Fault-tolerant embedded system design and optimization considering reliability estimation uncertainty

In this paper, we model embedded system design and optimization, considering component redundancy and uncertainty in the component reliability estimates. The systems being studied consist of software embedded in associated hardware components. Very often, component reliability values are not known exactly. Therefore, for reliability analysis studies and system optimization, it is meaningful to consider component reliability estimates as random variables with associated estimation uncertainty. In this new research, the system design process is formulated as a multiple-objective optimization problem to maximize an estimate of system reliability, and also, to minimize the variance of the reliability estimate. The two objectives are combined by penalizing the variance for prospective solutions. The two most common fault-tolerant embedded system architectures, N-Version Programming and Recovery Block, are considered as strategies to improve system reliability by providing system redundancy. Four distinct models are presented to demonstrate the proposed optimization techniques with or without redundancy. For many design problems, multiple functionally equivalent software versions have failure correlation even if they have been independently developed. The failure correlation may result from faults in the software specification, faults from a voting algorithm, and/or related faults from any two software versions. Our approach considers this correlation in formulating practical optimization models. Genetic algorithms with a dynamic penalty function are applied in solving this optimization problem, and reasonable and interesting results are obtained and discussed.     

Layout of production lines considering the material movement system

Summary An Algorithm to minimize the number of bends in a production line is developed. This algorithm can be combined with existing methods to lay out industrial plants.

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Zusammenfassung Es wird ein Algorithmus entwickelt, der die Zahl von Biegungen in einem Fließband minimiert. Der Algorithmus kann mit vorhandenen Layoutplanungsmethoden kombiniert werden.

     

Supply chain network optimization considering assembly line balancing and demand uncertainty

In supply chain optimisation problems, determining the location, number and capacity of facilities is concerned as strategic decisions, while mid-term and short-term decisions such as assembly policy, inventory levels and scheduling are considered as the tactical and operational decision levels. This paper addresses the optimisation of strategic and tactical decisions in the supply chain network design (SCND) under demand uncertainty. In this respect, a two-stage stochastic programming model is developed in which strategic location decisions are made in the first-stage, while the second-stage contains SCND problem and the assembly line balancing as a tactical decision. In the solution scheme, the combination of sample average approximation and Latin hypercube sampling methods is utilised to solve the developed two-stage mixed-integer stochastic programming model. Finally, computational experiments on randomly generated problem instances are presented to demonstrate the performance and power of developed model in handling uncertainty. Computational experiments showed that stochastic model yields better results compared with deterministic model in terms of objective function value, i.e. the sum of the first-stage costs and the expected second-stage costs. This issue proved that uncertainty would be a significant and fundamental element of developed model and improve the quality of solutions.     

Stress constrained topology optimization simultaneously considering the uncertainty of load positions

This study presents a topological optimization method simultaneously considering the stress constraint and the uncertainty of the load positions for practical applications. The phase field design method is used to derive the topologically optimal structure shape. The stress penalization function, which makes intermediate design variable values disproportionately expensive, is employed to ensure numerical stability and avoid the singularity during the optimization process. The adaptive mesh refinement and a modified P-norm stress with correction factor are also employed to reduce the computational cost. As numerical examples, cantilever beam, L-shaped, and MBB-beam are presented to verify the proposed design method. The open-source code FreeFEM++ is used for the finite element analysis and the design process.     

An entropy-based three-stage approach for multi-objective system reliability optimization considering uncertainty

This article presents a three-stage approach for solving multi-objective system reliability optimization problems considering uncertainty. The reliability of each component is considered in the formulation as a component reliability estimate in the form of an interval value and discrete values. Component reliability may vary owing to variations in the usage scenarios. Uncertainty is described by defining a set of usage scenarios. To address this problem, an entropy-based approach to the redundancy allocation problem is proposed in this study to identify the deterministic reliability of each component. In the second stage, a multi-objective evolutionary algorithm (MOEA) is applied to produce a Pareto-optimal solution set. A hybrid algorithm based on k-means and silhouettes is performed to select representative solutions in the third stage. Finally, a numerical example is presented to illustrate the performance of the proposed approach.     

