Research on Flexible Job Shop Scheduling Based on Improved Two-Layer Optimization Algorithm

To improve the productivity,the resource utilization and reduce the production cost of flexible job shops,this paper designs an improved two-layer optimization algorithm for the dual-resource scheduling optimization problem of flexible job shop considering workpiece batching.Firstly,a mathematical model is established to minimize the maximum completion time.Secondly,an improved two-layer optimization algorithm is designed:the outer layer algorithm uses an improved PSO(Particle Swarm Optimization)to solve the workpiece batching problem,and the inner layer algorithm uses an improved GA(Genetic Algorithm)to solve the dual-resource scheduling problem.Then,a rescheduling method is designed to solve the task disturbance problem,represented by machine failures,occurring in the workshop production process.Finally,the superiority and effectiveness of the improved two-layer optimization algorithm are verified by two typical cases.The case results show that the improved two-layer optimization algorithm increases the average productivity by 7.44% compared to the ordinary two-layer optimization algorithm.By setting the different numbers of AGVs(Automated Guided Vehicles)and analyzing the impact on the production cycle of the whole order,this paper uses two indicators,the maximum completion time decreasing rate and the average AGV load time,to obtain the optimal number of AGVs,which saves the cost of production while ensuring the production efficiency.This research combines the solved problem with the real production process,which improves the productivity and reduces the production cost of the flexible job shop,and provides new ideas for the subsequent research.

ATwo-LayerOptimal Scheduling Strategy forRural Microgrids Accounting for Flexible Loads

In the context of China’s“double carbon”goals and rural revitalization strategy,the energy transition promotes the large-scale integration of distributed renewable energy into rural power grids.Considering the operational characteristics of rural microgrids and their impact on users,this paper establishes a two-layer scheduling model incorporating flexible loads.The upper-layer aims to minimize the comprehensive operating cost of the rural microgrid,while the lower-layer aims to minimize the total electricity cost for rural users.An Improved Adaptive Genetic Algorithm(IAGA)is proposed to solve the model.Results show that the two-layer scheduling model with flexible loads can effectively smooth load fluctuations,enhance microgrid stability,increase clean energy consumption,and balance microgrid operating costs with user benefits.

MCWOA Scheduler:Modified Chimp-Whale Optimization Algorithm for Task Scheduling in Cloud Computing

Cloud computing provides a diverse and adaptable resource pool over the internet,allowing users to tap into various resources as needed.It has been seen as a robust solution to relevant challenges.A significant delay can hamper the performance of IoT-enabled cloud platforms.However,efficient task scheduling can lower the cloud infrastructure’s energy consumption,thus maximizing the service provider’s revenue by decreasing user job processing times.The proposed Modified Chimp-Whale Optimization Algorithm called Modified Chimp-Whale Optimization Algorithm(MCWOA),combines elements of the Chimp Optimization Algorithm(COA)and the Whale Optimization Algorithm(WOA).To enhance MCWOA’s identification precision,the Sobol sequence is used in the population initialization phase,ensuring an even distribution of the population across the solution space.Moreover,the traditional MCWOA’s local search capabilities are augmented by incorporating the whale optimization algorithm’s bubble-net hunting and random search mechanisms into MCWOA’s position-updating process.This study demonstrates the effectiveness of the proposed approach using a two-story rigid frame and a simply supported beam model.Simulated outcomes reveal that the new method outperforms the original MCWOA,especially in multi-damage detection scenarios.MCWOA excels in avoiding false positives and enhancing computational speed,making it an optimal choice for structural damage detection.The efficiency of the proposed MCWOA is assessed against metrics such as energy usage,computational expense,task duration,and delay.The simulated data indicates that the new MCWOA outpaces other methods across all metrics.The study also references the Whale Optimization Algorithm(WOA),Chimp Algorithm(CA),Ant Lion Optimizer(ALO),Genetic Algorithm(GA)and Grey Wolf Optimizer(GWO).

A Two-Layer Encoding Learning Swarm Optimizer Based on Frequent Itemsets for Sparse Large-Scale Multi-Objective Optimization

Traditional large-scale multi-objective optimization algorithms(LSMOEAs)encounter difficulties when dealing with sparse large-scale multi-objective optimization problems(SLM-OPs)where most decision variables are zero.As a result,many algorithms use a two-layer encoding approach to optimize binary variable Mask and real variable Dec separately.Nevertheless,existing optimizers often focus on locating non-zero variable posi-tions to optimize the binary variables Mask.However,approxi-mating the sparse distribution of real Pareto optimal solutions does not necessarily mean that the objective function is optimized.In data mining,it is common to mine frequent itemsets appear-ing together in a dataset to reveal the correlation between data.Inspired by this,we propose a novel two-layer encoding learning swarm optimizer based on frequent itemsets(TELSO)to address these SLMOPs.TELSO mined the frequent terms of multiple particles with better target values to find mask combinations that can obtain better objective values for fast convergence.Experi-mental results on five real-world problems and eight benchmark sets demonstrate that TELSO outperforms existing state-of-the-art sparse large-scale multi-objective evolutionary algorithms(SLMOEAs)in terms of performance and convergence speed.

