Traditional source search algorithms are prone to local optimization,and source search methods combining crowdsourcing and human-AI collaboration suffer from low cost-efficiency due to human intervention.In this study...Traditional source search algorithms are prone to local optimization,and source search methods combining crowdsourcing and human-AI collaboration suffer from low cost-efficiency due to human intervention.In this study,we proposed a lightweight human-AI collaboration framework that utilized multi-modal large language models(MLLMs)to achieve visual-language conversion,combined chain-of-thought(CoT)reasoning to optimize decision-making,and constructed a heuristic strategy that incorporated probability distribution filtering and a balance between exploitation and exploration.The effectiveness of the framework was verified by experiments.The human-AI alignment heuristic strategy with large language model adaptation design provides a new idea to reduce manual dependency for source search task in complex scenes.展开更多
The Cross-domain Heuristic Search Challenge(CHeSC)is a competition focused on creating efficient search algorithms adaptable to diverse problem domains.Selection hyper-heuristics are a class of algorithms that dynamic...The Cross-domain Heuristic Search Challenge(CHeSC)is a competition focused on creating efficient search algorithms adaptable to diverse problem domains.Selection hyper-heuristics are a class of algorithms that dynamically choose heuristics during the search process.Numerous selection hyper-heuristics have different imple-mentation strategies.However,comparisons between them are lacking in the literature,and previous works have not highlighted the beneficial and detrimental implementation methods of different components.The question is how to effectively employ them to produce an efficient search heuristic.Furthermore,the algorithms that competed in the inaugural CHeSC have not been collectively reviewed.This work conducts a review analysis of the top twenty competitors from this competition to identify effective and ineffective strategies influencing algorithmic performance.A summary of the main characteristics and classification of the algorithms is presented.The analysis underlines efficient and inefficient methods in eight key components,including search points,search phases,heuristic selection,move acceptance,feedback,Tabu mechanism,restart mechanism,and low-level heuristic parameter control.This review analyzes the components referencing the competition’s final leaderboard and discusses future research directions for these components.The effective approaches,identified as having the highest quality index,are mixed search point,iterated search phases,relay hybridization selection,threshold acceptance,mixed learning,Tabu heuristics,stochastic restart,and dynamic parameters.Findings are also compared with recent trends in hyper-heuristics.This work enhances the understanding of selection hyper-heuristics,offering valuable insights for researchers and practitioners aiming to develop effective search algorithms for diverse problem domains.展开更多
Heuristic optimization algorithms have been widely used in solving complex optimization problems in various fields such as engineering,economics,and computer science.These algorithms are designed to find high-quality ...Heuristic optimization algorithms have been widely used in solving complex optimization problems in various fields such as engineering,economics,and computer science.These algorithms are designed to find high-quality solutions efficiently by balancing exploration of the search space and exploitation of promising solutions.While heuristic optimization algorithms vary in their specific details,they often exhibit common patterns that are essential to their effectiveness.This paper aims to analyze and explore common patterns in heuristic optimization algorithms.Through a comprehensive review of the literature,we identify the patterns that are commonly observed in these algorithms,including initialization,local search,diversity maintenance,adaptation,and stochasticity.For each pattern,we describe the motivation behind it,its implementation,and its impact on the search process.To demonstrate the utility of our analysis,we identify these patterns in multiple heuristic optimization algorithms.For each case study,we analyze how the patterns are implemented in the algorithm and how they contribute to its performance.Through these case studies,we show how our analysis can be used to understand the behavior of heuristic optimization algorithms and guide the design of new algorithms.Our analysis reveals that patterns in heuristic optimization algorithms are essential to their effectiveness.By understanding and incorporating these patterns into the design of new algorithms,researchers can develop more efficient and effective optimization algorithms.展开更多
A well-designed production schedule for cold rolling can enhance steel enterprises'operational efficiency and profitability.Nevertheless,the intricate constraints and numerous steps involved in cold rolling pose c...A well-designed production schedule for cold rolling can enhance steel enterprises'operational efficiency and profitability.Nevertheless,the intricate constraints and numerous steps involved in cold rolling pose challenges to devising a rational scheduling plan.Therefore,considering the practical production constraints,this paper investigates a cold rolling scheduling problem for processing jobs with specific due dates and batch attributions on parallel heterogeneous machines with continuous production requirements.Firstly,the scheduling problem is formulated as a mixed integer linear program(MILP)model with an economic objective.Then,a modified genetic algorithm(GA)is proposed to search for the optimal solution to the MILP problem.Specifically,this method includes a heuristic initialization mechanism to generate feasible initial solutions,three heuristic mutation operators to generate promising candidate solutions,and a parallel computing mechanism to accelerate the evaluation process of the GA.The simulation results demonstrate that the proposed method can be effectively implemented to generate optimized scheduling schemes in the cold rolling process.展开更多
