Optimal Stochastic Hydro-Thermal Scheduling Using Non-Linear Programming Technique

We consider a class of k-server optimal task scheduling problems partitioning and scheduling N tasks with various real-time constrains and work loads on k servers with convex task processing cost function so as to minimize the total task processing cost while still guaranteeing satisfaction of all time constraints. This class has broad expressing power for practical scheduling problems in several areas such as real-time multimedia wireless transmission , CPU energy conservation, and warehouse order processing management, et. al. Our formulation is quite general such that most previous works can be readily reduced to a special case of the presented k-server optimal task scheduling problem. We show that, when k = 1, optimal solution can be obtained in computational complexity of O(N) and the corresponding optimal scheduling problem is equivalent to finding the shortest 2D Euclidean distance between two vertices inside a well-defined 2D polygon. However, when k 2, the optimal scheduling problem can be demonstrated to be NP-hard by reducing it to a well-known NP-complete bin-packing problem. Therefore, we conclude no polynomial time algorithm exists for a general k-server optimal task scheduling problem. We then construct approximation algorithms to solve the presented k-server problem in a practical way and illustrate its performance by simulation results and analysis.

This work studies the power optimal dynamic scheduling problem in multi-channel multi-user wireless access networks. Users have quality-of-service (QoS) requirements on the minimum rates with statistical delay guarantees. Only one user is allowed to transmit over a channel in a given time slot. This work considers two scenarios: homogeneous and heterogeneous users. For the former scenario, the optimal scheduling policy can be derived, and an online scheduling algorithm for the optimal policy is proposed using online time-averaging without requiring a-priori known fading statistics. For the latter scenario, the optimal scheduling problem is combinatorially hard; hence, even when the fading statistics are available, computing the optimal policy is intractable. Consequently, this work develops a sub-optimal online scheduling algorithm with linear complexity which does not require a-priori known fading statistics. Moreover, the scheduling algorithm satisfies the QoS constraints for the users. Illustrative results demonstrate the performance of the proposed scheduling algorithms in various settings.

This paper proposes a decentralized alternating direction method of multipliers (ADMM) algorithm for solving the optimization problem of energy scheduling in microgrids. Different from the other ADMM-based distributed approaches which decomposes the monolithic problem spatially into smaller tractable subproblems, the proposed method adopts a temporal decomposition on the scenario tree inherited from multi-stage stochastic programming. Each node in the scenario tree serves its own optimization with local variables and constraints, and iteratively updates information with adjacent nodes. By implementing the proposed ADMM algorithm in a rolling fashion, simulation results have shown the fast convergence of the temporal distribution framework, and comparisons on optimal value and computation time with other optimization approaches reveals its advantages and effectiveness.

In this paper we address the stochastic cyclic scheduling problem in synchronous assembly and production lines. Synchronous lines are widely used in the production and assembly of various goods such as automobiles and household appliances. We consider the cycle time (or throughput rate) performance criterion as the objective of the scheduling problem with the assumption that the processing times are independent random variables.

The roles of carbon capture, utilization and storage in the transition to a low-carbon energy system using a stochastic optimal scheduling approach

Approximate optimal periodic scheduling of multiple sensors with constraints

No framework or classification scheme has ever been introduced for stochastic scheduling problems. It is more difficult to develop such a scheme for stochastic scheduling problems than for deterministic scheduling problems. In order to characterize a stochastic scheduling problem more information is required. For example, the distributions of the processing times have to be specified as well as the distributions of the due dates (which may be different). It has to be specified whether the processing times of the n jobs are independent or correlated (e.g., equal to the same random variable) and also which class of policies is considered. For these reasons no framework has been introduced in this book either

The paper describes an efficient algorithm, based on a 1st-order gradient technique in conjunction with a nonlinear-programming technique, for the long-term scheduling of multistorage hydroelectric and multithermal systems for the minimum expected fuel cost under the constraints of expected water available for hydroelectric generation in a given period of time. The system variables are in a discrete form, and the water inflows and load demand are stochastic, their probability properties being pre-estimated from past history. It has been demonstrated through an example solved on an IBM 1130 digital computer that considerable saving in the cost can be achieved through the optimal allocation of the available water.

