Redundancy allocation of series-parallel systems using a variable neighborhood search algorithm

This paper presents a meta-heuristic algorithm, variable neighborhood search (VNS), to the redundancy allocation problem (RAP). The RAP, an NP-hard problem, has attracted the attention of much prior research, generally in a restricted form where each subsystem must consist of identical components. The newer meta-heuristic methods overcome this limitation and offer a practical way to solve large instances of the relaxed RAP where different components can be used in parallel. Authors’ previously published work has shown promise for the variable neighborhood descent (VND) method, the simplest version among VNS variations, on RAP. The variable neighborhood search method itself has not been used in reliability design, yet it is a method that fits those combinatorial problems with potential neighborhood structures, as in the case of the RAP. Therefore, authors further extended their work to develop a VNS algorithm for the RAP and tested a set of well-known benchmark problems from the literature. Results on 33 test instances ranging from less to severely constrained conditions show that the variable neighborhood search method improves the performance of VND and provides a competitive solution quality at economically computational expense in comparison with the best-known heuristics including ant colony optimization, genetic algorithm, and tabu search.     

Redundancy allocation for multi-state systems using physical programming and genetic algorithms

This paper proposes a multi-objective optimization model for redundancy allocation for multi-state series–parallel systems. This model seeks to maximize system performance utility while minimizing system cost and system weight simultaneously. We use physical programming as an effective approach to optimize the system structure within this multi-objective optimization framework. The physical programming approach offers a flexible and effective way to address the conflicting nature of these different objectives. Genetic algorithm (GA) is used to solve the proposed physical programming-based optimization model due to the following three reasons: (1) the design variables, the number of components of each subsystems, are integer variables; (2) the objective functions in the physical programming-based optimization model do not have nice mathematical properties, and thus traditional optimization approaches are not suitable in this case; (3) GA has good global optimization performance. An example is used to illustrate the flexibility and effectiveness of the proposed physical programming approach over the single-objective method and the fuzzy optimization method.     

A heuristic for solving the redundancy allocation problem for multi-state series-parallel systems

The redundancy allocation problem is formulated with the objective of minimizing design cost, when the system exhibits a multi-state reliability behavior, given system-level performance constraints. When the multi-state nature of the system is considered, traditional solution methodologies are no longer valid. This study considers a multi-state series-parallel system (MSPS) with capacitated binary components that can provide different multi-state system performance levels. The different demand levels, which must be supplied during the system-operating period, result in the multi-state nature of the system. The new solution methodology offers several distinct benefits compared to traditional formulations of the MSPS redundancy allocation problem. For some systems, recognizing that different component versions yield different system performance is critical so that the overall system reliability estimation and associated design models the true system reliability behavior more realistically. The MSPS design problem, solved in this study, has been previously analyzed using genetic algorithms (GAs) and the universal generating function. The specific problem being addressed is one where there are multiple component choices, but once a component selection is made, only the same component type can be used to provide redundancy. This is the first time that the MSPS design problem has been addressed without using GAs. The heuristic offers more efficient and straightforward analyses. Solutions to three different problem types are obtained illustrating the simplicity and ease of application of the heuristic without compromising the intended optimization needs.     

A joint reliability-redundancy optimization approach for multi-state series-parallel systems

In this paper, we present a practical approach for the joint reliability-redundancy optimization of multi-state series-parallel systems. In addition to determining the optimal redundancy level for each parallel subsystem, this approach also aims at finding the optimal values for the variables that affect the component state distributions in each subsystem. The key point is that technical and organizational actions can affect the state transition rates of a multi-state component, and thus affect the state distribution of the component and the availability of the system. Taking this into consideration, we present an approach for determining the optimal versions and numbers of components and the optimal set of technical and organizational actions for each subsystem of a multi-state series-parallel system, so as to minimize the system cost while satisfying the system availability constraint. The approach might be considered to be the multi-state version of the joint system reliability-redundancy optimization methods.     

