Cold-standby redundancy allocation problem with degrading components

Components in cold-standby state are usually assumed to be as good as new when they are activated. However, even in a standby environment, the components will suffer from performance degradation. This article presents a study of a redundancy allocation problem (RAP) for cold-standby systems with degrading components. The objective of the RAP is to determine an optimal design configuration of components to maximize system reliability subject to system resource constraints (e.g. cost, weight). As in most cases, it is not possible to obtain a closed-form expression for this problem, and hence, an approximated objective function is presented. A genetic algorithm with dual mutation is developed to solve such a constrained optimization problem. Finally, a numerical example is given to illustrate the proposed solution methodology.     

Solving reliability redundancy allocation problems using an artificial bee colony algorithm

This paper proposed a penalty guided artificial bee colony algorithm (ABC) to solve the reliability redundancy allocation problem (RAP). The redundancy allocation problem involves setting reliability objectives for components or subsystems in order to meet the resource consumption constraint, e.g. the total cost. RAP has been an active area of research for the past four decades. The difficulty that one is confronted with the RAP is the maintenance of feasibility with respect to three nonlinear constraints, namely, cost, weight and volume related constraints. In this paper nonlinearly mixed-integer reliability design problems are investigated where both the number of redundancy components and the corresponding component reliability in each subsystem are to be decided simultaneously so as to maximize the reliability of the system. The reliability design problems have been studied in the literature for decades, usually using mathematical programming or heuristic optimization approaches. To the best of our knowledge the ABC algorithm can search over promising feasible and infeasible regions to find the feasible optimal/near-optimal solution effectively and efficiently; numerical examples indicate that the proposed approach performs well with the reliability redundant allocation design problems considered in this paper and computational results compare favorably with previously-developed algorithms in the literature.     

An efficient heuristic for reliability design optimization problems

This paper develops an efficient heuristic to solve two typical combinatorial optimization problems frequently met when designing highly reliable systems. The first one is the redundancy allocation problem (RAP) of series-parallel binary-state systems. The design goal of the RAP is to select the optimal combination of elements and redundancy levels to maximize system reliability subject to the system budget and to the system weight. The second problem is the expansion-scheduling problem (ESP) of multi-state series-parallel systems. In this problem, the study period is divided into several stages. At each stage, the demand is represented as a piecewise cumulative load curve. During the system lifetime, the demand can increase and the total productivity may become insufficient to assume the demand. To increase the total system productivity, elements are added to the existing system. The objective in the ESP is to minimize the sum of costs of the investments over the study period while satisfying availability constraints at each stage. The heuristic approach developed to solve the RAP and the ESP is based on a combination of space partitioning, genetic algorithms (GA) and tabu search (TS). After dividing the search space into a set of disjoint subsets, this approach uses GA to select the subspaces, and applies TS to each selected subspace. Numerical results for the test problems from previous research are reported and compared. The results show the advantages of the proposed approach for solving both problems.     

Sequencing Optimization in k-out-of-n Cold-Standby Systems Considering Mission Cost

The k-out-of-n: G heterogeneous cold-standby system structure is a widely used fault-tolerant system design method, where the sequence in which the different system elements are initiated can greatly affect the system reliability and mission cost. This paper considers the optimal standby element sequencing problem (SESP) for such systems. Given the desired cold-standby redundancy level and fixed set of element choices, the objective of the optimal system design is to select the initiation sequence of the system elements so as to minimize the expected system mission cost while meeting a certain level of system reliability constraint. Based on a discrete approximation of time-to-failure distributions of the system elements, the system reliability and expected mission cost are evaluated simultaneously using a numerical method. A genetic algorithm is used as an optimization tool for solving the formulated SESP problem for k-out-of-n: G heterogeneous cold-standby systems. Examples are given to illustrate the considered problem and the proposed solution methodology.     

多目标粒子群算法在交叉培训规划中的应用

为了进一步提高人力资源交叉培训规划的实用性,增加了对于员工学习行为的考虑,提出了在保证任务覆盖水平的基础上,获得员工满意度最大和学习效率最高的多目标优化模型.本文针对问题的特征,采用多目标粒子群(MOPSO)算法对多目标优化模型进行了求解,并设计了多种算法策略,以适应不同的问题环境.通过数值实验,分析了不同问题规模下,针对不同性能指标算法参数和策略的适用性.最后,以柔性单元装配生产线为例,进行了数值实验,实验结果表明了模型的有效性和合理性.     

