Stochastic Scheduling Research Articles

Real-time multi-energy demand response for high-renewable buildings

Proactive demand response is a cost-effective approach to enhance energy flexibility of high-renewable urban energy systems. This paper proposes a two-stage real-time multi-energy demand response framework for a high-renewable building microgrid. In the first stage, a rolling horizon-based on-line scheduling model is formulated to economically optimize the building multi-energy converters and storages via a novel transactive pricing mechanism. In the second stage, the schedulable multi-energy flexibility for response devices is defined and evaluated via comprehensive information. After obtaining the stochastic optimal economical scheduling results in the first stage, the second stage performs a rule-based faster-time scale multi-energy allocation to offset the real-time mismatch energy due to supply–demand uncertainties. Case studies over a building microgrid are performed to validate the effective and superior performances of the proposed method on improvements of multi-energy economy and flexibility. Simulations results show that the system operating cost can be reduced by at most 36.9% with a higher operational flexibility.

Optimal operation and stochastic scheduling of renewable energy of a microgrid with optimal sizing of battery energy storage considering cost reduction

In order to alleviate worldwide worries about environmental issues, power system operators and planning entities are looking for new energy sources that will produce fewer emissions than conventional fossil-fuel power plants. When it comes to powering their systems, utilities are increasingly choosing renewable energy sources (RESs). Here, microgrids (MG) would furnish the ideal conditions for incorporating RESs. Thus, this study presents an seasonal optimization framework for the short-term operation of an MG, including energy storage and solar photovoltaic (PV) systems, while thoroughly exploring the effects of varying climatic factors on the optimal scheduling of resources. The day-ahead MG scheduling is addressed in this model, taking into account the impact of varying irradiances across a year. The resulting single-objective optimization problem is then tackled with the help of the converged barnacles mating optimizer (CBMO), as a robust and effective optimization method. The simulation findings show that the total operating cost of the grid-integrated microgrid is alleviated when a PV model is used in a real-world setting to raise the accuracy of the energy management system. In case 1, the CBMO reduces the operating cost of the MG by 262.784 €ct/day, which is less than the results obtained by some other algorithms. Using the hybrid CBMO, the reported costs for Case 2 is 298.8513 €ct/day. The CBMO approach yielded the best results of 352.1964 €ct on a warm sunny day, 285.2851 €ct on a cold sunny day, 257.7912 €ct on a warm cloudy day, and 252.135 €ct on a cold cloudy day. After running the simulations, it has been found out that the suggested CBMO has the shortest mean simulation time by 114.217 s in Case 3, while other algorithms need longer simulation time such that the GA needs 120.364 s, the PSO needs 118.487 s, the DE needs 118.039 s and the ICA needs 116.287 s. Therefore, the CBMO takes significantly less time than other methods.

Surrogate “Level-Based” Lagrangian Relaxation for mixed-integer linear programming

Mixed-Integer Linear Programming (MILP) plays an important role across a range of scientific disciplines and within areas of strategic importance to society. The MILP problems, however, suffer from combinatorial complexity. Because of integer decision variables, as the problem size increases, the number of possible solutions increases super-linearly thereby leading to a drastic increase in the computational effort. To efficiently solve MILP problems, a “price-based” decomposition and coordination approach is developed to exploit 1. the super-linear reduction of complexity upon the decomposition and 2. the geometric convergence potential inherent to Polyak’s stepsizing formula for the fastest coordination possible to obtain near-optimal solutions in a computationally efficient manner. Unlike all previous methods to set stepsizes heuristically by adjusting hyperparameters, the key novel way to obtain stepsizes is purely decision-based: a novel “auxiliary” constraint satisfaction problem is solved, from which the appropriate stepsizes are inferred. Testing results for large-scale Generalized Assignment Problems demonstrate that for the majority of instances, certifiably optimal solutions are obtained. For stochastic job-shop scheduling as well as for pharmaceutical scheduling, computational results demonstrate the two orders of magnitude speedup as compared to Branch-and-Cut. The new method has a major impact on the efficient resolution of complex Mixed-Integer Programming problems arising within a variety of scientific fields.