Data-driven Wasserstein distributionally robust chance-constrained optimization for crude oil scheduling under uncertainty

Crude oil scheduling optimization is an effective method to enhance the economic benefits of oil refining.But uncertainties,including uncertain demands of crude distillation units(CDUs),might make the production plans made by the traditional deterministic optimization models infeasible.A data-driven Wasserstein distributionally robust chance-constrained(WDRCC)optimization approach is proposed in this paper to deal with demand uncertainty in crude oil scheduling.First,a new deterministic crude oil scheduling optimization model is developed as the basis of this approach.The Wasserstein distance is then used to build ambiguity sets from historical data to describe the possible realizations of probability distributions of uncertain demands.A cross-validation method is advanced to choose suitable radii for these ambiguity sets.The deterministic model is reformulated as a WDRCC optimization model for crude oil scheduling to guarantee the demand constraints hold with a desired high probability even in the worst situation in ambiguity sets.The proposed WDRCC model is transferred into an equivalent conditional value-at-risk representation and further derived as a mixed-integer nonlinear programming counterpart.Industrial case studies from a real-world refinery are conducted to show the effectiveness of the proposed method.Out-of-sample tests demonstrate that the solution of the WDRCC model is more robust than those of the deterministic model and the chance-constrained model.

Energy-Saving Distributed Flexible Job Shop Scheduling Optimization with Dual Resource Constraints Based on Integrated Q-Learning Multi-Objective Grey Wolf Optimizer

The distributed flexible job shop scheduling problem(DFJSP)has attracted great attention with the growth of the global manufacturing industry.General DFJSP research only considers machine constraints and ignores worker constraints.As one critical factor of production,effective utilization of worker resources can increase productivity.Meanwhile,energy consumption is a growing concern due to the increasingly serious environmental issues.Therefore,the distributed flexible job shop scheduling problem with dual resource constraints(DFJSP-DRC)for minimizing makespan and total energy consumption is studied in this paper.To solve the problem,we present a multi-objective mathematical model for DFJSP-DRC and propose a Q-learning-based multi-objective grey wolf optimizer(Q-MOGWO).In Q-MOGWO,high-quality initial solutions are generated by a hybrid initialization strategy,and an improved active decoding strategy is designed to obtain the scheduling schemes.To further enhance the local search capability and expand the solution space,two wolf predation strategies and three critical factory neighborhood structures based on Q-learning are proposed.These strategies and structures enable Q-MOGWO to explore the solution space more efficiently and thus find better Pareto solutions.The effectiveness of Q-MOGWO in addressing DFJSP-DRC is verified through comparison with four algorithms using 45 instances.The results reveal that Q-MOGWO outperforms comparison algorithms in terms of solution quality.

An Elite-Class Teaching-Learning-Based Optimization for Reentrant Hybrid Flow Shop Scheduling with Bottleneck Stage

Bottleneck stage and reentrance often exist in real-life manufacturing processes;however,the previous research rarely addresses these two processing conditions in a scheduling problem.In this study,a reentrant hybrid flow shop scheduling problem(RHFSP)with a bottleneck stage is considered,and an elite-class teaching-learning-based optimization(ETLBO)algorithm is proposed to minimize maximum completion time.To produce high-quality solutions,teachers are divided into formal ones and substitute ones,and multiple classes are formed.The teacher phase is composed of teacher competition and teacher teaching.The learner phase is replaced with a reinforcement search of the elite class.Adaptive adjustment on teachers and classes is established based on class quality,which is determined by the number of elite solutions in class.Numerous experimental results demonstrate the effectiveness of new strategies,and ETLBO has a significant advantage in solving the considered RHFSP.

