Makespan Minimization Research Articles

An adaptive artificial bee colony for unrelated parallel machine scheduling with additional resource and maintenance

Unrelated parallel machine scheduling problem with additional resource (UPMSPR) has been extensively considered; however, UPMSPR with preventive maintenance (PM) is seldom studied; on the other hand, artificial bee colony (ABC) has potential advantages on solving UPMSPR with PM because of the extensive applications of ABC to unrelated parallel machine scheduling. In this paper, an adaptive artificial bee colony (AABC) algorithm is proposed to solve UPMSPR with PM and makespan minimization. A new solution representation is presented Evolution quality of population is evaluated and an adaptive onlooker bee phase is implemented, in which multiple search operators including reduced variable neighborhood search (RVNS) are constructed, the number of the used onlooker bees and search operator are dynamically determined. Historical optimization data and a new scout phase are also used. A number of experiments are conducted on 300 instances from the literature. The computational results demonstrate that the new strategies are effective and AABC can provide better results than the algorithms from the literature.

Effective deep Q-networks (EDQN) strategy for resource allocation based on optimized reinforcement learning algorithm

The healthcare industry has always been an early adopter of new technology and a big benefactor of it. The use of reinforcement learning in the healthcare system has repeatedly resulted in improved outcomes.. Many challenges exist concerning the architecture of the RL method, measurement metrics, and model choice. More significantly, the validation of RL in authentic clinical settings needs further work. This paper presents a new Effective Resource Allocation Strategy (ERAS) for the Fog environment, which is suitable for Healthcare applications. ERAS tries to achieve effective resource management in the Fog environment via real-time resource allocating as well as prediction algorithms. Comparing the ERAS with the state-of-the-art algorithms, ERAS achieved the minimum Makespan as compared to previous resource allocation algorithms, while maximizing the Average Resource Utilization (ARU) and the Load Balancing Level (LBL). For each application, we further compared and contrasted the architecture of the RL models and the assessment metrics. In critical care, RL has tremendous potential to enhance decision-making. This paper presents two main contributions, (i) Optimization of the RL hyperparameters using PSO, and (ii) Using the optimized RL for the resource allocation and load balancing in the fog environment. Because of its exploitation, exploration, and capacity to get rid of local minima, the PSO has a significant significance when compared to other optimization methodologies.

Single batch processing machine scheduling with sequence-dependent setup times and multi-material parts in additive manufacturing

Additive manufacturing has been a breakthrough revolution in the manufacturing world due to the ability to economically print parts with high geometric complexity, minimal vast and dissimilar materials in the same printing process. However, some problems arise with the usage of multi-materials in AM machines. This study aims to analyze the scheduling problem of a single AM machine for printing multi-material parts. We developed a mathematical model for a single AM machine to directly minimize the makespan of a production schedule of multi-material parts and indirectly minimize the material changeovers. IBM ILOG CPLEX Optimization Studio (v12.10) is used for the development stage of the model. Some numerical examples from AM literature were handled and solutions were gathered. Effects of material changeover costs for the different numbers of materials were investigated. Results indicated that setup time depending on material changeovers becomes a critical parameter for the minimization of makespan. Higher numbers of dissimilar materials increase the completion time of the schedule. While the developed model can be used for AM machines with different material changeover difficulties, it can also be used in the printing of parts that need to be uncontaminated finished products.

Dynamic scheduling of heterogeneous resources across mobile edge-cloud continuum using fruit fly-based simulated annealing optimization scheme

Achieving sustainable profit advantage, cost reduction and resource utilization are always a bottleneck for resource providers, especially when trying to meet the computing needs of resource hungry applications in mobile edge-cloud (MEC) continuum. Recent research uses metaheuristic techniques to allocate resources to large-scale applications in MECs. However, some challenges attributed to the metaheuristic techniques include entrapment at the local optima caused by premature convergence and imbalance between the local and global searches. These may affect resource allocation in MECs if continually implemented. To address these concerns and ensure efficient resource allocation in MECs, we propose a fruit fly-based simulated annealing optimization scheme (FSAOS) to serve as a potential solution. In the proposed scheme, the simulated annealing is incorporated to balance between the global and local search and to overcome its premature convergence. We also introduce a trade-off factor to allow application owners to select the best service quality that will minimize their execution cost. Implementation of the FSAOS is carried out on EdgeCloudSim Simulator tool. Simulation results show that the FSAOS can schedule resources effectively based on tasks requirement by returning minimum makespan and execution costs, and achieve better resource utilization compared to the conventional fruit fly optimization algorithm and particle swarm optimization. To further unveil how efficient the FSAOSs, a statistical analysis based on 95% confidential interval is carried out. Numerical results show that FSAOS outperforms the benchmark schemes by achieving higher confidence level. This is an indication that the proposed FSAOS can provide efficient resource allocation in MECs while meeting customers’ aspirations as well as that of the resource providers.