An improved greedy algorithm for stochastic online scheduling on unrelated machines

Most practical scheduling applications involve some uncertainty about the arriving times and lengths of the jobs. Stochastic online scheduling is a well-established model capturing this. Here the arrivals occur online, while the processing times are random. For this model, Gupta, Moseley, Uetz, and Xie recently devised an efficient policy for non-preemptive scheduling on unrelated machines with the objective to minimize the expected total weighted completion time. We improve upon this policy by adroitly combining greedy job assignment with αj-point scheduling on each machine. In this way we obtain a (3+5)(2+Δ)-competitive deterministic and an (8+4Δ)-competitive randomized stochastic online scheduling policy, where Δ is an upper bound on the squared coefficients of variation of the processing times. We also give constant performance guarantees for these policies within the class of all fixed-assignment policies. The αj-point scheduling on a single machine can be enhanced when the upper bound Δ is known a priori or the processing times are known to be δ-NBUE for some δ≥1. This implies improved competitive ratios for unrelated machines but may also be of independent interest.

Simulation of Job Sequencing for Stochastic Scheduling with a Genetic Algorithm

Sequencing is done to determine the order in which the jobs are to be processed. Extensive research has been carried out with an aim to tackle real-world scheduling problems. In industries, experimentation is performed before an ultimate choice is made to know the optimal priority sequencing rule. Therefore, an extensive approach to selecting the correct choice is necessary for the management decision-making perspective. In this research, the genetic algorithm (GA) and working of a simulation environment are explained, in which a scheduling operator, under any given circumstances, can obtain the appropriate sequence for job scheduling in a shop. The paper also explains the stochastic based linguistic, scenarios and probabilistic approaches to solve sequencing problem. The simulation environment allows the operator to select the tardiness and non-tardiness related performance measures. The simulator takes input values such as number of jobs, processing time and due date and discovers a near-optimal sequence for scheduling of jobs that minimizes the performance measures selected by the operator as per requirement. The case study considered is solved using scenarios based stochastic scheduling approach and results are shown. The results are compared with the classical method used in the company and observed that the proposed approach gives a better result.

Stochastic single machine scheduling with time-dependent deterioration or position-dependent learning effect

Stochastic single machine scheduling with time-dependent deterioration or position-dependent learning effect

STOCHOS: Stochastic opportunistic maintenance scheduling for offshore wind farms

Despite the promising outlook, the numerous economic and environmental benefits of offshore wind energy are still compromised by its high Operations and Maintenance (O&M) expenditures. On one hand, offshore-specific challenges such as site remoteness, harsh weather, transportation requirements, and production losses, significantly inflate the O&M costs relative to land-based wind farms. On the other hand, the uncertainties in weather conditions, asset degradation, and electricity prices largely constrain the farm operator’s ability to identify the time windows at which maintenance is possible, let alone optimal. In response, we propose STOCHOS, short for the stochastic holistic opportunistic scheduler—a maintenance scheduling approach tailored to address the unique challenges and uncertainties in offshore wind farms. Given probabilistic forecasts of key environmental and operational parameters, STOCHOS optimally schedules the offshore maintenance tasks by harnessing the opportunities that arise due to favorable weather conditions, on-site maintenance resources, and maximal operating revenues. STOCHOS is formulated as a two-stage stochastic mixed-integer linear program, which we solve using a scenario-based rolling horizon algorithm that aligns with the industrial practice. Tested on real-world data from the U.S. North Atlantic where several offshore wind farms are in-development, STOCHOS demonstrates considerable improvements relative to prevalent maintenance benchmarks, across various O&M metrics, including total cost, downtime, resource utilization, and maintenance interruptions.

