Optimal apportionment of reliability and redundancy in seriessystems under multiple objectives

A multiobjective reliability apportionment problem for a series system with time-dependent reliability is presented. The resulting mathematical programming formulation determines the optimal level of component reliability and the number of redundant components at each stage. The problem is a multiobjective, nonlinear, mixed-integer mathematical programming problem, subject to several design constraints. Sequential unconstrained minimization techniques in conjunction with heuristic algorithms are used to find an optimum solution. A generalization of the problem in view of inherent vagueness in the objective and the constraint functions results in an ill-structured reliability apportionment problem. This multiobjective fuzzy optimization problem is solved using nonlinear programming. The computational procedure is illustrated through a numerical example. The fuzzy optimization techniques can be useful during initial stages of the conceptual design of engineering systems where the design goals and design constraints have not been clearly identified or stated, and for decision making problems in ill-structured situations     

Reliability design of a standby system by a large-scale multiobjective optimization method

This paper deals with the reliability design of a standby redundancy system from a view point of large-scale multiobjective optimization. A large-scale multiobjective mathematical model is formulated and the problem considered is to optimize system reliability, cost, weight and volume, for a given mission time, subject to multiple constraints. A large-scale multiobjective optimization method is proposed by combined application of both surrogate worth trade-off method and dual decomposition method, and the preferred solution of the decision maker can effectively be obtained by using the proposed method. The method is illustrated by numerical examples.     

Optimal Reliability Allocation by Branch-and-Bound Technique

The paper presents an efficient method for finding the exact optimal solutions of reliability allocation problems that are formulated as an integer nonlinear programming problem generalized to handle nonlinear constraints and nonseparable problems. The method is based on branch-and-bound and developed by considering separation and relaxation techniques.     

Multiobjective Optimization by the Surrogate Worth Trade-off Method

This paper applies the Surrogate Worth Trade-off method to multiobjective reliability-allocation problems. A multiobjective mathematical model is formulated and the problem is to assign reliability to each stage of a series system such that system reliability is maximized and cost is minimized, subject to multiple constraints. The preferred solution of the decision-maker is obtained by using the Surrogate Worth Trade-off method. A numerical example illustrates the efficiency of the proposed method. Although only a problem with two objectives is considered, more than two objectives can be tackled by the same approach.     

Grid Implementation of a Parallel Multiobjective Genetic Algorithm for Optimized Allocation of Chlorination Stations in Drinking Water Distribution Systems: Chojnice Case Study

Solving multiobjective optimization problems requires suitable algorithms to find a satisfactory approximation of a globally optimal Pareto front. Furthermore, it is a computationally demanding task. In this paper, the grid implementation of a distributed multiobjective genetic algorithm is presented. The distributed version of the algorithm is based on the island algorithm with forgetting island elitism used instead of a genetic data exchange. The algorithm is applied to the allocation of booster stations in a drinking water distribution system. First, a multiobjective formulation of the allocation problem is further enhanced in order to handle multiple water demand scenarios and to integrate controller design into the allocation problem formulation. Next, the new grid-based algorithm is applied to a case study system. The results are compared with a nondistributed version of the algorithm.     

A cross-layer framework for multiobjective performance evaluation of wireless ad hoc networks

In this paper we address the problem of finding the optimal performance region of a wireless ad hoc network when multiple performance metrics are considered. Our contribution is to propose a novel cross-layer framework for deriving the Pareto optimal performance bounds for the network. These Pareto bounds provide key information for understanding the network behavior and the performance trade-offs when multiple criteria are relevant. Our approach is to take a holistic view of the network that captures the cross-interactions among interference management techniques implemented at various layers of the protocol stack (e.g. routing and resource allocation) and determines the objective functions for the multiple criteria to be optimized. The resulting complex multiobjective optimization problem is then solved by multiobjective search techniques. The Pareto optimal sets for an example sensor network are presented and analyzed when delay, reliability and energy objectives are considered.     

Optimal Reliability Allocation Under Preventive Maintenance Schedule

This paper considers a series system of components with time-dependent reliability and gives a new formulation of an optimal reliability allocation problem where an optimal preventive maintenance (PM) schedule is determined simultaneously. The importance of this formulation is shown in comparison with a conventional formulation where PM schedule is not taken into account. The optimization problem becomes a nonlinear mixed-integer programming problem. A simple approximate solution algorithm is given on the basis of a nonlinear programming (NLP) algorithm. The procedure is illustrated by use of a numerical example. Though we restrict our attention to the case where a preventive replacement is adopted as a PM policy, a similar discussion is possible for the as-good-as-new repair.     

