Recurrent neural network approach for cyclic job shop scheduling problem

While cyclic scheduling is involved in numerous real-world applications, solving the derived problem is still of exponential complexity. This paper focuses specifically on modelling the manufacturing application as a cyclic job shop problem and we have developed an efficient neural network approach to minimise the cycle time of a schedule. Our approach introduces an interesting model for a manufacturing production, and it is also very efficient, adaptive and flexible enough to work with other techniques. Experimental results validated the approach and confirmed our hypotheses about the system model and the efficiency of neural networks for such a class of problems.     

An evolving surrogate model-based differential evolution algorithm

Differential evolution (DE) is a simple and effective approach for solving numerical optimization problems. However, the performance of DE is sensitive to the choice of mutation and crossover strategies and their associated control parameters. Therefore, to achieve optimal performance, a time-consuming parameter tuning process is required. In DE, the use of different mutation and crossover strategies with different parameter settings can be appropriate during different stages of the evolution. Therefore, to achieve optimal performance using DE, various adaptation, self-adaptation, and ensemble techniques have been proposed. Recently, a classification-assisted DE algorithm was proposed to overcome trial and error parameter tuning and efficiently solve computationally expensive problems. In this paper, we present an evolving surrogate model-based differential evolution (ESMDE) method, wherein a surrogate model constructed based on the population members of the current generation is used to assist the DE algorithm in order to generate competitive offspring using the appropriate parameter setting during different stages of the evolution. As the population evolves over generations, the surrogate model also evolves over the iterations and better represents the basin of search by the DE algorithm. The proposed method employs a simple Kriging model to construct the surrogate. The performance of ESMDE is evaluated on a set of 17 bound-constrained problems. The performance of the proposed algorithm is compared to state-of-the-art self-adaptive DE algorithms: the classification-assisted DE algorithm, regression-assisted DE algorithm, and ranking-assisted DE algorithm.     

A three-fold approach for job shop problems: A divide-and-integrate strategy with immune algorithm

This paper presents a novel divide-and-integrate strategy based approach for solving large scale job-shop scheduling problems. The proposed approach works in three phases. First, in contrast to traditional job-shop scheduling approaches where optimization algorithms are used directly regardless of problem size, priority rules are deployed to decrease problem scale. These priority rules are developed with slack due dates and mean processing time of jobs. Thereafter, immune algorithm is applied to solve each small individual scheduling module. In last phase, integration scheme is employed to amalgamate the small modules to get gross schedule with minimum makespan. This integration is carried out in dynamic fashion by continuously checking the preceding module's machine ideal time and feasible slots (satisfying all the constraint). In this way, the proposed approach will increase the machine utilization and decrease the makespan of gross schedule. Efficacy of the proposed approach has been tested with extremely hard standard test instances of job-shop scheduling problems. Implementation results clearly show effectiveness of the proposed approach.     

An improved firefly algorithm for solving dynamic multidimensional knapsack problems

There is a wide range of publications reported in the literature, considering optimization problems where the entire problem related data remains stationary throughout optimization. However, most of the real-life problems have indeed a dynamic nature arising from the uncertainty of future events. Optimization in dynamic environments is a relatively new and hot research area and has attracted notable attention of the researchers in the past decade. Firefly Algorithm (FA), Genetic Algorithm (GA) and Differential Evolution (DE) have been widely used for static optimization problems, but the applications of those algorithms in dynamic environments are relatively lacking. In the present study, an effective FA introducing diversity with partial random restarts and with an adaptive move procedure is developed and proposed for solving dynamic multidimensional knapsack problems. To the best of our knowledge this paper constitutes the first study on the performance of FA on a dynamic combinatorial problem. In order to evaluate the performance of the proposed algorithm the same problem is also modeled and solved by GA, DE and original FA. Based on the computational results and convergence capabilities we concluded that improved FA is a very powerful algorithm for solving the multidimensional knapsack problems for both static and dynamic environments.     

差分进化混合粒子群算法求解装配式住宅项目进度优化问题

针对装配式住宅项目进度优化问题,提出了基于差分算法(DE)和粒子群算法(PSO)的差分粒子群混合算法(DEPSO)。建立了以项目工期最优为目标的进度优化模型,通过在DE和PSO之间建立信息交流机制,避免了单一算法容易落入局部最优和精度低的缺陷。最后以某装配式住宅项目为例,通过三种算法的比较,结果表明DEPSO在求解装配式住宅项目进度优化中合理高效、鲁棒性较强,能有效地解决装配式住宅项目工期优化问题,有较大的应用价值。     

Optimal short-term hydro-thermal scheduling using quasi-oppositional teaching learning based optimization