A stochastic optimal scheduling of distributed energy resources with electric vehicles based on microgrid considering electricity price

With the expanding demand for electrical energy across the world and the growing concern about environmental matters resulting from the widespread use of fossil fuels in the power system, it is necessary to find suitable alternatives to resolve the problem. In this regard, Renewable Energy Sources (RES) that produce almost no pollution have become the preferred means of supplying the global energy demand. In this paper, a novel approach is proposed for formulating the problem and reducing reliability costs to achieve the minimum total cost of the grid. Concurrently, the transportation system has been replacing conventional vehicles with Electric Vehicles (EVs), where Plug-in Electric Vehicles (PEVs) and Plug-in Hybrid Electric Vehicles (PHEVs) have got the public's attention. Thanks to the Grid-to-Vehicle (G2V) and Vehicle-to-Grid (V2G) technologies, it is technically possible and economically justified to plug in such vehicles to receive/inject power from/to the grid. Alternatively, an emerging concept in electric power systems, i.e. Microgrid (MG), was developed and employed to level up the RESs’ penetration rate and maximize the capabilities of EVs using the smart infrastructure. Indeed, the V2G option is utilized for mitigating operating costs in order to host PEVs in the network. Therefore, optimally scheduling the MG would be of utmost importance. Thus, an efficient day-ahead stochastic operation framework has been developed in this research work for an MG equipped with renewable energy-powered Distributed Generation (DG) units and EVs. The mentioned stochastic programming framework is based on the Unscented Transform (UT). It is worth mentioning that the problem has been formulated as a stochastic programming problem with the objective of optimizing the total operating cost. The studied problem is then tackled using a biomimicry well-known approach called the “Converged Barnacles Mating Optimizer (CBMO) algorithm” and the results derived from simulating the problem would be compared to the ones achieved by some prominent algorithms.

Forecast-Driven Stochastic Scheduling of a Virtual Power Plant in Energy and Reserve Markets

Virtual power plants (VPPs) offer a cost-effective solution to incentivize coordination between different resources participating in joint energy and reserve markets. However, emerging technologies such as storage and demand response cannot deliver flexibility over long periods due to inherent energy limitations. In this article, we, therefore, inform the day-ahead scheduling of VPPs with forecast scenarios of the balancing stage, which are complemented with information on nonshiftable load, renewable generation, and electricity prices. These multivariate scenarios (incorporating both time and cross-variable dependencies) are obtained using a machine learning framework in which probabilistic forecasts are converted into time trajectories using a copula-based sampling. The model is enriched with a detailed representation of the intraday decision stage wherein all flexible resources are dynamically allocated over the daily horizon. To ensure the reliability of the solution, we take into full consideration the revenues and unit-specific costs related to the activation of reserves. Outcomes show that improving the representation of the intraday dispatch stage while relying on representative balancing uncertainties are two complementary components for increasing the quality of the VPP day-ahead strategy, which ultimately fosters its economic value.

Simulation-based assessment on stochastic load scheduling for building cooling systems

To fill knowledge gaps related to stochastic load scheduling, we performed a comprehensive evaluation of the stochastic load scheduling for building cooling systems. Specifically, we studied the common uncertain variables in the load scheduling process for building cooling systems and categorized those variables based on their dynamic patterns. We then developed a generic stochastic load scheduling framework and applied it to building cooling systems that served a simulated community. This community consists of 100 heterogeneous houses and serves as a virtual testbed for evaluating the performance of stochastic load scheduling. In this evaluation, we considered representatives of uncertain variables with different dynamic patterns and included 100 realizations of the considered uncertainty in the evaluation to better catch the probability distribution of the control performance. The evaluation results suggest that deterministic load scheduling can reduce the operating energy cost by 18% but its performance can be affected by uncertainty. Stochastic load scheduling can further decrease the operating energy cost under uncertainty compared to deterministic load scheduling. We also found that the effectiveness of stochastic load scheduling in handling uncertainty is not directly associated with the number of uncertainty scenarios that are considered in its formulation.