Exactly Solving Hard Permutation Flowshop Scheduling Problems on Peta-Scale GPU-Accelerated Supercomputers

Makespan minimization in permutation flow-shop scheduling is a well-known hard combinatorial optimization problem. Among the 120 standard benchmark instances proposed by E. Taillard in 1993, 23 have remained unsolved for almost three decades. In this paper, we present our attempts to solve these instances to optimality using parallel Branch-and-Bound (BB) on the GPU-accelerated Jean Zay supercomputer. We report the exact solution of 11 previously unsolved problem instances and improved upper bounds for eight instances. The solution of these problems requires both algorithmic improvements and leveraging the computing power of peta-scale high-performance computing platforms. The challenge consists in efficiently performing parallel depth-first traversal of a highly irregular and fine-grained search tree on distributed systems composed of hundreds of massively parallel accelerator devices and multicore processors. We present and discuss the design and implementation of our permutation-based BB and experimentally evaluate its parallel performance on up to 384 V100 GPUs (2 million CUDA cores) and 3840 CPU cores. The optimality proof for the largest solved instance requires about 64 CPU-years of computation—using 256 GPUs and over 4 million parallel search agents, the traversal of the search tree is completed in 13 hours, exploring [Formula: see text] nodes.

Variable neighbourhood search for job scheduling with position-dependent deteriorating processing times

This article studies the problem of job scheduling in hand-intensive manufacturing with processing times that deteriorate depending on the sequence in order to minimize the maximum delay of the set of jobs. In the literature, only a small number of academic works has considered the assumption of non-stationary workers during the planning horizon. This problem is NP-hard since it is as an extension of the parallel machine scheduling problem with makespan minimization, which is itself NP-hard. A variable neighbourhood search (VNS) algorithm is presented to solve this problem; its efficiency is evaluated through an extended set of numerical experiments with random-generated datasets. Results are compared with an exact method based on mathematical programming. The results show that the VNS algorithm provides good solutions in reasonable computing times even for large problems.

A collaborative iterative greedy algorithm for the scheduling of distributed heterogeneous hybrid flow shop with blocking constraints

The hybrid flow shop and distributed flow shop problems have been extensively studied due to their wide industrial applications. However, the distributed heterogeneous hybrid flow shop problems (DHHFSP) with blocking constraints have not yet been well studied up to date. This paper considers how to arrange a variety of jobs to different heterogeneous factories, and each factory has a minimal makespan. The innovations of this paper lie in presenting a mathematical model of the DHHFSP with blocking constraints and designing a collaborative iterative greedy (CIG) algorithm. The CIG contains the problem-specific initialization strategy, the neighborhood search strategy, the destruction-reconstruction strategy, and the local intensification strategy. The cross-factory and inner-factory neighborhood search strategies based on two swap operators are adopted to reduce the blocking time. The local intensification strategy is developed to optimize the scheduling sequence of each factory. The proposed algorithm is empirically compared with five state-of-the-art algorithms on 60 different instance sets. The experimental results show that the proposed algorithm significantly outperforms the compared ones in terms of objective values and relative percentage deviation values.

Optimum scheduling of machines, automated guided vehicles and tools without tool delay in a multi‐machine flexible manufacturing system using symbiotic organisms search algorithm

AbstractThis article deals with machines, automated guided vehicles (AGVs) and tools simultaneous scheduling in multimachine flexible manufacturing system (FMS) with the lowest possible number of copies of every tool type without tool delay considering jobs' transport times among machines to minimize makespan (MSN). The tools are kept in a central tool magazine (CTM), which is shared by and serves many machines. Tool transporter (TT) and AGVs shift tools and jobs among machines respectively. This concurrent scheduling problem is extremely complex in nature as it involves determining the lowest possible tool copies of every type of tool, allocation of AGVs and tools copies to job‐operations, job‐operations sequencing on machines, and associated trip operations including the dead heading trip and loaded trip times of AGVs. This paper proposes nonlinear mixed integer programming (MIP) formulation to model this problem and symbiotic organisms search algorithm (SOSA) for solving this problem. Verification is carried out using an industrial problem in a manufacturing firm. The results show that employing two copies for one tool type and one copy each for the remaining tool types results in no tool delay and reduction in MSN which causes a reduction in cost, and SOSA is providing better solution than Jaya algorithm.