This paper presents a new approach for solving short-term hydrothermal scheduling (HTS) using an integrated algorithm based on teaching learning based optimization (TLBO) and oppositional based learning (OBL). The practical hydrothermal system is highly complex and possesses nonlinear relationship of the problem variables, cascading nature of hydro reservoirs, water transport delay and scheduling time linkage that make the problem of optimization difficult using standard optimization methods. To overcome these problems, the proposed quasi-oppositional teaching learning based optimization (QOTLBO) is employed. To show its efficiency and robustness, the proposed QOTLBO algorithm is applied on two test systems. Numerical results of QOTLBO are compared with those obtained by two phase neural network, augmented Lagrange method, particle swarm optimization (PSO), improved self-adaptive PSO (ISAPSO), improved PSO (IPSO), differential evolution (DE), modified DE (MDE), fuzzy based evolutionary programming (Fuzzy EP), clonal selection algorithm (CSA) and TLBO approaches. The simulation results reveal that the proposed algorithm appears to be the best in terms of convergence speed, solution time and minimum cost when compared with other established methods. This method is considered to be a promising alternative approach for solving the short-term HTS problems in practical power system.     

Dynamic supply chain scheduling

Based on a combination of fundamental results of modern optimal program control theory and operations research, an original approach to supply chain scheduling is developed in order to answer the challenges of dynamics, uncertainty, and adaptivity. Both supply chain schedule generation and execution control are represented as an optimal program control problem in combination with mathematical programming and interpreted as a dynamic process of operations control within an adaptive framework. Hence, the problems and models of planning, scheduling, and adaptation can be consistently integrated on a unified mathematical axiomatic of modern control theory. In addition, operations control and flow control models are integrated and applicable for both discrete and continuous processes. The application of optimal control for supply chain scheduling becomes possible by formulating the scheduling model as a linear non-stationary finite-dimensional controlled differential system with the convex area of admissible control and a reconfigurable structure. For this model class, theorems of optimal control existence can be used regarding supply chain scheduling. The essential structural property of this model are the linear right parts of differential equations. This allows applying methods of discrete optimization for optimal control calculation. The calculation procedure is based on applying Pontryagin’s maximum principle and the resulting essential reduction of problem dimensionality that is under solution at each instant of time. The gained insights contribute to supply chain scheduling theory, providing advanced insights into dynamics of the whole supply chains (and not any dyadic relations in them) and transition from a partial “one-way” schedule optimization to the feedback loop-based dynamic and adaptive supply chain planning and scheduling.     

A linear optimization approach to the heterogeneous r-cyclic hoist scheduling problem

The cyclic hoist scheduling problem is encountered in electroplating facilities, when mass production is required. This class of problems is a branch stemming from the Hoist Scheduling Problem (HSP) where automatic hoist is used for moving electroplates through chemical baths. A repetitive sequence of moves is searched for the hoist in cyclic schedule. To minimize the cycle time of r different part-jobs, we propose a linear optimization approach. An illustrative example is given in order to show some feedback of our exact solving method. Afterward, two comparisons are presented: firstly, between a two 1-cycle homogenous schedule and a 2-cycle heterogeneous part-job and secondly, between 2-cycle and 4-cycle heterogeneous part-job. These comparisons show how, by considering r-cyclic scheduling, we can optimize the cycle length considerably and then the throughput rate of the electroplating line.     

Push-Pull: Deterministic Search-Based DAG Scheduling for Heterogeneous Cluster Systems

Consider directed acyclic graph (DAG) scheduling for a large heterogeneous system, which consists of processors with varying processing capabilities and network links with varying bandwidths. The search space of possible task schedules for this problem is immense. One possible approach for this optimization problem, which is NP-hard, is to start with the best task schedule found by a fast deterministic task scheduling algorithm and then iteratively attempt to improve the task schedule by employing a general random guided search method. However, such an approach can lead to extremely long search times, and the solutions found are sometimes not significantly better than those found by the original deterministic task scheduling algorithm. In this paper, we propose an alternative strategy, termed Push-Pull, which starts with the best task schedule found by a fast deterministic task scheduling algorithm and then iteratively attempts to improve the current best solution using a deterministic guided search method. Our simulation results show that given similar runtimes, the Push-Pull algorithm performs well, achieving results similar to or better than all of the other algorithms being compared.     

