A spectral clustering algorithm for manufacturing cell formation

A graph clustering algorithm constructs groups of closely related parts and machines separately. After they are matched for the least intercell moves, a refining process runs on the initial cell formation to decrease the number of intercell moves. A simple modification of this main approach can deal with some practical constraints, such as the popular constraint of bounding the maximum number of machines in a cell. Our approach makes a big improvement in the computational time. More importantly, improvement is seen in the number of intercell moves when the computational results were compared with best known solutions from the literature.     

A minimum-cost network flow approach to preemptive parallel-machine scheduling

We model and solve the problems of preemptive scheduling of n independent jobs with release dates on m parallel machines with machine availability and eligibility constraints to minimize the makespan and maximum lateness as the minimum-cost network flow problem. We show that the approach can be extended to solve the corresponding scheduling problems on two uniform parallel machines.     

Machine cell formation in generalized group technology

In this paper, we study the configuration of machine cells in the presence of alternative routings for part types. The objective function is the minimization of transportation costs. Limits on cell sizes as well as separation constraints (i.e. machines that are not allowed to be placed in the same cell) and co-location constraints (i.e. machines that must be placed in the same cell) may be imposed. An efficient Tabu Search (TS) algorithm is proposed to solve this problem. Extensive computational experiences with large-size problems show that this method outperforms some existing Simulated Annealing (SA) approaches.     

An energy-aware scheduling algorithm under maximum power consumption constraints

This research investigates the production scheduling problems under maximum power consumption constraints. Probabilistic models are developed to model dispatching-dependent and stochastic machine energy consumption. A multi-objective scheduling algorithm called the energy-aware scheduling optimization method is proposed in this study to enhance both production and energy efficiency. The explicit consideration of the probabilistic energy consumption constraint and the following factors makes this work distinct from other existing studies in the literature: 1) dispatching-dependent energy consumption of machines, 2) stochastic energy consumption of machines, 3) parallel machines with different production rates and energy consumption pattern, and 4) maximum power consumption constraints. The proposed three-stage algorithm can quickly generate near-optimal solutions and outperforms other algorithms in terms of energy efficiency, makespan, and computation time. While minimizing the total energy consumption in the first and second stages, the proposed algorithm generates a detailed production schedule under the probabilistic constraint of peak energy consumption in the third stage. Numerical results show the superiority of the scheduling solution with regard to quality and computational time in real problems instances from manufacturing industry. While the scheduling solution is optimal in total energy consumption, the makespan is within 0.6 % of the optimal on average.     

Sensitivity bounds for machine scheduling with uncertain communication delays

The paper deals with the scheduling of tasks on a set of parallel machines subject to precedence constraints and communication delays, that are not fully known before the execution. This is usual in parallel computing (message passing) and in production workshops (part transportation). The goal is to give a priori informations on the behavior of different schedules computed before the execution. This sensitivity analysis helps to choose among different available algorithms. It also provides tools to decide whether it is justified to change the schedule structure at execution time (run-time scheduling).By hypothesis, the communication delays are within a given interval. Worst case sensitivity bounds are proposed that give the maximum loss of performance. These bounds hold for algorithms which are optimal in the deterministic case, but can be easily adapted to arbitrary algorithms. Some applications to specific problems are presented, namely two identical machines, and unbounded number of machines, for tree-like precedence constraints.     

Simultaneous machine-part grouping approach in manufacturing cells

We present a comprehensive model including all of the operational constraints for solving a cell formation problem in cellular manufacturing systems. It is formulated as a generalized quadratic binary programming model with the objective of minimizing total moves evaluated as a weighted sum of inter- and intracell moves. Two most significant operational constraints included in the model are the sequence of operations associated with each part and the capability of assigning machines of the same type to different cells if two or more machines are considered due to workload requirements. The original model is Transformed into a linear binary programming model, and an example problem is solved using a commercial programming package. The final assignment of parts and machines to cells result in a lower total move than that evaluated from a previous study for the same problem.     

On a parallel machine scheduling problem with precedence constraints

We characterize a nontrivial special case with a polynomial-time algorithm for a well-known parallel machine scheduling problem with precedence constraints, with a fixed number of machines, and with tasks of unit length. The special case is related to instances with given maximum path length and maximum degree of the task precedence graph. The method is based on the observation that the number of tasks is either small and bounded by a constant depending on the maximum path length and maximum degree, or alternatively, the number of tasks is large, giving a “dense” schedule.     