Co-design of scheduling protocol and fuzzy sliding mode controller under communication constraints

This paper investigates the co-design of scheduling protocol and sliding mode controller for interval type-2 T–S fuzzy systems under communication constraints. To reduce the transmission burden and relieve the data congestion, a stochastic scheduling protocol is established via Markov chain to determine the transmission of system state, under which only one sensor node is permitted to transmit the state signal at each instant. Different from the existing results, the key feature of the proposed protocol is that the transition probability matrix of Markov chain is co-designed with the controller, rather than given a priori. Moreover, the scheduling signal (also called token) reflecting the selected node is integrated to design a token-dependent sliding mode controller, where controller’s membership functions are constructed based on the available state. By establishing the relation between the membership functions in fuzzy system and the ones in controller, sufficient conditions are obtained to attain the stochastic stability of the closed-loop system and the reachability of the sliding domain. Moreover, an iterative optimization algorithm is proposed to search token-dependent parameters and sliding matrix with the objective of reducing the sliding domain. Finally, the effectiveness of the co-design control scheme is verified via simulation examples.

Hybrid Harmony Search for Stochastic Scheduling of Chemotherapy Outpatient Appointments

This research deals with the same-day chemotherapy outpatient scheduling problem that is recognized as a leading strategy to pursue the objective of reducing patient waiting time. Inspired by a real-world context and different from the other studies, we modeled a multi-stage chemotherapy ward in which the pharmacy is located away from the treatment area and drugs are delivered in batches. Processes in oncology wards are characterized by several sources of uncertainty that increase the complexity of the problem; thus, a stochastic approach was preferred to study the outpatient scheduling problem. To generate effective appointment schedules, we moved in two directions. First, we adopted a late-start scheduling strategy to reduce the idle times within and among the different stages, namely medical consultation, drug preparation and infusion. Then, since the problem is NP-hard in the strong sense, we developed a hybrid harmony search metaheuristic whose effectiveness was proved through an extended numerical analysis involving another optimization technique from the relevant literature. The outcomes from the numerical experiments confirmed the efficacy of the proposed scheduling model and the hybrid metaheuristic algorithm as well.

A simulated annealing based stochastic long-term production scheduling of open-pit mines with stockpiling under grade uncertainty

ABSTRACT This research presents a new Simulated Annealing based stochastic optimisation algorithm to integrate geological uncertainty into the optimization process through multiple equiprobable simulated realisations of an orebody while considering stockpiling options and other relevant constraints. The stockpiling option is included, increasing the chances of processing high-grade and most certain ore blocks in early periods. The efficiency of the proposed algorithm in creating a single good enough production schedule that minimises the risk of deviation from production targets while maximising the net present value of the operation is demonstrated through three case studies, i.e. case A with 2448 blocks, B with 6,578 and C with 10,810 blocks. The comparison of results with the two-stage stochastic model reveals that the proposed methodology reduces the risk of production deviation to a minimal and provides a near-optimal solution with an optimality gap of 3.53, −0.87, and 8.19% for cases A, B, and C within a reasonable amount of time.

Integrating geometallurgical ball mill throughput predictions into short-term stochastic production scheduling in mining complexes

This article presents a novel approach to integrate a throughput prediction model for the ball mill into short-term stochastic production scheduling in mining complexes. The datasets for the throughput prediction model include penetration rates from blast hole drilling (measurement while drilling), geological domains, material types, rock density, and throughput rates of the operating mill, offering an accessible and cost-effective method compared to other geometallurgical programs. First, the comminution behavior of the orebody was geostatistically simulated by building additive hardness proportions from penetration rates. A regression model was constructed to predict throughput rates as a function of blended rock properties, which are informed by a material tracking approach in the mining complex. Finally, the throughput prediction model was integrated into a stochastic optimization model for short-term production scheduling. This way, common shortfalls of existing geometallurgical throughput prediction models, that typically ignore the non-additive nature of hardness and are not designed to interact with mine production scheduling, are overcome. A case study at the Tropicana Mining Complex shows that throughput can be predicted with an error less than 30 t/h and a correlation coefficient of up to 0.8. By integrating the prediction model and new stochastic components into optimization, the production schedule achieves weekly planned production reliably because scheduled materials match with the predicted performance of the mill. Comparisons to optimization using conventional mill tonnage constraints reveal that expected production shortfalls of up to 7% per period can be mitigated this way.

Stochastic Event-Triggered Fault Detection and Isolation Based on Kalman Filter.