Vulnerability assessment is a systematic process to identify security gaps in the design and evaluation of physical protection systems.Adversarial path planning is a widely used method for identifying potential vulner...Vulnerability assessment is a systematic process to identify security gaps in the design and evaluation of physical protection systems.Adversarial path planning is a widely used method for identifying potential vulnerabilities and threats to the security and resilience of critical infrastructures.However,achieving efficient path optimization in complex large-scale three-dimensional(3D)scenes remains a significant challenge for vulnerability assessment.This paper introduces a novel A^(*)-algorithmic framework for 3D security modeling and vulnerability assessment.Within this framework,the 3D facility models were first developed in 3ds Max and then incorporated into Unity for A^(*)heuristic pathfinding.The A^(*)-heuristic pathfinding algorithm was implemented with a geometric probability model to refine the detection and distance fields and achieve a rational approximation of the cost to reach the goal.An admissible heuristic is ensured by incorporating the minimum probability of detection(P_(D)^(min))and diagonal distance to estimate the heuristic function.The 3D A^(*)heuristic search was demonstrated using a hypothetical laboratory facility,where a comparison was also carried out between the A^(*)and Dijkstra algorithms for optimal path identification.Comparative results indicate that the proposed A^(*)-heuristic algorithm effectively identifies the most vulnerable adversarial pathfinding with high efficiency.Finally,the paper discusses hidden phenomena and open issues in efficient 3D pathfinding for security applications.展开更多
As commercial drone delivery becomes increasingly popular,the extension of the vehicle routing problem with drones(VRPD)is emerging as an optimization problem of inter-ests.This paper studies a variant of VRPD in mult...As commercial drone delivery becomes increasingly popular,the extension of the vehicle routing problem with drones(VRPD)is emerging as an optimization problem of inter-ests.This paper studies a variant of VRPD in multi-trip and multi-drop(VRP-mmD).The problem aims at making schedules for the trucks and drones such that the total travel time is minimized.This paper formulate the problem with a mixed integer program-ming model and propose a two-phase algorithm,i.e.,a parallel route construction heuristic(PRCH)for the first phase and an adaptive neighbor searching heuristic(ANSH)for the second phase.The PRCH generates an initial solution by con-currently assigning as many nodes as possible to the truck–drone pair to progressively reduce the waiting time at the rendezvous node in the first phase.Then the ANSH improves the initial solution by adaptively exploring the neighborhoods in the second phase.Numerical tests on some benchmark data are conducted to verify the performance of the algorithm.The results show that the proposed algorithm can found better solu-tions than some state-of-the-art methods for all instances.More-over,an extensive analysis highlights the stability of the pro-posed algorithm.展开更多
The increasing penetration of second-life battery energy storage systems(SLBESS)in power grids presents substantial challenges to system operation and control due to the heterogeneous characteristics and uncertain deg...The increasing penetration of second-life battery energy storage systems(SLBESS)in power grids presents substantial challenges to system operation and control due to the heterogeneous characteristics and uncertain degradation patterns of repurposed batteries.This paper presents a novel model-free adaptive voltage controlembedded dung beetle-inspired heuristic optimization algorithmfor optimal SLBESS capacity configuration and power dispatch.To simultaneously address the computational complexity and ensure system stability,this paper develops a comprehensive bilevel optimization framework.At the upper level,a dung beetle optimization algorithmdetermines the optimal SLBESS capacity configuration byminimizing total lifecycle costswhile incorporating the charging/discharging power trajectories derived from the model-free adaptive voltage control strategy.At the lower level,a health-priority power dispatch optimization model intelligently allocates power demands among heterogeneous battery groups based on their real-time operational states,state-of-health variations,and degradation constraints.The proposed model-free approach circumvents the need for complex battery charging/discharging power controlmodels and extensive historical data requirements whilemaintaining system stability through adaptive controlmechanisms.A novel cycle life degradation model is developed to quantify the relationship between remaining useful life,depth of discharge,and operational patterns.The integrated framework enables simultaneous strategic planning and operational control,ensuring both economic efficiency and extended battery lifespan.The effectiveness of the proposed method is validated through comprehensive case studies on hybrid energy storage systems,demonstrating superior computational efficiency,robust performance across different network configurations,and significant improvements in battery utilization compared to conventional approaches.展开更多
