Application of genetic algorithms with dominant genes in a distributed scheduling problem in flexible manufacturing systems

Multi-factory production networks have increased in recent years. With the factories located in different geographic areas, companies can benefit from various advantages, such as closeness to their customers, and can respond faster to market changes. Products (jobs) in the network can usually be produced in more than one factory. However, each factory has its operations efficiency, capacity, and utilization level. Allocation of jobs inappropriately in a factory will produce high cost, long lead time, overloading or idling resources, etc. This makes distributed scheduling more complicated than classical production scheduling problems because it has to determine how to allocate the jobs into suitable factories, and simultaneously determine the production scheduling in each factory as well. The problem is even more complicated when alternative production routing is allowed in the factories. This paper proposed a genetic algorithm with dominant genes to deal with distributed scheduling problems, especially in a flexible manufacturing system (FMS) environment. The idea of dominant genes is to identify and record the critical genes in the chromosome and to enhance the performance of genetic search. To testify and benchmark the optimization reliability, the proposed algorithm has been compared with other approaches on several distributed scheduling problems. These comparisons demonstrate the importance of distributed scheduling and indicate the optimization reliability of the proposed algorithm.     

Hybrid TSSA algorithm-based approach to solve warehouse-scheduling problems

Managing a supply chain efficiently is one of the most promising tasks for enterprises these days. Therefore, all the major factors that contribute to the success of the supply chain have to be handled carefully. Warehousing being the vital component of the supply chain contributes towards the storage and timely and efficient delivery of products. The role of warehouses in the overall success of the supply chain has shifted the inclination of researchers towards finding ways that can ease the complexities prevailing under such a scenario. Motivated by these facts, the present paper deals with the issues pertaining to the modelling of the warehouse management system. The paper emphasizes various matters related to warehouse scheduling and aims for an overall minimization of tardiness. It also proposes a Tabu sample-sort simulated annealing (TSSA) algorithm to solve the complex warehouse-scheduling problems. The comparative result with simulated annealing (SA), Tabu search (TS), and hybrid Tabu-SA algorithms at the end of the proposed work reveals the efficacy and robustness of the TSSA algorithm.     

考虑任务拆分特性与簇准备时间的并行机调度

在印制电路板钻孔任务调度等工程实际中,普遍存在一类具有任务拆分特性与簇准备时间的并行机调度问题,尚缺乏高效的优化模型和方法。针对该问题,首先建立以总拖期最小为目标的数学模型,以约束的形式将两个现有优势定理嵌入其中。为了高效求解实际规模问题,进一步提出嵌入优势定理的模拟退火算法。最后,基于随机生成的算例构造计算实验,以验证所建模型和算法的有效性。实验结果表明,嵌入优势定理的数学模型在问题求解规模和计算效率方面均优于现有数学模型,嵌入优势定理的模拟退火算法同样优于现有模拟退火算法。     

Resource-constrained project scheduling by simulated annealing

This paper presents a new adaptation of the simulated annealing algorithm for solving non-preemptive resource-constrained project scheduling problems in which resources are limited but renewable from period to period. This algorithm is able to handle single-mode and multi-mode problems and to optimize different objective functions. Statistical experiments show the efficiency of the proposed algorithm even in comparison to some Tabu search heuristics.     

Integrated multi-factory production and distribution scheduling applying vehicle routing approach

This paper introduces a new integrated multi-factory production and distribution scheduling problem in supply chain management. This supply chain consists of a number of factories joined together in a network configuration. The factories produce intermediate or finished products and supply them to other factories or to end customers that are distributed in various geographical zones. The problem consists of finding a production schedule together with a vehicle routing solution simultaneously to minimise the sum of tardiness cost and transportation cost. A mixed-integer programming model is developed to tackle the small-sized problems using CPLEX, optimally. Due to the NP-hardness, to deal with medium- and large-sized instances, this paper develops a novel Improved Imperialist Competitive Algorithm (IICA) employing a local search based on simulated annealing algorithm. Performance of the proposed IICA is compared with the optimal solution and also with four variants of population-based metaheuristics: Imperialist Competitive Algorithm, Genetic Algorithm, Particle Swarm Optimisation (PSO), and Improved PSO. Based on the computational results, it is statistically shown that quality of the IICA’s solutions is the same as optimal ones solving small problems. It also outperforms other algorithms in finding near-optimal solutions dealing with medium and large instances in a reasonably short running time.     

Hybrid metaheuristic techniques for optimising sugarcane rail operations

Mixed integer programming and parallel-machine job shop scheduling are used to solve the sugarcane rail transport scheduling problem. Constructive heuristics and metaheuristics were developed to produce a more efficient scheduling system and so reduce operating costs. The solutions were tested on small and large size problems. High-quality solutions and improved CPU time are the result of developing new hybrid techniques which consist of different ways of integrating simulated annealing and Tabu search techniques.     

