Optimal Scheduling Problem Research Articles

Bi-level energy management system for optimal real time operation of grid tied multi-nanogrids

• Proposing an efficient on-line EMS considering uncertainties of weather conditions, load demand and electricity price during real time. • Introducing an efficient day-ahead scheduling of interconnected nano-grids using an improved version of Aquila Optimization (IAO) algorithm. • Presenting demand side management to enhance the efficiency of the proposed EMS. • Exploiting the cooperation between the nano-grids for economic operation. Integrating distributed energy resources (DERs) utilizing renewable energy sources enhances the performance and efficiency of the power system. Nano-grid (NG) comprises a small scale DERs at a small building. This paper presents an efficient bi-level energy management system (EMS), day-ahead and real time scheduling, for economic operation of grid tied multi-interconnected NGs. Balancing between generation and consumption is secured through exchanging power with the utility grid so the daily energy consumption cost could be optimized. The proposed day-ahead scheduling is applied through two stages. The first is demand side management (DSM) while the second is determining the optimal set-points of different sources in NGs. The optimal set-points obtained from day-ahead scheduling are rescheduled and updated during real time to keep the economic operation under uncertainties of weather conditions, grid tariff and load demand. Advanced meta-heuristic techniques can handle with energy scheduling optimization problem, complex non-linear optimization problem, efficiently considering the different operation constraints. Comparative performance study of the original Aquila optimizer (AO), improved aquila optimizer (IAO), and particle swarm optimization technique (PSO) is investigated in this paper. Results obtained demonstrate that the interconnection between NGs with an IAO based bi-level EMS provides the optimal economic operation.

A Continuous-Time-Based MILP Model for Production and Transportation Scheduling in Nonpipelined Wells in Low-Permeability Oil Fields

Abstract The marginal wells in low-permeability oilfields are characterized by small storage size, scattered distribution, large regional span, low production, intermittent production, etc. The production mode of these wells is nonpipeline mode. In our previous work (Zhang et al., 2019), a novel mixed-integer linear programming (MILP) model using a discrete-time representation was presented for the operation scheduling of nonpipelined wells. However, too many discretization time points are required to ensure the accuracy of the model. Even for moderately sized problems, computationally intractable models can arise. The present paper describes a new continuous-time representation method to reformulate this schedule optimization problem. By introducing the continuous-time representation, the binary variables are largely reduced. The solution effect for different model sizes is also investigated. When the model size increases to a certain degree, a feasible solution cannot be obtained within a limited time. The results of a case study originated from a real oilfield in China show that the continuous-time model requires less time to obtain the optimal solution compared to the discrete-time model. In details, considering a same scale problem, the solution based on the continuous-time model saves 52.25% of the time comparing with the discrete-time model. The comparison validates the new model’s superiority.

Robust metro train scheduling integrated with skip-stop pattern and passenger flow control strategy under uncertain passenger demands

As the passenger demands, especially commuters, in the megacities increase dramatically, the congestion problem of metro lines becomes severe and affects passengers’ travel experience. More and more metro stations have adopted passenger flow control measures to ensure operational security or implemented skip-stop patterns to ease transportation pressure. This paper investigates the collaborative optimization problem of timetable scheduling, passenger flow control, and skip-stop pattern on a metro line. A mixed integer nonlinear programming (MINLP) model is proposed to require a performance balance between service level and operation costs. The collaborative optimization model is constructed to optimize the train timetable by determining arrival and departure times with bounded dwell time and running time at intervals. Specifically, time-dependent passenger arrival rates are regarded as uncertain parameters here. The scenario-based robust optimization (SBRO) model with nonlinear constraints is further transformed into a model with linear constraints, which can be directly solved by commercial solvers. Finally, several sets of numerical experiments according to the actual data about the Beijing Changping metro line are performed to demonstrate the validity of the proposed model and method. The optimized train timetable integrated with the skip-stop pattern and passenger flow control strategy can effectively ease the congestion of stations and improve the safety and service quality of the metro system. The tradeoff between solution robustness and model robustness is obtained with critical practical insights.