In an aircraft final assembly line(AFAL),the rational scheduling of assembly workers to complete tasks in an orderly manner is crucial for enhancing production efficiency.This paper addresses the multi-skilled worker ...In an aircraft final assembly line(AFAL),the rational scheduling of assembly workers to complete tasks in an orderly manner is crucial for enhancing production efficiency.This paper addresses the multi-skilled worker scheduling problem in the AFAL,where the processing time of each task varies due to the assigned workers’skill levels,referred to as variable duration.The objective is to minimize the makespan,i.e.,the total time required for all workers to complete all tasks.A mixed integer linear programming model is formulated under complex constraints including assembly precedence relations,skill requirements,worker skill capabilities,and workspace capacities.To solve the model effectively,a multi-pass priority rule-based heuristic(MPRH)algorithm is proposed.This algorithm integrates 14 activity priority rules and nine worker priority rules with worker weights.Extensive experiments iteratively the best-performing priority rules,and the most effective rule subsets are integrated through a lightweight multi-pass mechanism to enhance its efficiency.The computational results demonstrate that the MPRH can find high-quality solutions effectively within very short central processing unit central processing unit(CPU)time compared to GUROBI.A case study based on real data obtained from an AFAL confirms the necessity and the feasibility of the approach in practical applications.Sensitivity analyses provide valuable insights to real production scenarios.展开更多
Transfer learning is the predominant method for adapting pre-trained models on another task to new domains while preserving their internal architectures and augmenting them with requisite layers in Deep Neural Network...Transfer learning is the predominant method for adapting pre-trained models on another task to new domains while preserving their internal architectures and augmenting them with requisite layers in Deep Neural Network models.Training intricate pre-trained models on a sizable dataset requires significant resources to fine-tune hyperparameters carefully.Most existing initialization methods mainly focus on gradient flow-related problems,such as gradient vanishing or exploding,or other existing approaches that require extra models that do not consider our setting,which is more practical.To address these problems,we suggest employing gradient-free heuristic methods to initialize the weights of the final new-added fully connected layer in neural networks froma small set of training data with fewer classes.The approach relies on partitioning the output values from pre-trained models for a small set into two separate intervals determined by the targets.This process is framed as an optimization problem for each output neuron and class.The optimization selects the highest values as weights,considering their direction towards the respective classes.Furthermore,empirical 145 experiments involve a variety of neural networkmodels tested acrossmultiple benchmarks and domains,occasionally yielding accuracies comparable to those achieved with gradient descent methods by using only small subsets.展开更多
Combining the heuristic algorithm （HA） developed based on the specific knowledge of the cooperative multiple target attack （CMTA） tactics and the particle swarm optimization （PSO）, a heuristic particle swarm opt...Combining the heuristic algorithm （HA） developed based on the specific knowledge of the cooperative multiple target attack （CMTA） tactics and the particle swarm optimization （PSO）, a heuristic particle swarm optimization （HPSO） algorithm is proposed to solve the decision-making （DM） problem. HA facilitates to search the local optimum in the neighborhood of a solution, while the PSO algorithm tends to explore the search space for possible solutions. Combining the advantages of HA and PSO, HPSO algorithms can find out the global optimum quickly and efficiently. It obtains the DM solution by seeking for the optimal assignment of missiles of friendly fighter aircrafts （FAs） to hostile FAs. Simulation results show that the proposed algorithm is superior to the general PSO algorithm and two GA based algorithms in searching for the best solution to the DM problem.展开更多
Traditional models for project management have not adequately incorporated a number of factors that are important for resource allocation. This paper proposed a unified timed Petri net model in which scheduling and pl...Traditional models for project management have not adequately incorporated a number of factors that are important for resource allocation. This paper proposed a unified timed Petri net model in which scheduling and planning were collectively carried out to take full advantages of the flexibility of the FMS. Through the lens of system theory, two types of resources were distinguished: major role and auxiliary role, and the major role was used to construct the FMS' Petri net. The method simplified the Petri net's construction and gave a clear flow chart for scheduling. Hence, the auxiliary resource allocation could be easily carried out according to the schedule, which was proposed by heuristic search algorithm. At last, the efficacy of the Petri net model for online scheduling in a resource constrained environment was discussed.展开更多
基金National Natural Science Foundation of China (62202477)。
文摘Traditional source search algorithms are prone to local optimization,and source search methods combining crowdsourcing and human-AI collaboration suffer from low cost-efficiency due to human intervention.In this study,we proposed a lightweight human-AI collaboration framework that utilized multi-modal large language models(MLLMs)to achieve visual-language conversion,combined chain-of-thought(CoT)reasoning to optimize decision-making,and constructed a heuristic strategy that incorporated probability distribution filtering and a balance between exploitation and exploration.The effectiveness of the framework was verified by experiments.The human-AI alignment heuristic strategy with large language model adaptation design provides a new idea to reduce manual dependency for source search task in complex scenes.