Distributed Robust Scheduling Optimization ofWind-Thermal-Storage System Based on Hybrid Carbon Trading andWasserstein Fuzzy Set

A robust scheduling optimization method for wind–fire storage system distribution based on the mixed carbon trading mechanism is proposed to improve the rationality of carbon emission quota allocation while reducing the instability of large-scale wind power access systems.A hybrid carbon trading mechanism that combines shortterm and long-term carbon trading is constructed,and a fuzzy set based onWasserstein measurement is proposed to address the uncertainty of wind power access.Moreover,a robust scheduling optimization method for wind–fire storage systems is formed.Results of the multi scenario comparative analysis of practical cases show that the proposed method can deal with the uncertainty of large-scale wind power access and can effectively reduce operating costs and carbon emissions.

An Improved Harris Hawk Optimization Algorithm for Flexible Job Shop Scheduling Problem

Flexible job shop scheduling problem(FJSP)is the core decision-making problem of intelligent manufacturing production management.The Harris hawk optimization(HHO)algorithm,as a typical metaheuristic algorithm,has been widely employed to solve scheduling problems.However,HHO suffers from premature convergence when solving NP-hard problems.Therefore,this paper proposes an improved HHO algorithm(GNHHO)to solve the FJSP.GNHHO introduces an elitism strategy,a chaotic mechanism,a nonlinear escaping energy update strategy,and a Gaussian random walk strategy to prevent premature convergence.A flexible job shop scheduling model is constructed,and the static and dynamic FJSP is investigated to minimize the makespan.This paper chooses a two-segment encoding mode based on the job and the machine of the FJSP.To verify the effectiveness of GNHHO,this study tests it in 23 benchmark functions,10 standard job shop scheduling problems(JSPs),and 5 standard FJSPs.Besides,this study collects data from an agricultural company and uses the GNHHO algorithm to optimize the company’s FJSP.The optimized scheduling scheme demonstrates significant improvements in makespan,with an advancement of 28.16%for static scheduling and 35.63%for dynamic scheduling.Moreover,it achieves an average increase of 21.50%in the on-time order delivery rate.The results demonstrate that the performance of the GNHHO algorithm in solving FJSP is superior to some existing algorithms.

Optimal Scheduling Strategy of Source-Load-Storage Based onWind Power Absorption Benefit

In recent years,the proportion of installed wind power in the three north regions where wind power bases are concentrated is increasing,but the peak regulation capacity of the power grid in the three north regions of China is limited,resulting in insufficient local wind power consumption capacity.Therefore,this paper proposes a two-layer optimal scheduling strategy based on wind power consumption benefits to improve the power grid’s wind power consumption capacity.The objective of the uppermodel is tominimize the peak-valley difference of the systemload,which ismainly to optimize the system load by using the demand response resources,and to reduce the peak-valley difference of the system load to improve the peak load regulation capacity of the grid.The lower scheduling model is aimed at maximizing the system operation benefit,and the scheduling model is selected based on the rolling schedulingmethod.The load-side schedulingmodel needs to reallocate the absorbed wind power according to the response speed,absorption benefit,and curtailment penalty cost of the two DR dispatching resources.Finally,the measured data of a power grid are simulated by MATLAB,and the results show that:the proposed strategy can improve the power grid’s wind power consumption capacity and get a large wind power consumption benefit.

Enhanced Hybrid Equilibrium Strategy in Fog-Cloud Computing Networks with Optimal Task Scheduling

More devices in the Intelligent Internet of Things(AIoT)result in an increased number of tasks that require low latency and real-time responsiveness,leading to an increased demand for computational resources.Cloud computing’s low-latency performance issues in AIoT scenarios have led researchers to explore fog computing as a complementary extension.However,the effective allocation of resources for task execution within fog environments,characterized by limitations and heterogeneity in computational resources,remains a formidable challenge.To tackle this challenge,in this study,we integrate fog computing and cloud computing.We begin by establishing a fog-cloud environment framework,followed by the formulation of a mathematical model for task scheduling.Lastly,we introduce an enhanced hybrid Equilibrium Optimizer(EHEO)tailored for AIoT task scheduling.The overarching objective is to decrease both the makespan and energy consumption of the fog-cloud system while accounting for task deadlines.The proposed EHEO method undergoes a thorough evaluation against multiple benchmark algorithms,encompassing metrics likemakespan,total energy consumption,success rate,and average waiting time.Comprehensive experimental results unequivocally demonstrate the superior performance of EHEO across all assessed metrics.Notably,in the most favorable conditions,EHEO significantly diminishes both the makespan and energy consumption by approximately 50%and 35.5%,respectively,compared to the secondbest performing approach,which affirms its efficacy in advancing the efficiency of AIoT task scheduling within fog-cloud networks.