Casualty scheduling optimisation with facility disruptions under grey information in early stage of post-earthquake relief

PurposeThe purpose of this paper is to propose a new casualty scheduling optimisation problem and to effectively treat casualties in the early stage of post-earthquake relief.Design/methodology/approachDifferent from previous studies, some new characteristics of this stage are considered, such as the grey uncertainty information of casualty numbers, the injury deterioration and the facility disruption scenarios. Considering these new characteristics, we propose a novel casualty scheduling optimisation model based on grey chance-constrained programming (GCCP). The model is formulated as a 0–1 mixed-integer nonlinear programming (MINP) model. An improved particle swarm optimisation (PSO) algorithm embedded in a grey simulation technique is proposed to solve the model.FindingsA case study of the Lushan earthquake in China is given to verify the effectiveness of the model and algorithm. The results show that (1) considering the facility disruption in advance can improve the system reliability, (2) the grey simulation technology is more suitable for dealing with the grey uncertain information with a wider fluctuation than the equal-weight whitening method and (3) the authors' proposed PSO is superior to the genetic algorithm and immune algorithm.Research limitations/implicationsThe casualty scheduling problem in the emergency recovery stage of post-earthquake relief could be integrated with our study to further enhance the research value of this paper.Practical implicationsConsidering the facility disruption in advance is beneficial to treat more patients. Considering the facility disruption in the design stage of the emergency logistics network can improve the reliability of the system.Originality/value(1) The authors propose a new casualty scheduling optimisation problem based on GCCP in the early stage of post-earthquake relief. The proposed problem considers many new characteristics in this stage. To the best of the authors' knowledge, the authors are the first to use the GCCP to study the casualty scheduling problem under the grey information. (2) A MINP model is established to formulate the proposed problem. (3) An improved integer-encoded particle swarm optimisation (PSO) algorithm embedded grey simulation technique is designed in this paper.

Distributionally Robust Unit Commitment with N-k Security Criterion and Operational Flexibility of CSP

In order to reduce the conservatism of the robust optimization method and the complexity of the stochastic optimization method and to enhance the ability of power systems to deal with occasional line fault disturbance, this paper proposes a distributionally robust unit commitment (DRUC) model with concentrating solar power (CSP) operational flexibility and N-k safety criterion under distributed uncertainty. According to the limited historical sample data, under the condition of satisfying a certain confidence level, based on the imprecise Dirichlet model (IDM), an ambiguity set is constructed to describe the uncertainty of transmission line fault probability. Through the identification of the worst probability distribution in the ambiguity set, the adaptive robust optimal scheduling problem is transformed into a two-stage robust optimization decision model under the condition of deterministic probability distribution. The CSP flexibility column and constraint generation (C&CG) algorithm is used to process the model and the main problem and subproblem are solved by using the Big-M method, linearization technique, and duality principle. Then, a mixed integer linear programming problem (MILP) model is obtained, which effectively reduces the difficulty of solving the model. Finally, case studies on the IEEE 14 bus system and the IEEE 118 bus system demonstrate the efficiency of the proposed method, such as enhancing the ability of power systems to cope with occasional line fault disturbances and reducing the conservatism of the robust optimization method.

Double-Layer Q-Learning-Based Joint Decision-Making of Dual Resource-Constrained Aircraft Assembly Scheduling and Flexible Preventive Maintenance

This study investigates an integrated optimization problem of aircraft assembly scheduling and flexible preventive maintenance (PM) with decision-making (FPM/DM), in which both machine flexibility and worker flexibility are considered. A mixed integer linear programming (MILP) model targeted at minimizing the assembly cycle is first established to formulate the problem. Then, CPLEX is used for solving the exact solution of the MILP model, however, it is time-consuming and difficult to apply to complex scenarios. For the tradeoff between solution quality and computational efficiency, an improved double-layer Q-learning (QL) algorithm with PM decision-making (IDLQL/PM) is further designed. Specifically, upper-layer QL is responsible for learning a proper machine selection heuristic from the given action set to ensure the machine load balance, and lower-layer QL provides a proper action (either an operation or a PM) for the selected machine to reduce unnecessary idle time and PM. Next, some instances are generated to evaluate the performance of IDLQL/PM. In a small-sized instance compared to CPLEX, the average solution gap is 1.8%, while the model solving time is reduced by 481%. As for 16 large-sized instances, IDLQL/PM presents a clear advantage over the well-known genetic algorithm and two other QL-based approaches. In addition, three state-of-the-art maintenance strategies are selected as rivals to validate the effectiveness of FPM/DM. It is observed that the proposed FPM/DM strategy can avoid improper maintenance during aircraft final assembly and ensure higher assembly efficiency.