基金funded by Ministry of Higher Education(MoHE)Malaysia,under Transdisciplinary Research Grant Scheme(TRGS/1/2019/UKM/01/4/2).
文摘The Cross-domain Heuristic Search Challenge(CHeSC)is a competition focused on creating efficient search algorithms adaptable to diverse problem domains.Selection hyper-heuristics are a class of algorithms that dynamically choose heuristics during the search process.Numerous selection hyper-heuristics have different imple-mentation strategies.However,comparisons between them are lacking in the literature,and previous works have not highlighted the beneficial and detrimental implementation methods of different components.The question is how to effectively employ them to produce an efficient search heuristic.Furthermore,the algorithms that competed in the inaugural CHeSC have not been collectively reviewed.This work conducts a review analysis of the top twenty competitors from this competition to identify effective and ineffective strategies influencing algorithmic performance.A summary of the main characteristics and classification of the algorithms is presented.The analysis underlines efficient and inefficient methods in eight key components,including search points,search phases,heuristic selection,move acceptance,feedback,Tabu mechanism,restart mechanism,and low-level heuristic parameter control.This review analyzes the components referencing the competition’s final leaderboard and discusses future research directions for these components.The effective approaches,identified as having the highest quality index,are mixed search point,iterated search phases,relay hybridization selection,threshold acceptance,mixed learning,Tabu heuristics,stochastic restart,and dynamic parameters.Findings are also compared with recent trends in hyper-heuristics.This work enhances the understanding of selection hyper-heuristics,offering valuable insights for researchers and practitioners aiming to develop effective search algorithms for diverse problem domains.
文摘Heuristic optimization algorithms have been widely used in solving complex optimization problems in various fields such as engineering,economics,and computer science.These algorithms are designed to find high-quality solutions efficiently by balancing exploration of the search space and exploitation of promising solutions.While heuristic optimization algorithms vary in their specific details,they often exhibit common patterns that are essential to their effectiveness.This paper aims to analyze and explore common patterns in heuristic optimization algorithms.Through a comprehensive review of the literature,we identify the patterns that are commonly observed in these algorithms,including initialization,local search,diversity maintenance,adaptation,and stochasticity.For each pattern,we describe the motivation behind it,its implementation,and its impact on the search process.To demonstrate the utility of our analysis,we identify these patterns in multiple heuristic optimization algorithms.For each case study,we analyze how the patterns are implemented in the algorithm and how they contribute to its performance.Through these case studies,we show how our analysis can be used to understand the behavior of heuristic optimization algorithms and guide the design of new algorithms.Our analysis reveals that patterns in heuristic optimization algorithms are essential to their effectiveness.By understanding and incorporating these patterns into the design of new algorithms,researchers can develop more efficient and effective optimization algorithms.
基金Supported by National Natural Science Foundation of China(Grant No.62273362)National Key Research and Development Program of China(Grant No.2024YFB3312100)。
文摘A well-designed production schedule for cold rolling can enhance steel enterprises'operational efficiency and profitability.Nevertheless,the intricate constraints and numerous steps involved in cold rolling pose challenges to devising a rational scheduling plan.Therefore,considering the practical production constraints,this paper investigates a cold rolling scheduling problem for processing jobs with specific due dates and batch attributions on parallel heterogeneous machines with continuous production requirements.Firstly,the scheduling problem is formulated as a mixed integer linear program(MILP)model with an economic objective.Then,a modified genetic algorithm(GA)is proposed to search for the optimal solution to the MILP problem.Specifically,this method includes a heuristic initialization mechanism to generate feasible initial solutions,three heuristic mutation operators to generate promising candidate solutions,and a parallel computing mechanism to accelerate the evaluation process of the GA.The simulation results demonstrate that the proposed method can be effectively implemented to generate optimized scheduling schemes in the cold rolling process.