A two-stage three-machine assembly scheduling problem with a position-based learning effect

The two-stage assembly scheduling problem has attracted increasing research attention. In many such problems, job processing times are commonly assumed to be fixed. However, this assumption does not hold in many real production situations. In fact, processing times usually decrease steadily when the same task is performed repeatedly. Therefore, in this study, we investigated a two-stage assembly position-based learning scheduling problem with two machines in the first stage and an assembly machine in the second stage. The objective was to complete all jobs as soon as possible (or to minimise the makespan, implying that the system can perform better and efficient task planning with limited resources). Because this problem is NP-hard, we derived some dominance relations and a lower bound for the branch-and-bound method for finding the optimal solution. We also propose three heuristics, three versions of the simulated annealing (SA) algorithm, and three versions of cloud theory-based simulated annealing algorithm for determining near-optimal solutions. Finally, we report the performance levels of the proposed algorithms.     

A genetic algorithm for the multi-stage and parallel-machine scheduling problem with job splitting – A case study for the solar cell industry

This paper studies a multi-stage and parallel-machine scheduling problem with job splitting which is similar to the traditional hybrid flow shop scheduling (HFS) in the solar cell industry. The HFS has one common hypothesis, one job on one machine, among the research. Under the hypothesis, one order cannot be executed by numerous machines simultaneously. Therefore, multiprocessor task scheduling has been advocated by scholars. The machine allocation of each order should be scheduled in advance and then the optimal multiprocessor task scheduling in each stage is determined. However, machine allocation and production sequence decisions are highly interactive. As a result, this study, motivated from the solar cell industry, is going to explore these issues. The multi-stage and parallel-machine scheduling problem with job splitting simultaneously determines the optimal production sequence, multiprocessor task scheduling and machine configurations through dynamically splitting a job into several sublots to be processed on multiple machines. We formulate this problem as a mixed integer linear programming model considering practical characteristics and constraints. A hybrid-coded genetic algorithm is developed to find a near-optimal solution. A preliminary computational study indicates that the developed algorithm not only provides good quality solutions but outperforms the classic branch and bound method and the current heuristic in practice.     

面向印制电路板钻孔任务动态调度的短视策略

印制电路板钻孔任务因随机到达和工艺要求而难以调度。考虑该问题的NP难性质,提出基于优先规则和智能算法的短视策略。该策略采用事件驱动的再调度机制,在任务到达和任务完工时触发优化算法对当前未开工任务进行决策。为了高效求解每个决策时刻的优化问题,构建了嵌入局部优势定理的模拟退火和变邻域搜索算法,其初始解由优先规则获得。通过计算实验,在不同调度环境下对比两种智能算法与经典优先规则的表现。实验结果表明,智能算法在多数目标下的优化效果较优先规则可提升20%以上,变邻域搜索的优化效果略好于模拟退火,但是模拟退火的计算效率高一倍。     

Meta-heuristics for the distributed two-stage assembly scheduling problem with bi-criteria of makespan and mean completion time

This paper focuses on the distributed two-stage assembly flowshop scheduling problem for minimising a weighted sum of makespan and mean completion time. This problem involves two inter-dependent decision sub-problems: (1) how to allocate jobs among factories and (2) how to schedule the assigned jobs at each factory. A mathematical model is formulated for solving the small-sized instances of the problem. Since the NP-hardness of the problem, we also proposed a variable neighbourhood search (VNS) algorithm and a hybrid genetic algorithm combined with reduced variable neighbourhood search (GA-RVNS) to solve the distributed two-stage assembly flowshop scheduling problems and approximately optimise makespan and mean completion time simultaneously. Computational experiments have been conducted to compare the performances of the model and proposed algorithms. For a set of small-sized instances, both the model and the proposed algorithms are effective. The proposed algorithms are further evaluated on a set of large-sized instances. The results statistically show that both GA-RVNS and VNS obtain much better performances than the GA without RVNS-based local search step (GA-NOV). For the instances with small numbers of jobs, VNS achieves better performances than GA-RVNS. However, for the instances with large numbers of jobs, GA-RVNS yields better performances than the VNS. It is also shown that the overall performances of VNS are very close to GA-RVNS with different numbers of factories, weights given to makespan and numbers of machines at the first stage.     