Algebraic Solution to Optimal Scheduling Problems Taking into Account the Scheduled Start Time of Jobs in Projects

Algebraic Solution to Optimal Scheduling Problems Taking into Account the Scheduled Start Time of Jobs in Projects

Energy saving and pollution reduction through optimal scheduling of cleaning actions in a heat exchanger network

Heat exchanger fouling may impair energy recovery in Heat Exchanger Networks (HENs), thereby increasing the energy intensity of production processes. Fouling growth on the heat-transfer surfaces of the exchangers can be monitored to mitigate its adverse effects, using measurement data that also enable scheduling exchanger cleaning when economically justified. The research builds on the authors’ previous work devoted to different measurement-aided monitoring methods of fouling thermal resistance, where the method based on the least-square approach to measurement data is the preferred one. The aim is to apply the preferred approach to and perform a case study on the optimization of scheduling of cleaning actions on heat exchangers operated in a HEN. The avoided HEN operating cost is employed as an objective function to be maximized by the optimal cleaning schedule that also has to satisfy a set of constraints related to the timing of cleaning actions. The mathematical formulation of the schedule optimization problem is simplified to make solution finding easier. The case study uses historical operation records covering three years of the real-life HEN composed of 26 shell-and-tube heat exchangers working continuously in connection with a Crude Distillation Unit. Having identified historical time characteristics of the thermal resistance of fouling in all the heat exchangers, one can retroactively determine optimal HEN cleaning schedules. The optimization results are discussed, considering their economic aspects and potential for energy saving and pollution reduction.

Multi-agent deep reinforcement learning for online request scheduling in edge cooperation networks

Edge computing as a complementary paradigm of cloud computing has gained more attention by providing mobile users with diversified services at the network edge. However, the increasingly complex mobile applications put a heavier load on edge networks. It is challenging to provide concurrency requests with high-quality service processing, especially when the edge networks are dynamically changing. To address the above issues, this paper investigates the online concurrent user requests scheduling optimization problem in edge cooperation networks. We model it as an online multi-stage decision-making problem, where requests are divided into a group of independent and logically related sub-tasks. We proposed a centralized training distributed execution based multi-agent deep reinforcement learning technique to realize the implicit cooperation scheduling decision-making policy learning among edge nodes. At the centralized training stage of the proposed mechanism, a value-decomposition-based policy learning technique is adopted to improve the long-term system performance, while at the distributed execution stage, only local environment status information is needed for each edge node to make the request scheduling decision. Extensive experiments are conducted, and simulation results demonstrate that the proposed mechanism outperforms other request scheduling mechanisms in reducing the long-term average system delay and energy consumption while improving the throughput rate of the system.

Consensus-based dispatch optimization of a microgrid considering meta-heuristic-based demand response scheduling and network packet loss characterization