基金supported by the fundings from 2024 Young Talents Program for Science and Technology Thinking Tanks(No.XMSB20240711041)2024 Student Research Program on Dynamic Simulation and Force-on-Force Exercise of Nuclear Security in 3D Interactive Environment Using Reinforcement Learning,Natural Science Foundation of Top Talent of SZTU(No.GDRC202407)+2 种基金Shenzhen Science and Technology Program(No.KCXFZ20240903092603005)Shenzhen Science and Technology Program(No.JCYJ20241202124703004)Shenzhen Science and Technology Program(No.KJZD20230923114117032)。
文摘Vulnerability assessment is a systematic process to identify security gaps in the design and evaluation of physical protection systems.Adversarial path planning is a widely used method for identifying potential vulnerabilities and threats to the security and resilience of critical infrastructures.However,achieving efficient path optimization in complex large-scale three-dimensional(3D)scenes remains a significant challenge for vulnerability assessment.This paper introduces a novel A^(*)-algorithmic framework for 3D security modeling and vulnerability assessment.Within this framework,the 3D facility models were first developed in 3ds Max and then incorporated into Unity for A^(*)heuristic pathfinding.The A^(*)-heuristic pathfinding algorithm was implemented with a geometric probability model to refine the detection and distance fields and achieve a rational approximation of the cost to reach the goal.An admissible heuristic is ensured by incorporating the minimum probability of detection(P_(D)^(min))and diagonal distance to estimate the heuristic function.The 3D A^(*)heuristic search was demonstrated using a hypothetical laboratory facility,where a comparison was also carried out between the A^(*)and Dijkstra algorithms for optimal path identification.Comparative results indicate that the proposed A^(*)-heuristic algorithm effectively identifies the most vulnerable adversarial pathfinding with high efficiency.Finally,the paper discusses hidden phenomena and open issues in efficient 3D pathfinding for security applications.
文摘As commercial drone delivery becomes increasingly popular,the extension of the vehicle routing problem with drones(VRPD)is emerging as an optimization problem of inter-ests.This paper studies a variant of VRPD in multi-trip and multi-drop(VRP-mmD).The problem aims at making schedules for the trucks and drones such that the total travel time is minimized.This paper formulate the problem with a mixed integer program-ming model and propose a two-phase algorithm,i.e.,a parallel route construction heuristic(PRCH)for the first phase and an adaptive neighbor searching heuristic(ANSH)for the second phase.The PRCH generates an initial solution by con-currently assigning as many nodes as possible to the truck–drone pair to progressively reduce the waiting time at the rendezvous node in the first phase.Then the ANSH improves the initial solution by adaptively exploring the neighborhoods in the second phase.Numerical tests on some benchmark data are conducted to verify the performance of the algorithm.The results show that the proposed algorithm can found better solu-tions than some state-of-the-art methods for all instances.More-over,an extensive analysis highlights the stability of the pro-posed algorithm.
基金Financial support was provided by the State Grid Sichuan Electric Power Company Science and Technology Project“Key Research on Development Path Planning and Key Operation Technologies of New Rural Electrification Construction”under Grant No.52199623000G.
文摘The increasing penetration of second-life battery energy storage systems(SLBESS)in power grids presents substantial challenges to system operation and control due to the heterogeneous characteristics and uncertain degradation patterns of repurposed batteries.This paper presents a novel model-free adaptive voltage controlembedded dung beetle-inspired heuristic optimization algorithmfor optimal SLBESS capacity configuration and power dispatch.To simultaneously address the computational complexity and ensure system stability,this paper develops a comprehensive bilevel optimization framework.At the upper level,a dung beetle optimization algorithmdetermines the optimal SLBESS capacity configuration byminimizing total lifecycle costswhile incorporating the charging/discharging power trajectories derived from the model-free adaptive voltage control strategy.At the lower level,a health-priority power dispatch optimization model intelligently allocates power demands among heterogeneous battery groups based on their real-time operational states,state-of-health variations,and degradation constraints.The proposed model-free approach circumvents the need for complex battery charging/discharging power controlmodels and extensive historical data requirements whilemaintaining system stability through adaptive controlmechanisms.A novel cycle life degradation model is developed to quantify the relationship between remaining useful life,depth of discharge,and operational patterns.The integrated framework enables simultaneous strategic planning and operational control,ensuring both economic efficiency and extended battery lifespan.The effectiveness of the proposed method is validated through comprehensive case studies on hybrid energy storage systems,demonstrating superior computational efficiency,robust performance across different network configurations,and significant improvements in battery utilization compared to conventional approaches.