三台等级机器上带重排的半在线问题

研究了3台机上带2种等级的重排问题,当所有工件都被分配之后,在等级约束下,可以重排一台机器上的最后一个工件,目标是最小化最大完工时间。3台机上带2种等级分为2种情形：第1种是有1台机器的等级为1,另2台机器的等级为2;第2种是2台机器的等级为1,另1台机器的等级为2。针对第1种情形给出了一个竞争比下界为3/2,并提出了一个竞争比至多为5/3的在线算法;针对第2种情形给出了一个竞争比下界为3/2,并提出了一个竞争比至多为12/7的在线算法。     

Genetic algorithm for balancing reconfigurable machining lines

We consider the problem of designing a reconfigurable machining line. Such a line is composed of a sequence of workstations performing specific sets of operations. Each workstation is comprised of several identical CNC machines (machining centers). The line is required to satisfy the given precedence order, inclusion, exclusion and accessibility constraints on the given set of operations. Inclusion and exclusion are zoning constraints which oblige or forbid certain operations to be performed on the same workstation. The accessibility constraints imply that each operation has a set of possible part positions under which it can be performed. All the operations performed on the same workstation must have a common part position. Workstation times are computed taking into account processing and setup times for operations and must not exceed a given bound. The number of CNC machines at one workstation is limited, and the total number of machines must be minimized. A genetic algorithm is proposed. This algorithm is based on the permutation representation of solutions. A heuristic decoder is suggested to construct a solution from a permutation, so that the output solution is feasible w.r.t. precedence, accessibility, cycle time, and exclusion constraints. The other constraints are treated with a penalty approach. For a local improvement of solutions, a mixed integer programming model is suggested for an optimal design of workstations if the order of operations is fixed. An experimental evaluation of the proposed GA on large scale test instances is performed.     

Maximum Entropy Models with Inequality Constraints: A Case Study on Text Categorization

Data sparseness or overfitting is a serious problem in natural language processing employing machine learning methods. This is still true even for the maximum entropy (ME) method, whose flexible modeling capability has alleviated data sparseness more successfully than the other probabilistic models in many NLP tasks. Although we usually estimate the model so that it completely satisfies the equality constraints on feature expectations with the ME method, complete satisfaction leads to undesirable overfitting, especially for sparse features, since the constraints derived from a limited amount of training data are always uncertain. To control overfitting in ME estimation, we propose the use of box-type inequality constraints, where equality can be violated up to certain predefined levels that reflect this uncertainty. The derived models, inequality ME models, in effect have regularized estimation with L ₁ norm penalties of bounded parameters. Most importantly, this regularized estimation enables the model parameters to become sparse. This can be thought of as automatic feature selection, which is expected to improve generalization performance further. We evaluate the inequality ME models on text categorization datasets, and demonstrate their advantages over standard ME estimation, similarly motivated Gaussian MAP estimation of ME models, and support vector machines (SVMs), which are one of the state-of-the-art methods for text categorization.     

A multiple-objective grouping genetic algorithm for the cell formation problem with alternative routings

This paper addresses the cell formation problem with alternative part routings, considering machine capacity constraints. Given processes, machine capacities and quantities of parts to produce, the problem consists in defining the preferential routing for each part optimising the grouping of machines into manufacturing cells. The main objective is to minimise the inter-cellular traffic, while respecting machine capacity constraints. To solve this problem, the authors propose an integrated approach based on a multiple-objective grouping genetic algorithm for the preferential routing selection of each part (by solving an associated resource planning problem) and an integrated heuristic for the cell formation problem.     

Can mature patch constraints mitigate the fragmenting effects of harvest opening size restrictions?

Harvest scheduling models often include maximum harvest opening size constraints, a restriction generally imposed for legal or policy reasons. The maximum harvest opening size restriction can greatly affect the spatial layout of the forest, with the dispersed harvesting increasing forest fragmentation. Because they can offset the negative impacts of maximum harvest opening size constraints, mature patch size constraints, which require a certain amount of the forest to be in patches meeting both minimum size and age requirements, have also been included in these models. This paper looks at the economic and spatial effects of ten harvest scheduling formulations with these two constraint sets on 21 hypothetical forest landscapes. Analyses of their age‐class distributions, border distributions, and patch size distributions at the end of a 60‐year planning horizon confirm that maximum harvest opening size constraints tend to fragment forest landscapes and that mature patch constraints can significantly reduce these effects.     

Scheduling jobs on identical machines with agreement graph

We consider the following problem of scheduling with agreements: a set of jobs must be scheduled non-preemptively on identical machines subject to constraints that only some specific jobs can be scheduled concurrently on different machines. These constraints are represented by an agreement graph and the aim is to minimize the makespan. This problem is NP-hard. We study the complexity of the problem for two machines and arbitrary bipartite agreement graphs, in particular we prove the NP-hardness of the open problem proposed in the literature which is the case of two machines with processing times at most 3. We propose list algorithms with empirical results for the problem in the general case.     