Homogeneous redundancy optimization in multi-state series-parallel systems: A heuristic approach

This paper presents a heuristic for a series-parallel system, exhibiting a multi-state behavior, minimizing the cost in order to provide a desired level of reliability. System reliability is defined as the ability to satisfy consumer demands which is presented as a piecewise cumulative load curve. The components are binary and chosen from a list of products available on the market, and are characterized in terms of their feeding capacity, reliability and cost. The solution approach makes use of a homogeneous collection of components to provide redundancy in a subsystem. The algorithm is applied to power systems found in the literature for various levels of reliability requirement. The heuristic offers a straightforward analysis and is efficient both in terms of solution quality and computational time, as compared to existing genetic algorithms and heuristics. Thus, the developed heuristic is attractive, and it can be easily and efficiently applied to numerous real-life systems.     

Reliability optimization of series-parallel systems with a choice of redundancy strategies using a genetic algorithm

This paper proposes a genetic algorithm (GA) for a redundancy allocation problem for the series-parallel system when the redundancy strategy can be chosen for individual subsystems. Majority of the solution methods for the general redundancy allocation problems assume that the redundancy strategy for each subsystem is predetermined and fixed. In general, active redundancy has received more attention in the past. However, in practice both active and cold-standby redundancies may be used within a particular system design and the choice of the redundancy strategy becomes an additional decision variable. Thus, the problem is to select the best redundancy strategy, component, and redundancy level for each subsystem in order to maximize the system reliability under system-level constraints. This belongs to the NP-hard class of problems. Due to its complexity, it is so difficult to optimally solve such a problem by using traditional optimization tools. It is demonstrated in this paper that GA is an efficient method for solving this type of problems. Finally, computational results for a typical scenario are presented and the robustness of the proposed algorithm is discussed.     

Reactive power cost allocation by using a value-based approach

This study proposes a value-based approach to allocate the cost of reactive power production/absorption and the useful VAr reserve provided by the generators. Reactive power support can be segregated into two broad categories: the utilised component of the support and the reactive power reserve component for system security. The utilised reactive power capacity can be decomposed further into the support required for meeting the reactive power loads and that required to meet additional reactive power transmission losses for the MW load shipment. A value-based sensitivity approach has been utilised to compute utilisation factors (UFs) for allocation of the cost of reactive power production/absorption and reserve provision. This method provides transparency in determining the relative utilisation and supply of reactive power by sources to the customers. System operator (SO) can utilise this method for allocation of the cost incurred by the reactive power providers to the load serving entities. Case studies on five-bus test system, IEEE 24-bus reliability test system (RTS) and 75-bus Indian system demonstrate the proposed approach.     

Darwinian approach for dynamic spectrum allocation in next generation systems

The authors present the use of a genetic algorithm (GA) model as a solution approach to the dynamic spectrum allocation (DSA) problem considered as a difficult combinatorial optimisation problem. The proposed multi-objective GA model enhances overall spectral efficiency of the network, while optimising its own spectrum utilisation to generate accessible spectrum opportunities for other radio technologies. A novel two-dimensional encoding technique is defined to represent solutions in the problem domain and the technique enables significantly shorter convergence times. A simulation tool has been developed to model the GA-based DSA and to compare the new scheme with the conventional fixed spectrum allocation (FSA) scheme under both uniform and non-uniform traffic distributions. The proposed scheme significantly outperformed the FSA scheme both in terms of spectral efficiency gain and spectral utilisation.     

Redundancy model for water distribution systems

This paper presents a model, based on head driven simulation, for assessing the redundancy of water distribution systems (WDS). The formulation recognises the pressure dependency of water consumption in the solution procedure. A new algorithm for pressure dependent modelling of WDS has, therefore, been developed. Notable features of the proposed network analysis technique include the introduction of a new subcategory of nodes called key partial-flow nodes and the use of a joint head-flow system of equations. The algorithm is reliable, quick and easy-to-implement.The redundancy assessment methodology addresses the randomness of component failure or unavailability. Results are presented which demonstrate the suitability and meaning of the redundancy measure. In particular, it is recommended that redundancy be evaluated along with reliability when assessing system performance. The computer program developed can seamlessly calculate several performance indicators including reliability.     

