遗传算法在系统可靠性优化中的应用

研究性等价、体积和重量约束条件下，多级串联系统和桥式网络系统可靠性优化问题.使用遗传算法对该问题进行求解，利用基于排名的选择方法和最优保存策略，改善了遗传算法的收敛性能。计算机仿真实验结果表明，用遗传算法求解该问题是有效的。     

串并联系统中支持实时替换的混合冗余策略优化

在需要长时间可靠运行的软件系统中,由于持续运行时间和任务响应速度的要求增加,工作组件在被探测到失效后将被冗余组件实时替换.但现有可靠性优化研究通常假设冷备份冗余在所有积极冗余组件失效后才使用.针对支持实时替换的混合冗余策略,对其冗余度优化分配进行研究.该策略不仅能够保障系统可靠性,而且能够保障系统性能,故选用实时可用性和任务完成效率两类约束条件,建立冗余配置代价最小化模型.基于马尔可夫链理论对可靠性及性能两类系统指标进行定量分析;采用数值计算方法对非线性的状态分析模型进行计算;改进二元组编码遗传算法对上述优化问题进行求解.采用实例对串并联系统中实时可用性及任务完成效率的分析进行了说明,并对优化冗余分配模型进行了验证.实验结果表明,在相同冗余度下,支持实时替换的混合冗余策略在任务完成效率方面优于传统的混合冗余策略.所以,在相同约束条件下不同混合冗余策略需要采用不同的冗余优化配置方案.     

Multi-objective reliability-redundancy allocation problem using particle swarm optimization

This paper considers the multi-objective reliability redundancy allocation problem of a series system where the reliability of the system and the corresponding designing cost are considered as two different objectives. Due to non-stochastic uncertain and conflicting factors it is difficult to reduce the cost of the system and improve the reliability of the system simultaneously. In such situations, the decision making is difficult, and the presence of multi-objectives gives rise to multi-objective optimization problem (MOOP), which leads to Pareto optimal solutions instead of a single optimal solution. However in order to make the model more flexible and adaptable to human decision process, the optimization model can be expressed as fuzzy nonlinear programming problems with fuzzy numbers. Thus in a fuzzy environment, a fuzzy multi-objective optimization problem (FMOOP) is formulated from the original crisp optimization problem. In order to solve the resultant problem, a crisp optimization problem is reformulated from FMOOP by taking into account the preference of decision maker regarding cost and reliability goals and then particle swarm optimization is applied to solve the resulting fuzzified MOOP under a number of constraints. The approach has been demonstrated through the case study of a pharmaceutical plant situated in the northern part of India.     

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.     

Bi-objective optimization of the reliability-redundancy allocation problem for series-parallel system

The main objective of this paper is to solve the bi-objective reliability redundancy allocation problem for series-parallel system where reliability of the system and the corresponding designing cost are considered as two different objectives. In their formulation, reliability of each component is considered as a triangular fuzzy number. In order to solve the problem, developed fuzzy model is converted to a crisp model by using expected values of fuzzy numbers and taking into account the preference of decision maker regarding cost and reliability goals. Finally the obtained crisp optimization problem has been solved with particle swarm optimization (PSO) and compared their results with genetic algorithm (GA). Examples are shown to illustrate the method. Finally statistical simulation has been performed for supremacy the approach.     

一种求解软件可靠性分配的近似算法

在考虑开发成本约束的基础上,通过建立一种开发成本-可靠度-满意度三者平衡的软件可靠性分配和优化模型,将对软件可靠性最优分配问题转化为对模糊非线性规划问题的求解,从而为软件可靠性分配的最优化问题提供了一种新方法。为获得具有实际意义的数值解,提出一种沿着加权梯度方向进行变异的特殊遗传算法。最后结合实例,证明了该方法的有效性和合理性。     

Simultaneous parameter and tolerance optimization of structures via probability-interval mixed reliability model