Two-Stage Optimal Scheduling of Community Integrated Energy System

From the perspective of a community energy operator,a two-stage optimal scheduling model of a community integrated energy system is proposed by integrating information on controllable loads.The day-ahead scheduling analyzes whether various controllable loads participate in the optimization and investigates the impact of their responses on the operating economy of the community integrated energy system(IES)before and after;the intra-day scheduling proposes a two-stage rolling optimization model based on the day-ahead scheduling scheme,taking into account the fluctuation of wind turbine output and load within a short period of time and according to the different response rates of heat and cooling power,and solves the adjusted output of each controllable device.The simulation results show that the optimal scheduling of controllable loads effectively reduces the comprehensive operating costs of community IES;the two-stage optimal scheduling model can meet the energy demand of customers while effectively and timely suppressing the random fluctuations on both sides of the source and load during the intra-day stage,realizing the economic and smooth operation of IES.

Multi-Time Scale Optimal Scheduling of a Photovoltaic Energy Storage Building System Based on Model Predictive Control

Building emission reduction is an important way to achieve China’s carbon peaking and carbon neutrality goals.Aiming at the problem of low carbon economic operation of a photovoltaic energy storage building system,a multi-time scale optimal scheduling strategy based on model predictive control(MPC)is proposed under the consideration of load optimization.First,load optimization is achieved by controlling the charging time of electric vehicles as well as adjusting the air conditioning operation temperature,and the photovoltaic energy storage building system model is constructed to propose a day-ahead scheduling strategy with the lowest daily operation cost.Second,considering inter-day to intra-day source-load prediction error,an intraday rolling optimal scheduling strategy based on MPC is proposed that dynamically corrects the day-ahead dispatch results to stabilize system power fluctuations and promote photovoltaic consumption.Finally,taking an office building on a summer work day as an example,the effectiveness of the proposed scheduling strategy is verified.The results of the example show that the strategy reduces the total operating cost of the photovoltaic energy storage building system by 17.11%,improves the carbon emission reduction by 7.99%,and the photovoltaic consumption rate reaches 98.57%,improving the system’s low-carbon and economic performance.

Optimized scheduling of integrated energy systems for low carbon economy considering carbon transaction costs

With the introduction of the“dual carbon”goal and the continuous promotion of low-carbon development,the integrated energy system(IES)has gradually become an effective way to save energy and reduce emissions.This study proposes a low-carbon economic optimization scheduling model for an IES that considers carbon trading costs.With the goal of minimizing the total operating cost of the IES and considering the transferable and curtailable characteristics of the electric and thermal flexible loads,an optimal scheduling model of the IES that considers the cost of carbon trading and flexible loads on the user side was established.The role of flexible loads in improving the economy of an energy system was investigated using examples,and the rationality and effectiveness of the study were verified through a comparative analysis of different scenarios.The results showed that the total cost of the system in different scenarios was reduced by 18.04%,9.1%,3.35%,and 7.03%,respectively,whereas the total carbon emissions of the system were reduced by 65.28%,20.63%,3.85%,and 18.03%,respectively,when the carbon trading cost and demand-side flexible electric and thermal load responses were considered simultaneously.Flexible electrical and thermal loads did not have the same impact on the system performance.In the analyzed case,the total cost and carbon emissions of the system when only the flexible electrical load response was considered were lower than those when only the flexible thermal load response was taken into account.Photovoltaics have an excess of carbon trading credits and can profit from selling them,whereas other devices have an excess of carbon trading and need to buy carbon credits.

Three-Level Optimal Scheduling and Power Allocation Strategy for Power System ContainingWind-Storage Combined Unit

To mitigate the impact of wind power volatility on power system scheduling,this paper adopts the wind-storage combined unit to improve the dispatchability of wind energy.And a three-level optimal scheduling and power allocation strategy is proposed for the system containing the wind-storage combined unit.The strategy takes smoothing power output as themain objectives.The first level is the wind-storage joint scheduling,and the second and third levels carry out the unit combination optimization of thermal power and the power allocation of wind power cluster(WPC),respectively,according to the scheduling power of WPC and ESS obtained from the first level.This can ensure the stability,economy and environmental friendliness of the whole power system.Based on the roles of peak shaving-valley filling and fluctuation smoothing of the energy storage system(ESS),this paper decides the charging and discharging intervals of ESS,so that the energy storage and wind power output can be further coordinated.Considering the prediction error and the output uncertainty of wind power,the planned scheduling output of wind farms(WFs)is first optimized on a long timescale,and then the rolling correction optimization of the scheduling output of WFs is carried out on a short timescale.Finally,the effectiveness of the proposed optimal scheduling and power allocation strategy is verified through case analysis.