Reliability and cost optimization of electronic devices considering the component failure rate uncertainty

The objective of this paper is to present an efficient computational methodology to obtain the optimal system structure of electronic devices by using either a single or a multiobjective optimization approach, while considering the constraints on reliability and cost. The component failure rate uncertainty is taken under consideration and it is modeled with two alternative probability distribution functions. The Latin hypercube sampling method is used to simulate the probability distributions. An optimization approach was developed using the simulated annealing algorithm because of its flexibility to be applied in various system types with several constraints and its efficiency in computational time. This optimization approach can handle efficiently either the single or the multiobjective optimization modeling of the system design. The developed methodology was applied to a power electronic device and the results were compared with the results of the complete enumeration of the solution space. The stochastic nature of the best solutions for the single objective optimization modeling of the system design was sampled extensively and the robustness of the developed optimization approach was demonstrated.     

A robust optimization approach for the capacitated vehicle routing problem with demand uncertainty

In this paper we introduce a robust optimization approach to solve the Vehicle Routing Problem (VRP) with demand uncertainty. This approach yields routes that minimize transportation costs while satisfying all demands in a given bounded uncertainty set. We show that for the Miller-Tucker-Zemlin formulation of the VRP and specific uncertainty sets, solving for the robust solution is no more difficult than solving a single deterministic VRP. Our computational results on benchmark instances and on families of clustered instances show that the robust solution can protect from unmet demand while incurring a small additional cost over deterministic optimal routes. This is most pronounced for clustered instances under moderate uncertainty, where remaining vehicle capacity is used to protect against variations within each cluster at a small additional cost. We compare the robust optimization model with classic stochastic VRP models for this problem to illustrate the differences and similarities between them. We also observe that the robust solution amounts to a clever management of the remaining vehicle capacity compared to uniformly and non-uniformly distributing this slack over the vehicles.     

Cellular manufacturing systems design with routing flexibility,machine procurement,production planning and dynamic system reconfiguration

This paper investigates the problem of designing cellular manufacturing systems with multi-period production planning, dynamic system reconfiguration, operation sequence, duplicate machines, machine capacity and machine procurement. An important aspect of this problem is the introduction of routing flexibility in the system by the formation of alternate contingency process routings in addition to alternate main process routings for all part types. Contingency routings serve as backups so as to effectively address the reality of part process routing disruptions (in the main routings) owing to machine breakdowns and allow the cellular manufacturing system to operate in a continuous manner even in the event of such breakdowns. The paper also provides in-depth discussions on the trade-off between the increased flexibility obtained versus the additional cost to be incurred through the formation of contingency routings for all parts. Some sensitivity analysis is also performed on some of the model parameters. The problem is modelled and solved through a comprehensive mixed integer programming formulation. Computational results presented by solving some numerical examples show that the routing and process flexibilities can be incorporated within the cellular manufacturing system design without significant increase in the system cost.     

Cause of failure and optimization of a V-belt pulley considering fatigue life uncertainty in automotive applications

High accuracy of dimensions and strength in design requirements are required to produce reliable automotive components with consistent strength distribution. For example, a V-belt pulley is widely used to transmit power between rotational mechanical elements. However, due to defects from the manufacturing process and heterogeneity of materials, different kinds of failure damage may occur in pulleys of identical shape and material. Common applications in the automotive industry include crankshafts, water pumps, air-conditioner compressors and power steering pumps. Although the shape and the usage of pulleys are very simple, evaluating the pulley design is difficult because the loading conditions and installation environment are complicated. This paper focuses on the clutch pulley in the A/C compressor system of automotives and cause of failure was investigated. The applied stress distribution of the pulley under high-tension and torque was obtained by using finite element analysis (FEA) and based on theses results, the life of the pulley with variation in fatigue strength was estimated with a durability analysis simulator. The results for failure probabilities of 50% and 1% were compared with the fatigue life. Incidentally, the purpose of this study was to optimize the fatigue life of vehicle components from the stochastic point of view. The fatigue life was obtained by an approximation function, and the optimum design was verified by fatigue tests considering durability and validity. The design optimization of a V-belt pulley was performed using an approximation function, which improved the fatigue life. A new shape optimization procedure was presented to improve the fatigue life of the pulley in automotive applications and the shape control concept was introduced to reduce the shape design variables. Design of experiment (DOE) was employed to evaluate the design sensitivity of fatigue life with respect to shape design variables.     