A surrogate-assisted evolution strategy for constrained multi-objective optimization

In many real-world optimization problems, several conflicting objectives must be achieved and optimized simultaneously and the solutions are often required to satisfy certain restrictions or constraints. Moreover, in some applications, the numerical values of the objectives and constraints are obtained from computationally expensive simulations. Many multi-objective optimization algorithms for continuous optimization have been proposed in the literature and some have been incorporated or used in conjunction with expert and intelligent systems. However, relatively few of these multi-objective algorithms handle constraints, and even fewer, use surrogates to approximate the objective or constraint functions when these functions are computationally expensive. This paper proposes a surrogate-assisted evolution strategy (ES) that can be used for constrained multi-objective optimization of expensive black-box objective functions subject to expensive black-box inequality constraints. Such an algorithm can be incorporated into an intelligent system that finds approximate Pareto optimal solutions to simulation-based constrained multi-objective optimization problems in various applications including engineering design optimization, production management and manufacturing. The main idea in the proposed algorithm is to generate a large number of trial offspring in each generation and use the surrogates to predict the objective and constraint function values of these trial offspring. Then the algorithm performs an approximate non-dominated sort of the trial offspring based on the predicted objective and constraint function values, and then it selects the most promising offspring (those with the smallest predicted ranks from the non-dominated sort) to become the actual offspring for the current generation that will be evaluated using the expensive objective and constraint functions. The proposed method is implemented using cubic radial basis function (RBF) surrogate models to assist the ES. The resulting RBF-assisted ES is compared with the original ES and to NSGA-II on 20 test problems involving 2–15 decision variables, 2–5 objectives and up to 13 inequality constraints. These problems include well-known benchmark problems and application problems in manufacturing and robotics. The numerical results showed that the RBF-assisted ES generally outperformed the original ES and NSGA-II on the problems used when the computational budget is relatively limited. These results suggest that the proposed surrogate-assisted ES is promising for computationally expensive constrained multi-objective optimization.     

Intuitionistic fuzzy optimization technique for solving multi-objective reliability optimization problems in interval environment

In designing phase of systems, design parameters such as component reliabilities and cost are normally under uncertainties. This paper presents a methodology for solving the multi-objective reliability optimization model in which parameters are considered as imprecise in terms of triangular interval data. The uncertain multi-objective optimization model is converted into deterministic multi-objective model including left, center and right interval functions. A conflicting nature between the objectives is resolved with the help of intuitionistic fuzzy programming technique by considering linear as well as the nonlinear degree of membership and non-membership functions. The resultants max–min problem has been solved with particle swarm optimization (PSO) and compared their results with genetic algorithm (GA). Finally, a numerical instance is presented to show the performance of the proposed approach.     

Elite-guided multi-objective artificial bee colony algorithm

Multi-objective optimization has been a difficult problem and a research focus in the field of science and engineering. This paper presents a novel multi-objective optimization algorithm called elite-guided multi-objective artificial bee colony (EMOABC) algorithm. In our proposal, the fast non-dominated sorting and population selection strategy are applied to measure the quality of the solution and select the better ones. The elite-guided solution generation strategy is designed to exploit the neighborhood of the existing solutions based on the guidance of the elite. Furthermore, a novel fitness calculation method is presented to calculate the selecting probability for onlookers. The proposed algorithm is validated on benchmark functions in terms of four indicators: GD, ER, SPR, and TI. The experimental results show that the proposed approach can find solutions with competitive convergence and diversity within a shorter period of time, compared with the traditional multi-objective algorithms. Consequently, it can be considered as a viable alternative to solve the multi-objective optimization problems.     

基于正交设计NSGA-II算法的制动器多目标优化*

针对汽车鼓式制动器,以制动效能因数最大、制动鼓体积最小和制动器温升最低为目标,建立了多目标优化模型。针对传统NSGA-II算法求解3目标优化问题的不足,引入正交设计策略,提出了改进的NSGA-II算法。将改进算法与目前三种经典的多目标优化算法在DTLZ系列测试函数上进行性能测试,结果表明改进算法在求解3目标优化问题上有更好的性能。用改进算法和NSGA-II两种算法同时求解制动器多目标优化设计实例,改进算法得到了分布更好的Pareto前端,表明改进算法对此类问题求解行之有效。     

正交设计的E占优策略求解高维多目标优化问题研究

在实际应用中,传统多目标演化算法面临着高维多目标优化问题。针对这一缺陷,提出正交E占优(Orthogo-nality E-dominant,OE)策略。在OE策略的理论优越性设计的基础上,改进了当前5种具有代表性的演化多目标优化算法。改进前后的算法求解DTLZ1-6(20)测试问题的数值对比试验显示,OE策略改进后的算法在不同程度上提高了算法求解高维多目标优化问题的效果,从而证实了OE策略对演化多目标优化算法改进的有效性。