Pseudo‐spectral method for controlling the drug dosage in cancer

A mixed chemotherapy–immunotherapy treatment protocol is developed for cancer treatment. Chemotherapy pushes the trajectory of the system towards the desired equilibrium point, and then immunotherapy alters the dynamics of the system by affecting the parameters of the system. A co‐existing cancerous equilibrium point is considered as the desired equilibrium point instead of the tumour‐free equilibrium. Chemotherapy protocol is derived using the pseudo‐spectral (PS) controller due to its high convergence rate and simple implementation structure. Thus, one of the contributions of this study is simplifying the design procedure and reducing the controller computational load in comparison with Lyapunov‐based controllers. In this method, an infinite‐horizon optimal control problem is proposed for a non‐linear cancer model. Then, the infinite‐horizon optimal control of cancer is transformed into a non‐linear programming problem. The efficient Legendre PS scheme is suggested to solve the proposed problem. Then, the dynamics of the system is modified by immunotherapy is another contribution. To restrict the upper limit of the chemo‐drug dose based on the age of the patients, a Mamdani fuzzy system is designed, which is not present yet. Simulation results on four different dynamics cases how the efficiency of the proposed treatment strategy.Inspec keywords: patient treatment, cancer, convergence, linear programming, optimal control, nonlinear programming, nonlinear control systems, Lyapunov methods, drugs, tumoursOther keywords: nonlinear programming problem, efficient Legendre PS scheme, chemo‐drug dose, Mamdani fuzzy system, treatment strategy, pseudospectral method, drug dosage, mixed chemotherapy–immunotherapy treatment protocol, cancer treatment, desired equilibrium point, immunotherapy alters, cancerous equilibrium point, tumour‐free equilibrium, chemotherapy protocol, pseudospectral controller, high convergence rate, simple implementation structure, controller computational load, Lyapunov‐based controllers, infinite‐horizon optimal control problem, nonlinear cancer model     

Reliability and redundancy apportionment using crisp and fuzzy multiobjective optimization approaches

The reliability of a multistage system with several components in each stage can be improved either by using more reliable components, or by adding redundant components in parallel in any stage. In many practical situations where reliability enhancement is involved, the decision making is complicated because of the presence of several mutually conflicting goals. For example, in the reliability based design of a system, the designer may be required to maximize the reliability and minimize the cost, weight or volume. This work considers the problem of reliability allocation for multistage systems with components having time-dependent reliability. Two multiobjective optimization techniques are presented, coupled with heuristic procedures, to solve the mixed integer nonlinear programming problems. A generalization of the problem in the presence of vague information results in an ill-structured reliability apportionment problem. The solution of such multiobjective problems is also presented in the present work using the techniques of fuzzy optimization.     

Bayes approach in RDT using accelerated and long-term life data

A common problem of reliability demonstration testing (RDT) is the magnitude of total time on test required to demonstrate reliability to the consumer’s satisfaction, particularly in the case of high reliability components. One solution is the use of accelerated life testing (ALT) techniques. Another is to incorporate prior beliefs, engineering experience, or previous data into the testing framework. This may have the effect of reducing the amount of testing required in the RDT in order to reach a decision regarding conformance to the reliability specification. It is in this spirit that the use of a Bayesian approach can, in many cases, significantly reduce the amount of testing required.We demonstrate the use of this approach to estimate the acceleration factor in the Arrhenius reliability model based on long-term data given by a manufacturer of electronic components (EC). Using the Bayes approach we consider failure rate and acceleration factor to vary randomly according to some prior distributions. Bayes approach enables for a given type of technology the optimal choice of test plan for RDT under accelerated conditions when exacting reliability requirements must be met. These requirements are given by a hypothetical consumer by two different ways. The calculation of posterior consumer’s risk is demonstrated in both cases.The test plans are optimum in that they take into account Var{λ|data}, posterior risk, E{λ|data}, Median λ or other percentiles of λ at data observed at the accelerated conditions. The test setup assumes testing of units with time censoring.     

具有非负困难度的符号几何规划的一种分解方法

本文针对具有非负困难度的符号几何规划问题提出了一种新的分解方法.该方法首先利用指数变换及矩阵理论,将原问题等价地转化为一个非线性程度较低的町分离规划,然后,将所得等价问题分解成一系列易于求解的子问题,并且当困难度为零时,文中给出了求解子问题精确解的方法.最后,通过数值实例验证了新方法的有效性和可行性.     

