Makespan Minimization Research Articles

Integrated Optimization of Process Planning and Scheduling for Aerospace Complex Component Based on Honey-Bee Mating Algorithm

To cope with the problems of poor matching between processing characteristics and manufacturing resources, low production efficiency, and the hard-to-meet dynamic and changeable model requirements in multi-variety and small batch aerospace enterprises, an integrated optimization method of complex component process planning and workshop scheduling for aerospace manufacturing enterprises is proposed. This paper considers the process flexibility of aerospace complex components comprehensively, and an integrated optimization model for the process planning and production scheduling of aerospace complex components is established with the optimization objectives of achieving a minimum makespan, machining time and machining cost. A honey-bee mating optimization algorithm (HBMO) combined with the greedy algorithm was proposed to solve the model. Then, it formulated a four-layer encoding method based on a feature-processing sequence, processing method, and machine tool, a tool was designed, and five worker bee cultivation strategies were designed to effectively solve the problems of infeasible solutions and local optimization when a queen bee mated to a drone. Finally, taking the complex component parts of an aerospace enterprise as an example, the integrated optimization of process planning and workshop scheduling is carried out. The results demonstrate that the proposed model and algorithm can effectively shorten the makespan and machining time, and reduce the machining cost.

Solving an Industrial-Scale Warehouse Delivery Problem with Answer Set Programming Modulo Difference Constraints

A warehouse delivery problem consists of a set of robots that undertake delivery jobs within a warehouse. Items are moved around the warehouse in response to events. A solution to a warehouse delivery problem is a collision-free schedule of robot movements and actions that ensures that all delivery jobs are completed and each robot is returned to its docking station. While the warehouse delivery problem is related to existing research, such as the study of multi-agent path finding (MAPF), the specific industrial requirements necessitated a novel approach that diverges from these other approaches. For example, our problem description was more suited to formalizing the warehouse in terms of a weighted directed graph rather than the more common grid-based formalization. We formalize and encode the warehouse delivery problem in Answer Set Programming (ASP) extended with difference constraints. We systematically develop and study different encoding variants, with a view to computing good quality solutions in near real-time. In particular, application specific criteria are contrasted against the traditional notion of makespan minimization as a measure of solution quality. The encoding is tested against both crafted and industry data and experiments run using the Hybrid ASP solver clingo[dl].

Solving a job shop scheduling problem

ABSTRACT Job shop scheduling is a highly nondeterministic polynomial combinatorial issue. In this regard, optimization is essential for reducing the time consumed to perform a task. This research paper proposes an evolved social spider optimization method to deal with the job shop scheduling problem. The evolved social spider optimization method was developed by combining both the differential evolutionary and the social spider optimizations. The key proposal is to minimize the makespan time and solve Job shop scheduling problems to improve productivity. The differential evolutionary algorithm is integrated into the spider position update to boost the exploration capabilities of the social spider optimization algorithm. The time taken for ‘‘i’ jobs and ‘‘j’ machines to perform their tasks is studied. Consequently, 23 benchmark problems were prosperously studied utilizing the proposed techniques, and the computational results were compared with previous Meta heuristics methods. An all-inclusive comparison process was carried out to rate the efficiency of the existing optimization techniques in solving job shop scheduling problems. The proposed method of evolved social spider optimization has emerged as the most promising methodology in solving the job shop scheduling problem by consuming minimum makespan time.

Efficient Dependent Task Offloading for Multiple Applications in MEC-Cloud System

With the proliferation of versatile mobile applications, offloading compute-intensive tasks to the MEC/Cloud becomes a dramatic technique due to the limited resources and high user experience requirements at mobile devices. However, most existing works design their task offloading schemes without considering the dependence of tasks and the orchestration of the MEC and Cloud, and thus may limit the system performance. In this paper, we propose a dependent task offloading framework for multiple mobile applications, named COFE, where mobile devices can offload their compute-intensive tasks with dependent constraints to the MEC-Cloud system. It can assign the offloaded tasks to the MEC and Cloud adaptively to improve the user experience. Based on COFE, we formulate the task offloading problem as an average makespan minimization problem, which is proved to be NP-hard. Then, we propose a heuristic ranking-based algorithm to assign the offloaded tasks according to their bottom levels. Theoretical analysis proves the stability of the system under the proposed algorithm and extensive simulations validate that the proposed algorithm can significantly reduce the average makespan and deadline violation probabilities of offloaded applications.

