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

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.

Approximate optimal periodic scheduling of multiple sensors with constraints

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.

SummaryModern power systems are being shifted its attention towards distributed generations (DGs). DGs have allured more concern as an auspicious opportunity with considerable economic profits. To minimize the power generation costs of DGs, day‐to‐day operation scheduling is essential. The role of this study is to offer an optimal operation schedule for DG with several energy sources including renewable energy sources (RES), considering economic facets. In order to achieve the cost minimization along with optimal scheduling, an objection function has been formulated and solved using the optimization algorithms. This study aims to present the applications of differential evolution (DE) algorithm and its variants such as opposition‐based differential evolution (ODE), self‐adaptive differential evolution (SaDE), improved differential evolution (IDE), and cultivated differential evolution (CuDE) for scheduling DG optimally. A scheme for optimal scheduling of thermal, wind power, and solar PV generators has been evaluated. The simulations have been carried out on IEEE 14 bus system, IEEE 30 bus system, IEEE 57 bus system, and Tamil Nadu Generation and Distribution Corporation Limited (TANGEDCO), as a real part of 62 bus Indian utility system (IUS). The novelty of this study lies in simulating a real‐time system for solving optimal scheduling problem, in that way helping decision makers to choose the optimal operation points. The results indicate that the SaDE outperformed other DE variants by giving the best fitness value and convergence rate.

Approximation algorithms for multi-agent scheduling to minimize total weighted completion time

Convexification of an optimal scheduling algorithm for distributed energy storage (DES) in radial distribution systems with high penetration of photovoltaic resources is studied. The AC power flow equalities are taken into account as constraints in the optimization model. Different from the typical optimal power flow problem, the objective function of a DES optimal scheduling (DESOS) problem varies with changing operational requirements. In this paper, three frequently-used objective functions are considered for the DESOS problem. Two of them are monotonic over the feasible set while the third is not. An illustrative example elucidates that the descent direction of a chosen objective function significantly impacts the efficiency of the second-order cone programming (SOCP) relaxation for the DESOS problem. To obtain tighter semidefinite programming (SDP) relaxations for the DESOS cases where the SOCP relaxation is not exact, this paper looks for computationally efficient convex constraints that can approximate the rank-1 constraint in the non-iterative framework. The designed non-iterative enhanced SDP relaxations are compared in terms of tightness of convexification for the DESOS problems considering the three objective functions independently. The comparison is performed on several radial IEEE test systems and a real world distribution feeder.

Two preemptive single-machine bicriteria scheduling problems with release dates and deadlines are considered in this paper. Each criterion is formulated as a maximum cost. In the first problem the cost of both criteria depends on the completion time of the tasks. This problem can be solved by enumerating all the Pareto optimal points with an approach proposed by Hoogeveen (1996) for the nonpreemptive problem without release dates. In the second problem, the costs of one criterion are dependent on the completion times of the tasks and the costs of the other criterion are dependent on the start times. This problem is more difficult but an efficient algorithm is proposed for a sub-problem with heads, tails, release dates and deadlines that appears in the job-shop scheduling problem.

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.

Order acceptance and scheduling (OAS) problems are realistic for enterprises. They have to select the appropriate orders according to their capacity limitations and profit consideration, and then complete these orders by their due dates or no later than their deadlines. OAS problems have attracted significant attention in supply chain management. However, there is an issue that has not been studied well. To our best knowledge, no prior research examines the carbon emission cost and the time-of-use electricity cost in the OAS problems. The carbon emission during the on-peak hours is lower than the one in mid-peak and off-peak hours. However, the electricity cost during the on-peak hours is higher than the one during mid-peak and off-peak hours when time-of-use electricity (TOU) tariff is used. There is a trade-off between sustainable scheduling and the electricity cost. To calculate the objective value, a carbon tax and carbon dioxide emission factor are included when we evaluate the carbon emission cost. The objective function is to maximize the total revenue of the accepted orders and then subtract the carbon emission cost and the electricity cost under different time intervals on a single machine with sequence-dependent setup times and release date. This research proposes a mixed-integer linear programming model (MILP) and a relaxation method of MILP model to solve this problem. It is of importance because the OAS problems are practical in industry. This paper could attract the attention of academic researchers as well as the practitioners.