An integrated emergency ordering and production planning optimization model with demand and yield uncertainty

This paper proposes an integrated emergency ordering and production planning scheme for a multi-item, multi-product problem in which each product is composed of several ingredients. Each item can be supplied from both cheap unreliable suppliers prone to yield uncertainty and expensive reliable suppliers. A two-stage decision-making process is proposed in which orders are placed to the unreliable suppliers during the first stage and an emergency order can be placed in the second stage. In addition, a flexible backup ordering contract between the buyer and emergency supplier is proposed. A similar two-stage decision-making process is considered for production planning, where in the first stage, the main production plan is determined and in the second stage, the decision about a limited increase in the production plan is made as an emergency decision. An integrated ordering and production planning decision process is proposed for the problem. The value of emergency decisions, including the value of emergency ordering and the value of emergency production planning evaluates the effectiveness of the emergency decisions. Due to the staggering size of the problem, sample average approximation method is used to solve the problem.     

Surface roughness modelling considering uncertainty in measurements

Surface finish tends to be decisive in a large number of applications and, in general, it must be corrected by means of finishing operations. It is also highly important that the characteristics required from the products obtained should be determined beforehand, and on this basis the operating conditions that most closely suit the materials to be employed and their characteristics should be chosen. Factorial design will be employed to study the effects of these operating conditions. Although factorial design is a known technique for analysing the effect of variables over an objective function, the uncertainty of these variables is often ignored. This means that the true behaviour of the objective function cannot be explained. Most of the previous investigators have studied the effect of cutting variables on surface roughness and many different models have been proposed, but they do not take uncertainty in the measurements into accountand this uncertainty is often ignored - in order to perform the regression analysis. In this paper, a development of models that would allow us to determine the surface quality of parts, obtained by turning processes, is carried out, using the response surface methodology and considering the uncertainty due to the process and the measuring instruments. In addition, a methodology for determining the capability of manufacturing processes is presented.     

Pricing optimization,channel and uncertainty

This paper conducts a state-of-the-art review for a particular emerging field of Production Research: pricing optimisation, channel and uncertainty. This is achieved by presenting a set of state-of-the-art papers accepted to this special issue, and co-word analysis to trace the development of this research field. Data for co-word analysis is based on literature search in the International Journal of Production Research, since 1961 using Web of Science with the Keywords ‘pricing optimization’, ‘channel’ or ‘uncertainty’. Pricing approaches and tools have attracted more and more attentions from multiple disciplinary such as supply-chain management and marketing. The objective of this special issue is to contribute new insights to the extant body of knowledge in pricing optimisation, channel and uncertainty, specifically for 55th anniversary of International Journal of Production Research.     

The effects of routing flexibility in a multi-stage pull-type system

The pull-type manufacturing system is known for its need for a frozen schedule, balanced work load and inability to handle fluctuations in demand. But today research and development are addressing ways to handle a pull-type system to accommodate greater fluctuations. One approach is to design the system with machines that have a greater routing flexibility in what work they can perform. However, most of the existing literature dealing with routing flexibility has primarily been devoted to the push-type production systems. This research examined the effects of routing flexibility for a multi-stage kanban-controlled pull-type system.     

Optimization of laminated composite structure considering uncertainty effects

In this paper, the most conservative Tsai–Wu failure envelopes are obtained for laminated composite considering material as well as ply angle uncertainty. The uncertainty analysis is performed using Monte Carlo simulation (MCS). The obtained failure envelopes are then used as the constraint functions to perform the minimum weight design optimization problem using particle swarm optimization (PSO). Results show increase in weight of the laminate from the deterministic results and it varies from 4% to 50% depending upon the stacking sequence and loading condition. Substantial effects of uncertainty on the failure envelope and optimal design are quantified.     