Semi-Online Scheduling on Two Identical Parallel Machines with Initial-Lookahead Information

This work investigates a new semi-online scheduling problem with lookahead. We focus on job scheduling on two identical parallel machines, where deterministic online algorithms only know the information of [Formula: see text] initial jobs (i.e., the initial-lookahead information), while the following jobs still arrive one-by-one in an over-list fashion. We consider makespan minimization as the objective. The study aims at revealing the value of knowing [Formula: see text] initial jobs, which are used to improve the competitive performance of those online algorithms without such initial-lookahead information. We provide the following findings: (1) For the scenario where the [Formula: see text] initial jobs are all the largest jobs with length [Formula: see text], we prove that the classical LIST algorithm is optimal with competitive ratio [Formula: see text]; (2) For the scenario where the total length of these [Formula: see text] jobs is at least [Formula: see text], we show that any online algorithm has a competitive ratio at least 3/2, implying that the initial-lookahead knowledge is powerless since there exists a 3/2-competitive online algorithm without such information; (3) For the scenario where the total length of these [Formula: see text] jobs is at least [Formula: see text] ([Formula: see text]), we propose an online algorithm, named as LPT-LIST, with competitive ratio of [Formula: see text], implying that the initial-lookahead information indeed helps to improve the competitiveness of those online algorithms lacking such information.

Load Balancing in Distributed Cloud Computing: A Reinforcement Learning Algorithms in Heterogeneous Environment

Balancing load in cloud based is an important aspect that plays a vital role in order to achieve sharing of load between different types of resources such as virtual machines that lay on servers, storage in the form of hard drives and servers. Reinforcement learning approaches can be adopted with cloud computing to achieve quality of service factors such as minimized cost and response time, increased throughput, fault tolerance and utilization of all available resources in the network, thus increasing system performance. Reinforcement Learning based approaches result in making effective resource utilization by selecting the best suitable processor for task execution with minimum makespan. Since in the earlier related work done on sharing of load, there are limited reinforcement learning based approaches. However this paper, focuses on the importance of RL based approaches for achieving balanced load in the area of distributed cloud computing. A Reinforcement Learning framework is proposed and implemented for execution of tasks in heterogeneous environments, particularly, Least Load Balancing (LLB) and Booster Reinforcement Controller (BRC) Load Balancing. With the help of reinforcement learning approaches an optimal result is achieved for load sharing and task allocation. In this RL based framework processor workload is taken as an input. In this paper, the results of proposed RL based approaches have been evaluated for cost and makespan and are compared with existing load balancing techniques for task execution and resource utilization..

A Hybrid Evolutionary Algorithm Using Two Solution Representations for Hybrid Flow-Shop Scheduling Problem.

As an extension of the classical flow-shop scheduling problem, the hybrid flow-shop scheduling problem (HFSP) widely exists in large-scale industrial production systems and has been considered to be challenging for its complexity and flexibility. Evolutionary algorithms based on encoding and heuristic decoding approaches are shown effective in solving the HFSP. However, frequently used encoding and decoding strategies can only search a limited area of the solution space, thus leading to unsatisfactory performance during the later period. In this article, a hybrid evolutionary algorithm (HEA) using two solution representations is proposed to solve the HFSP for makespan minimization. First, the proposed HEA searches the solution space by a permutation-based encoding representation and two heuristic decoding methods to find some promising areas. Afterward, a Tabu search (TS) procedure based on a disjunctive graph representation is introduced to expand the searching space for further optimization. Two classical neighborhood structures focusing on critical paths are extended to the problem-specific backward schedules to generate candidate solutions for the TS. The proposed HEA is tested on three public HFSP benchmark sets from the existing literature, including 567 instances in total, and is compared with some state-of-the-art algorithms. Extensive experimental results indicate that the proposed HEA performs much better than the other algorithms. Moreover, the proposed method finds new best solutions for 285 hard instances.

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.