Efficiently Solving the Redundancy Allocation Problem Using Tabu Search

A tabu search meta-heuristic has been developed and successfully demonstrated to provide solutions to the system reliability optimization problem of redundancy allocation. Tabu search is particularly well-suited to this problem and it offers distinct advantages compared to alternative optimization methods. While there are many forms of the problem, the redundancy allocation problem generally involves the selection of components and redundancy levels to maximize system reliability given various system-level constraints. This is a common and extensively studied problem involving system design, reliability engineering and operations research. It is becoming increasingly important to develop efficient solutions to this reliability optimization problem because many telecommunications (and other) systems are becoming more complex, yet with short development schedules and very stringent reliability requirements. Tabu search can be applied to a more diverse problem domain compared to mathematical programming methods, yet offers the potential of greater efficiency compared to population-based search methodologies, such as genetic algorithms. The tabu search is demonstrated on numerous variations of three different problems and compared to integer programming and genetic algorithm solutions. The results demonstrate the benefits of tabu search for solving this type of problem.     

Jointly solving the group scheduling and machining speed selection problems: A hybrid tabu search and simulated annealing approach

In a cellular manufacturing environment, once the machines and parts have been grouped the remaining tasks are sequencing part families and scheduling operations for the parts within each part family so that some planning goals such as minimization of tardiness can be achieved. This type of problem is called group scheduling and will be analysed in this paper. The solution of the group scheduling is affected by the machining speed specified for each operation since the completion time of each operation is a function of machining speed. As such, the group scheduling and machining speed selection problems should be simultaneously solved to provide meaningful solutions. This, however, further complicates the solution procedure. In view of this, a hybrid tabu-simulated annealing approach is proposed to solve the group scheduling problem. The main advantage of this approach is that a short term memory provided by the tabu list can be used to avoid solution re-visits while preserving the stochastic nature of the simulated annealing method. The performance of this new method has been tested and favourably compared with two other algorithms using tabu search and simulated annealing alone.     

A two-stage three-machine assembly scheduling problem with deterioration effect

The two-stage assembly scheduling problem has received growing attention in the research community. Furthermore, in many two-stage assembly scheduling problems, the job processing times are commonly assumed as a constant over time. However, it is at odds with real production situations some times. In fact, the dynamic nature of processing time may occur when machines lose their performance during their execution times. In this case, the job that is processed later consumes more time than another one processed earlier. In view of these observations, we address the two-stage assembly linear deterioration scheduling problem in which there are two machines at the first stage and an assembly machine at the second stage. The objective is to complete all jobs as soon as possible (or to minimise the makespan, implies that the system can yield a better and efficient task planning to limited resources). Given the fact that this problem is NP-hard, we then derive some dominance relations and a lower bound used in the branch-and-bound method for finding the optimal solution. We also propose three metaheuristics, including dynamic differential evolution (DDE), simulated annealing (SA) algorithm, and cloud theory-based simulated annealing (CSA) algorithm for find near-optimal solutions. The performances of the proposed algorithms are reported as well.     

基于密度峰值聚类的VRPTW问题研究

提出一种密度峰值聚类 (density peak clustering, DPC)与遗传算法(genetic algorithm, GA)相结合的新型混合算法(density peak clustering with genetic algorithm, DGA),求解带时间窗的车辆路径问题。首先应用DPC对客户进行聚类以缩减问题规模,再将聚类后的客户用GA进行线路优化。结果表明：DGA在9个数据集上的平均值比模拟退火(simulated annealing, SA)和禁忌搜索(Tabu)分别提高了13.41%和4.7%,单个数据集最大提高了26.4%。这证明了该算法是求解车辆调度问题的高效算法。     

Enhanced Heap-Based Optimizer Algorithm for Solving Team FormationProblem

Team Formation (TF) is considered one of the most significant problems in computer science and optimization. TF is defined as forming the best team of experts in a social network to complete a task with least cost. Many real-world problems, such as task assignment, vehicle routing, nurse scheduling, resource allocation, and airline crew scheduling, are based on the TF problem. TF has been shown to be a Nondeterministic Polynomial time (NP) problem, and high-dimensional problem with several local optima that can be solved using efficient approximation algorithms. This paper proposes two improved swarm-based algorithms for solving team formation problem. The first algorithm, entitled Hybrid Heap-Based Optimizer with Simulated Annealing Algorithm (HBOSA), uses a single crossover operator to improve the performance of a standard heap-based optimizer (HBO) algorithm. It also employs the simulated annealing (SA) approach to improve model convergence and avoid local minima trapping. The second algorithm is the Chaotic Heap-based Optimizer Algorithm (CHBO). CHBO aids in the discovery of new solutions in the search space by directing particles to different regions of the search space. During HBO’s optimization process, a logistic chaotic map is used. The performance of the two proposed algorithms (HBOSA) and (CHBO) is evaluated using thirteen benchmark functions and tested in solving the TF problem with varying number of experts and skills. Furthermore, the proposed algorithms were compared to well-known optimization algorithms such as the Heap-Based Optimizer (HBO), Developed Simulated Annealing (DSA), Particle Swarm Optimization (PSO), Grey Wolf Optimization (GWO), and Genetic Algorithm (GA). Finally, the proposed algorithms were applied to a real-world benchmark dataset known as the Internet Movie Database (IMDB). The simulation results revealed that the proposed algorithms outperformed the compared algorithms in terms of efficiency and performance, with fast convergence to the global minimum.     

