An algorithm to solve integer programming problems: An efficient tool for reliability design

In many reliability design problems, the decision variables can only have integer values. The redundancy allocation is an example of one such problem; others include spare parts allocation, or repairmen allocation, which necessitate an integer programming formulation. In other words, integer programming plays an important role in system reliability optimization. In this paper, an algorithm is presented which provides an exact, simple and economical solution to any general class of integer programming problems and thereby offers reliability designers an efficient tool for system design. The algorithm can be used effectively to solve a wide variety of reliability design problems. The scope of use of this algorithm is also indicated and the procedure is illustrated by an example.     

Application-Specific MPSoC Reliability Optimization

This paper presents modeling and estimation techniques permitting the temperature-aware optimization of application-specific multiprocessor system-on-chip (MPSoC) reliability. Technology scaling and increasing power densities make MPSoC lifetime reliability problems more severe. MPSoC reliability strongly depends on system-level MPSoC architecture, redundancy, and thermal profile during operation. We propose an efficient temperature-aware MPSoC reliability analysis and prediction technique that enables MPSoC reliability optimization via redundancy and temperature-aware design planning. Reliability, performance, and area are concurrently optimized. Simulation results indicate that the proposed approach has the potential to substantially improve MPSoC system mean time to failure with small area overhead.     

A bound dynamic programming for solving reliability redundancy optimization

This paper presents a bound dynamic programming for solving reliability optimization problems, in which the optimal solution is obtained in the bound region of the problem by using dynamic programming. This algorithm is based on the studies of the characters of the problem and Misra [IEEE Trans. Reliability 40, 81–91 (1991)] bound search technique. With some examples, the proposed algorithm has been found to be more economical and effective than Misra integer programming to obtain the exact solutions of reliability redundancy optimization problems.     

A framework for reliability-aware design exploration on MPSoC based systems

Applying system-level fault-tolerant techniques such as active redundancy is a promising way to enhance the system reliability for safety-related applications. Embedded system design using active redundancy is a challenging task that involves solving two major problems, namely finding the optimal redundancy configuration and mapping/scheduling of the application (including the redundant components) to the platform under timing and reliability constraints. This paper presents a framework for automatic synthesis of fault-tolerant designs on multiprocessor platforms. The core of the framework consists of: (1) a reliability analysis, that computes the system-level reliability in the presence spatial and temporal redundancy, and (2) an optimization approach for reliability-aware design space exploration. The proposed approach considers both transient and permanent faults and is among the first to support system design using imperfect fault detectors. The framework takes an application model, a platform model and a set of application requirements as input, and generates the recommended design parameters, including task-to-processor binding, task schedule and the selection/placement of redundancy. The effectiveness of our approach is illustrated using several case studies.     

基于GA的系统冗余可靠性设计多目标优化模型

系统冗余可靠性多目标设计是一个复合最优化问题。传统的用于解决此类问题的方法,如拉格朗日乘子法、动态规划法、直接寻查法等,在系统单元较多的情况下存在着计算量大、难以获取全局最优解等问题。针对此问题,本文建立了基于遗传算法（GA）的系统冗余可靠性设计的多目标优化模型,该模型可在系统可靠性约束条件下,使系统的成本费用、体积、重量等指标达到最优设计。     

Multiple Weighted Objectives Heuristic for the Redundancy Allocation Problem

A new heuristic is proposed and tested for system reliability optimization. The multiple weighted objective heuristic is based on a transformation of the problem into a multiple objective optimization problem, and then ultimately, transformation into a different single objective problem. The multiple objectives are to simultaneously maximize the reliability of each individual subsystem. This is a logical approach because system reliability is the product of the subsystem reliabilities, so if they are maximized, the system reliability will also be high. This new formulation and associated heuristic are then based on solving a sequence of linear programming problems. It is one of the very few optimization approaches that allow for linear programming algorithms and software to be used for the redundancy allocation problem when mixing of functionally equivalent components is allowed. Thus, it represents an efficient solution method that relies on readily available optimization tools. The heuristic is tested on many example problems, and compared to competing solution approaches. Overall, the heuristic performance is observed to be very good on the tested problem, and superior to the max-min heuristic regarding both efficiency, and performance.     

Computer Redundancy: Design, Performance, and Future

The literature on the theoretical aspects of redundancy in digital computers is extensive providing a sound basis for highly reliable design. This paper describes the design problems, the reliability prediction, the field performance, and the future application of redundancy techniques to digital systems. Triple modular redundancy (TMR) is described using the logic of the Launch Vehicle Digital Computer utilized in the uprated Saturn I and the Saturn V vehicles. The self-correcting memory of this computer is described along with the associated design problems and the design verification based on production experience. Consideration is given to system design problems involved with TMR logic. A Monte Carlo technique for predicting computer reliability is considered in a design engineering rather than programmer approach. The unique means of indicating single-channel malfunctions, while continuing to mask these single-channel malfunctions with respect to system operation, is introduced. The result of field operation are given and compared with predicted reliability. Quad redundancy at the component part level is described using the circuitry of the primary processor and data storage (PPDS) for NASA's Orbital Astronomical Observatory. The process of arriving at a quad redundancy implementation is considered in light of the constraints of cost, schedule, and an initial reliability requirement of 95 percent for a year's operation in space. The circuit and system design problems associated with quad redundancy such as impedance and part parameter variations, power consumption, fan out limitations, and testing restrictions are indicated. The results of field operation are given and compared with predicted reliability.     