LS-HH: A Learning-Based Selection Hyper-Heuristic for Distributed Heterogeneous Hybrid Blocking Flow-Shop Scheduling

As the development of economic globalization, the distributed manufacturing has become common in modern industries. The scheduling of production resources in multiple production centers becomes an emerging topic. This paper is the first attempt to address a distributed heterogeneous hybrid blocking flow-shop scheduling problem (DHHFSP-B) with the minimization of makespan. Compared with the traditional single flow-shop scheduling, DHHFSP-B considers the collaborative production of multiple hybrid flow lines with heterogeneous layout and processing performance as well as no intermediate buffers. We firstly present a mixed-integer linear programming model to formulate DHHFSP-B and then propose a learning-based selection hyper-heuristic framework (LS-HH) for solving it. The LS-HH contains high-level strategy and low-level heuristics. In the high-level strategy, a learning probability model is built to provide the guidance to choose the suitable perturbation heuristic during the optimization process. A simulated annealing-like move acceptance is employed to determine the updating of incumbent domain solution and prevent the search from trapping into local optimum. In the low-level heuristics, a constructive heuristic is proposed based on a novel assignment rule to create the initial domain solution. Four problem-specific perturbation heuristics and a variable neighborhood search-based improvement operator are employed to search the solution space. A comprehensive computational experiment is conducted. The comparative results show that the LS-HH significantly outperforms the Gurobi solver and several closely relevant optimization methods in solving the DHHFSP-B.

Logic-based Benders decomposition for the preemptive flexible job-shop scheduling problem

In this paper, we focus on exact methods to solve the preemptive flexible job-shop scheduling problem with makespan minimisation objective function. Mathematical and constraint programming models enable the resolution of this problem for small instances. However, as an NP-hard problem, the cost of solving grows rapidly when considering larger instances. In this regard, we propose a logic-based Benders decomposition that relies on an efficient branch-and-bound procedure to solve the subproblem representing a pure (non-flexible) preemptive job-shop scheduling problem. Computational experiments are carried out and show the very good performance of our proposals.

An enhanced ordinal optimization with lower scheduling overhead based novel approach for task scheduling in cloud computing environment

Efficient utilization of available computing resources in Cloud computing is one of the most challenging problems for cloud providers. This requires the design of an efficient and optimal task-scheduling strategy that can play a vital role in the functioning and overall performance of the cloud computing system. Optimal Schedules are specifically needed for scheduling virtual machines in fluctuating & unpredictable dynamic cloud scenario. Although there exist numerous approaches for enhancing task scheduling in the cloud environment, it is still an open issue. The paper focuses on an improved & enhanced ordinal optimization technique to reduce the large search space for optimal scheduling in the minimum time to achieve the goal of minimum makespan. To meet the current requirement of optimal schedule for minimum makespan, ordinal optimization that uses horse race conditions for selection rules is applied in an enhanced reiterative manner to achieve low overhead by smartly allocating the load to the most promising schedule. This proposed ordinal optimization technique and linear regression generate optimal schedules that help achieve minimum makespan. Furthermore, the proposed mathematical equation, derived using linear regression, predicts any future dynamic workload for a minimum makespan period target.

A new job priority rule for the NEH-based heuristic to minimize makespan in permutation flowshops

The permutation flowshop scheduling problem is a vital production management concern of industries such as electronic product manufacturing and integrated circuit fabrication. In many studies, jobs are prioritized independently according to their features or properties. This article develops a new perspective by introducing the self-attention mechanism into scheduling for the first time. The job similarities are characterized by the dot-product of processing time matrices and taken as job priorities. Based on this idea, a new priority rule denoted by PRSAT is proposed, and a heuristic named NEHLJP2 is presented with makespan minimization. The computational results with the Taillard and VRF benchmarks and 640 random instances demonstrate that the new priority rule and heuristic dominate the existing ones at a nominal cost of computation time.

