Energy-efficient Scheduling Problem Research Articles

An Adaptive Two-Class Teaching-Learning-Based Optimization for Energy-Efficient Hybrid Flow Shop Scheduling Problems with Additional Resources

Energy-efficient scheduling problems with additional resources are seldom studied in hybrid flow shops. In this study, an energy-efficient hybrid flow shop scheduling problem (EHFSP) with additional resources is studied in which there is asymmetry in the machine. An adaptive two-class teaching-learning-based optimization (ATLBO) which has multiple teachers is proposed to simultaneously minimize the makespan and the total energy consumption. After two classes are formed, a teacher phase is first executed, which consists of teacher self-learning and teacher training. Then, an adaptive learner phase is presented, in which the quality of two classes is used to adaptively decide the learner phase or the reinforcement search of the temporary solution set. An adaptive formation of classes is also given. Extensive experiments were conducted and the computational results show that the new strategies are effective and that ATLBO was able to provide better results than comparative algorithms reported in the literature in at least 54 of 68 instances.

Energy-Efficient Scheduling for Search-Space Periods in NB-IoT Networks

One of the significant properties of narrowband Internet of Things (NB-IoT) devices is supporting a long battery life. In the NB-IoT, devices have different search-space periods based on channel qualities. However, because a subframe of 180 kHz is a basic unit in the downlink, a base station can generally only simultaneously schedule devices with the same search-space period and allocate radio resources at the start of the period. If scheduling does not consider search-space periods, a base station will miss the start of the search-space period of some devices or sacrifice some devices. Massive devices will attempt multiple periods for blind decoding (BD), resulting in huge energy consumption. This article investigates a new direction in reducing the energy consumption of devices by reducing the BD and idle time for the NB-IoT. The challenge of the target energy-efficient scheduling problem is how to schedule search-space periods to reduce each device's BD and idle time subject to the data requirements. We propose an algorithm to determine each device's search-space period and an energy-efficient scheduling algorithm to schedule the search-space periods. The simulation results show that, compared with two baselines, the proposed algorithms reduce the energy consumption by 77%.

A cooperative coevolutionary algorithm with problem-specific knowledge for energy-efficient scheduling in seru system

With the increasingly prominent issues about the global environment, green manufacturing has become a research hotspot. To cope with the turbulent market environment, seru production system (SPS) as an innovative manufacturing mode has attracted much attention, yet energy consumption is still rarely considered in SPS. This paper addresses an energy-efficient scheduling problem in seru system (EESPSS) with the minimization of energy consumption and makespan simultaneously. It contains three coupled subproblems, i.e., worker-seru assignment, batch-seru assignment, and worker-task assignment. To tackle the problem effectively, we build a mathematical model and design a cooperative coevolutionary algorithm (CCA) with three phases: hybrid initialization, multi-population cooperation exploration with feedback, and knowledge-guided greedy search. Firstly, a knowledge-based rule is designed to produce high-quality initial solutions. Secondly, multi-population cooperation is proposed to achieve subproblem co-optimization. Specifically, two populations are constructed for adjusting worker-seru assignment and batch-seru assignment and an elite population is applied for information sharing by individual migration. Moreover, to enhance algorithm search capability, a feedback strategy is designed for operator selection and population size adjustment. Thirdly, to exploit the nondominated solutions effectively, several properties are derived as the problem-specific knowledge to design a greedy search for the batch-seru assignment and worker-task assignment. Numerical tests and statistical comparisons are carried out, which demonstrate the effectiveness of the specific designs of the CCA and its superiority to the existing algorithms in solving the EESPSS.