In this article, the robust fault detection and isolation (FDI) Kalman filter is extended based on stochastic event-triggered schedulers for discrete linear systems consisting of deterministic/stochastic unknown inputs with nonzero mean and colored measurement noise. In the proposed FDI method, first, a subspace of the main system that significantly attenuates disturbance effects is proposed. After that, the fusion method is proposed for dealing with the colored measurement-noise problem in designing the Kalman filter and preventing from leading to measurement noise with zero mean and zero covariance. The stochastic event-triggered schedulers are considered as Gaussian functions. Therefore, the Gaussian property of innovation sequence is preserved, and consequently, the recursive equation of the Kalman filter need not be extended based on approximation techniques. Finally, design parameters are chosen based on the convex optimization problem such that the lowest communication rate between the sensor node and FDI filter, and also the best FDI performance are achieved. The proposed FDI method is evaluated to detect and isolate stator interturn short circuit and broken rotor bars faults with unbalanced voltage as disturbance in three-phase induction motors.

A SVM-based implicit stochastic joint scheduling method for ‘wind-photovoltaic-cascaded hydropower stations’ systems

With the gradual expansion of the development scale of wind power and photovoltaic (PV) power plants, the multi-energy complementary power generation system, typically represented by hydro-PV/hydro-wind/hydro-wind-PV, has become an important part of modern power systems. Aiming at the joint operation of the cascaded hydropower stations after wind-PV grid connection, a medium- and long-term implicit stochastic joint dispatching function model for wind-PV-cascaded hydropower stations based on the SVM(support vector machine) method is developed in this paper, which selects the final water levels of the reservoirs as the dependent variables, and the initial water levels of the reservoirs, the reservoir inflow, the interval inflow as well as the wind and PV output are independent variables. First, the optimization of main parameters C (Penalty coefficient), g (Kernel function parameter) and p (Insensitive loss coefficient) of the model are achieved by particle swarm algorithm. The Gaussian radial basis function is then used to fit the scheduling function proposed in this paper. Finally, the rolling simulation calculation and correction of the obtained scheduling function are realized by C# programming language of VS2017 platform. The results show that the proposed scheduling function is an effective method for scheduling decision-making, and the revised water level process, output process as well as annual electricity production of the scheduling model are not significantly different from the optimal scheduling results. Moreover, the simulation results conform to the existing scheduling rules, which has shown it can be used to inform the operation of cascaded hydropower stations under the multi-energy complementary system.

Solving a stochastic hierarchical scheduling problem by VNS-based metaheuristic with locally assisted algorithms

High-end equipment manufacture has features of intensive technology, uncertain process, and large scale. Hence, the scheduling of the High-end equipment manufacture is challenging. Large ships are a type of High-end equipment that is tied to national maritime security. In this paper, we study a stochastic hierarchical scheduling problem with serial-batch processing machines and the deterioration effect in ship manufacture. In the studied problem, the job processing time is uncertain and follows a normal probability distribution. Under the deterioration effect, the actual processing time of jobs is formulated as a function of the start time. The first objective is to maximize the robustness of the manufacturing system. The second objective is to minimize the total inventory cost subjected to the optimization of the first objective. The robustness of the manufacturing system is measured by the worst level of completion probability. The total inventory cost is measured by the difference between the job delivery time and the job completion time. The mathematical model for the studied problem is formulated. Some structural properties are derived to solve the problem. Based on the properties, the optimal sequence for the first objective can be obtained and a heuristic algorithm is designed to optimize the second objective. The considered problem is NP-hard involving several non-linearities. Hence, a variable neighborhood search (VNS) algorithm is developed to solve the problem in a reasonable time, which is integrated with three local search strategies and a heuristic algorithm. Various problem instances are generated and extensive computational experiments verify that the proposed VNS algorithm outperforms other compared algorithms and has strong robustness.