Modified benders decomposition and metaheuristics for multi-machine parallel-batch scheduling and resource allocation under deterioration effect

Batch scheduling problem is a common difficulty in mass production, which includes many decisions such as grouping, batch ordering, and resource allocation. Motivated by the semiconductor burn-in test process, this paper investigates a combinatorial optimization problem considering the deterioration effect and resource allocation. The objective is to design an appropriate job sequencing and resource allocation scheme to achieve an overall minimization of makespan and resource costs. The problem, subject to parallel-batch, multi-machine, deterioration effect, and resource constraints, is NP-hard. We decompose it into a master problem and a sub-problem based on Benders Decomposition (BD). A cut filtering rule that limits the number of cuts is proposed to control the complexity of the problem. Meanwhile, some structural properties are deduced to guide the design of two algorithms combined with Variable Neighborhood Search (VNS). We conduct extensive simulation experiments on instances of different scales, and the results demonstrate that the cut filtering method can effectively reduce the solution time. In large-scale computational experiments, it is more obvious that the proposed algorithms have good convergence and robustness.

An Experimental Study of Grouping Mutation Operators for the Unrelated Parallel-Machine Scheduling Problem

The Grouping Genetic Algorithm (GGA) is an extension to the standard Genetic Algorithm that uses a group-based representation scheme and variation operators that work at the group-level. This metaheuristic is one of the most used to solve combinatorial optimization grouping problems. Its optimization process consists of different components, although the crossover and mutation operators are the most recurrent. This article aims to highlight the impact that a well-designed operator can have on the final performance of a GGA. We present a comparative experimental study of different mutation operators for a GGA designed to solve the Parallel-Machine scheduling problem with unrelated machines and makespan minimization, which comprises scheduling a collection of jobs in a set of machines. The proposed approach is focused on identifying the strategies involved in the mutation operations and adapting them to the characteristics of the studied problem. As a result of this experimental study, knowledge of the problem-domain was gained and used to design a new mutation operator called 2-Items Reinsertion. Experimental results indicate that the state-of-the-art GGA performance considerably improves by replacing the original mutation operator with the new one, achieving better results, with an improvement rate of 52%.

Bicriteria multi-machine scheduling with equal processing times subject to release dates

<abstract><p>This paper addresses the problem of scheduling $ n $ equal-processing-time jobs with release dates non-preemptively on identical machines to optimize two criteria simultaneously or hierarchically. For simultaneous optimization of total completion time (and makespan) and maximum cost, an algorithm is presented which can produce all Pareto-optimal points together with the corresponding schedules. The algorithm is then adapted to solve the hierarchical optimization of two min-max criteria, and the final schedule has a minimum total completion time and minimum makespan among the hierarchical optimal schedules. The two algorithms provided in this paper run in $ O(n^3) $ time.</p></abstract>

Service scheduling optimization for multiple tower cranes considering the interval time of the cross-tasks.

The key issues that have always affected the production yield of the construction industry are delays and cost overruns, especially when dealing with large-scale projects and super-high buildings in which multiple tower cranes with overlapping areas are often deployed because of urgent due date and limited space. The service scheduling of tower cranes, which act as the crucial site equipment for lifting and transporting materials, is one of the main problems not only related to the construction progress and project cost but also affecting equipment health, and it may bring security risks. The current work presents a multi-objective optimization model for a multiple tower cranes service scheduling problem (MCSSP) with overlapping areas while achieving maximum interval time of cross-tasks and minimum makespan. For the solving procedure, NSGA-Ⅱ is employed with double-layer chromosome coding and simultaneous coevolutionary strategy design, which can obtain a satisfactory solution through effectively allocating tasks within overlapping areas to each crane and then prioritizing all the assigned tasks. The makespan was minimized, and stable operation of tower cranes without collision was achieved by maximizing the cross-tasks interval time. A case study of the megaproject Daxing International Airport in China has been conducted to evaluate the proposed model and algorithm. The computational results illustrated the Pareto front and its non-dominant relationship. The Pareto optimal solution outperforms the results of the single objective classical genetic algorithm in terms of overall performance of makespan and interval time of cross-tasks. It also can be seen that significant improvement in the time interval of cross-tasks can be achieved at the cost of a tiny increase in makespan, which means effective avoidance of the tower cranes entering the overlapping area at the same time. This can help eliminate collision, interference and frequent start-up and braking of tower cranes, leading to safe, stable and efficient operation on the construction site.