Dynamic energy-efficient scheduling of multi-variety and small batch flexible job-shop: A case study for the aerospace industry

In the context of the global implementation of carbon peaking and carbon neutrality, energy-aware production scheduling has attracted world-wide attention. The optimal scheduling problem for a multi-variety and small-batch dynamic flexible job shop scheduling is challenging in aerospace industry. This paper considers an energy-efficient scheduling problem with multi-resource constraints of multi-variety and small-batch dynamic flexible job shop (α-shop for short). First, it formulates a mathematical model of energy efficient α-shop with the objectives of minimum total energy consumption (TEC), makespan and machining cost. Next, a novel multi-objective bi-population differential artificial bee colony (BDABC) algorithm is proposed to solve the model. Then, the design of experiment Taguchi method is performed to calibrate the parameter setting of the proposed algorithm. Finally, comparative experiments of the proposed algorithm with other popular algorithms such as large-scale multi-objective optimization framework (LSMOF), large-scale multi-objective competitive swarm optimizer (LMOCSO), as well as some known algorithms including multi-objective evolutionary algorithm based on decomposition (MOEA/D), multi-objective particle swarm optimization (MOPSO) and multi-objective artificial bee colony (MOABC) are carried out to assess the effectiveness of the proposed algorithm in an aerospace plant of China based on a number of well-recognized metrics. The experimental results demonstrate that our proposed algorithm is effective reported for this real-life scheduling problem.

Unrelated parallel machine energy-efficient scheduling considering sequence-dependent setup times and time-of-use electricity tariffs

Given that about half of the produced energy in the world is consumed in industries, there has been an increasing concern about optimizing energy consumption in manufacturing sectors. As one of the most effective ways, proper production scheduling to reduce energy consumption is of crucial importance among researchers and manufacturers. This paper addresses an unrelated parallel machine energy-efficient scheduling problem with sequence-dependent setup times by considering different energy consumption tariffs. The setup times are studied in two modes: disjointed from/jointed to processing time. For each one of these problems, two mixed-integer linear programming models have been formulated. The presented models for the problem with setup time disjointed from processing time can solve up to 16 machines and 45 jobs. In contrast, this capability is changed to 20 machines and 40 jobs for processing time jointed to the setup time problem. Furthermore, a fix and relax heuristic algorithm is presented for large-size instances, which can solve instances of up to 20 machines and 100 jobs for each of the two considered problems.

Energy-efficient unrelated parallel machine scheduling with general position-based deterioration

ABSTRACT This paper investigates an energy-efficient scheduling problem on unrelated parallel machines considering general position-based deterioration which arises from the labour-intensive textile industry. The actual processing time of a job is not only associated with the job and the machine but also with its position in the processing sequence. The objective is to minimise the total energy consumption with a bounded makespan. To address this problem, we first establish a mixed-integer linear programming (MILP) model. Afterwards, the initial model is improved by deriving lower and upper bounds on the makespan, and an upper bound on the number of jobs processed on each machine. We also develop an iterative heuristic embedded with a variable neighbourhood search procedure (IHVNS). The algorithm obtains initial solutions iteratively by solving assignment problems and then repairs and improves them with the VNS procedure. Computational results demonstrate that the improved model is up to 230 times faster than the original one. Moreover, the proposed heuristic yields excellent solutions with average gaps of less than 0.73% for large-scale instances. Especially, the results reveal that the IHVNS algorithm is more suitable than MILP models for solving large-scale problems with tight makespan restrictions.

Improved NSGA-II for energy-efficient distributed no-wait flow-shop with sequence-dependent setup time

This paper addresses a multi-objective energy-efficient scheduling problem of the distributed permutation flowshop with sequence-dependent setup time and no-wait constraints (EEDNWFSP), which have important practical applications. Two objectives minimization of both makespan and total energy consumption (TEC) are considered simultaneously. To address this problem, a new mixed-integer linear programming (MILP) model is formulated. Considering the issues faced in solving large-scale instances, an improved non-dominated sorting genetic algorithm (INSGA-II) is further proposed that uses two variants of the Nawaz-Enscore-Ham heuristic (NEH) to generate high-quality initial population. Moreover, two problem-specific speed adjustment heuristics are presented, which can enhance the qualities of the obtained non-dominated solutions. In addition, four local and two global search operators are designed to improve the exploration and exploitation abilities of the proposed algorithm. The effectiveness of the proposed algorithm was verified using extensive computational tests and comparisons. The experimental results show that the proposed INSGA-II is more effective compared to other efficient multi-objective algorithms.