基金supported by the National Natural Science Foundation of China(52175475).
文摘In an aircraft final assembly line(AFAL),the rational scheduling of assembly workers to complete tasks in an orderly manner is crucial for enhancing production efficiency.This paper addresses the multi-skilled worker scheduling problem in the AFAL,where the processing time of each task varies due to the assigned workers’skill levels,referred to as variable duration.The objective is to minimize the makespan,i.e.,the total time required for all workers to complete all tasks.A mixed integer linear programming model is formulated under complex constraints including assembly precedence relations,skill requirements,worker skill capabilities,and workspace capacities.To solve the model effectively,a multi-pass priority rule-based heuristic(MPRH)algorithm is proposed.This algorithm integrates 14 activity priority rules and nine worker priority rules with worker weights.Extensive experiments iteratively the best-performing priority rules,and the most effective rule subsets are integrated through a lightweight multi-pass mechanism to enhance its efficiency.The computational results demonstrate that the MPRH can find high-quality solutions effectively within very short central processing unit central processing unit(CPU)time compared to GUROBI.A case study based on real data obtained from an AFAL confirms the necessity and the feasibility of the approach in practical applications.Sensitivity analyses provide valuable insights to real production scenarios.
基金supported by the BK21 FOUR project(AI-driven Convergence Software Education Research Program)funded by the Ministry of Education,School of Computer Science and Engineering,Kyungpook National University,Republic of Korea(4120240214871)supported by the New Faculty Start Up Fund from LSU Health Sciences New Orleans,LA,USA.
文摘Transfer learning is the predominant method for adapting pre-trained models on another task to new domains while preserving their internal architectures and augmenting them with requisite layers in Deep Neural Network models.Training intricate pre-trained models on a sizable dataset requires significant resources to fine-tune hyperparameters carefully.Most existing initialization methods mainly focus on gradient flow-related problems,such as gradient vanishing or exploding,or other existing approaches that require extra models that do not consider our setting,which is more practical.To address these problems,we suggest employing gradient-free heuristic methods to initialize the weights of the final new-added fully connected layer in neural networks froma small set of training data with fewer classes.The approach relies on partitioning the output values from pre-trained models for a small set into two separate intervals determined by the targets.This process is framed as an optimization problem for each output neuron and class.The optimization selects the highest values as weights,considering their direction towards the respective classes.Furthermore,empirical 145 experiments involve a variety of neural networkmodels tested acrossmultiple benchmarks and domains,occasionally yielding accuracies comparable to those achieved with gradient descent methods by using only small subsets.
文摘Combining the heuristic algorithm （HA） developed based on the specific knowledge of the cooperative multiple target attack （CMTA） tactics and the particle swarm optimization （PSO）, a heuristic particle swarm optimization （HPSO） algorithm is proposed to solve the decision-making （DM） problem. HA facilitates to search the local optimum in the neighborhood of a solution, while the PSO algorithm tends to explore the search space for possible solutions. Combining the advantages of HA and PSO, HPSO algorithms can find out the global optimum quickly and efficiently. It obtains the DM solution by seeking for the optimal assignment of missiles of friendly fighter aircrafts （FAs） to hostile FAs. Simulation results show that the proposed algorithm is superior to the general PSO algorithm and two GA based algorithms in searching for the best solution to the DM problem.
文摘Traditional models for project management have not adequately incorporated a number of factors that are important for resource allocation. This paper proposed a unified timed Petri net model in which scheduling and planning were collectively carried out to take full advantages of the flexibility of the FMS. Through the lens of system theory, two types of resources were distinguished: major role and auxiliary role, and the major role was used to construct the FMS' Petri net. The method simplified the Petri net's construction and gave a clear flow chart for scheduling. Hence, the auxiliary resource allocation could be easily carried out according to the schedule, which was proposed by heuristic search algorithm. At last, the efficacy of the Petri net model for online scheduling in a resource constrained environment was discussed.