Optimal load distribution in series-parallel systems

This paper presents an algorithm for determining an optimal loading of elements in series-parallel systems. The optimal loading is aimed at achieving the greatest possible expected system performance subject to repair resource constraint. The model takes into account the dependence of elements’ failure rates on their load. The optimization algorithm uses a universal generating function technique for evaluating the expected system performance, and a genetic algorithm for determining the optimal load distribution. An illustrative example of load distribution optimization is presented.     

An exact algorithm for preventive maintenance planning of series-parallel systems

Reliability is a meaningful parameter in assessing the performance of systems such as chemical processing facilities, power plant, aircrafts, ships, etc. In the literature, reliability optimization is widely considered during the system design phase and it is carried out by an opportune selection of both system components and redundancy. On the other hand, the problem of maintaining a required level of reliability by an opportune maintenance policy has been poorly examined. The paper tackles this problem for a system whose major components can be maintained only during a planned system downtime. An exact algorithm is proposed in order to single out the set of components that must be maintained to guarantee a required reliability level up to the next planned stop with the minimum cost. In order to verify the algorithm effectiveness, it has been applied to a complex real case regarding ship maintenance.     

Optimal resource allocation on grid systems for maximizing service reliability using a genetic algorithm

Grid computing system is different from conventional distributed computing systems by its focus on large-scale resource sharing and open architecture for services. The global grid technologies and the Globus Toolkit in particular, are evolving toward an open grid service architecture (OGSA) with which a grid system provides an extensible infrastructure so that various organizations can offer their own services and integrate their resources. Hence, this paper aims at solving the problem of optimally allocating services on the grid to maximize the grid service reliability. Since no existing study has analyzed the grid service reliability, this paper develops initial modeling and evaluation algorithms to evaluate the grid service reliability. Based on the grid service reliability evaluation, we present an optimization model for the grid service allocation problem and develop a genetic algorithm (GA) to effectively solve it. A numerical example is given to show the modeling procedures and efficiency of the GAs.     

A segmentation approach for solving buffer allocation problems in large production systems

Buffer space allocation is an important step in production line design. In this paper, we focus on maximising the profit rate of a line subject to a production rate constraint. We describe a newly observed property of production line optimisation. The property is that the production rate constraint, if it is effective, allows an original line to be decoupled into several short lines for optimisation. An approximation method is developed from this property. Instead of optimising a long line, the method divides it into several short lines, optimises them separately and combines their optimal buffer distributions to find the optimal or near optimal buffer distribution of the original line. The method greatly improves the computation efficiency for solving buffer allocation problem for long lines, while ensuring the accuracy of the optimal buffer distribution. A heuristic explanation is proposed. Numerical experiments are provided to show the accuracy and efficiency of the method. The effect of the number and length of line segments on the performance of the method is discussed.     

The classes of asymptotic reliability functions for series-parallel and parallel-series systems

In this paper ten-element classes of limit reliability functions for series-parallel and parallel-series systems with identical components are presented. Next, the results are transferred to the systems with non-identical components. These systems are such that at least the number of their series or the number of their parallel components tends to infinity. The classes are more extensive than the known classes of limit distributions of minimax and maximin statistics of independent random variables with the same distributions. The results can be useful in the reliability evaluation of large systems, especially in design problems.     

Multiresponse systems optimization using a goal attainment approach

A goal attainment approach to optimize multiresponse systems is presented. This approach aims to identify the settings of control factors to minimize the overall weighted maximal distance measure with respect to individual response targets. Based on a nonlinear programming technique, a sequential quadratic programming algorithm, the method is proved to be robust and can achieve good performance for multiresponse optimization problems with multiple conflicting goals. Moreover, the optimization formulation may include some prior work as special cases by assigning proper response targets and weights. Fewer assumptions are needed when using the approach as compared to other techniques. Furthermore, the decision-maker's preference and the model's predictive ability can easily be incorporated into the weights' adjustment schemes with explicit physical interpretation. The proposed approach is investigated and compared with other techniques through various classical examples in the literature.     