Mixed-Integer Nonlinear Programming for Energy-Efficient Container Handling: Formulation and Customized Genetic Algorithm

Energy consumption is expected to be reduced while maintaining high productivity for container handling. This paper investigates a new energy-efficient scheduling problem of automated container terminals, in which quay cranes (QCs) and lift automated guided vehicles (AGVs) cooperate to handle inbound and outbound containers. In our scheduling problem, operation times and task sequences are both to be determined. The underlying optimization problem is mixed-integer nonlinear programming (MINLP). To deal with its computational intractability, a customized and efficient genetic algorithm (GA) is developed to solve the studied MINLP problem, and lexicographic and weighted-sum strategies are further considered. An <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\epsilon $ </tex-math></inline-formula> -constraint algorithm is also developed to analyze the Pareto frontiers. Comprehensive experiments are tested on a container handling benchmark system, and the results show the effectiveness of the proposed lexicographic GA, compared to results obtained with two commonly-used metaheuristics, a commercial MINLP solver, and two state-of-the-art methods.

Energy Efficient AoI Minimization in Opportunistic NOMA/OMA Broadcast Wireless Networks

The concept of Age of Information (AoI) minimization in wireless networks has garnered huge interest in recent times. While current literature focuses on scheduling for AoI minimization, there is also a need to efficiently utilize the underlying physical layer resources. In this paper, we consider the problem of energy-efficient scheduling for AoI minimization in an opportunistic NOMA/OMA downlink broadcast wireless network, where the user equipment operate with diverse QoS requirements. We first formulate a resource allocation problem to minimize the average AoI of the network, with energy-efficiency factored in by restricting the long term average transmit power to a predetermined threshold. A heuristic adaptation of the drift-plus-penalty approach from the Lyapunov framework is then utilized to solve the original long-term mixed-integer nonlinear problem on a per time-slot basis. The single time-slot problem is further decomposed into multiple sub-problems, solving for power allocation and user scheduling separately. However, the attained power allocation sub-problems being non-convex, we propose an efficient piece-wise linear approximation to obtain a tractable solution. The scheduling sub-problem is solved optimally by using the integrality property of the linear program. Finally, we provide extensive numerical simulations to show that our proposed approach outperforms the state of the art.

A memetic algorithm for energy-efficient scheduling of integrated production and shipping

ABSTRACT Energy-efficient manufacturing is critical as the industrial sector accounts for a substantial portion of global energy consumption. This research aims to address an energy-efficient scheduling problem of production and shipping for minimizing both makespan and energy consumption. It contributes to an integrated energy-efficient production and shipping system, which is separately studied in most existing research. The production stage allocates jobs onto unrelated parallel machines that can be shut off and adjust their cutting speed to save energy. The shipping stage aims to allocate jobs to vehicles of various sizes with varied unit energy consumption. The problem is modelled as a mixed-integer quadratic program. Considering its complexity, a memetic algorithm (MA) is proposed to incorporate a knowledge-driven local search strategy considering the balance between exploration and exploitation. Two dominance rules are derived from the characteristics of the specific problem and embedded into the proposed MA to enhance its performance. Experimental results demonstrate that the proposed MA outperforms two other population-based algorithms, genetic algorithm and traditional MA, in terms of performance and computing time. This research practically contributes to improving productivity and energy efficiency for the production-shipping supply chain of make-to-order products.

Efficient multiobjective optimization for an AGV energy-efficient scheduling problem with release time

In recent years, green manufacturing has attracted wide attention from researchers. However, the energy efficiency problem in matrix manufacturing workshops is still a blank area. This paper considers a novel automatic guided vehicle (AGV) energy-efficient scheduling problem with release time (AGVEESR) to optimize the three objectives of energy consumption, number of AGVs used and customer satisfaction simultaneously. Considering the development of the AGVEESR, we extract problem-specific knowledge, establish a multiobjective mathematical model, and design a hybrid constructive heuristic. Due to the complexity of the problem, we propose an efficient multiobjective greedy algorithm (MOGA) with effective strategies such as new population initialization, greedy operation, and self-adaptive multiple neighbourhood local search. Meanwhile, an ideal-point-based construction operator in the greedy operation phase is presented to lower the computational complexity. Simulation results show that the proposed MOGA has a tremendously superior performance to the five state-of-the-art algorithms in solving the problem considered.