Equity Metrics With Risk, Performance, and Cost Objectives for the Prioritization of Transportation Projects

Prioritizing and selecting a few critical transportation projects from several competing projects is a multiobjective combinatorial optimization problem (MOCO). Transportation planners and managers are always interested in analyzing and visualizing the tradeoffs involved, but equity issues in distribution of resources are given much less attention. This paper develops a methodology for integrating equity metrics with traditional metrics for planning and prioritizing a large and diverse portfolio of transportation investment projects. The methodology serves to help planners, managers, and engineers to visualize and compare measures of the distributed equity of the allocation along with cost-benefit tradeoffs. It is based on incorporating network-level equity metrics along with traditional metrics in formulating a generic multiobjective combinatorial optimization (MOCO) problem and visualizing multiobjective tradeoffs on the spatial network. A case study of a region demonstrates the use of the methodology in tradeoff analysis for prioritizing and selecting transportation projects. The approach is adaptable to other manufacturing and service industries where consideration of the distributed equity of allocation is an important issue.     

Review of Optimal Reliability Design, Fundamentals and Applications

This reference covers the extent of the state-of-the-art in optimizing systems reliability. The book consists of fifteen chapters and an appendix. The main part of the book is organized by problem type and solution method. Some of the topics covered include: redundancy allocation methods using heuristics, dynamic programming solutions and discrete optimization methods; reliability optimization using nonlinear programming and meta-heuristic algorithms; and methods to solve reliability-redundancy optimization. The book may serve as a textbook for students or as a reference for researchers and practitioners. It is a comprehensive book that is recommended for anyone concerned with designing reliable systems.     

可靠性分配中存在的问题及其对策

针对可靠性分配中运用工程加权因子分配法所存在的问题,给出正确进行可靠性分配的方法。     

Virtual network function–forwarding graph embedding: A genetic algorithm approach

Network function virtualization (NFV) provides a simple and effective mean to deploy and manage network and telecommunications' services. A typical service can be expressed in the form of a virtual network function–forwarding graph (VNF‐FG). Allocating a VNF‐FG is equivalent to place VNFs and virtual links onto a given substrate network considering resources and quality‐of‐service (QoS) constraints. The deployment of VNF‐FGs in large‐scale networks, such that QoS measures and deployment cost are optimized, is an emerging challenge. Single‐objective VNF‐FGs allocation has been addressed in existing literature; however, there is still a lack of studies considering multiobjective VNF‐FGs allocation. In addition, it is not trivial to obtain optimal VNF‐FGs allocation due to its high computational complexity even in case of single‐objective VNF‐FGs allocation. Genetic algorithms (GAs) have been proved its ability in coping with multiobjective optimization problems; thus, we propose a GA‐based scheme to solve multiobjective VNF‐FGs allocation problem in this paper. The numerical results confirm that the proposed scheme can provide near Pareto‐optimal solutions within a short execution time.     

基于构件的软件测试中测试用例分配优化研究

探讨了软件测试中每个构件软件的可靠性灵敏度已知,而测试资源受约束时,如何合理分配测试用例以提高构件软件可靠性的最优化问题.分析了传统的基于可靠性灵敏度的构件软件可靠性优化方法(RPP策略),在此基础上提出一种考虑测试代价的改进的构件软件可靠性优化方法(RPP-c策略).证明了RPP-c策略中带约束的测试用例最优分配问题是一个NPC问题,给出了动态规划求解方法,从理论上验证了RPP-c策略是最优的.     

A decomposition method for optimization of large-system reliability

The authors consider a decomposition approach for optimization of the reliability of a large system with a general network structure. A three-level methodology is developed for optimal allocation of available resources among subsystems in order to ensure maximization of system reliability. The decentralized nature of this methodology greatly reduces the complexity of the large problem and facilitates seeking the optimal solution. Two examples show that the complexity of a large system can be greatly reduced by solving several smaller-dimensional subproblems iteratively. Subproblems whose dimensions are small can be efficiently solved by an existing nonlinear programming method. Another important feature of the approach is the possible simplification of the objective function during the solution. This leads in some cases to an analytic solution for the lower-level optimization problems in the three-level decomposition solution     

Techniques for Optimum Spares Allocation: A Tutorial Review

In many modern complex systems the problem of achieving high reliability leads to the use of interchangeable modular components accompanied by a stock of spare parts. This paper examines, compares, and assesses several of the techniques presented in the literature for allocating the numbers of spares of each part type to be stocked in order to maximize the system reliability subject to constraints on resources (i.e., weight, volume, cost, etc.). The problem of optimum spares allocation is complicated since resources are consumed in a discrete fashion and the expression for the system reliability is a nonlinear transcendental function. The classical dynamic programming algorithm produces all optimal spares allocations; however, the solution can become computationally intractable even with the aid of a modern high-speed digital computer. In the case of multiple constraints the time problem is vastly exacerbated. In such a case one must turn to a procedure that yields a near-optimal solution in a reasonable amount of computer time. Two approximate methods discussed in this paper are the incremental reliability per pound algorithm and the Lagrange multiplier algorithm. These algorithms are readily adaptable to handle multiple constraints. Computer programs are developed for each of the three optimization algorithms and are utilized to obtain the spares allocation for a few systems. The optimization theory presented is directly applicable to series or parallel systems. A concluding example illustrates how this can be extended to certain series-parallel systems.     

