Stochastic Machine Research Articles

A knowledge-based evolutionary proactive scheduling approach in the presence of machine breakdown and deterioration effect

This paper considers proactive scheduling in response to stochastic machine breakdown under deteriorating production environments, where the actual processing time of a job gets longer along with machine's usage and age. It is assumed that a job's processing time is controllable by allocating extra resources and the machine breakdown can be described using a given probability distribution. If a machine breaks down, it needs to be repaired and is no longer available during the repair. To absorb the repair duration, the subsequent unfinished jobs are compressed as much as possible to match up the baseline schedule. This work aims to find the optimal baseline sequence and the resource allocation strategy to minimize the operational cost consisting of the total completion time cost and the resource consumption cost of the baseline schedule, and the rescheduling cost consisting of the match-up time cost and additional resource cost. To this end, an efficient multi-objective evolutionary algorithm based on elitist non-dominated sorting is proposed, in which a support vector regression (SVR) surrogate model is built to replace the time-consuming simulations in evaluating the rescheduling cost, which represents the solution robustness of the baseline schedule. In addition, a priori domain knowledge is embedded in population initialization and offspring generation to further enhance the performance of the algorithm. Comparative results and statistical analysis show that the proposed algorithm is effective in finding non-dominated tradeoff solutions between operational cost and robustness in the presence of machine breakdown and deterioration effect.

A Novel Hyper-Active Algorithm to Estimate Missing Microarray Attributes

Classification the Microarray dataset is a powerful method used in clinical and biomedical studies, to estimate and diagnose some diseases like (cancer, non-cancer) depending on Gene expression. To be full beneficial, the gene expression dataset should be complete; i.e. with no missing data. Several approaches were proposed to deal with these missing values. In this paper, a robust algorithm is proposed based on the optimal fitting analysis to estimate the missing values in the microarray data. Then, the complete dataset is used to estimate the probability of lung cancer occurrence based on stochastic algorithm and support vector machine (SVM). The designed algorithm has been applied on different types of datasets varies from complete to different percent of missing data. Comparisons have been done with different other algorithms from the accuracy and error rates perspectives. The experimental results indicate that the proposed algorithm surpass other tested methods.

Perturbative theory for Brownian vortexes.

Brownian vortexes are stochastic machines that use static nonconservative force fields to bias random thermal fluctuations into steadily circulating currents. The archetype for this class of systems is a colloidal sphere in an optical tweezer. Trapped near the focus of a strongly converging beam of light, the particle is displaced by random thermal kicks into the nonconservative part of the optical force field arising from radiation pressure, which then biases its diffusion. Assuming the particle remains localized within the trap, its time-averaged trajectory traces out a toroidal vortex. Unlike trivial Brownian vortexes, such as the biased Brownian pendulum, which circulate preferentially in the direction of the bias, the general Brownian vortex can change direction and even topology in response to temperature changes. Here we introduce a theory based on a perturbative expansion of the Fokker-Planck equation for weak nonconservative driving. The first-order solution takes the form of a modified Boltzmann relation and accounts for the rich phenomenology observed in experiments on micrometer-scale colloidal spheres in optical tweezers.

A Generalizable Brain-Computer Interface (BCI) Using Machine Learning for Feature Discovery.

This work describes a generalized method for classifying motor-related neural signals for a brain-computer interface (BCI), based on a stochastic machine learning method. The method differs from the various feature extraction and selection techniques employed in many other BCI systems. The classifier does not use extensive a-priori information, resulting in reduced reliance on highly specific domain knowledge. Instead of pre-defining features, the time-domain signal is input to a population of multi-layer perceptrons (MLPs) in order to perform a stochastic search for the best structure. The results showed that the average performance of the new algorithm outperformed other published methods using the Berlin BCI IV (2008) competition dataset and was comparable to the best results in the Berlin BCI II (2002–3) competition dataset. The new method was also applied to electroencephalography (EEG) data recorded from five subjects undertaking a hand squeeze task and demonstrated high levels of accuracy with a mean classification accuracy of 78.9% after five-fold cross-validation. Our new approach has been shown to give accurate results across different motor tasks and signal types as well as between subjects.