Source-Load Coordinated Optimal Scheduling Considering the High Energy Load of Electrofused Magnesium and Wind Power Uncertainty

In fossil energy pollution is serious and the“double carbon”goal is being promoted,as a symbol of fresh energy in the electrical system,solar and wind power have an increasing installed capacity,only conventional units obviously can not solve the new energy as the main body of the scheduling problem.To enhance the systemscheduling ability,based on the participation of thermal power units,incorporate the high energy-carrying load of electro-melting magnesiuminto the regulation object,and consider the effects on the wind unpredictability of the power.Firstly,the operating characteristics of high energy load and wind power are analyzed,and the principle of the participation of electrofusedmagnesiumhigh energy-carrying loads in the elimination of obstructedwind power is studied.Second,a two-layer optimization model is suggested,with the objective function being the largest amount of wind power consumed and the lowest possible cost of system operation.In the upper model,the high energy-carrying load regulates the blocked wind power,and in the lower model,the second-order cone approximation algorithm is used to solve the optimizationmodelwithwind power uncertainty,so that a two-layer optimizationmodel that takes into account the regulation of the high energy-carrying load of the electrofused magnesium and the uncertainty of the wind power is established.Finally,the model is solved using Gurobi,and the results of the simulation demonstrate that the suggested model may successfully lower wind abandonment,lower system operation costs,increase the accuracy of day-ahead scheduling,and lower the final product error of the thermal electricity unit.

Hybrid ant colony optimization for the resource-constrained project scheduling problem

To solve the resource-constrained project scheduling problem （RCPSP）, a hybrid ant colony optimization （HACO） approach is presented. To improve the quality of the schedules, the HACO is incorporated with an extended double justification in which the activity splitting is applied to predict whether the schedule could be improved. The HACO is tested on the set of large benchmark problems from the project scheduling problem library （PSPLIB）. The computational result shows that the proposed algo- rithm can improve the quality of the schedules efficiently.

Joint optimization scheduling for water conservancy projects incomplex river networks

In this study, we simulated water flow in a water conservancy project consisting of various hydraulic structures, such as sluices, pumping stations, hydropower stations, ship locks, and culverts, and developed a multi-period and multi-variable joint optimization scheduling model for flood control, drainage, and irrigation. In this model, the number of sluice holes, pump units, and hydropower station units to be opened were used as decision variables, and different optimization objectives and constraints were considered. This model was solved with improved genetic algorithms and verified using the Huaian Water Conservancy Project as an example. The results show that the use of the joint optimization scheduling led to a 10% increase in the power generation capacity and a 15% reduction in the total energy consumption. The change in the water level was reduced by 0.25 m upstream of the Yundong Sluice, and by 50% downstream of pumping stations No. 1, No. 2, and No. 4. It is clear that the joint optimization scheduling proposed in this study can effectively improve power generation capacity of the project, minimize operating costs and energy consumption, and enable more stable operation of various hydraulic structures. The results may provide references for the management of water conservancy projects in complex river networks.

Blending Scheduling under Uncertainty Based on Particle Swarm Optimization Algorithm

Blending is an important unit operation in process industry. Blending scheduling is nonlinear optimiza- tion problem with constraints. It is difficult to obtain optimum solution by other general optimization methods. Particle swarm optimization (PSO) algorithm is developed for nonlinear optimization problems with both contin- uous and discrete variables. In order to obtain a global optimum solution quickly, PSO algorithm is applied to solve the problem of blending scheduling under uncertainty. The calculation results based on an example of gasoline blending agree satisfactory with the ideal values, which illustrates that the PSO algorithm is valid and effective in solving the blending scheduling problem.

APPLYING PARTICLE SWARM OPTIMIZATION TO JOB-SHOPSCHEDULING PROBLEM

A new heuristic algorithm is proposed for the problem of finding the minimummakespan in the job-shop scheduling problem. The new algorithm is based on the principles ofparticle swarm optimization (PSO). PSO employs a collaborative population-based search, which isinspired by the social behavior of bird flocking. It combines local search (by self experience) andglobal search (by neighboring experience), possessing high search efficiency. Simulated annealing(SA) employs certain probability to avoid becoming trapped in a local optimum and the search processcan be controlled by the cooling schedule. By reasonably combining these two different searchalgorithms, a general, fast and easily implemented hybrid optimization algorithm, named HPSO, isdeveloped. The effectiveness and efficiency of the proposed PSO-based algorithm are demonstrated byapplying it to some benchmark job-shop scheduling problems and comparing results with otheralgorithms in literature. Comparing results indicate that PSO-based algorithm is a viable andeffective approach for the job-shop scheduling problem.