A hybrid differential evolution algorithm for a two-stage flow shop on batch processing machines with arbitrary release times and blocking

Batch processing machines (BPMs) have important applications in a variety of industrial systems. This paper considers the problem of scheduling two BPMs in a flow shop with arbitrary release times and blocking such that the makespan is minimised. The problem is formulated as a mixed integer programming model. Subsequently, a hybrid discrete differential evolution (HDDE) algorithm is proposed. In the algorithm, individuals in the population are first represented as discrete job sequences, and mutation and crossover operators are applied based on the representation. Second, after using the first-fit rule to form batches, a novel least idle/blocking time heuristic is developed to schedule the batches in the flow shop. Furthermore, an effective local search technique is embedded in the algorithm to enhance the exploitation ability. The performance of the proposed algorithm is evaluated by comparing its results to a commercial solver (CPLEX), a genetic algorithm and a simulated annealing algorithm. Computational experiments demonstrate the superiority of the HDDE algorithm in terms of solution quality, robustness and run time.     

Mathematical model and metaheuristics for simultaneous balancing and sequencing of a robotic mixed-model assembly line

This article presents the first method to simultaneously balance and sequence robotic mixed-model assembly lines (RMALB/S), which involves three sub-problems: task assignment, model sequencing and robot allocation. A new mixed-integer programming model is developed to minimize makespan and, using CPLEX solver, small-size problems are solved for optimality. Two metaheuristics, the restarted simulated annealing algorithm and co-evolutionary algorithm, are developed and improved to address this NP-hard problem. The restarted simulated annealing method replaces the current temperature with a new temperature to restart the search process. The co-evolutionary method uses a restart mechanism to generate a new population by modifying several vectors simultaneously. The proposed algorithms are tested on a set of benchmark problems and compared with five other high-performing metaheuristics. The proposed algorithms outperform their original editions and the benchmarked methods. The proposed algorithms are able to solve the balancing and sequencing problem of a robotic mixed-model assembly line effectively and efficiently.     

Parallel flowshop scheduling using Tabu search

Production scheduling problems in manufacturing systems with parallel machine flowshops are discussed. A mathematical programming model for combined part assignment and job scheduling is developed. The objective of solving the scheduling problem is to minimize a weighted sum of production cost and the cost incurred from late product delivery. The solution of the model is NP-hard. To solve the problem efficiently, a heuristic algorithm combining Tabu search and Johnson's method was proposed. Several numerical examples are presented to illustrate the developed model and the algorithm. Computational results from these example problems are very encouraging.     

考虑运输时间的绿色作业车间调度问题研究

针对制造车间能量消耗大、利用率低的现状,以作业车间为研究对象,建立了一种AGV (automated guided vehicle)运输与加工资源集成调度的模型。首先,通过考虑机器间利用AGV运输工件所需的时间与对应的能耗构建了车间总能耗和完工时间的多目标优化模型,并设置权重系数来调节优化目标的偏好。其次,提出了一种融入模拟退火搜索策略的分布估计算法对模型进行求解。该算法主要是利用分布估计算法全局搜索能力快和模拟退火算法突跳性强的特点构建的一种新的混合算法。同时设计新的退火函数来进一步提高算法深度搜索能力。最后,通过实例验证所提算法的可行性和模型节能的有效性。     

Task assignment problems in distributed computing systems by simulated annealing

Abstract

The stochastic, heuristic search algorithm called simulated annealing is considered for the problems of static task assignment in distributed computing systems. The purposes of task assignment problems are to assign modules of programs over a set of interconnected processors in order to both maximize the utilization of processors and minimize interprocessor communication costs. This problem has been proven to be NP‐hard. Although simulated annealing has been applied to a broad class of combinatorial optimization problems, but it requires a long computation time in order to converge to the globally optimal solution. In this paper, we design a very efficient annealing schedule with good move generation strategies and use the concept of specific heat and the frozen condition to obtain near‐optimal solutions for task assignment problems with a significantly large reduction in the number of iterations.