Dynamic Power Management for Portable Hybrid Power-Supply Systems Utilizing Approximate Dynamic Programming

Recently, the optimization of power flows in portable hybrid power-supply systems (HPSSs) has become an important issue with the advent of a variety of mobile systems and hybrid energy technologies. In this paper, a control strategy is considered for dynamically managing power flows in portable HPSSs employing batteries and supercapacitors. Our dynamic power management strategy utilizes the concept of approximate dynamic programming (ADP). ADP methods are important tools in the fields of stochastic control and machine learning, and the utilization of these tools for practical engineering problems is now an active and promising research field. We propose an ADP-based procedure based on optimization under constraints including the iterated Bellman inequalities, which can be solved by convex optimization carried out offline, to find the optimal power management rules for portable HPSSs. The effectiveness of the proposed procedure is tested through dynamic simulations for smartphone workload scenarios, and simulation results show that the proposed strategy can successfully cope with uncertain workload demands.

A Dynamic Algorithm for Distributed Feedback Control for Manufacturing Production, Capacity, and Maintenance

We propose a dynamic algorithm for distributed feedback control which unifies the functions of production and maintenance scheduling at the shop floor level, and machinery capacity control at the CNC level, which are usually considered in isolation in practice. A continuous-time control theoretic approach is used to model dynamics of these three functions in a unified manner, considering stochastic machine failures and a corresponding maintenance interval. Theories of nonlinear control and discontinuous differential equations are used to analytically predict the system dynamics including the resulting discontinuous dynamics.

A bi-stable neuronal model of Gibbs distribution

In this paper we present a bi-stable neuronal model consistent with the Gibbs distribution. Our approach utilizes a formalism used in stochastic (Boltzmann) machines with a bistable-neuron algorithm in which each neuron can exist in either an ON or an OFF state. The transition between the system’s states is composed of two random processes, the first one decides which state transition should be attempted and the second one decides if the transition is accepted or not. Our model can be easily extended to systems with asymmetrical weight matrices.

QoS Evaluation of End-to-End Services in Virtualized Computing Environments

Quality of service (QoS) optimization for end-to-end (e2e) services always depends on performance analysis in cloud-based service delivery industry. However, performance analysis of e2e services becomes difficult as the scale and complexity of virtualized computing environments increase. In this paper, the authors present a novel hierarchical stochastic approach to evaluate the QoS of e2e virtualized cloud services using Quasi-Birth Death structures, where jobs arrive according to a stochastic process and request virtual machines (VMs), which are specified in terms of resources, i.e., VM-configuration. To reduce the complexity of performance evaluation, the overall virtualized cloud services are partitioned into three sub-hierarchies. The authors analyze each individual sub-hierarchy using stochastic queueing approach. Thus, the key performance metrics of e2e cloud service QoS, such as acceptance probability and e2e response delay incurred on user requests, are obtained.

Deep Cutting Plane Inequalities for Stochastic Non-Preemptive Single Machine Scheduling Problem

We study the classical single machine scheduling problem but with uncertainty. A robust optimization model is presented, and an effective deep cut is derived. Numerical experiments show effectiveness of the derived cut.

Robust scheduling for flexible job shop problems with random machine breakdowns using a quantum behaved particle swarm optimisation

This paper addresses a robust schedule for a flexible job shop scheduling problem with random machine breakdown. A multi objective framework based on quantum particle swarm optimisation (QPSO) is proposed to generate the predictive schedules that can simultaneously optimise the makespan and the robust measures. The results indicate that the proposed QPSO algorithm is quite effective in reducing makespan in the event that uncertainty is encountered in terms of stochastic machine breakdown. An exhaustive experimental study is conducted to study the effect of different proposed robustness measures on the generated schedules using benchmark problems.