A new hybridization of adaptive large neighborhood search with constraint programming for open shop scheduling with sequence-dependent setup times

In recent years, researchers have been paying special attention to scheduling problems with setup times and costs, aiming to adopt more realistic assumptions. This paper aims at presenting a new hybridization of an adaptive large neighborhood search (ALNS) with constraint programming (CP) as a local search phase for open shop scheduling with non-anticipatory sequence-dependent setup time. An integer linear programming model is presented based on the classic open shop model, and a new CP model is proposed with non-anticipatory setup times. The proposed CP model has not been addressed in the revised literature and outperforms all other exact methods. The objective function adopted is makespan minimization, and we use the relative deviation as performance criteria. Since the problem under study is NP-hard, we test many approximations and exact algorithms to obtain high-quality solutions in acceptable computational times. The extensive computational experience shows that the proposed hybridization of metaheuristic and constraint programming is promising for solving large-sized instances.

A Greedy heuristic for solving scheduling problems with bounded rejection cost

We study single machine scheduling problems with the option of job rejection. The scheduling measures considered are: makespan, total completion time, total tardiness and number of tardy jobs. Following many real-life settings, the total permitted rejection cost is assumed to be bounded. All the problems are known to be NP-hard. The paper focuses on the introduction of an efficient greedy-type heuristic, and performing an extensive numerical study. For makespan minimization, the heuristic is proved to be asymptotically optimal under very general conditions. For each of the problems, a pseudo-polynomial dynamic programming algorithm is introduced, and consequently, the results obtained by the greedy heuristic are compared to the optimum. We show that the greedy heuristic leads to very small optimality gaps in all our tests, and that the dynamic programming algorithms can solve medium and large size instances in reasonable times.

A Hybrid Approach for Task Scheduling Based Particle Swarm and Chaotic Strategies in Cloud Computing Environment

This paper presents a hybrid approach based discrete Particle Swarm Optimization (PSO) and chaotic strategies for solving multi-objective task scheduling problem in cloud computing. The main purpose is to allocate the summited tasks to the available resources in the cloud environment with minimum makespan (i.e. schedule length) and processing cost while maximizing resource utilization without violating Service Level Agreement (SLA) among users and cloud providers. The main challenges faced by Particle Swarm Optimization (PSO) when used to solve scheduling problems are premature convergence and trapping into local optimum. This paper presents an enhanced Particle Swarm Optimization algorithm hybridized with Chaotic Map strategies. The proposed approach is called Enhanced Particle Swarm Optimization based Chaotic Strategies (EPSOCHO) algorithm. Our proposed approach suggests two Chaotic Map strategies: sinusoidal iterator and Lorenz attractor to enhanced PSO algorithm in order to get good convergence and diversity for optimizing the task scheduling in cloud computing. The proposed approach is simulated and implemented in Cloudsim simulator. The performance of the proposed approach is compared with the standard PSO algorithm, the improved PSO algorithm with Longest job to fastest processor (LJFP-PSO), and the improved PSO algorithm with minimum completion time (MCT-PSO) using different sizes of tasks and various benchmark datasets. The results clearly demonstrate the efficiency of the proposed approach in terms of makespan, processing cost and resources utilization.

Task Pattern Identification and Scheduling Using Equal Opportunity Model for Minimization of Makespan and Task Diversity in Cloud Computing

Task Pattern Identification and Scheduling Using Equal Opportunity Model for Minimization of Makespan and Task Diversity in Cloud Computing

Simultaneous Scheduling of Machines and Tools in a Multi-Machine FMS with Alternate Machines Using Crow Search Algorithm

Scheduling jobs and tools is a significant problem for manufacturing systems. Inefficient job scheduling and tool loading planning may result in under utilization of capital intensive machines and a high level of machine idle time. Therefore, efficient scheduling of jobs and tools enables a manufacturing system to increase machines’ utilization and decrease their idle times. This paper addresses machines’ and tools’ joint scheduling with alternate machines in a multimachine flexible manufacturing system (FMS) to minimize makespan (MSN). Only one copy of each type of tool is made available in FMS where tools are expensive. The tools are stored in the central tool magazine (CTM), which shares and serves them to several machines in order to reduce the cost of duplicating the tools in every machine. The problem is to select machines from alternate machines for job-operations, allocation of tools to the job-operations and job-operations’ sequencing on machines for MSN minimization. This paper presents nonlinear mixed integer programming (MIP) formulation to model this simultaneous scheduling problem and crow search algorithm (CSA) built on the crows’ intelligent behavior for solving this problem. The results show that CSA is providing better solutions than Jaya algorithm and the usage of alternate machines for the operations can reduce MSN.