Towards Energy-Efficient Scheduling of UAV and Base Station Hybrid Enabled Mobile Edge Computing

Mobile edge computing (MEC) has been considered as a promising paradigm to support the growing popularity of mobile devices (MDs) with similar capabilities as cloud computing. Most existing research focuses on MEC enabled by terrestrial base stations (BSs), which is unable to work in certain scenarios, e.g., disaster rescue and field operation. Some researchers have been making efforts on studying MEC assisted by unmanned-aerial-vehicles (UAVs) and developed lots of efficient scheduling algorithms. However, MEC assisted only by UAVs has limited capability and is unsuitable for heavy-computation applications. To address the issue, this paper proposes a novel UAV-and-BS hybrid enabled MEC system, where multiple UAVs and one BS are deployed to facilitate the provisioning of MEC services either directly from UAVs or indirectly from the BS. Considering maximizing the lifetime of all MDs, the energy-efficient scheduling problem is formulated as minimizing the energy consumption of all MDs by jointly optimizing UAV trajectories, task associations, computing-and-transmitting resource allocations. The optimization problem is further decomposed into three sub-problems and solved by the proposed hybrid heuristic and learning based scheduling algorithms to reduce the complexity. Experimental results show that the proposed algorithm can achieve promising performance improvements over baseline algorithms, including local-computing, random-offloading and greedy-offloading.

Permutation flow shop energy-efficient scheduling with a position-based learning effect

Severe environmental problems have made green scheduling an emerging research hotspot. In this paper, a permutation flow shop energy-efficient scheduling problem that considers multiple criteria is investigated. The aim is to find the optimal job processing sequence and conveyor speed that minimise both the makespan and total energy consumption. In addition to two types of common criteria, namely, machine-based criterion (i.e. sequence-dependent setup time) and energy-based criteria (including both the transportation time control strategy and machine shutdown strategy), a human-based criterion (i.e. a position-based learning effect) is introduced. A bi-objective programming model is developed, and a multi-objective iterated greedy (MOIG) is designed to reach the Pareto front of the model. Considering that there are two types of decisions in the model (i.e. job sequence and conveyor speed), two algorithm alternatives are designed based on the job sequence and conveyor speed, respectively. Meanwhile, an acceptance criterion with advantages in terms of the convergence speed and solution diversity is proposed. Existing algorithms, including NSGA-II and MOEA/D, are introduced to evaluate the performance of the MOIG. The results emphasise the efficiency of the MOIG. Overall, the model and MOIG effectively improve the green efficiency of enterprises and can reasonably control operating costs.

An Energy-Efficient Scheduling Algorithm for Shared Facility Supercomputer Centers

The evolution of high-performance computing is associated with the growth of energy consumption. Performance of cluster computes (is increased via rising in performance and the number of used processors, GPUs, and coprocessors. An increment in the number of computing elements results in significant growth of energy consumption. Power grids limits for supercomputer centers (SCC) are driving the transition to more energy-efficient solutions. Often upgrade of computing resources is done step-by-step, i.e. parts of older supercomputers are removed from service and replaced with newer ones. A single SCC at any time can operate several computing systems with different performance and power consumption. That is why the problem of scheduling parallel programs execution on SCC resources to optimize energy consumption and minimize the increase in execution time (energy-efficient scheduling) is important. The goal of the presented work was the development of a new energy-efficient algorithm for scheduling computing resources at SCC. To reach the goal the authors analyzed methods of scheduling computing resources in a shared facility, including energy consumption minimizing methods. The study made it possible to formulate the problem of energy-efficient scheduling for a set of CCs and propose an algorithm for its solution. Experiments on NPB benchmarks allowed achieving significant reduction in energy consumption with a minor increase of runtime.