Reoptimization framework and policy analysis for maritime inventory routing under uncertainty

We study a maritime inventory routing problem, in which shipments between production and consumption nodes are carried out by a fleet of vessels. The vessels have specific capacities and can be chartered under different agreements. The inventory levels of all consumption nodes and some production nodes should be maintained within specified bounds; for the remaining production nodes, orders should be picked up within pre-defined time windows. We propose a discrete-time mixed-integer programming model. In the face of new information and uncertainty, this optimization model has to be re-solved, as the horizon is rolled forward. We discuss how to account for different sources of uncertainty. We present a rolling-horizon reoptimization framework that allows us to study different policies that impact the quality of the implemented solution, so we can identify the optimal set of policies.     

Study on the vehicle routing problem considering congestion and emission factors

To meet the requirement of greening transportation in poor traffic condition, vehicle routing problem (VRP) with consideration of fuel consumption and congestion is studied. We formulated a time-dependent green vehicle routing problem (TD-GVRP) model with minimised total cost as the objective function which includes fuel consumption cost, and the measurement of fuel consumption is based on the Comprehensive Modal Emissions Model (CMEM). In the model, the situation of waiting at customer nodes to avoid bad traffic is defined. To solve this model, a Response Surface Method (RSM)-based hybrid algorithm (HA) that combines genetic algorithm (GA) and particle swarm optimisation (PSO) is constructed. Finally, using instances from PRPLIB database, the following experiments are carried out and the corresponding conclusions are drawn. (i) Comparison of the proposed objective and traditional VRP objectives shows that fuel consumption can be greatly reduced by introducing fuel consumption factor into the objective function. (ii) Sensitivity analysis of congestion duration provides the influence of congestion duration on fuel consumption and travel time. (iii) Experiments based on different waiting time reveal that the optimisation of departure time can reduce fuel consumption and total cost to some extent.     

Aerospace applications of optimization under uncertainty

The Multidisciplinary Optimization (MDO) Branch at NASA Langley Research Center develops new methods and investigates opportunities for applying optimization to aerospace vehicle design. This paper describes MDO Branch experiences with three applications of optimization under uncertainty: (1) improved impact dynamics for airframes, (2) transonic airfoil optimization for low drag, and (3) coupled aerodynamic and structures optimization of a 3-D wing. For each case, a brief overview of the problem and references to previous publications are provided. The three cases are aerospace examples of the challenges and opportunities presented by optimization under uncertainty. The present paper will illustrate a variety of needs for this technology, summarize promising methods, and uncover fruitful areas for new research.     

Multifidelity approaches for optimization under uncertainty

It is important to design robust and reliable systems by accounting for uncertainty and variability in the design process. However, performing optimization in this setting can be computationally expensive, requiring many evaluations of the numerical model to compute statistics of the system performance at every optimization iteration. This paper proposes a multifidelity approach to optimization under uncertainty that makes use of inexpensive, low‐fidelity models to provide approximate information about the expensive, high‐fidelity model. The multifidelity estimator is developed based on the control variate method to reduce the computational cost of achieving a specified mean square error in the statistic estimate. The method optimally allocates the computational load between the two models based on their relative evaluation cost and the strength of the correlation between them. This paper also develops an information reuse estimator that exploits the autocorrelation structure of the high‐fidelity model in the design space to reduce the cost of repeatedly estimating statistics during the course of optimization. Finally, a combined estimator incorporates the features of both the multifidelity estimator and the information reuse estimator. The methods demonstrate 90% computational savings in an acoustic horn robust optimization example and practical design turnaround time in a robust wing optimization problem. Copyright © 2014 John Wiley & Sons, Ltd.     

A mathematical model for vehicle routing problem under endogenous uncertainty

In this study, a multistage stochastic programming (SP) model is presented for a variant of single-vehicle routing problem with stochastic demands from a dynamic viewpoint. It is assumed that the actual demand of a customer becomes known only when the customer is visited. This problem falls into the category of SP with endogenous uncertainty and hence, the scenario tree is decision-dependent. Therefore, nonanticipativity of decisions is ensured by conditional constraints making up a large portion of total constraints. Thus, a novel approach is proposed that considerably reduces the problem size without any effect on the solution space. Computational results on some test problems are reported.