Energy expenditure and makespan multi-objective optimization for cobots systems design

Nowadays, we are living a transitional period from Industry 4.0, with its principles of high productivity and high flexibility of modern production systems due to the mass customization, to Industry 5.0, that aims to realize a more human-centered design of the workplace in order to improve the operators’ wellness. For this purpose, new technologies such as collaborative robots are always more integrated since they are able to guarantee, at the same time, productivity and flexibility but they can also perform the more burdensome tasks, leaving to the operators the more challenging ones. However, since these systems are thought to work directly with human operators, it is fundamental to consider the human-robot collaboration, in order to correctly assign the tasks to the resources. This is the cornerstone of Industry 5.0, that points toward the realization of human-centered systems.For this purpose, the here presented paper proposed a bi-objective optimization for task allocation, aiming at minimizing both the time required to assemble the parts, including so the makespan minimization as objective function, and the energy required by the operator during the work. Multi-objective optimization has already been extensively studied, however, there is still no research concerning this for collaborative systems. Hence, the objective functions are described, followed by the problem statement with the constraints included. Moreover, characteristics indexes are analyzed to evaluate the performance of the method.A case study is finally reported to demonstrate the practical implication of the research, proposing a different set of optimal solutions, which may be selected according to specific needs.

Improved Chameleon Swarm Optimization-Based Load Scheduling for IoT-Enabled Cloud Environment

Internet of things (IoT) and cloud computing (CC) becomes widespread in different application domains such as business, e-commerce, healthcare, etc. The recent developments of IoT technology have led to an increase in large amounts of data from various sources. In IoT enabled cloud environment, load scheduling remains a challenging process which is applied for ensuring network stability with maximum resource utilization. The load scheduling problem was regarded as an optimization problem that is solved by metaheuristics. In this view, this study develops a new Circle Chaotic Chameleon Swarm Optimization based Load Scheduling (C3SOA-LS) technique for IoT enabled cloud environment. The proposed C3SOA-LS technique intends to effectually schedule the tasks and balance the load uniformly in such a way that maximum resource utilization can be accomplished. Besides, the presented C3SOA-LS model involves the design of circle chaotic mapping (CCM) with the traditional chameleon swarm optimization (CSO) algorithm for improving the exploration process, shows the novelty of the work. The proposed C3SOA-LS model computes an objective with the minimization of energy consumption and makespan. The experimental outcome implied that the C3SOA-LS model has showcased improved performance and uniformly balances the load over other approaches.

Modified multi-objective simulated annealing algorithm for scheduling a flow shop production system with setup times

The presence of setup times and multiple objectives makes the scheduling problem complex. This paper presents two algorithms namely: multi-objective simulated annealing (MOSA) and modified MOSA for the simultaneous minimisation of makespan and mean tardiness in scheduling a flow shop production system wherein setup times depend on processing sequence. The modified MOSA algorithm is developed by hybridising MOSA with variable neighbourhood search. Benchmark problems are used to conduct computational experiments. The analysis of the algorithms reveals that modified MOSA outperforms MOSA for the measures considered. Hybridisation improves the performance of MOSA. The proposed algorithms are applied on scheduling a real-world SDST flow shop and the results indicate superior performance of modified MOSA.

Environmentally friendly strategy for hybrid flow shop scheduling with the unrelated parallel machines

With the increasing environmental pressure, reducing the environmental impact on hybrid flow shops (HFS) has attracted extensive attention because of its broad industrial applications. The selection of machines in the implementation of HFS is a complex decision-making process that hinders the optimization efficiency in shops. However, this issue has not been addressed thoroughly. In light of this, a multi-objective mathematical model is formulated for the minimization of makespan and energy consumption of the hybrid flow shop scheduling problem (HFSP). The environmental performance of machines is calculated by the proposed evaluation index and is ranked on the basis of the integrated entropy and fuzzy technique for order performance by similarity to ideal solution method. Moreover, to solve the multi-objective model of HFSP, an improved differential evolution algorithm with a heuristic active decoding rule that incorporates the ranking of environmental performance of machines into the iterative process of the algorithm is presented. Finally, a case study is presented to evaluate the effectiveness of the proposed method and to prove the feasibility of the ranking-based differential evolution algorithm (RBDE). The result shows that the proposed RBDE outperforms RBNSGA-II and RBPSO in searching for non-dominated solutions that can solve the environmental production of HFSP effectively.