Energy-efficient scheduling of flexible job shops with complex processes: A case study for the aerospace industry complex components in China

As an effective means to reduce enterprise energy consumption, job-shop scheduling has received extensive attention in the industry. This paper focuses on a real case energy-efficient scheduling problem for aerospace complex components in a flexible job-shop with complex processes. To handle the issues of low production efficiency, high energy consumption and processing cost in the job-shop, an aerospace complex components lot-splitting scheduling model is formulated with the optimization objectives of total energy consumption, makespan, and processing cost for the first time. A novel improved crossover artificial bee colony algorithm is presented to cope with the combinatorial optimization problem in the model. Specifically, a multi-objective process tree algorithm is introduced to address the poor quality of random initial solutions, and the crossover and mutation are designed in the global search of employed bees to improve the population diversity. Moreover, the parameter setting of the proposed algorithm is calibrated by a new assessment metrics ASQ and the DOE Taguchi method. In this way, the Pareto optimal solution set is obtained. Then, a comparative experiment of the proposed algorithm and other famous optimization algorithms including ABC, MOBA, NSGA-II, as well as heuristic scheduling methods including RANDOM+LPP and RANDOM+SPT is designed to verify the energy-saving effect of the proposed model and the feasibility of the algorithm. The results show that the proposed algorithm is a very competitive algorithm for this real-world instance. Finally, the Plant Simulation is used to verify the practicability of the proposed energy-efficient model and algorithm. The simulation results show that the model and algorithm in this work can effectively reduce energy consumption, shorten the production makespan and improve the utilization of various resources in the job shop. The research results of this paper established a quick response, high efficiency, and flexible job-shop scheduling scheme for the aerospace complex components manufacturer, and lay a foundation for other multi-variety, single-piece and small-batch manufacturers to solve similar problems in the future.

Expected Energy Optimization for Real-Time Multiprocessor SoCs Running Periodic Tasks with Uncertain Execution Time

Energy optimization plays an increasingly critical role in designing an embedded real-time multiprocessor System on Chip (MPSoC). Dynamic Voltage Frequency Scaling (DVFS) and Dynamic Power Management (DPM) are preferable techniques to optimize energy consumption. However, previous DVFS and DPM algorithms were mostly designed for inter-task scheduling, without sufficient exploration on intra-task scheduling for further energy reduction. This paper presents a new intra-task scheduling approach considering the probabilistic distribution of task execution time, and it optimizes the mathematical expectation of power consumption (expected power consumption) for periodic dependent tasks with uncertain execution time running on MPSoCs using DVFS and DPM. The energy-efficient scheduling problem can be formulated by means of mixed integer linear programming (MILP) with the proposed technique. Moreover, we also propose a technique to compress the exploration space by reorganizing the probabilistic profiling information of all tasks. Our experimental results on synthetic and realistic benchmarks show that the proposed approach achieves up to 30 percent energy savings compared with other existing methods.

A Knowledge-Based Two-Population Optimization Algorithm for Distributed Energy-Efficient Parallel Machines Scheduling.

In recent years, both distributed scheduling problem and energy-efficient scheduling have attracted much attention. As the integration of these two problems, the distributed energy-efficient scheduling problem is of great realistic significance. To the best of our knowledge, the distributed energy-efficient parallel machines scheduling problem (DEPMSP) has not been studied yet. This article aims to solve DEPMSP by integrating factory assignment and machine assignment into an extended machine assignment to handle the coupled relations of subproblems. A knowledge-based two-population optimization (KTPO) algorithm is proposed to minimize total energy consumption and total tardiness simultaneously. Five properties are derived by analyzing the characteristics of DEPMSP. The population is initialized by using two heuristics based on problem-specific knowledge and a random heuristic. The nondominated sorting genetic algorithm-II and differential evolution perform cooperatively on the population in parallel. Moreover, two knowledge-based local search operators are proposed to enhance the exploitation. Extensive simulation experiments are conducted by comparing KTPO with four algorithms from the literature. The comparative results and statistical analysis demonstrate the effectiveness and advantages of KTPO in solving DEPMSP.

Last train station-skipping, transfer-accessible and energy-efficient scheduling in subway networks

Abstract Station-skipping and deadheading for subway operation regulations are two effective ways to reduce the effects of train variations, such as large passenger flow and unexpected incidents. These variations, if not properly eliminated through strategies, will lead to a gap in the train and eventually increase passenger waiting time and energy consumption. This paper addresses the last-train station-skipping, transfer-accessible, and energy-efficient scheduling problem for the subway system by optimizing the subway schedule and the last train station-skipping scheme. First, an integrated last train operational model was developed to achieve energy savings and better performance of transfer waiting and in-train travel times by adjusting train acceleration, cruising, coasting, and braking times on each rail segment. Second, a heuristic evaluation-based optimization algorithm was designed to solve a real-life case study of the Beijing Subway to demonstrate the effectiveness of our methods. Two operational strategies (station-skipping and deadheading) for the last trains were designed and compared quantitatively. The results indicate that the station-skipping plan shows an advantage in minimizing the in-train travel time and energy consumption.