Multi-objective genetic algorithm for solving N-version program design problem

N-version programming (NVP) is a programming approach for constructing fault tolerant software systems. Generally, an optimization model utilized in NVP selects the optimal set of versions for each module to maximize the system reliability and to constrain the total cost to remain within a given budget. In such a model, while the number of versions included in the obtained solution is generally reduced, the budget restriction may be so rigid that it may fail to find the optimal solution. In order to ameliorate this problem, this paper proposes a novel bi-objective optimization model that maximizes the system reliability and minimizes the system total cost for designing N-version software systems. When solving multi-objective optimization problem, it is crucial to find Pareto solutions. It is, however, not easy to obtain them. In this paper, we propose a novel bi-objective optimization model that obtains many Pareto solutions efficiently.We formulate the optimal design problem of NVP as a bi-objective 0–1 nonlinear integer programming problem. In order to overcome this problem, we propose a Multi-objective genetic algorithm (MOGA), which is a powerful, though time-consuming, method to solve multi-objective optimization problems. When implementing genetic algorithm (GA), the use of an appropriate genetic representation scheme is one of the most important issues to obtain good performance. We employ random-key representation in our MOGA to find many Pareto solutions spaced as evenly as possible along the Pareto frontier. To pursue improve further performance, we introduce elitism, the Pareto-insertion and the Pareto-deletion operations based on distance between Pareto solutions in the selection process.The proposed MOGA obtains many Pareto solutions along the Pareto frontier evenly. The user of the MOGA can select the best compromise solution among the candidates by controlling the balance between the system reliability and the total cost.     

Reliability analysis of the dynamic system for the Chen model through sequential order statistics

Recently, the two-parameter Chen distribution has widely been used for reliability studies in various engineering fields. In this article, we have developed various statistical inferences on the composite dynamic system, assuming Chen distribution as a baseline model. In this dynamic system, failure of a component induces a higher load on the surviving components and thus increases component hazard rate through a power-trend process. The classical and Bayesian point estimates of the unknown parameters of the composite system are obtained by the method of maximum likelihood and Markov chain Monte Carlo techniques, respectively. In the Bayesian framework, we have used gamma priors to obtain Bayes estimates of unknown parameters under the squared error and generalized entropy loss functions. The interval estimates of the baseline reliability function are obtained by using the Fisher information matrix and Bayesian method. A parametric hypothesis test is presented to test whether the failed components change the hazard rate function. A compact simulation study is carried out to examine the behavior of the proposed estimation methods. Finally, one real data analysis is performed for illustrative purposes.     

Polymorphic uncertain nonlinear programming approach for maximizing the capacity of V-belt driving

In this paper, a polymorphic uncertain nonlinear programming (PUNP) approach is developed to formulate the problem of maximizing the capacity in a system of V-belt driving with uncertainties. The constructed optimization model is found to consist of a nonlinear objective function and some nonlinear constraints with some parameters which are of uncertain nature. These uncertain parameters are interval parameters, random interval parameters, fuzzy parameters or fuzzy interval parameters. To find a robust solution of the problem, a deterministic equivalent formulation (DEF) is established for the polymorphic uncertain nonlinear programming model. For a given satisfaction level, this DEF turns out to be a nonlinear programming involving only interval parameters. A solution method, called a sampling based interactive method, is developed such that a robust solution of the original model with polymorphic uncertainties is obtained by using standard smooth optimization techniques. The proposed method is applied into a real-world design of V-belt driving, and the results indicate that both the PUNP approach and the developed algorithm are useful to the optimization problem with polymorphic uncertainty.     

Combining stochastic programming and optimal control to decompose multistage stochastic optimization problems

The paper suggests a possible cooperation between stochastic programming and optimal control for the solution of multistage stochastic optimization problems. We propose a decomposition approach for a class of multistage stochastic programming problems in arborescent form (i.e. formulated with implicit non-anticipativity constraints on a scenario tree). The objective function of the problem can be either linear or nonlinear, while we require that the constraints are linear and involve only variables from two adjacent periods (current and lag 1). The approach is built on the following steps. First, reformulate the stochastic programming problem into an optimal control one. Second, apply a discrete version of Pontryagin maximum principle to obtain optimality conditions. Third, discuss and rearrange these conditions to obtain a decomposition that acts both at a time stage level and at a nodal level. To obtain the solution of the original problem we aggregate the solutions of subproblems through an enhanced mean valued fixed point iterative scheme.     

Lagrangian relaxation and cut generation for sequence-dependent setup time flowshop scheduling problems to minimise the total weighted tardiness

The Lagrangian relaxation and cut generation technique is applied to solve sequence-dependent setup time flowshop scheduling problems to minimise the total weighted tardiness. The original problem is decomposed into individual job-level subproblems that can be effectively solved by dynamic programming. Two types of additional constraints for the violation of sequence-dependent setup time constraints are imposed on the decomposed subproblems in order to improve the lower bound. The decomposed subproblem with the additional setup time constraints on any subset of jobs is also effectively solved by a novel dynamic programming. Computational results show that the lower bound derived by the proposed method is much better than those of CPLEX and branch and bound for problem instances with 50 jobs and five stages with less computational effort.     