In this paper, we consider the problem of dynamic programming when supremum terms appear in the objective function. Such terms can represent overhead costs associated with the underlying state variables. Specifically, this form of optimization problem can be used to represent optimal scheduling of batteries such as the Tesla Powerwall for electrical consumers subject to demand charges — a charge based on the maximum rate of electricity consumption. These demand charges reflect the cost to the utility of building and maintaining generating capacity. Unfortunately, we show that dynamic programming problems with supremum terms do not satisfy the principle of optimality. However, we also show that the supremum is a special case of the class of forward separable objective functions. To solve the dynamic programming problem, we propose a general class of optimization problems with forward separable objectives. We then show that for any problem in this class, there exists an augmented-state dynamic programming problem which satisfies the principle of optimality and the solutions to which yield solutions to the original forward separable problem. We further generalize this approach to stochastic dynamic programming problems and apply the results to the problem of optimal battery scheduling with demand charges using a data-based stochastic model for electricity usage and solar generation by the consumer.

In order to reasonably quantify the influence of wind and photovoltaic power output uncertainty on optimal scheduling, a day-ahead optimal scheduling model of wind-photovoltaic-thermal-energy storage combined power generation system considering opportunity-constrained programming is established. The model takes the system operation cost, which contains the operation cost of thermal power units, the penalty cost of pollutants, the operation cost of energy storage system and the penalty cost of new energy curtailment, as the optimization goal. In order to characterize the influence of wind and photovoltaic power prediction errors on the optimal scheduling, an opportunity-constrained programming method is used to calculate the rotating reserve capacity of the system in each period. The simulation calculation is performed on a typical day. The results show that the established model can realize the multi-energy complementary operation of the wind-photovoltaic-thermal-energy storage system. By reasonably quantifying the influence of the wind and photovoltaic power prediction error on the optimal scheduling, the system operation cost can be reduced, which verifies the validity of the model.

Optimal day-ahead scheduling of microgrid with hybrid electric vehicles using MSFLA algorithm considering control strategies

A stochastic scheduling, allocation, and inventory replenishment problem for battery swap stations

Pareto optimization for the two-agent scheduling problems with linear non-increasing deterioration based on Internet of Things

This paper addresses the stochastic optimal day-ahead microgrid (MG) energy resources scheduling, considering the uncertain load, price of electricity, and generated electrical power by wind and solar units. Moreover, the vehicle-to-grid (V2G) implementation, load curtailment cost, and spinning reserve requirements are modeled to make the results more practical and applicable. Furthermore, the price elasticity of supply is considered to explore the relation between V2G capability and the optimization process. The stochastic energy resources scheduling problem is formulated in a two-level optimization framework. The unit commitment of dispatchable resources is analyzed in the upper level, and the lower level is formulated as a scenario-based two-stage stochastic programming problem that minimizes the operation cost of MG considering all the constraints. The risk of attaining unfavorable high costs of MG scheduling is considered using the variance approach. The generated scenarios are reduced by using the backward reduction method for each uncertain variable at each hour, independently. The artificial intelligent-based methods, including differential evolution algorithm (DEA), particle swarm optimization (PSO), and covariance matrix adaptation evolution strategy (CMAES) are applied to solve the problem. The effectiveness of the proposed approaches is confirmed by simulations on a modified 13-bus IEEE test system, in two cases of neglecting the risk and including the managed risk by applying the real-world data. The results confirmed the better performance of CMAES for solving such optimization problems.

Energy-efficient scheduling of stochastic tasks is considered in this paper. The main characteristic of a stochastic task is that its execution time is a random variable whose actual value is not known in advance, but only its probability distribution. Our performance measures are the probability that the total execution time does not exceed a given bound and the probability that the total energy consumption does not exceed a given bound. Both probabilities need to be maximized. However, maximizations of the two performance measures are conflicting objectives. Our strategy is to fix one and maximize the other. Our investigation includes the following two aspects, with the purpose of maximizing the probability for the total execution time not to exceed a given bound, under the constraint that the probability for the total energy consumption not to exceed a given bound is at least certain value. First, we explore the technique of optimal processor speed setting for a given set of stochastic tasks on a processor with variable speed. It is found that the simple equal speed method (in which all tasks are executed with the same speed) yields high quality solutions. Second, we explore the technique of optimal stochastic task scheduling for a given set of stochastic tasks on a multiprocessor system, assuming that the equal speed method is used. We propose and evaluate the performance of several heuristic stochastic task scheduling algorithms. Our simulation studies identify the best methods among the proposed heuristic methods.