The uncertainty inherent in power load forecasts represents a major factor in the mismatches between supply and demand in renewables-rich electricity networks, which consequently increases the energy bills and curtailed generation. As the transition to a power grid founded on the so-called grid-of-grids becomes more evident, the need for distributed control algorithms capable of handling computationally challenging problems in the energy sector does so as well. In this light, the consensus-based distributed algorithm has recently been shown to provide an effective platform for solving the complex energy management problem in microgrids. More specifically, in a microgrid context, the consensus-based distributed algorithm requires reliable information exchange with customers to achieve convergence. However, packet losses remain an important issue, which can potentially result in the failure of the overall system. In this setting, this paper introduces a novel method to effectively characterize such packet losses during information exchange between the customers and the microgrid operator, whilst solving the microgrid scheduling optimization problem for a multi-agent-based microgrid. More specifically, the proposed framework leverages the virulence optimization algorithm and the earth-worm optimization algorithm to optimally shift the energy consumption during peak periods to lower-priced off-peak hours. The effectiveness of the proposed method in minimizing the overall active power mismatches in the presence of packet losses has also been demonstrated based on benchmarking the results against the business-as-usual iterative scheduling algorithm. Also, the robustness of the overall meta-heuristic- and multi-agent-based method in producing optimal results is confirmed based on comparing the results obtained by several well-established meta-heuristic optimization algorithms, including the binary particle swarm optimization, the genetic algorithm, and the cuckoo search optimization.

Optimal Driving Strategies for a Fleet of Trains on Level Track with Prescribed Intermediate Signal Times and Safe Separation

We propose an analytic solution to the problem of finding optimal driving strategies that minimize total tractive energy consumption for a fleet of trains traveling on the same track in the same direction subject to clearance-time equality constraints that ensure safe separation and compress the headway timespan. We assume the track is divided into sections by a set of trackside signals at fixed positions. For each intermediate signal there is an associated signal segment consisting of the two adjacent sections. Successive trains are safely separated only if the leading train leaves the signal segment before the following train enters. Although the fleet can be safely separated by a complete set of clearance times and associated clearance-time inequality constraints the problem of finding optimal schedules with safe separation rapidly becomes intractable as the number of trains and signals increases. The main difficulty is in distinguishing between active equality constraints and inactive inequality constraints. The curse of dimensionality means it is not feasible to check every different combination of active constraints, find the optimal strategies for each train, optimize the corresponding prescribed times and calculate the cost. Nevertheless we can formulate and solve an alternative problem with active clearance-time equality constraints for successive trains defined at selected signals. We show that this problem can be formulated as an unconstrained convex optimization and propose a solution algorithm that finds the optimal schedule and the associated optimal strategies for each train. Finally we find optimal schedules for a case study using realistic parameters on a busy metropolitan line.

Energy-conscious maintenance and production scheduling for single machine systems under time-of-use tariffs

In view of the joint optimization problem of preventive maintenance and production scheduling for modern production systems under time-of-use tariffs, a two-stage joint decision-making policy is proposed to achieve the peak-shifting reduction of production power. In the first stage, a dynamic preventive maintenance schedule is sequentially obtained based on the availability of machine. In the second stage, the production scheduling optimization of multi-workpiece processing is further carried out. The power consumption cost and the delay penalty cost under the time-of-use electricity tariff are considered, and the mixed integer programming model is established to achieve the balance of energy consumption and production delay. Numerical experiments have shown that by reasonably planning the idle time at the time of production batch conversion, the proposed model can effectively shift the on-peak power demand to off-peak, meet the stable electricity demand of enterprises, and improve the sustainable utilization level of power.

Optimal Dynamic Transmission Scheduling for Wireless Networked Control Systems

Wireless networked control systems (WNCSs) have the potential to revolutionize industrial automation in smart factories. Optimizing closed-loop performance while maintaining stability is a fundamental challenge in WNCS due to limited bandwidth and nondeterministic link quality of wireless networks. In order to bridge the gap between network design and control system performance, we propose an optimal dynamic transmission scheduling strategy that optimizes the performance of multiloop control systems by allocating network resources based on predictions of both link quality and control performance at run time. We formulate the optimal dynamic scheduling problem as a nonlinear integer programming problem, which is relaxed to a linear programming problem. We further extend the optimization problem to balance control performance and communication cost. The proposed optimal dynamic scheduling strategy renders the closed-loop system mean-square stable under mild assumptions. Its efficacy is demonstrated by simulating a four-loop control system over an IEEE 802.15.4 wireless network simulator—TOSSIM. The run-time network reconfiguration protocol tailored for optimal scheduling is designed and implemented on a real wireless network consisting of IEEE 802.15.4 devices. Hybrid simulations integrating a real wireless network and simulated physical plant control are performed. Simulation and experimental results show that the optimal dynamic scheduling can enhance control system performance and adapt to both constant and variable wireless interference and physical disturbance to the plant.