Neural network optimization for redundancy allocation

System reliability optimization problems such as redundancy allocation are hard to solve exactly. Neural networks offer an alternative computational model for obtaining good approximate solutions for such problems. In this paper we present a neural network for solving the redundancy allocation problem for a n-stage parallel redundant system with separable objective function and constraints. The problem is formulated as a 0–1 integer programming problem and solved using the network. The performance of the network compare favourably with that of the best fit algorithm. The number of iterations taken by the network increases very slowly with increase in number of variables. Hence the network can easily solve large problems.     

Multilevel Redundancy Allocation Optimization Using Hierarchical Genetic Algorithm

This paper proposes a generalized formulation for multilevel redundancy allocation problems that can handle redundancies for each unit in a hierarchical reliability system, with structures containing multiple layers of subsystems and components. Multilevel redundancy allocation is an especially powerful approach for improving the system reliability of such hierarchical configurations, and system optimization problems that take advantage of this approach are termed multilevel redundancy allocation optimization problems (MRAOP). Despite the growing interest in MRAOP, a survey of the literature indicates that most redundancy allocation schemes are mainly confined to a single level, and few problem-specific MRAOP have been proposed or solved. The design variables in MRAOP are hierarchically structured. This paper proposes a new variable coding method in which these hierarchical design variables are represented by two types of hierarchical genotype, termed ordinal node, and terminal node. These genotypes preserve the logical linkage among the hierarchical variables, and allow every possible combination of redundancy during the optimization process. Furthermore, this paper developed a hierarchical genetic algorithm (HGA) that uses special genetic operators to handle the hierarchical genotype representation of hierarchical design variables. For comparison, the customized HGA, and a conventional genetic algorithm (GA) in which design variables are coded in vector forms, are applied to solve MRAOP for series systems having two different configurations. The solutions obtained when using HGA are shown to be superior to the conventional GA solutions, indicating that the HGA here is especially suitable for solving MRAOP for series systems.      

Self-Organizing Migrating Strategies Applied to Reliability-Redundancy Optimization of Systems

The reliability-redundancy allocation problem is a mixed-integer programming problem. It has been solved by using optimization techniques such as dynamic programming, integer programming, mixed-integer non-linear programming, heuristics, and meta-heuristics. Meanwhile, the development of meta-heuristics has been an active research area in optimizing system reliability wherein the redundancy, the component reliability, or both are to be determined. In recent years, a broad class of stochastic algorithms, such as simulated annealing, evolutionary computation, and swarm intelligence algorithms, has been developed for reliability-redundancy optimization of systems. Recently, a new class of stochastic optimization algorithm called SOMA (Self-Organizing Migrating Algorithm) has emerged. SOMA works on a population of potential solutions called specimen, and is based on the self-organizing behavior of groups of individuals in a "social environment". This paper introduces a modified SOMA approach based on a Gaussian operator to solve reliability-redundancy optimization problems. In this context, three examples of mixed integer programming in reliability-redundancy design problems are evaluated. In this application domain, SOMA was found to outperform the previously best-known solutions available.     

A procedure for solving general integer programming problems

Recently, Misra [Microelectron. Reliab. 31, 285–294 (1991)] introduced a procedure for solving a variety of reliability optimization problems. In the present paper, the authors demonstrate that this procedure can also be used for solving a general class of integer programming problems, which are usually encountered in many allocation problems. System reliability design is only one of the applications. The algorithm, while being simple, has been found to be an economical and exact solution to the integer programming problem. The algorithm solves a very wide variety of the problems which otherwise cannot be easily solved through any of the existing search methods. Several illustrations are provided to establish the superiority of the approach.     

A heuristic task assignment algorithm to maximize reliability of adistributed system

Distributed systems potentially provide high reliability owing to the program and data-file redundancy possible. In many applications, high reliability is the major consideration for system design. Previous work has shown that the distribution of programs and data-files can affect the system reliability appreciably, and that redundancy in resources such as computers, programs, and data-files can improve the reliability of a distributed system. This work formulates a practical application for a reliability-oriented distributed task assignment problem which is NP-hard. Then, to cope with this challenging problem, a greedy algorithm is proposed, based on some heuristics, to find an approximate solution. The simulation shows that, in most cases tested, the algorithm finds suboptimal solutions efficiently; therefore, it is a desirable approach to solve these problems     

Markov model for k-out-of-n:G systems with built-in-test

This paper considers some new variations when the Built-In-Test technique is applied to k-out-of-n:G systems. A complete Markov model for the reliability and availability analysis of k-out-of-n:G systems with BIT is developed. Both fault coverage and false alarm are considered. A new inverse Laplace transform formula is derived to solve the differential simultaneous equations. Finally, generalized analytical functions for system reliability and availability are obtained. Our approach and solution are helpful and applicable for analyzing the impact of BIT design parameters on k-out-of-n:G system RAM and optimizing the redundancy management strategy.     