Evaluation of the expected makespan of a set of non-resumable jobs on parallel machines with stochastic failures

In this paper we consider a production process at operative level on m identical parallel machines, which are subject to stochastic machine failures. To avoid long downtime of the machines, caused by unexpected failures, preventive maintenance activities are planned and conducted, but if a failure could not be averted a corrective maintenance has to be performed. Both maintenance activities are assumed to restore the machine to be “as good as new”. The maintenance activities, the number of jobs and their allocation to machines as well as their sequence have a large impact on the performance of the production process and the delivery dates.We study an order of n jobs, scheduled for a frozen period on the machines. It is assumed that jobs, interrupted by machine failure, have to get repeated right after the corrective maintenance is finished (non-resumable case). We first derive an exact formula for the expected makespan. Since the exact evaluation of a schedule is highly complex, we propose two approximations for the expected makespan. The excellent performance of the approximations is illustrated in a numerical study.

Hybrid simulation and MIP based heuristic algorithm for the production and distribution planning in the soft drink industry

This study addresses the production and distribution planning problem in the soft drink industry. The problem involves the allocation of production volumes among the different production lines in the manufacturing plants, and the delivery of products to the distribution centers (DCs). A mixed integer linear programming (MILP) model is developed for the problem.In this paper, we present a hybrid solution methodology combining simulation and mixed integer programming (MIP) based Fixed and Optimize heuristic to solve the considered problem. First, MIP based Fix and Relax (F&R), Fix and Optimize (F&O) heuristics are proposed. The solution quality and performance of the proposed heuristics are analyzed with the randomly generated demand figures for the three granularity categories and various capacity load scenarios. Computational performances of these heuristic procedures are compared with the standard MIP results. The computational experiments carried out on a large set of instances have shown that the F&O heuristic algorithm provides good quality solutions in a reasonable amount of time. Second, simulation model is introduced to represent the problem with stochastic machine failures. Hybrid methodology combining the MIP based F&O heuristic and simulation model is implemented. The optimization model uses an F&O heuristic to determine the production and delivered quantity. Subsequently the simulation model is applied to capture the uncertainty in the production rate. Numerical studies from the data which have a tight production capacity and high demand granularity demonstrate that the developed hybrid approach is capable of solving real sized instance within a reasonable amount of time and demonstrate the applicability of the proposed approach.

Stochastic Machine Scheduling to Minimize Waiting Time Related Objectives with Emergency Jobs

We consider a new scheduling model where emergency jobs appear during the processing of current jobs and must be processed immediately after the present job is completed. All jobs have random processing times and should be completed on a single machine. The most common case of the model is the surgery scheduling problem, where some elective surgeries are to be arranged in an operation room when emergency cases are coming during the operating procedure of the elective surgeries. Two objective functions are proposed to display this practice in machine scheduling problem. One is the weighted sum of the waiting times and the other is the weighted discounted cost function of the waiting times. We address some optimal policies to minimize these objectives.

On the exploration of convexity about the expected total cost per unit time of replenishment run time problem with machine breakdown and failure in rework

Recently, Chiu et al. [Expert Systems with Applications 39 (2012) 1291-1297] study the optimal replenishment run time for a production system with stochastic machine breakdown and failure in rework. Basically, their model is rather interesting. However, their solution procedure based on Theorem 1 of Chiu et al. (2012) has shortcomings from the fundamentals of mathematics. The main purpose of this paper not only indicates its shortcomings but also presents the correct solution procedure for Chiu et al. (2012).

On the convexity for the expected total cost per unit time of the EPQ model with scrap, rework and stochastic machine breakdown

This study explores the economic production quantity model with scrap, rework and stochastic machine breakdown. The main purpose of this paper is twofold:(P1) This paper will adopt the rigorous methods of mathematics to demonstrate that the expected total cost per unit time is convex on all positive numbers to improve the conditional convexity in Theorem 1 of Chiu et al. (2010) [7].(P2) This paper gives the concrete proof to provide bounds for the optimal production run time to remove the logical shortcomings of mathematics presented in proof of Theorem 2 of Chiu et al. (2010) [7].