Static Scheduling of Conditional Branches in Parallel Programs

The problem of scheduling non-deterministic graphs arises in several situations in scheduling parallel programs, particularly in the cases of loops and conditional branching. When scheduling loops in a parallel program, non-determinism arises because the number of loop iterations may not be known before the execution of the program. However, since loops from a restricted class of conditional branching, there is a higher degree of non-determinism associated with scheduling conditional branching. In this case, the direction of every branch remains unknown before run time. It follows that entire subprograms of the parallel program may or may not get executed, which in turn increases the amount of non-determinism and complicates the scheduling process. Thus, the term non-determinism is frequently associated with conditional branching in the literature. In this paper, we study the problem of constructing a static schedule for task graphs that contain conditional branching on parallel computers. Generally, it is difficult to obtain optimal solutions for solving various scheduling problems, even in the deterministic case. When non-determinism is added to the scheduling problem through conditional branching, an optimal solution will be even harder to obtain. We start the paper with a brief discussion of the scheduling problem, then we introduce a model for representing parallel programs that contain branches. We present a two-step scheduling technique which employs two different approaches: a graph theoretic appraoch and a multi-phase approach. The first approach is based on exploring several graph theoretic properties of the model. This approach is used as a preprocessing step to decrease the amount of non-determinism before applying the multi-phase approach. In the second step, several execution instances of the program are generated, a schedule for every instance is obtained, and a unified schedule is constructed by merging the obtained schedules. Finally, we report the results of the experiments that we conducted to measure the performance of the techniques introduced in this paper.     

云计算中基于NSGA Ⅱ的虚拟资源调度算法

云计算环境下将物理资源抽象为同一的虚拟资源,如何将虚拟资源调度到物理资源上是云计算中一个基本且复杂的问题.对虚拟资源的调度进行建模并证明其难解性,将该模型的求解转化以系统负载均衡为优化目标的多目标优化问题,提出采用改进的基于非支配排序的遗传算法(NSGA Ⅱ)来求解该问题.与针对具体环境的调度算法相比,抽象的模型更能代表典型的云计算环境中的虚拟资源调度问题.对提出模型进行了仿真,实验结果表明了该模型的有效性和NSGA Ⅱ算法求解该问题的可行性,同时对比随机算法、静态算法和排序匹配调度算法,NSGA Ⅱ算法优于其他算法.     

On solving permutation scheduling problems with ant colony optimization

A new approach for solving permutation scheduling problems with ant colony optimization (ACO) is proposed in this paper. The approach assumes that no precedence constraints between the jobs have to be fulfilled. It is tested with an ACO algorithm for the single-machine total weighted deviation problem. In the new approach the ants allocate the places in the schedule not sequentially, as in the standard approach, but in random order. This leads to a better utilization of the pheromone information. It is shown by experiments that adequate combinations between the standard approach which can profit from list scheduling heuristics and the new approach perform particularly well.     

Sensitivity Analysis for Scheduling Problems

This paper represents a first attempt at a systematic study of sensitivity analysis for scheduling problems. Because schedules contain both combinatorial and temporal structures, scheduling problems present unique issues for sensitivity analysis. Some of the issues that we discuss have not been considered before. Others, while studied before, have not been explored in the context of scheduling. The applicability of these issues is illustrated using well-known scheduling models. We provide fast methods to determine when a previously optimal schedule remains optimal. Other methods restore an optimal schedule after a parameter change. The value of studying the sensitivity of an optimal sequence instead of the sensitivity of an optimal schedule is demonstrated. We show that, for some problems, sensitivity analysis results depend on the positions of jobs with changed parameters. We identify scheduling problems where performing additional or different computations during optimization facilitates sensitivity analysis. To improve the robustness of an optimal schedule, selection among multiple optimal schedules is considered. We discuss which types of sensitivity analysis questions are intractable because the scheduling problem itself is intractable. We also study how heuristic error bounds vary when the data of a scheduling problem is continuously modified. Although we focus on scheduling problems, several of the issues we discuss and our classification scheme can be extended to other optimization problems.     

带约束的清洁排班问题模型及其求解

保洁服务公司的清洁任务往往具有不同级别、不同时长和不同周期等特点,缺乏通用清洁排班问题模型,现阶段主要依赖人工排班方案,存在耗时费力且排班质量不稳定等问题.因此提出了属于NP难问题的带约束的清洁排班问题的数学模型,并使用模拟退火算法(SA)、蜂群算法(BCO)、蚁群算法(ACO)和粒子群优化算法(PSO)对该模型进行求...     

Multi-operator based evolutionary algorithms for solving constrained optimization problems

Over the last two decades, many sophisticated evolutionary algorithms have been introduced for solving constrained optimization problems. Due to the variability of characteristics in different COPs, no single algorithm performs consistently over a range of problems. In this paper, for a better coverage of the problem characteristics, we introduce an algorithm framework that uses multiple search operators in each generation. The appropriate mix of the search operators, for any given problem, is determined adaptively. The framework is tested by implementing two different algorithms. The performance of the algorithms is judged by solving 60 test instances taken from two constrained optimization benchmark sets from specialized literature. The first algorithm, which is a multi-operator based genetic algorithm (GA), shows a significant improvement over different versions of GA (each with a single one of these operators). The second algorithm, using differential evolution (DE), also confirms the benefit of the multi-operator algorithm by providing better and consistent solutions. The overall results demonstrated that both GA and DE based algorithms show competitive, if not better, performance as compared to the state of the art algorithms.     