Stochastic scheduling of generating units with weekly energy storage: A hybrid decomposition approach

We propose a solution method for the large-scale stochastic unit commitment (SUC) problem with weekly-dispatched energy storage and significant weather-dependent stochastic generating capacity. Weekly storage facilities that mostly charge during weekends and discharge during weekdays require a weekly scheduling of generating units, which result in a large-scale optimization problem. This SUC problem is formulated as a two-stage stochastic model and we use the conditional value-at-risk as a risk measure. Using a Benders framework, the proposed solution method decomposes the problem into a mixed-integer linear master problem and linear and continuous subproblems. The master problem corresponds to the first-stage decisions throughout the week and includes all the commitment (binary) variables and their corresponding constraints. The subproblems correspond to the actual dispatch of the generating units on a weekly basis. Based on the success of column-and-constraint generation algorithms to solve robust optimization problems, we improve the low communication between the master problem and the subproblems in the standard Benders decomposition by adding primal variables and constraints from the subproblems to the master problem, which provides a better approximation of the recourse function. Our computational experiments demonstrate the effectiveness of the proposed decomposition method using an instance of the South Carolina synthetic system with 90 generating units under 40 scenarios.

Stochastic scheduling of energy storage systems in harmonic polluted active distribution networks

Harmonics originating from non-linear loads in distribution systems will cause undesired effects and malfunctions of equipment. It is important to use efficient techniques for eliminating the voltage and current harmonic components. However, the uncertain nature of the active distribution networks (ADN) makes it difficult to apply these techniques, efficiently. Renewable energy sources (RESs), such as wind turbines (WTs) besides load fluctuations are the most important uncertainty sources. This study employs energy storage systems (ESS) to reduce total harmonic distortion (THD) as well as the ADN operating costs. In addition to the ESS, network structure reconfiguration and reactive power scheduling is presented for a more efficient operation of ADN. Also, the uncertainty of the network is modelled by the K-means and LHS methods. This methodology is conducted under a multi-objective optimization problem, which is handled by a multi-objective particle swarm optimization (MOPSO) algorithm. Furthermore, a technique for order of preference by similarity to ideal solution (TOPSIS) approach is applied to obtain the best compromise between two objectives. The efficacy of the proposed methodology is investigated in the IEEE 33 bus test system. Also, for validating the results, a large-scale network, the IEEE 118 bus test system is surveyed, too.

Learning-Based Grey Wolf Optimizer for Stochastic Flexible Job Shop Scheduling

This work considers a stochastic flexible job shop scheduling with limited extra resources and machine-dependent setup time in a semiconductor manufacturing environment, which is an NP-hard problem. In order to obtain its reliable and high-performance schedule in a reasonable time, a learning-based grey wolf optimizer is proposed. In it, an optimal computing budget allocation-based approach, which is designed for two scenarios from real manufacturing environments, is proposed to intelligently allocate computing budget and improve search efficiency. It extends the application area of optimal computing budget allocation by laying a theoretic foundation. Besides, to obtain proper control parameters iteratively, a reinforcement learning algorithm with a newly designed delay update strategy is used to build a parameter tuning scheme of a grey wolf optimizer. The scheme acts as a guide for balancing global and local search, thereby enhancing effectiveness of the proposed algorithm. The theoretic interpretation of the developed optimal computing budget allocation-based approach and the convergence analysis results of the proposed algorithm are presented. Various experiments with benchmarks and randomly generated cases are performed to compare it with several updated algorithms. The results shows its superiority over them. Note to Practitioners—Meta-heuristic are often deployed to solve semiconductor manufacturing scheduling problems. However, they face to two thorny issues when they face stochastic manufacturing environments. 1) their computational efficiency is quite low, thus requiring substantial improvement, since a stochastic optimization problem requires Monte Carlo sampling to estimate the actual objective function values in a precise manner; and 2) most of them are parameter-sensitive, and choosing their proper parameters is highly challenging in such environments. To address the first issue, we develop an optimal computing budget allocation-based method for deciding the optimal numbers of sampling times based on both prior knowledge and simulation results. To address the second one, we propose a reinforcement learning algorithm to self-adjust the parameters of our proposed method called Learning-based Grey Wolf Optimizer. In addition, we design a delay update strategy to enhance its robustness, and thus, a feasible and high-quality schedule can be founded in a short time for real-time scheduling problems. Theoretic proofs and experimental results show that the proposed method is effective and efficient. Consequently, it can be readily applicable to practical semiconductor manufacturing systems.