Both structural sizes and dimensional tolerances strongly influence the manufacturing cost and the functional performance of a practical product. This paper presents an optimization method to simultaneously find the optimal combination of structural sizes and dimensional tolerances. Based on a probability-interval mixed reliability model, the imprecision of design parameters is modeled as interval uncertainties fluctuating within allowable tolerance bounds. The optimization model is defined as to minimize the total manufacturing cost under mixed reliability index constraints, which are further transformed into their equivalent formulations by using the performance measure approach. The optimization problem is then solved with the sequential approximate programming. Meanwhile, a numerically stable algorithm based on the trust region method is proposed to efficiently update the target performance points (TPPs) and the worst case points (WCPs), which shows better performance than traditional approaches for highly nonlinear problems. Numerical results reveal that reasonable dimensions and tolerances can be suggested for the minimum manufacturing cost and a desirable structural safety.     

Cost-oriented task allocation and hardware redundancy policies in heterogeneous distributed computing systems considering software reliability

Task allocation policy and hardware redundancy policy for distributed computing system (DCS) are of great importance as they affect many system characteristics such as system cost, system reliability and performance. In recent years, abundant research has been carried out on the optimal task allocation and/or hardware redundancy problem, most of which took a reliability-oriented approach, i.e., the optimization criterion was system reliability maximization. Nevertheless, besides system reliability, other system characteristics such as system cost may be of great concern to management. In this paper, we take a cost-oriented approach to the optimal task allocation and hardware redundancy problem for DCS, which addresses both system cost and system reliability issues. A system cost model which could reflect the impact of system unreliability on system cost is developed, and by minimizing the total system cost, a satisfactory level of system reliability could be reached simultaneously. In the reliability modeling and analysis of DCS, we take both hardware reliability and software reliability into account. Two numerical examples are given to illustrate the formulation and solution procedures, in which genetic algorithm is used. Results show that based on the developed system cost model, appropriate decision-makings on task allocation and hardware redundancy policies for DCS could be made, and the result obtained seems to be a fairly good trade-off between system cost and system reliability.     

Penalty guided bees search for redundancy allocation problems with a mix of components in series–parallel systems

This paper uses a penalty guided strategy based on an artificial bee colony algorithm (PGBC) to solve the redundancy allocation problem (RAP) in reliability series–parallel systems. The penalty strategy was designed to eliminate the equalities in constraints and formulate new objective operators which guarantee feasibility within a reasonable execution time. The PGBC is used to deal with two kinds of RAPs with a mix of components. In the first example, the RAPs are designed to find the appropriate mix of components and redundancies within a system in order to either minimize the cost in the context of a minimum level of reliability, or maximize reliability subject to a maximum cost and weight. The second example involves RAPs of multi-state series–parallel reliability structures, wherein each subsystem can consist of a maximum of two types of redundant components. The objective is to minimize the total investment cost of system design while satisfying system reliability constraints and the consumer load demands. There are five multi-state system design problems which have been solved for illustration in this example. The experimental results show that the PGBC can significantly outperform other existing methods in the literature with less cost, higher reliability, and a significantly shorter computational time.     

An improved fruit fly optimization algorithm to solve the homogeneous fuzzy series–parallel redundancy allocation problem under discount strategies

In this paper, a mathematical formulation is first derived for a homogenous fuzzy series–parallel redundancy allocation problem, where both the system and its subsystems can only take two states of complete perfect and complete failure. Identical redundant components are included in order to achieve desirable system reliability. The components of each subsystem characterized by their cost, weight, and reliability, are purchased from the market under all-unit discount and incremental quantity discount strategies. The goal is to find the optimum combination of the number of components for each subsystem that maximizes the system reliability under total fuzzy cost and weight constraints. An improved fruit fly optimization algorithm (IFOA) is proposed to solve the problem, where a particle swarm optimization, a genetic algorithm, and a Tabu search algorithm are utilized to validate the results obtained. These algorithms are the most common ones in the literature to solve series–parallel redundancy allocation problems. Moreover, design of experiments using the Taguchi approach is employed to calibrate the parameters of the algorithms. At the end, some numerical examples are solved to demonstrate the applicability of the proposed methodology. The results are generally in favor IFOA.     