Minimizing makespan subject to minimum flowtime on two identical parallel machines

We consider the problem of scheduling jobs on two parallel identical machines where an optimal schedule is defined as one that gives the smallest makespan (the completion time of the last job) among the set of schedules with optimal total flowtime (the sum of the completion times of all jobs). We propose an algorithm to determine optimal schedules for the problem, and describe a modified multifit algorithm to find an approximate solution to the problem in polynomial computational time. Results of a computational study to compare the performance of the proposed algorithms with a known heuristic shows that the proposed heuristic and optimization algorithms are quite effective and efficient in solving the problem.Scope and purposeMultiple objective optimization problems are quite common in practice. However, while solving scheduling problems, optimization algorithms often consider only a single objective function. Consideration of multiple objectives makes even the simplest multi-machine scheduling problems NP-hard. Therefore, enumerative optimization techniques and heuristic solution procedures are required to solve multi-objective scheduling problems. This paper illustrates the development of an optimization algorithm and polynomially bounded heuristic solution procedures for the scheduling jobs on two identical parallel machines to hierarchically minimize the makespan subject to the optimality of the total flowtime.     

组合优化调度问题求解方法

1.引言优化是指一个从一组解中选取出最优解或最适应解的过程。优化方法涉及的工程领域很广,问题种类与性质繁多。归纳而言,最优化问题可分为函数优化问题和组合优化问题。其中函数优化的对象是一定区间内的连续变量,而组合优化的对象则是解空间中的离散状态。函数优化问题通常可描述为:令S为R~n上的有界子集(即变量的定义域),f:S→R为n维     

A framework for reinforcement-based scheduling in parallelprocessor systems

Task scheduling is important for the proper functioning of parallel processor systems. The static scheduling of tasks onto networks of parallel processors is well-defined and documented in the literature. However, in many practical situations a priori information about the tasks that need to be scheduled is not available. In such situations, tasks usually arrive dynamically and the scheduling should be performed on-line or “on the fly”. In this paper, we present a framework based on stochastic reinforcement learning, which is usually used to solve optimization problems in a simple and efficient way. The use of reinforcement learning reduces the dynamic scheduling problem to that of learning a stochastic approximation of an unknown average error surface. The main advantage of the proposed approach is that no prior information is required about the parallel processor system under consideration. The learning system develops an association between the best action (schedule) and the current state of the environment (parallel system). The performance of reinforcement learning is demonstrated by solving several dynamic scheduling problems. The conditions under which reinforcement learning can used to efficiently solve the dynamic scheduling problem are highlighted     

Real coded chemical reaction based optimization for short-term hydrothermal scheduling

This paper presents a real coded chemical reaction based (RCCRO) algorithm to solve the short-term hydrothermal scheduling (STHS) problem. Hydrothermal system is highly complex and related with every problem variables in a nonlinear way. The objective of the hydro thermal scheduling is to determine the optimal hourly schedule of power generation for different hydrothermal power system for certain intervals of time such that cost of power generation is minimum. Chemical reaction optimization mimics the interactions of molecules in term of chemical reaction to reach a low energy stable state. A real coded version of chemical reaction optimization, known as real-coded chemical reaction optimization (RCCRO) is considered here. To check the effectiveness of the RCCRO, 3 different test systems are considered and mathematical remodeling of the algorithm is done to make it suitable for solving short-term hydrothermal scheduling problem. Simulation results confirm that the proposed approach outperforms several other existing optimization techniques in terms quality of solution obtained and computational efficiency. Results also establish the robustness of the proposed methodology to solve STHS problems.     

Balancing and scheduling of flexible mixed model assembly lines

Mixed model assembly line literature involves two problems: balancing and model sequencing. The general tendency in current studies is to deal with these problems in different time frames. However, in today’s competitive market, the mixed model assembly line balancing problem has been turned into an operational problem. In this paper, we propose mixed integer programming (MIP) and constraint programming (CP) models which consider both balancing and model sequencing within the same formulation along with the optimal schedule of tasks at a station. Furthermore, we also compare the proposed exact models with decomposition schemes developed for solving different instances of varying sizes. This is the first paper in the literature which takes into account the network type precedence diagrams and limited buffer capacities between stations. Besides, it is the first study that CP method is applied to balancing and scheduling of mixed model assembly lines. Our empirical study shows that the CP approach outperforms the MIP approach as well as the decomposition schemes.