An energy-efficient bi-objective no-wait permutation flowshop scheduling problem to minimize total tardiness and total energy consumption

In manufacturing scheduling, sustainability concerns that raise from the service-oriented performance criteria have seldom been studied in the literature. This study aims to fill this gap in the literature by integrating the different energy consumption levels at the operational level. Since energy-efficient scheduling ideas have recently been increasing its popularity in industry due to the need for sustainable production, this study will be a good resource for future energy-efficient scheduling problems. Energy consumption in high volume manufacturing is a significant cost item in most industries. Potential energy saving mechanisms are needed to be integrated into manufacturing facilities for cost minimization at the operational level. A leading energy-saving mechanism in manufacturing is to be able to adapt/change the machine speed levels which exactly determines the energy consumption of the machines. Hence, in this study, the afore-mentioned framework is applied to the no-wait permutation flowshop scheduling problem (NWPFSP) which is a variant of classical permutation flowshop scheduling problems. However, it has various critical applications in industries such as chemical, pharmaceutical, food-processing, etc. This study proposes both mixed-integer linear programming (MILP) and constraint programming (CP) model formulations for the energy-efficient bi-objective no-wait permutation flowshop scheduling problems (NWPFSPs) considering the total tardiness and the total energy consumption minimization simultaneously. This problem treats total energy consumption as a second objective. Thus, the trade-off between the total tardiness – a service level measurement indicator – and the total energy consumption – a sustainability level indicator – is analyzed in this study. Furthermore, due to the NP-hardness nature of the first objective of the problem, a novel multi-objective discrete artificial bee colony algorithm (MO-DABC), a traditional multi-objective genetic algorithm (MO-GA) and a variant of multi-objective genetic algorithm with a local search (MO-GALS) are proposed for the bi-objective no-wait permutation flowshop scheduling problem. Besides the proposed algorithms are compared with the multi-objective energy-efficient algorithms from the literature. Consequently, a comprehensive comparative metaheuristic analysis is carried out. The computational results indicate that the proposed MO-DABC algorithm outperforms MILP, CP, MO-GA, MO-GALS, and algorithms from the literature in terms of both cardinality and quality of the solutions. The powerful results of this study show that the proposed models and algorithms can be adapted to other energy-efficient scheduling problems such as no-idle flowshop, blocking flowshop and job-shop scheduling problems or to other higher-level integrated manufacturing problems.

Parallel approaches of genetic algorithm in the MIC architecture of the Intel Xeon Phi

Today, genetic algorithms are widely used in many fields such as bioinformatics, computer science, artificial intelligence, finance ... Genetic algorithms are applied to create high quality solutions for complex optimization problems in the above industries. There have been many studies based on the proposed new hardware architecture that aims to speed up the execution of genetic algorithms as quickly as possible. Some studies suggest parallel genetic algorithms on systems with multicore CPUs and / or graphics processing units (GPUs). However, very few solutions propose a genetic algorithm that can be run on systems that use the new Intel Xeon Phi co-processor (Intel Many-Integrated Core (MIC) architecture). For that reason, we propose and develop the study of the genetic algorithm on high-performance computing systems with Intel Xeon Phi co-processors. This study will present the results of parallel approaches of genetic algorithm on one and more Intel Xeon Phi co-processors by the following methods: (i) Intel Xeon Phi programming model Offload and Native; and (ii) a combined model of MPI and OpenMP. The proposed genetic algorithm can find the optimal schedule for the energy-efficient scheduling problem of virtual machines on physical machines with the goal of minimization total energy consumption. The results of the simulations show the feasibility of implementing a genetic algorithm on one or many Intel Xeon Phi. Genetic algorithm on one or more distributed Intel Xeon Phi always results in faster algorithm execution time than sequential genetic algorithm and the ability to find better solutions using more Intel Xeon Phi. This research result can be applied to other meta-heuristic like TABU search, Ant Colony Optimization.