一种子载波配对和功率分配联合最优算法

在基于正交频分复用的多载波两跳中继系统中有两个关键的问题亟需解决:子载波间的功率分配和子载波配对.子载波功率分配和配对之间存在复杂的耦合关系,通过现有的方法对子载波功率分配和配对进行联合优化比较困难.在深入研究这种耦合关系的基础上,针对解码转发,利用凸优化思想,提出一种功率受限下的子载波配对和功率分配联合最优算法.仿真结果表明,本算法可以有效提升中继系统的系统容量.     

基于社会认知算法的软件可靠性分配问题研究

针对软件可靠性分配问题中求解全局最优解的困难,在保证系统开发费用最低的前提条件下,将可靠性指标分配到每个模块中,并利用一种新的智能优化算法——社会认知算法来搜索模型的最优解。实验结果表明了社会认知算法在求解软件可靠性分配问题中的有效性。     

连锁零售供应链多级库存协同决策研究

针对连锁零售供应链多级库存资源的动态优化配置问题,提出了在上层对库存策略和下层对物流分配方案协同寻优的多级库存双层规划模型。借鉴细粒度模型遗传算法的遗传操作具有局部性的特点,模拟微观群体交互作用的局部性,基于细粒度模型遗传算法的Agent群体行为优化算法和基于复杂适应系统涌现机理的协同决策机制,进行连锁零售供应链多级库存协同决策研究。通过算例实验对模型的有效性进行了验证。仿真实验结果表明,通过连锁零售供应链微观个体Agent的群体行为优化,从系统工程的角度,实现了连锁零售供应链多级库存的动态资源优化配置和信息共享,降低了多级库存管理与运营的总成本。     

Reliability evaluation and optimal design in heterogeneous multi-state series-parallel systems

This paper addresses the heterogeneous redundancy allocation problem in multi-state series-parallel reliability structures with the objective to minimize the total cost of system design satisfying the given reliability constraint and the consumer load demand. The demand distribution is presented as a piecewise cumulative load curve and each subsystem is allowed to consist of parallel redundant components of not more than three types. The system uses binary capacitated components chosen from a list of available products to provide redundancy so as to increase system performance and reliability. The components are characterized by their feeding capacity, reliability and cost. A system that consists of elements with different reliability and productivity parameters has the capacity strongly dependent upon the selection of constituent components. A binomial probability based method to compute exact system reliability index is suggested. To analyze the problem and suggest an optimal/near-optimal system structure, an ant colony optimization algorithm has been presented. The solution approach consists of a series of simple steps as used in early ant colony optimization algorithms dealing with other optimization problems and offers straightforward analysis. Four multi-state system design problems have been solved for illustration. Two problems are taken from the literature and solved to compare the algorithm with the other existing methods. The other two problems are based upon randomly generated data. The results show that the method can be appealing to many researchers with regard to the time efficiency and yet without compromising over the solution quality.     

Optimal control laws for lot-sizing and timing of jobs on a single production facility

The optimal control of a single machine processing a certain number of jobs and modeled as a discrete-event dynamic system is considered. The number of jobs and their sequence are fixed, whereas their timing and sizes represent the control variables of the system. The objective function to be optimized is a weighted sum of the quadratic earliness and tardiness of each job, and of the quadratic deviations of job lot sizes and actual machine service speeds from those specified by the production demand and by the regular machine speeds. An optimization problem with quadratic cost function and nonlinear constraints is stated and formalized as a multistage optimal control problem. Necessary conditions to be satisfied by an optimal control sequence are derived. A simpler model is also considered in which the machine speeds are fixed; in this case, the control problem is solved by a procedure making use of dynamic programming techniques. The optimal control laws at each stage are thus obtained.     