Simplified algorithm for optimum availability allocation and redundancy optimization subject to cost constraint

A simplified algorithm is described for optimum availability allocation and redundancy optimization subject to cost constraint. A series reliability structure is considered and the problems of optimum availability allocation and redundancy optimization have been tackled separately. The algorithm basically involves the evaluation of selection factor d_i for the ith sybsystem. The fixed cost increment or the redundant unit is assigned to that subsystem for which d_i is a maximum.     

A new partial bound enumeration technique for solving reliability redundancy optimization

A new partial bound enumeration technique is introduced to solve reliability redundancy optimization problems. The algorithm is based on the studies of the characters of the problems and the bound dynamic programming and the Misra integer programming. Some examples show that the proposed algorithm can obtain economically and effectively exact solutions of reliability redundancy optimization problems in many cases, especially when the numbers of the dimension size or the feasible region of the problem are very large.     

Formulation of the drift reliability optimization problem

Drift Reliabilty (DR) of a system is related to that part of the overal system reliability that is concerned with the system element ageing and parameter dependence on such environmental conditions as temperature, level of radiation, humidity, etc. Its maximization during the system design phase is of great economic importance for the manufacturers of electronic products and other equipment. In this paper the DR optimization problem is mathematically formulated in the context of parametric manufacturing yield optimization, and some algorithmic aspects of its solution are discussed. It is shown that it is possible to formulate the problem in such a way that some measures of both the yield and the average time to failure (due to the system element drift) can be maximized, and different trade-off situations investigated. The existing efficient gradient based yield optimization algorithms can be used after only some relatively simple modifications of the gradient estimation formulas.     

A Radial Basis Function Approach to Pattern Recognition and Its Applications

Pattern recognition is one of the most common problems encountered in engineering and scientific disciplines, which involves developing prediction or classification models from historic data or training samples. This paper introduces a new approach, called the Representational Capability (RC) algorithm, to handle pattern recognition problems using radial basis function (RBF) models. The RC algorithm has been developed based on the mathematical properties of the interpolation and design matrices of RBF models. The model development process based on this algorithm not only yields the best model in the sense of balancing its parsimony and generalization ability, but also provides insights into the design process by employing a design parameter (δ). We discuss the RC algorithm and its use at length via an illustrative example. In addition, RBF classification models are developed for heart disease diagnosis.     

Connection of users with a telecommunications network: Multicriteria assignment problem

The problem of connection of users with access points of a wireless telecommunications network is analyzed. An approach is based on the multicriteria assignment problem. A set of criteria involves the maximum bandwidth, the number of simultaneously served users, service reliability requirements, etc. Restrictions on the number of users served by access points and the frequency spectrum width of an access point are discussed. The combinatorial optimization problem employed belongs to the NP-hard class, and its solution is sought via the proposed heuristic methods. The proposed approach is illustrated by a numerical example.     

A Broadband High Gain Tapered Slot Antenna for Underwater Communication in Microwave Band

Named Data Networking (NDN), an emerging communication model in the content centric networks, has recently presented a solid framework for the future Internet. The NDN exploits content name instead of host name (IP address) and content caching. These features make NDN particularly efficient in networks with intermittent connectivity and dynamic topologies such as mobile ad hoc networks (MANETs). Due to the structure of NDN nodes, design of forwarding strategies has a vital impact on the network performance. In this paper, we propose a new forwarding strategy: redundancy elimination forwarding (REF). In REF, the NDN node structure and the operation of the data structures are modified. These modifications improve network performance in terms of throughput, overhead and resource requirements. REF strategy is simulated in different scenarios based on ndnSIM and the results demonstrate that it provides robust performance for various environments.

     

Reliability allocation through cost minimization

This paper considers the allocation of reliability and redundancy to parallel-series systems, while minimizing the cost of the system. It is proven that under usual conditions satisfied by cost functions, a necessary condition for optimal reliability allocation of parallel-series systems is that the reliability of the redundant components of a given subsystem are identical. An optimal algorithm is proposed to solve this optimization problem. This paper proves that the components in each stage of a parallel-series system must have identical reliability, under some nonrestrictive condition on the component's reliability cost functions. This demonstration provides a firm grounding for what many authors have hitherto taken as a working hypothesis. Using this result, an algorithm, ECAY, is proposed for the design of systems with parallel-series architecture, which allows the allocation of both reliability and redundancy to each subsystem for a target reliability for minimizing the system cost. ECAY has the added advantage of allowing the optimal reliability allocation in a very short time. A benchmark is used to compare the ECAY performance to LM-based algorithms. For a given reliability target, ECAY produced the lowest reliability costs and the optimum redundancy levels in the successive reliability allocation for all cases studied, viz, systems of 4, 5, 6, 7, 8, 9 stages or subsystems. Thus ECAY, as compared with LM-based algorithms, yields a less costly reliability allocation within a reasonable computing time on large systems, and optimizes the weight and space-obstruction in system design throughout an optimal redundancy allocation.