基于多目标进化策略算法的DNA核酸编码设计

设计高质量的核酸分子集合能有效提高DNA计算的可靠性、有效性和可求解问题的规模。DNA分子需要满足热力学约束、相似度约束、GC含量约束等多个相互冲突的目标函数,是典型的多目标优化问题。该文提出一种多目标进化策略(MOES)算法求解DNA分子序列设计问题,算法设计了随机碱基变异算子实现高效的局部搜索和全局搜索。改进的评价函数综合考虑了候选解的支配关系和冲突目标的平衡程度,选取符合DNA编码约束的核酸序列。实验结果证明,该文提出的算法具有高效的搜索效率和快速收敛能力,可以产生高质量的DNA序列集合,优于其他对比算法产生的DNA分子序列集合。     

Random Walk Guided Decap Embedding for Power/Ground Network Optimization

The reliability of power/ground networks is becoming significantly important in modern integrated circuits, while decap insertion is a main approach to enhance the power grid safety. In this brief, we propose a fast and efficient decap allocation algorithm, and adequately consider the leakage effect of decap. This approach borrows the idea of random walks to perform circuit partitioning and does subsequent decap insertion based on locality property of partitioned area, which avoids solving a large nonlinear programming problem in traditional decap optimization process. The optimization flow also integrates a refined leakage current model for decaps which makes it more practical. Experimental results show that our proposed method can achieve approximate 15 X speed up over the optimal budget method within the acceptable error tolerance. Also this algorithm only causes a few penalty area to compensate the leakage effect.     

Resource allocation with proportional rate fairness in orthogonal frequency division multiple access relay networks

We address the problem of subchannel and transmission power allocation in orthogonal frequency division multiple access relay networks with an aim to maximize the sum rate and maintain proportional rate fairness among users. Because the formulated problem is a mixed‐integer nonlinear optimization problem with an extremely high computational complexity, we propose a low‐complexity suboptimal algorithm, which is a two‐step separated subchannel and power allocation algorithm. In the first step, subchannels are allocated to each user, whereas in the second step, the optimal power allocation is carried out on the basis of the given subchannel allocation and the nonlinear interval Gauss–Seidel method. Simulation results have demonstrated that the proposed algorithm can achieve a good trade‐off between the efficiency and the fairness compared with two other existing relevant algorithms. In particular, the proposed algorithm can always achieve 100% fairness under various conditions. Copyright © 2012 John Wiley & Sons, Ltd.     

Crow–penguin optimizer for multiobjective task scheduling strategy in cloud computing

Task scheduling in the cloud is the multiobjective optimization problem, and most of the task scheduling problems fail to offer an effective trade‐off between the load, resource utilization, makespan, and Quality of Service (QoS). To bring a balance in the trade‐off, this paper proposes a method, termed as crow–penguin optimizer for multiobjective task scheduling strategy in cloud computing (CPO‐MTS). The proposed algorithm decides the optimal execution of the available tasks in the available cloud resources in minimal time. The proposed algorithm is the fusion of the Crow Search optimization Algorithm (CSA) and the Penguin Search Optimization Algorithm (PeSOA), and the optimal allocation of the tasks depends on the newly designed optimization algorithm. The proposed algorithm exhibits a better convergence rate and converges to the global optimal solution rather than the local optima. The formulation of the multiobjectives aims at a maximum value through attaining the maximum QoS and resource utilization and minimum load and makespan, respectively. The experimentation is performed using three setups, and the analysis proves that the method attained a better QoS, makespan, Resource Utilization Cost (RUC), and load at a rate of 0.4729, 0.0432, 0.0394, and 0.0298, respectively.     

Multiobjective decision making for traffic assignment

The use of traffic assignment methods with multiobjective decision making to remedy the shortcomings of conventional traffic assignment methods is discussed. The optimal flow patterns are determined using three objectives: total travel time for road users; air pollution for nonusers; and travel distance for government. By using multiobjective decision making and nonlinear programming techniques, a series of noninferior solutions is generated. By combining an eigenvector weighting method with pairwise comparison, a compromise solution for the flow pattern is obtained. As an application example the Taipei network system is discussed. The results show that if other nontraffic-related factors are taken into account, the multiobjective traffic assignment approach is more reasonable and suitable than conventional approaches     

Solving the Redundancy Allocation Problem With a Mix of Components Using the Improved Surrogate Constraint Method

When designing a system, there are two methods that can be used to improve the system's reliability without changing the nature of the system: 1) using more reliable components, and/or 2) providing redundant components within the system. The redundancy allocation problem attempts to find the appropriate mix of components & redundancies within a system in order to either minimize cost subject to a minimum level of reliability, or maximize reliability subject to a maximum cost and weight. Redundancy allocation problems can be classified into two groups; one allows the system to have a mix of components with different characteristics incorporated in the system, while the other only allows one type of each component. The former group has a much larger solution space compared to the latter, and therefore obtaining an exact optimal or even a high quality solution for this problem may be more difficult. Optimization techniques, based on meta-heuristic approaches, have recently been proposed to solve the redundancy allocation problem with a mix of components. However, an exact solution method has not been developed. In this paper, we develop an exact solution method, based on the improved surrogate constraint (ISC) method, and use this method to find optimal solutions to problems previously presented in the literature