Analysis of Smith’s rule in stochastic machine scheduling

In a landmark paper from 1986, Kawaguchi and Kyan show that scheduling jobs according to ratios weight over processing time–also known as Smith’s rule–has a tight performance guarantee of (1+2)/2≈1.207 for minimizing the weighted sum of completion times in parallel machine scheduling. We prove the counterintuitive result that the performance guarantee of Smith’s rule is not better than 1.243 when processing times are exponentially distributed.

EPQ Model for Trended Demand with Rework and Random Preventive Machine Time

Economic production quantity (EPQ) inventory model for trended demand has been analyzed with rework facility and stochastic preventive machine time. Due to the complexity of the model, search method is proposed to determine the best optimal solution. A numerical example and sensitivity analysis are carried out to validate the proposed model. From the sensitivity analysis, it is observed that the rate of change of demand has significant impact on the optimal inventory cost. The model is very sensitive to the production and demand rate.

Stochastic machines as a colocalization mechanism for scaffold protein function

The axis inhibition (Axin) scaffold protein colocalizes β-catenin, casein kinase Iα, and glycogen synthetase kinase 3β by their binding to Axin’s long intrinsically disordered region, thereby yielding structured domains with flexible linkers. This complex leads to the phosphorylation of β-catenin, marking it for destruction. Fusing proteins with flexible linkers vastly accelerates chemical interactions between them by their colocalization. Here we propose that the complex works by random movements of a “stochastic machine,” not by coordinated conformational changes. This non-covalent, modular assembly process allows the various molecular machine components to be used in multiple processes.

Stochastic bicriteria single machine scheduling with quadratic cost functions

In real world scheduling systems, job attributes are stochastic and schedulers are required to consider multiple criteria before arriving at some decisions. Moreover, schedulers incorporate their risk taking behaviour, characterised by their cost (or disutility) functions, into scheduling decisions. This paper deals with a single machine scheduling problem in which job attributes are random variables and a scheduler’s cost function for sequence evaluation is quadratic in two criteria. The objective is to determine the optimal sequence that minimises the scheduler’s expected cost of the criteria. The problem is NP-hard; however, it can be solved exactly when at least one of the criteria is a regular measure. We show that some cases have exact polynomial time solutions, while the rest can be formulated as quadratic assignment problems that are solvable either exactly or approximately. The results demonstrate that the schedulers’ risk taking behaviour, the stochasticity of job attributes, and the two criteria affect scheduling decisions. Our computational experiments on the cases with quadratic assignment formulations indicate that the proposed heuristic performs well in producing good sequences within reasonable amounts of time.

An integrated neural network–simulation algorithm for performance optimisation of the bi-criteria two-stage assembly flow-shop scheduling problem with stochastic activities

This paper presents an integrated computer simulation and Artificial Neural Network (ANN) algorithm for a stochastic Two-Stage Assembly Flow-Shop Scheduling Problem (TSAFSP) with setup times under a weighted sum of makespan and mean completion time (MCT) criteria, known as bi-criteria. Significantly, it should be noted that there is no mathematical model to analyse the stochastic model, therefore simulation is used to solve the problem. The simulation model enables decision makers to consider the influence of job scheduling on machines in order to examine both criteria simultaneously. Since it is not possible to evaluate all sequence combinations using the simulation model in a reasonable time, multilayered neural network meta-models have been trained and used to estimate objective function values composed of both makespan and mean completion time criteria for the stochastic TSAFSP. To the best of the authors’ knowledge, this is the first study that considers stochastic machine breakdown, processing times, setup times, makespan and mean completion time as objectives concurrently. The TSAFSP is modelled by Visual SLAM simulation software. The simulation output results are then given to the ANN as inputs to build the meta-model. This meta-model is then used to obtain the results with the optimum values. The advantage of these meta-model applications is a reduction in the number of simulation runs and consequently a reduced run time. Also, this is the first study that introduces an intelligent and flexible algorithm for handling stochastic TSAFSP.