A two-stage hybrid flowshop scheduling problem with a function constraint and unrelated alternative machines

This article addresses a two-stage hybrid flowshop scheduling problem with unrelated alternative machines. The problem to be studied has m unrelated alternative machines at the first machine center followed by a second machine center with a common processing machine in the system. The objective is to minimize the makespan of the system. For the processing of any job, it is assumed that the operation can be partially substituted by other machines in the first center, depending on its machining constraints. Such scheduling problems occur in certain practical applications such as semiconductors, electronics manufacturing, airplane engine production, and petrochemical production. We demonstrate that the addressed problem is NP-hard and then provide some heuristic algorithms to solve the problem efficiently. The experimental results show that the combination of the modified Johnson's rule and the First-Fit rule provides the best solutions within all proposed heuristics.Scope and purpose     

Efficient symmetry breaking formulations for the job grouping problem

The job grouping problem consists of assigning a set of jobs, each with a specific set of tool requirements, to machines with a limited tool capacity in order to minimize the number of machines needed. Traditionally, a formulation has been used that assigns jobs to machines. However, such a formulation contains a lot of symmetry since the machines are identical and they can be permuted in any feasible solution. We propose a new formulation for this problem, based on the asymmetric representatives formulation (ARF) idea. This formulation eliminates the symmetry between the identical machines. We further propose various symmetry breaking constraints, including variable reduction and lexicographic ordering constraints, which can be added to the traditional formulation. These formulations are tested on a data set from the literature and newly generated data sets using a state-of-the-art commercial solver, which includes symmetry breaking features.     

Relaxed constraints support vector machine

This paper presents a new model of support vector machines (SVMs) that handle data with tolerance and uncertainty. The constraints of the SVM are converted to fuzzy inequality. Giving more relaxation to the constraints allows us to consider an importance degree for each training samples in the constraints of the SVM. The new method is called relaxed constraints support vector machines (RSVMs). Also, the fuzzy SVM model is improved with more relaxed constraints. The new model is called fuzzy RSVM. With this method, we are able to consider importance degree for training samples both in the cost function and constraints of the SVM, simultaneously. In addition, we extend our method to solve one‐class classification problems. The effectiveness of the proposed method is demonstrated on artificial and real‐life data sets.     

Using column generation to solve parallel machine scheduling problems with minmax objective functions

In this paper we consider the parallel machine scheduling problem of minimizing an objective function of the minmax type, like maximum lateness, subject to release dates, deadlines, and/or generalized precedence constraints. We use a destructive strategy to compute a lower bound. Here we test the feasibility of a decision problem by applying column generation to compute a bound on the number of machines that we need to feasibly accommodate all jobs. After having derived the lower bound, we try to find a matching upper bound by identifying a feasible schedule with objective function value equal to this lower bound. Our computational results show that our lower bound is so strong that this is almost always possible. We are able to solve problems with up to 160 jobs and 10 machines in 10 minutes on average.     

改进布谷鸟算法求解双资源约束柔性车间调度问题

针对双资源约束的柔性车间调度问题（DRCFJSP）,以优化最大完工时间为目标,设计出一种具有改进解码方案的布谷鸟算法对其进行求解。由于DRCFJSP除了需要考虑机器的分配,还需要兼顾工人的加工情况,所以改进了传统解码方式以避免机器和工人在加工时间上的冲突,同时在解码时尽可能利用机器和工人的空闲时间。在布谷鸟算法核心框架下,将布谷鸟种群随机划分为三个子群,每个子群采用不同Lévy飞行方式独立进行寻优,并通过差分算子实现子群间信息交流,不仅增强了算法的全局搜索能力也平衡了算法的局部搜索能力。最后通过基准测试算例进行实验仿真分析并与其他算法进行对比,验证了改进布谷鸟算法和改进解码方法的有效性优越性。     

Topology optimization of continuum structures with local and global stress constraints

Topology structural optimization problems have been usually stated in terms of a maximum stiffness (minimum compliance) approach. The objective of this type of approach is to distribute a given amount of material in a certain domain, so that the stiffness of the resulting structure is maximized (that is, the compliance, or energy of deformation, is minimized) for a given load case. Thus, the material mass is restricted to a predefined percentage of the maximum possible mass, while no stress or displacement constraints are taken into account. This paper presents a different strategy to deal with topology optimization: a minimum weight with stress constraints Finite Element formulation for the topology optimization of continuum structures. We propose two different approaches in order to take into account stress constraints in the optimization formulation. The local approach of the stress constraints imposes stress constraints at predefined points of the domain (i.e. at the central point of each element). On the contrary, the global approach only imposes one global constraint that gathers the effect of all the local constraints by means of a certain so-called aggregation function. Finally, some application examples are solved with both formulations in order to compare the obtained solutions.     

Application of a genetic algorithm in solving the capacity allocation problem with machine dedication in the photolithography area

Wafer fabrication is a complicated manufacturing process with high process capability. Hence, maximizing machine capacity to meet customer deadlines is a very important issue in this field. This study proposes an integer programming model and a heuristic algorithm approach to solve the loading balance problem for the photolithography area in the semiconductor manufacturing industry. Considering process capability, machine dedication, and reticle constraints, we aim to minimize the difference in loading between machines. Process capability means that each product must be processed in machines that meet the process specification. Machine dedication means that if the first critical layer of a wafer is assigned to a certain machine, then the following critical layers of such wafer must be processed in this certain machine to ensure wafer quality. This research compares the results of two methods and finds the best parameter settings of the genetic algorithm (GA). The computational performance results of the GA shows that we can find the near-optimal solution within a reasonable amount of time. Finally, this research analyzes machine capability and reticle flexibility to determine the best percentage that can be used as reference for application in the semiconductor industry.