Genetic algorithm based multi-objective reliability optimization in interval environment

In most of the real world design or decision making problems involving reliability optimization, there are simultaneous optimization of multiple objectives such as the maximization of system reliability and the minimization of system cost, weight and volume. In this paper, our goal is to solve the constrained multi-objective reliability optimization problem of a system with interval valued reliability of each component by maximizing the system reliability and minimizing the system cost under several constraints. For this purpose, four different multi-objective optimization problems have been formulated with the help of interval mathematics and our newly proposed order relations of interval valued numbers. Then these optimization problems have been solved by advanced genetic algorithm and the concept of Pareto optimality. Finally, to illustrate and also to compare the results, a numerical example has been solved.     

基于群智能的模糊多目标软件可靠性冗余分配

针对软件可靠性冗余分配问题,建立了一种模糊多目标分配模型,并提出了基于分布估计的细菌觅食优化算法求解该模型。将软件可靠性和成本作为模糊目标函数,通过三角形隶属函数对模糊多目标进行处理,用高斯分布对细菌觅食算法进行优化,并将该优化算法用来求解多目标软件可靠性冗余分配问题,设置不同的隶属函数参数可以得到不同的Pareto最优解,实验数据验证了该群智能算法对解决多目标软件可靠性分配的有效性和正确性,Pareto最优解可为在可靠性和成本之间决策提供依据。     

改进PSO算法在多无人机协同任务分配中的应用

针对多无人机协同任务分配越来越复杂的问题,采用一种改进的阶层分级粒子群优化算法（HGIWPSO）获得最优分配方案。首先,根据粒子适应度值将种群动态划分为三个不同阶层,依据不同阶层粒子特性选择合适的学习模型,并引入独立权重思想调节惯性权重大小,平衡算法全局与局部搜索能力,提高算法性能;然后,建立协同多任务分配问题模型,采用多余负载竞拍方案减少非法劣解,通过实数编码建立粒子和实际分配方案之间的映射关系,解决实际分配问题。实验结果表明,该算法能够有效解决复杂约束条件下多无人机协同任务分配问题,得到最优分配序列,具有一定的理论以及实际意义。     

基于软件架构的可靠性分配算法

研究软件可靠性分配中的软件开发成本最小化问题.将软件系统的成本最小化问题表达为一类带约束条件的组合优化问题,并且提出了基于架构的软件可靠性与开发成本评估及分配思想,建立了基于软件架构的可靠性-成本模型,提出了基于该模型的可靠性最优分配算法.该算法可以求解在给定可靠性目标前提下的可靠性分配问题,使得软件系统预期开发成本最小.     

Application of a mixed fuzzy decision making and optimization programming model to the empty container allocation

Containerization transportation has been growing fast in the past few decades. International trades have been growing fast since the globalization of world economies intensified in the early 1990s. However, these international trades are typically imbalanced in terms of the numbers of import and export containers. As a result, the relocation of empty containers has become one of the important problems faced by liner shipping companies. In this paper, we consider the empty container allocation problem where we need to determine the optimal volume of empty containers at a port and to reposition empty containers between ports to meet exporters’ demand over time. We formulate this empty container allocation problem as a two-stage model: in stage one, we propose a fuzzy backorder quantity inventory decision making model for determining the optimal quantity of empty container at a port; whereas in stage two, an optimization mathematical programming network model is proposed for determining the optimal number of empty containers to be allocated between ports. The parameters such as the cost of loading container, cost of unloading container, leasing cost of empty container, cost of storing container, supplies, demands and ship capacities for empty containers are considered in this model. By taking advantages of the fuzzy decision making and the network structure, we show how a mixed fuzzy decision making and optimization programming model can be applied to solve the empty container allocation problem. The utilization of the proposed model is demonstrated with a case of trans-Pacific liner route in the real world. Six major container ports on the trans-Pacific route are considered in the case study, including the Port of Kaohsiung, the Port of Hong Kong, the Port of Keelung, the Port of Kobe, the Port of Yokohama and the Port of Los Angles. The results show that the proposed mixed fuzzy decision making and optimization programming model can be used to solve the empty container allocation problem well.