A Cloud Computing-Based Modified Symbiotic Organisms Search Algorithm (AI) for Optimal Task Scheduling.

The search algorithm based on symbiotic organisms’ interactions is a relatively recent bio-inspired algorithm of the swarm intelligence field for solving numerical optimization problems. It is meant to optimize applications based on the simulation of the symbiotic relationship among the distinct species in the ecosystem. The task scheduling problem is NP complete, which makes it hard to obtain a correct solution, especially for large-scale tasks. This paper proposes a modified symbiotic organisms search-based scheduling algorithm for the efficient mapping of heterogeneous tasks to access cloud resources of different capacities. The significant contribution of this technique is the simplified representation of the algorithm’s mutualism process, which uses equity as a measure of relationship characteristics or efficiency of species in the current ecosystem to move to the next generation. These relational characteristics are achieved by replacing the original mutual vector, which uses an arithmetic mean to measure the mutual characteristics with a geometric mean that enhances the survival advantage of two distinct species. The modified symbiotic organisms search algorithm (G_SOS) aims to minimize the task execution time (makespan), cost, response time, and degree of imbalance, and improve the convergence speed for an optimal solution in an IaaS cloud. The performance of the proposed technique was evaluated using a CloudSim toolkit simulator, and the percentage of improvement of the proposed G_SOS over classical SOS and PSO-SA in terms of makespan minimization ranges between 0.61–20.08% and 1.92–25.68% over a large-scale task that spans between 100 to 1000 Million Instructions (MI). The solutions are found to be better than the existing standard (SOS) technique and PSO.

New efficient heuristics for scheduling open shops with makespan minimization

This paper deals with the so-called Open Shop Scheduling Problem (OSSP) with makespan objective, which consists of scheduling a set of jobs that must visit a set of machines in no established order so the maximum completion time among the jobs is minimized. This problem is known to be NP-hard, and the absence of specific routes for the processing of the jobs makes its solution space extremely large. In this work we propose several efficient constructive heuristics that exploit some specific properties of the OSSP. We carry out an extensive computational experience using problem instances taken from the related literature to assess the performance of the proposed algorithms as compared to existing ones with respect to the quality of the solutions and the CPU time required. The extensive computational tests show the excellent performance of the heuristics proposed, resulting in the best-so-far heuristics for the problem.

Scheduling of semi-automatic carousels with fixed production sequences

Rotary transfer machines are widely used in different industrial sectors. A rich literature concerning their design and optimisation is available, but mainly dedicated to integrated machining systems. This machine architecture is also implemented in the aluminium gravity die casting technology where the specificity of the casting process needs an appropriate design. In particular, the constraints related to processing times and the rigidity of the production sequence impose a specific approach to schedule the production for achieving an optimal cycle time. We approach this problem with an optimisation perspective: first we propose a mixed-integer linear programming formulation for defining the sequencing and scheduling of the machine in order to obtain a specified production with minimum makespan, and discuss strategies for enumerating the variables of the formulation. Second, we describe a heuristic algorithm as an alternative to the solution of the formulation through a general-purpose solver. Eventually, we present extensive computational experiments on a set of instances generated from real data, comparing these alternative approaches.

Ant colony optimization with a new exploratory heuristic information approach for open shop scheduling problem

This work proposes a new metaheuristic algorithm (ACONEH) for open shop scheduling problem (OSSP) with makespan minimization. The aim is to improve the exploration capability of ant colony optimization (ACO) and also solve OSSP more effectively. This is achieved by introducing a new heuristic information approach that utilizes three exploratory characteristics. The first is randomness: the heuristic information should be generated randomly. The second is diversity: each ant acquires different information. The third is improvability: each ant improves its information periodically. ACONEH is tested on three well-known benchmark problem sets that include 175 instances. The proposed heuristic approach is compared with a traditional one. The results show that the proposed approach produces considerable improvements. These improvements are 91% in the average relative deviation of the best solution and 63% in the average relative deviation of the average solution. ACONEH is compared with other six recent and best-so-far metaheuristic algorithms. The results show that it produces better solutions than all of them in a reasonable computational time. Moreover, the improvements in the average relative deviation of the best solution achieved on the best-so-far ACO and the best-so-far metaheuristic algorithm are 75% and 46%, respectively. Therefore, ACONEH can be considered as the best-so-far metaheuristic algorithm for OSSP.