We consider two-machine flow shop scheduling problems with storage to minimize the makespan. Under a storage constraint, each job has its own size, and the total size of the job(s) being processed on the machine(s) and the job(s) waiting for the second operation cannot exceed the given capacity. It is known that the computational complexity is strongly NP-hard and in general an optimal schedule does not exist in the set of schedules with the same job sequences on two machines, referred to as a permutation set. Thus, we consider two cases such that an optimal schedule exists in the permutation set. These two cases have the special structure of processing times. In the first case, the processing times of two machines for each job are identical, while in the second case, machine 2 dominates machine 1, that is, the smallest processing time of the second group of operations is larger than or equal to the largest one of the first group of operations. We show that the first case is strongly NP-hard and admits a polynomial-time approximation scheme (PTAS), while the second case is solved in polynomial time.

This paper considers a multi-agent scheduling problem, in which each agent has a set of non-preemptive jobs, and all jobs are to be processed on two uniform parallel machines with the objective to minimize the makespan of each agent. Given an instance of the multi-agent scheduling problem, we first devise a measure on the optimal makespan of the single-agent instance for each agent. Then an approximation algorithm is proposed for the multi-agent scheduling problem, in which agents are scheduled in the non-decreasing order of the measure values, and all jobs of each agent are scheduled generally subject to the longest processing time first (LPT) rule. In the obtained schedule, we prove the makespan of the ith completed agent is at most $$i+ \frac{\sqrt{17}-3}{4}$$ times its optimal makespan, in which $$\frac{\sqrt{17}-3}{4}$$ is the relative error of the LPT rule for the single-agent problem $$Q2||C_{\max }$$ . Furthermore, an example is introduced to show the tightness of the performance analysis.

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

Routing Protocol for Low-Power and Lossy Networks (RPL) is an IPv6 routing protocol that is standardized for the Internet of Things (IoT) by Internet-Engineering Task Force (IETF). RPL forms a tree-like topology which is based on different optimizing process called Objective Function (OF). In most cases, IoT has to deal with low power devices and lossy networks. So, the major constraints of the RPL are limited power source, network life time and reliability of the network. OFs depend on different metrics like Expected Transmission Count (ETX), Energy, Received Signal Strength Indicator (RSSI) for route optimization. In this work, the ETX and Energy based OF have been evaluated in terms of energy-efficiency and reliability. For one sink and nine senders, the simulated average power consumption is 1.291 mW and 1.56 mW respectively, for ETX OF and Energy OF. On the other hand, the average hop count for ETX OF is 1.89, which is 3.01 for Energy OF. Thus, ETX OF is more energy-efficient but it is not reliable as it takes fewer hops with long distances. Moreover, it does not take load balancing and link quality into account. However, Energy OF is more reliable due to short hops, but it is not energy efficient and sometimes it might take unnecessary hops.

In order to solve the problem of slow resource scheduling in the process of smart city management, the author proposes a smart city information extraction and data planning system based on the Internet of Things. IoT requires different technologies for analysis for different data types. Managers use different IoT applications to analyze data from different devices and integrate relevant data for possible machine failure or emergency in smart home applications. Situation is predicted. The system includes a cloud platform intelligence center, uses the cloud management module to monitor various hardware devices, constructs the cloud computing resource scheduling objective function, uses the cultural particle swarm algorithm to solve the objective function, and obtains the cloud computing resource scheduling scheme. The experimental results show that the overall utilization rate of the system is the best, close to 100%. Conclusion. The system can realize the effective management of the smart city and monitor the city situation in real time. When implementing resource scheduling, the task completion time is short, the system utilization rate is high, and the resources can be maximized.

Anomaly detection is an important security mechanism for the Internet of Things (IoT). Existing works have been focused on developing accurate anomaly detection models. However, due to the resource-constrained nature of IoT networks and the requirement of real-time security operation, cost efficient (regarding computational efficiency and memory-consumption efficiency) approaches for anomaly detection are highly desirable in IoT applications. In this paper, we investigated machine learning (ML) enabled anomaly detection models for the IoT with regard to multi-objective optimization (Pareto optimization) that minimizes the detection error, execution time, and memory consumption simultaneously. Making use of well-known datasets consisting of network traffic traces captured in an IoT environment, we studied a variety of machine learning algorithms through the world-class H2O AI platform. Our experimental results show that the Gradient Boosting Machine, Random Forest, and Deep Learning models are the most accurate and fastest anomaly detection models; the Gradient Boosting Machine and Random Forest are the most accurate and memory-efficient models. These ML models form the Pareto-optimal set of anomaly detection models. Our results can be used by the industry to facilitate their selection of ML models for anomaly detection on various IoT networks based on their security requirements and system constraints.