Unit commitment in oligopolistic markets by nonlinear mixed variable programming

In the paper we consider the unit commitment problem in oligopolistic markets. The formulation of the problem involves both integer and continuous variables and nonlinear functions as well, thus yielding a nonlinear mixed variable programming problem. Our formulation takes into account all technical constraints for the generating units, such as ramp rate and minimum up and down time constraints, considers the uncertainty related to the selling prices and allows modeling their dependence on the total output of a producer. The objective function is the expected value of the revenue over the different scenarios minus a term which takes into account the risk related to the decision. To solve the problem we adopt a recently proposed method for mixed integer nonlinear programming problems and use a derivative free algorithm to solve the continuous subproblems. We report results for two operators: one managing a single unit and the other managing three units. Numerical results give evidence to the features of the modeling and show viability of the adopted algorithm.     

Redundancy allocation for series-parallel systems using a max-min approach

The redundancy allocation problem is formulated with the objective of maximizing the minimum subsystem reliability for a series-parallel system. This is a new problem formulation that offers several distinct benefits compared to traditional problem formulations. Since time-to-failure of the system is dictated by the minimum subsystem time-to-failure, a logical design strategy is to increase the minimum subsystem reliability as high as possible, given constraints on the system. For some system design problems, a preferred design objective may be to maximize the minimum subsystem reliability. Additionally, the max-min formulation can serve as a useful and efficient surrogate for optimization problems to maximize system reliability. This is accomplished by sequentially solving a series of max-min subproblems by fixing the minimum subsystem reliability to create a new problem. For this new formulation, it becomes possible to linearize the problem and use integer programming methods to determine system design configurations that allow mixing of functionally equivalent component types within a subsystem. This is the first time the mixing of component types has been addressed using integer programming. The methodology is demonstrated on three problems.     

基于灰色聚类评估的配送中心选址模糊多目标优化模型

将多属性决策方法与最优化方法相集成,研究了多配送中心选址优化问题。首先采用灰色聚类决策计算各候选地定性属性的综合评估值。再以选定配送中心的评估值均值最大化、系统成本最小化,以及配送中心容量利用率最大化作为3个优化目标,建立一个考虑需求点模糊需求、供应点与候选配送中心容量限制的三级供应链系统多配送中心选址模型。该模型被描述成了一个多目标的非线性混合整数规划模型。采用机会约束规划对模糊需求进行清晰化处理,并应用目标加权的方法将问题转化为单目标问题。通过算例验证了所提模型的可行性。在实际工作中,可根据决策者权重偏好得出令人满意的结果。     

BARP—A PC-based Bayesian reliability program allowing engineers to think in the language of probability curves

In addition to the misunderstandings and conceptual controversies that have swirled around Bayes theorem for more than 200 years, one of the factors that have kept it from assuming its proper role in an engineer's tool chest is the tedium of doing the probabilistic calculations, curve plotting, etc. The computer program BARP has been developed to eliminate this problem. The program combines the ability to construct priors and do Bayesian updates with the ability to do probabilistic arithmetic via the discrete probability distribution (DPD) method. This combined ability allows us, among other things, to do Bayesian assessments of the reliabilities of individual components of a system, and then combine these into an assessment of the reliability for the system as a whole. The interface with the user is menu driven and highly graphical, making the personal computer like a slide rule that works in terms of probability curves. Experience with this tool allows the engineer, after a while, to begin to think in terms of probability curves, thus promoting what we consider to be a favorable state of mind for people doing risk and reliability work.     

Evaluation of operational system structures based on reliability data

Systems of components have a structure that plays an important role in determining how the reliability of the individual components relates to the reliability of the system. The system reliability can be computed from component reliabilities using results from basic probability theory in the simplest case with all of the components assumed to act independently of one another. However, in the case of dependence, such calculations can be much more involved. When reliability data have been independently collected on both the system and each component in the system, it can be difficult to model any possible dependence between components. Established methods use the known structure of a system, along with these data, to assess whether the reliability of the individual components are mutually independent. In this paper, we expand this methodology to include an assessment of the type of dependence that may exist between the components. This is based on finding the system structure that would most likely produce the observed reliability data, under independence. In the frequentist setting, the likelihood approach is used to find these structures and an observed confidence measure is used to assess the strength of the statistical evidence in favor of each possible structure. In the Bayesian setting, posterior probabilities along with Bayes factors are used. An example demonstrates how these methods can be used in an applied setting.     