Effective prediction and resource allocation method (EPRAM) in fog computing environment for smart healthcare system

Recently, many concepts in technology has been changed. According to the digital transformation trends, Internet of Things (IoT) represents an interested research issue. As the IoT grows, the data and the processes will need more space. The data in cases like healthcare, smart cities, autonomous vehicles, smart agriculture, etc. needs to be analyzed and processed in real-time. Cisco refers to the dependence of edge and cloud as “The Fog”. The data can be analyzed at the fog layer to maximize data utilization. This paper presents a new Effective Prediction and Resource Allocation Methodology (EPRAM) for Fog environment, which is suitable for Healthcare applications. Resource Allocation (RA) represents a hard mission as it involves a set of various resources and fog nodes to achieve the required computations for IoT systems. EPRAM tries to achieve effective resource management in Fog environment via real-time resource allocating as well as prediction algorithm. EPRAM is composed of three main modules, namely: (i) Data Preprocessing Module (DPM), (ii) Resource Allocation Module (RAM) and (ii) Effective Prediction Module (EPM). The EPM uses the PNN to predict a target field, using one or more predictors. In order to detect the probability of the heart attack, PNN is trained using the training dataset. Then PNN will be tested using the user’s sensing data coming from the IoT layer to predict the probability of heart attack and then take the most appropriate action accordingly. The main goal of the system is to achieve a low latency while improving the Quality of Service (QoS) metrics such as (the allocation cost, the response time, bandwidth efficiency and energy consumption). Unlike other RA techniques, EPRAM employs deep Reinforcement Learning (RL) algorithm in a new manner. It also uses the PNN for the prediction algorithm. It has achieved such acceptable performance due to using deep RL and PNN. Deep RL has shown impressive promises in resource allocation. PNN generates accurate predicted target and is much faster than multilayer perceptron networks. Comparing the EPRAM with the state-of-the-art algorithms, EPRAM achieved the minimum Makespan as compared to previous LB algorithms, while maximizing the Average Resource Utilization (ARU) and the Load Balancing Level (LBL). Accordingly, EPRAM is a suitable algorithm in the case of real-time systems in FC which leads to load balancing. ERAM is effective in monitoring and predicting the status of the patient accurately and quickly.

A Theoretical Framework for Instance Complexity of the Resource-Constrained Project Scheduling Problem

The resource-constrained project scheduling problem (RCPSP) addresses the problem of constructing a schedule with minimum makespan for a set of activities, subject to precedence and resource constraints. Recent research introduced a data set with small instances that cannot be solved by the state-of-the-art algorithms, revealing a gap in our understanding of instance complexity. We propose a new theoretical framework for the instance complexity for the RCPSP, consecutively incorporating precedence constraints, resource constraints, and activity durations. Our approach contributes to the existing knowledge base in two ways. First, it is independent from solution algorithms, which enables generalisable conclusions. Second, the theoretical perspective enables a deeper understanding of the drivers of instance complexity. We evaluate the performance of our approach with a series of computational experiments. These show that our framework is a strong discriminator between easy and hard instances and explains a large fraction of CPU times of optimal solution algorithms.

The distributed flowshop scheduling problem with delivery dates and cumulative payoffs

In the classic distributed permutation flowshop scheduling problem (DPFSP), there are more studies on the minimization of makespan, total flow time, total tardiness, etc. This paper studies a new problem with a new optimization goal, the DPFSP with delivery dates and cumulative payoffs. It is a variation of the DPFSP with job release dates that maximizes the total payoff with a stepwise job objective function. The main contributions are summarized as follows. (1) A mathematical model is built to formulate the new problem. (2) The characteristics of the problem are explored, and the upper and lower bounds of the problem are given. Based on the problem-specific knowledge, an algorithm named Insert-Pruning is proposed to improve the efficiency of search. (3) Nine heuristic algorithms are proposed, including DRI, DRA, DEI, DEA, DNI, DNA, DII, DIA and DFF. (4) Combined with the characteristics of the problem, some modifications and improvements have been made to the IG algorithm to solve it, including the destruction method, the local search method and the acceptance criterion. (5) The experimental results show that the presented algorithm significantly outperforms the existing algorithms in the literature. In comparison with other competing algorithms in different dimensions, our algorithm has shown better performance, which verifies the effectiveness of this algorithm.