Multicontractor multiproject matching optimization for planning modular school construction programs

In a practical context of construction management, a number of special contractors are selected to deliver a multiproject program in a definitive time frame. Research has yet to address how well contractors are matched to projects in scheduling and how to evaluate this criterion in scheduling optimization analysis. This research formulates a novel resource scheduling optimization problem termed multicontractor multiproject matching optimization problem (MCMPMO) based on the current practice of planning modular school development programs. The particular goal of MCMPMO is to determine which contractor is a better match for delivering which project in such a way that the program would be completed by available resources in time, resulting in the highest chances of completing the whole program to the satisfaction of all the stakeholders. A bi-objective optimization formulation for MCMPMO is proposed in the application context of planning modular school development programs. A computer program was prototyped to identify a Pareto front of the MCMPMO problem in a case study.

Economic and low-carbon island operation scheduling strategy for microgrid with renewable energy

With the advancement of supply-side reforms in the energy and power fields, a comprehensive energy system that integrates various energy sources such as electricity, heat, and natural gas has become the main development trend. Based on this, this paper proposes a combined heat and power(CHP) microgrid model with renewable energy. Based on the improved particle swarm algorithm, the optimal scheduling problem of the microgrid model is calculated, and a feasible optimal scheduling strategy considering both economy and low carbon is proposed. Finally, the economy and correctness of the optimal scheduling strategy proposed in this paper are verified by simulation.

Real‐time active power dispatch of virtual power plant based on distributed model predictive control

With the increasing penetration of renewable energy, virtual power plants (VPP) reduce the impact on the power grid by integrating massive distributed resources for unified management. However, the optimal scheduling of a large number of distributed resources in VPP has become a new problem in recent years. Therefore, aiming at the real-time optimal scheduling problem in the optimal scheduling of virtual power plant, this letter regards the virtual power plant as a multi-agent system and proposes a novel real-time active power dispatch scheme of virtual power plant based on distributed model predictive control (DMPC), so that each agent can not only calculate its own optimization function relatively independently, but also fully refer to the neighbour information. Simulation results show the feasibility and effectiveness of the proposed method.

An adaptive heuristic algorithm based on reinforcement learning for ship scheduling optimization problem

Due to the development of ship sizes and the traffic increase in port, ships having long turnaround time in port often result in port congestion, which seriously affects the efficiency of the ship navigation and environmental sustainability of port, it has been evident that effective ship scheduling presents a solution of the fundamental and strategic importance to port congestion. In this paper, a mixed-integer linear programming mathematical model is proposed to realize the optimization of the ship scheduling in port to minimize the total time spent by ships in port. Its methodological novelty is gained by an innovative adaptive genetic simulated annealing algorithm based on a reinforcement learning algorithm (GSAA-RL) to support the developed mathematical model, in which the genetic algorithm is considered as the basic optimization algorithm, and Q-learning with a unique property of selecting suitable parameters dynamically is developed to adjust the parameters of crossover and mutation to improve the search ability of the algorithm. Meanwhile, the dynamic parameter turning process is formulated into a Markov decision process (MDP) model with well defining the state, action, and reward function in GSAA-RL. Specifically, the state sets are proposed by analyzing the key factors affecting the scheduling efficiency and a new reward mechanism that can reduce the objective value significantly based on the quality of selected parameters is designed. The annealing operation is performed on some excellent individuals to further expand the search scope. Simulation experiments demonstrate that the proposed GSAA-RL algorithm can significantly shorten the total time spent by ships in port compared to existing approaches. This study hence helps port operators/planners to improve operational efficiency and reduce port congestion, reduce ship fuel consumption, and deliver goods to cargo owners in a timely manner, which has important practical significance for achieving the “dual carbon” goal.