Bundle strength of polyester fibers determined using a series-parallel combination model

This paper describes the bundle strengths of PET filaments from a statistical point of view. A bundle is an arrangement of a number of filaments. We applied the weakest-link theory and probabilistic load-sharing rules to estimate the bundle strength from the breaking strength data of PET filaments. We analyzed the breaking behavior of 12 filament bundles according to their length and number of filaments and compared the breaking behavior of a prepared specimen yarn with that of a commercial PET filament yarn. The breaking strength of the PET filaments, which we tested using a MANTIS® tester, was compared with that of the actual yarn. We compared the actual tested values obtained by INSTRON® with the expected values, which we calculated from the MANTIS® data by using Peirce's theory and Knox's hazard function. The key effects that determine the actual random breakage behavior of a bundle include not only the load-sharing rules in the constituent filaments but also the slippage and friction between adjacent filaments, the appearance of which we distinguished especially in the bundle consisting of a large number of filaments and in small-denier filaments. The PET filaments were better approximated when using the Peirce's weakest-link theory than they were by Knox's hazard function. In a series-parallel model, we found that the number of parallel filaments and their load-sharing behavior had larger effects on the bundle strength than did the weakest-link effects of continuous elements.     

Life assessment prognostic modelling for multi-layered coating systems using a multidisciplinary approach

The multidisciplinary approach has been adopted to model the formation and propagation of blistering effect for evaluation of useful coating life in the multi-layered coating–substrate system. A prognostic model of de-bonding driving force has been formulated as a function of material science, solid mechanics and fracture mechanics properties to estimate critical, safe and fail conditions of the coating–substrate system. The blister growth velocity rate is also included in the developed model to estimate the blister propagation as a function of diffusion-induced stress and residual stress. The proposed prognostic modelling for the formation and propagation of blistering effect are combined to form an assessment model for the evaluation of useful coating life of the multi-layered coating–substrate system and validated through experimental observation.     

Response probability estimation for randomly excited quasi-linear systems using a neural network approach

A quasi-linear system is referred to as a system linear in properties and subjected to multiplicative random excitations appearing also in the linear terms. It is known that exact solutions for the stationary moments can be obtained analytically for such a quasi-linear system if the excitations are Gaussian white noises. However, the exact response probability, which is non-Gaussian, is not obtainable analytically. In this paper, a neural network approach is proposed to evaluate the stationary response probability for quasi-linear systems under both additive and multiplicative excitations of Gaussian white noises based on the obtained exact statistical moments. Numerical examples show that the procedure yields accurate results if an appropriate form is assumed for the probability density function. The accuracy of the results is substantiated by comparing them with those obtained from Monte Carlo simulations.     

Selective maintenance optimisation for series-parallel systems alternating missions and scheduled breaks with stochastic durations

This paper deals with the selective maintenance problem for a multi-component system performing consecutive missions separated by scheduled breaks. To increase the probability of successfully completing its next mission, the system components are maintained during the break. A list of potential imperfect maintenance actions on each component, ranging from minimal repair to replacement is available. The general hybrid hazard rate approach is used to model the reliability improvement of the system components. Durations of the maintenance actions, the mission and the breaks are stochastic with known probability distributions. The resulting optimisation problem is modelled as a non-linear stochastic programme. Its objective is to determine a cost-optimal subset of maintenance actions to be performed on the components given the limited stochastic duration of the break and the minimum system reliability level required to complete the next mission. The fundamental concepts and relevant parameters of this decision-making problem are developed and discussed. Numerical experiments are provided to demonstrate the added value of solving this selective maintenance problem as a stochastic optimisation programme.     

Inspection allocation for multistage deteriorating production systems

The paper deals with the layout and operation of an inspection system used for detecting malfunctioning processors in a multistage production system. This problem involves three inter-related decisions: (i) the overall inspection capacity; (ii) the assignment of inspection tasks to inspectors; and (iii) the scheduling of the inspector's tasks. These decisions require a trade-off between the cost of inspectors and the loss associated with non-conforming products. A hierarchical heuristic solution procedure is proposed to support these three related decisions. Numerical experiments demonstrate the performance of the heuristic, showing that solution criteria are very close to their lower bounds. Although we use production terminology, the results might be applicable to any organization, which inspects and maintains a variety of characteristics of its branches or activities.