-agent system that react and re-optimize the scheduling plan in case of disturbances and unpredicted events. The proposed solution demonstrated superior performance in terms of makespan in the majority of dynamic scenarios tested when compared to previous studies in the literature. This improved performance is attributed to the solution’s ability to combine the scheduling plan both statically and dynamically.

Efficient Multi-Objective Optimization on Dynamic Flexible Job Shop Scheduling Using Deep Reinforcement Learning Approach

Previous research focuses on approaches of deep reinforcement learning (DRL) to optimize diverse types of the single-objective dynamic flexible job shop scheduling problem (DFJSP), e.g., energy consumption, earliness and tardiness penalty and machine utilization rate, which gain many improvements in terms of objective metrics in comparison with metaheuristic algorithms such as GA (genetic algorithm) and dispatching rules such as MRT (most remaining time first). However, single-objective optimization in the job shop floor cannot satisfy the requirements of modern smart manufacturing systems, and the multiple-objective DFJSP has become mainstream and the core of intelligent workshops. A complex production environment in a real-world factory causes scheduling entities to have sophisticated characteristics, e.g., a job’s non-uniform processing time, uncertainty of the operation number and restraint of the due time, avoidance of the single machine’s prolonged slack time as well as overweight load, which make a method of the combination of dispatching rules in DRL brought up to adapt to the manufacturing environment at different rescheduling points and accumulate maximum rewards for a global optimum. In our work, we apply the structure of a dual layer DDQN (DLDDQN) to solve the DFJSP in real time with new job arrivals, and two objectives are optimized simultaneously, i.e., the minimization of the delay time sum and makespan. The framework includes two layers (agents): the higher one is named as a goal selector, which utilizes DDQN as a function approximator for selecting one reward form from six proposed ones that embody the two optimization objectives, while the lower one, called an actuator, utilizes DDQN to decide on an optimal rule that has a maximum Q value. The generated benchmark instances trained in our framework converged perfectly, and the comparative experiments validated the superiority and generality of the proposed DLDDQN.

Multitask Multiobjective Genetic Programming for Automated Scheduling Heuristic Learning in Dynamic Flexible Job-Shop Scheduling.

Evolutionary multitask multiobjective learning has been widely used for handling more than one multiobjective task simultaneously. However, it is rarely used in dynamic combinatorial optimization problems, which have valuable practical applications such as dynamic flexible job-shop scheduling (DFJSS) in manufacturing. Genetic programming (GP), as a popular hyperheuristic approach, has been used to learn scheduling heuristics for generating schedules for multitask single-objective DFJSS only. Searching in the heuristic space with GP is more difficult than in the solution space, since a small change on heuristics can lead to ineffective or even infeasible solutions. Multiobjective DFJSS is more challenging than single DFJSS, since a scheduling heuristic needs to cope with multiple objectives. To tackle this challenge, we first propose a multipopulation-based multitask multiobjective GP algorithm to preserve the quality of the learned scheduling heuristics for each task. Furthermore, we develop a multitask multiobjective GP algorithm with a task-oriented knowledge-sharing strategy to further improve the effectiveness of learning scheduling heuristics for DFJSS. The results show that the designed multipopulation-based GP algorithms, especially the one with the task-oriented knowledge-sharing strategy, can achieve good performance for all the examined tasks by maintaining the quality and diversity of individuals for corresponding tasks well. The learned Pareto fronts also show that the GP algorithm with task-oriented knowledge-sharing strategy can learn competitive scheduling heuristics for DFJSS on both of the objectives.

An immune-based multi-agent system for flexible job shop scheduling problem in dynamic and multi-objective environments

In this paper, a biological immune-based multi agent system (IMAS) is developed to overcome the multi-objectivity and dynamicity of the multi-objective dynamic flexible job shop scheduling (MODFJSS) problem. In modeling the MODFJSS problem, four objectives, i.e., makespan, total weighted tardiness, maximal machine workload, and schedule stability, are considered for simultaneous optimization. In the proposed IMAS architecture, immune agents are coordinated to identify the environment, generate a set of non-dominated schedules, and select a utility optimal schedule. In addition, these agents have the ability of self-adaptation and flexible coordination to adapt to the environment of MODFJSS problem. The performance of the proposed method was evaluated on dynamic versions of the five commonly used benchmark instance sets in comparison with three state-of-the-art algorithms. The obtained results showed that the proposed IMAS outperformed the competitors in most of the experiments conducted in this study.

Dynamic scheduling for flexible job shop using a deep reinforcement learning approach

Due to the influence of dynamic changes in the manufacturing environment, a single dispatching rule (SDR) cannot consistently attain better results than other rules for dynamic scheduling problems. Dynamic selection of the most appropriate rule from several SDRs based on the Deep Q-Network (DQN) offers better scheduling performance than using an individual SDR. However, the discreteness of action space caused by the DQN and the simplicity of the action as an SDR limit the selection range and restrict performance improvement. Thus, in this paper, we propose a scheduling method based on deep reinforcement learning for the dynamic flexible job-shop scheduling problem (DFJSP), aiming to minimize the mean tardiness. Firstly, a Markov decision process with composite scheduling action is provided to elaborate the flexible job-shop dynamic scheduling process and transform the DFJSP into an RL task. Subsequently, a composite scheduling action aggregated by SDRs and continuous weight variables is designed to provide a continuous rule space and SDR weight selection. Moreover, a reward function related to mean tardiness performance criteria is designed such that maximizing the cumulative reward is equivalent to minimizing the mean tardiness. Finally, a policy network with states as inputs and weights as outputs is constructed to generate the scheduling decision at each decision point. Also, the deep deterministic policy gradient (DDPG) algorithm is used to train the policy network to select the most appropriate weights at each decision point, thereby aggregating the SDRs into a better rule. Results from numerical experiments reveal that the proposed scheduling method achieves significantly better scheduling results than an SDR and the DQN-based method in dynamically changeable manufacturing environments.

Dynamic energy-efficient scheduling of multi-variety and small batch flexible job-shop: A case study for the aerospace industry

In the context of the global implementation of carbon peaking and carbon neutrality, energy-aware production scheduling has attracted world-wide attention. The optimal scheduling problem for a multi-variety and small-batch dynamic flexible job shop scheduling is challenging in aerospace industry. This paper considers an energy-efficient scheduling problem with multi-resource constraints of multi-variety and small-batch dynamic flexible job shop (α-shop for short). First, it formulates a mathematical model of energy efficient α-shop with the objectives of minimum total energy consumption (TEC), makespan and machining cost. Next, a novel multi-objective bi-population differential artificial bee colony (BDABC) algorithm is proposed to solve the model. Then, the design of experiment Taguchi method is performed to calibrate the parameter setting of the proposed algorithm. Finally, comparative experiments of the proposed algorithm with other popular algorithms such as large-scale multi-objective optimization framework (LSMOF), large-scale multi-objective competitive swarm optimizer (LMOCSO), as well as some known algorithms including multi-objective evolutionary algorithm based on decomposition (MOEA/D), multi-objective particle swarm optimization (MOPSO) and multi-objective artificial bee colony (MOABC) are carried out to assess the effectiveness of the proposed algorithm in an aerospace plant of China based on a number of well-recognized metrics. The experimental results demonstrate that our proposed algorithm is effective reported for this real-life scheduling problem.