Integrated freight car routing and train scheduling

Rail freight transportation is involved with highly complex logistical processes and requires a lot of resources such as locomotives or wagons. Thus, cost-efficient strategies for routing freight cars in a cargo network are of great interest for railway companies. When it comes to single wagon load traffic, trains are usually formed by collecting individual freight cars into batches at shunting yards, in order to transport them jointly to their destinations. The problem of finding optimal routes and schedules for single freight cars is typically solved in two steps: (i) determining routes for the freight cars in the railway network by solving the Single-freight car routing problem (SCRP), and (ii) deciding on time schedules for trains by solving the freight train scheduling problem (FTSP). Since train departure and arrival times, as well as freight car routes are highly interdependent, one aims to solve the SCRP and the FTSP simultaneously. For smooth and convenient operational processes many railway companies apply the concept of a routing matrix. This matrix defines unique routes between all shunting yards that are used for all shipments. In this work, we present an integrated mathematical model based on time discretization, that jointly solves the SCRP and FTSP and enforces the routing matrix concept. To the best of our knowledge, this is the first work that combines all three aspects. The approach is tailored for Rail Cargo Austria’s (RCA) needs, incorporating train capacities, yard capacities, and restrictions regarding travel times. We perform an extensive computational study based on real-world data provided by RCA. Besides the performance we analyze the utilization of trains, waiting times of freight cars, and the number of shunting processes.

The Low-Carbon Scheduling Optimization of Integrated Multispeed Flexible Manufacturing and Multi-AGV Transportation

As low-carbon and sustainable manufacturing becomes the mainstream development direction of the current manufacturing industry, the traditional heavy industry manufacturing enterprises in China urgently need to transform. For the heavy cement equipment manufacturing enterprise investigated here, there is a large amount of energy waste during the manufacturing operation due to scheduling confusion. In particular, the multispeed, multi-function machining and the transportation of multiple automated guided vehicles (multi-AGV) are the main influencing factors. Therefore, this paper addresses a novel low-carbon scheduling optimization problem that integrated multispeed flexible manufacturing and multi-AGV transportation (LCSP-MSFM & MAGVT). First, a mixed-integer programming (MIP) model is established to minimize the comprehensive energy consumption and makespan in this problem. In the MIP model, a time-node model is built to describe the completion time per workpiece, and a comprehensive energy consumption model based on the operation process of the machine and the AGV is established. Then, a distribution algorithm with a low-carbon scheduling heuristic strategy (EDA-LSHS) is estimated to solve the proposed MIP model. In EDA-LSHS, the EDA with a novel probability model is used as the main algorithm, and the LSHS is presented to guide the search direction of the EDA. Finally, the optimization effect and actual performance of the proposed method are verified in a case study. The experimental results show that the application of the proposed method in actual production can save an average of 43.52% comprehensive energy consumption and 64.43% makespan, which effectively expands the low-carbon manufacturing capacity of the investigated enterprise.

A chaotic sine cosine algorithm with crossover operator for microgrid energy scheduling considering uncertainty

Microgrid (MG) systems are growing at a rapid pace since they can accommodate the high amount of renewable energy. Since the MG consists of small distributed generators (DG) with volatile characteristics, an efficient energy management system is the main requisite in MG. In this paper, a chaotic sine cosine algorithm with crossover operator (CSCAC) is proposed for the day-ahead MG optimal energy scheduling problem. CSCAC includes a novel non-linear transition parameter based on the chaos system which can help the algorithm escape from local optima. A chaotic search operator is proposed to enhance the local search ability. Furthermore, a crossover operator is devised to combine the advantages of different search strategies and achieve a comparatively better balance of exploration and exploitation. First, the effectiveness of CSCAC is validated on several benchmark functions. Then, it is applied to the day-ahead energy scheduling in a MG with three wind power plants, two photovoltaic power plants and a combined heat and power plant (CHP). Furthermore, it is implemented in two more cases considering the uncertainty and stochastic nature of the renewable power sources. Experimental results demonstrate the superiority of CSCAC over other comparative algorithms in the optimal MG energy management problem.