Inexact rough-interval type-2 fuzzy stochastic optimization model supporting municipal solid waste management under uncertainty

In this study, an inexact rough-interval type-2 fuzzy stochastic linear programming (IRIT2FSLP) approach is developed for addressing uncertainties presented as rough-interval, type-2 fuzzy and random variables. The proposed method is applied to the case of a long-term municipal solid waste management system. The IRIT2FSLP approach is an extension of the inexact interval linear programming for handling nonlinear stochastic optimization problems where rough-interval and type-2 fuzzy parameters are integrated into a general framework. The results indicate that IRIT2FSLP normally leads to rough-interval solutions. Comparisons of the proposed model with scenarios without rough-interval and type-2 fuzzy parameters are also conducted. The results indicate the significant impact of dual-uncertain information on the system, which implies the reliability of IRIT2FSLP in handling waste flow allocation.     

考虑V2G模式的电动汽车与可再生能源协同调度

为减小地区电网负荷峰谷差,增强电力系统接纳可再生能源的能力,同时提高电动汽车用户响应积极性,以地区电网等效负荷波动最小和用户充电费用最低为目标函数,建立了考虑电动汽车与电网互动(vehicle-to-grid,V2G)模式并计及风电和光伏出力的多目标协同调度模型,以合理安排电动汽车的充放电行为.定义了各目标的隶属度函数,通过运用最大模糊满意度法,将该多目标优化问题转化为单目标非线性优化问题,并应用自适应权重粒子群寻优算法进行求解,得到最优调度方案.算例结果验证了模型的有效性和求解方法的可行性.     

Fuzzy Regression Analysis by Quadratic Programming Reflecting Central Tendency

In this paper, we propose fuzzy regression analysis based on a quadratic programming approach. In fuzzy regression analysis, a quadratic programming approach gives more diverse spread coefficients than a linear programming approach. Moreover, a quadratic programming approach can integrate the central tendency of least squares and the possibilistic properties of fuzzy regression. Due to the characteristic of the quadratic programming problem, the proposed approach can obtain the optimal regression model representing possibilistic properties with the central tendency. In this approach, we classify the given data into two groups, i.e., the center-located group and the remaining group. Then, the upper and the lower approximation models can be obtained based on the classification result. By changing the weight coefficients of the objective function in the quadratic programming problem, we can analyze the given data in various angles.

     

Filter allocation and replacement strategies in fluid power system under uncertainty: a fuzzy robust nonlinear programming approach

A fuzzy robust nonlinear programming model is developed for the assessment of filter allocation and replacement strategies in hydraulic systems under uncertainty. It integrates the methods of fuzzy mathematic programming (FMP) and robust programming (RP) within the mixed integer nonlinear programming framework, and can facilitate dynamic analysis and optimization of filters allocation and replacement planning where the uncertainties are expressed as fuzzy membership functions. In modeling formulation, theory of contamination wear of typical hydraulic components is introduced to strengthen the presentation of relationship between system contamination and work performance. The fuzzy decision space is delimited into a more robust one by specifying the uncertainties through dimensional enlargement of the original fuzzy constraints. The piecewise linearization approach is employed to handle the nonlinearities of problem. The developed method has been applied to a case of planning filter allocation and replacement strategies under uncertainty and the generated optimal solution will help to reduce the total system cost and failure-risk level of the FPS.     

Fuzzy belief propagation in constrained Bayesian networks with application to maintenance decisions

Bayesian networks have been widely applied to domains such as medical diagnosis, fault analysis, and preventative maintenance. In some applications, because of insufficient data and the complexity of the system, fuzzy parameters and additional constraints derived from expert knowledge can be used to enhance the Bayesian reasoning process. However, very few methods are capable of handling the belief propagation in constrained fuzzy Bayesian networks (CFBNs). This paper therefore develops an improved approach which addresses the inference problem through a max-min programming model. The proposed approach yields more reasonable inference results and with less computational effort. By integrating the probabilistic inference drawn from diverse sources of information with decision analysis considering a decision-maker's risk preference, a CFBN-based decision framework is presented for seeking optimal maintenance decisions in a risk-based environment. The effectiveness of the proposed framework is validated based on an application to a gas compressor maintenance decision problem.     

Soft computing approach for reliability optimization: State-of-the-art survey

In the broadest sense, reliability is a measure of performance of systems. As systems have grown more complex, the consequences of their unreliable behavior have become severe in terms of cost, effort, lives, etc., and the interest in assessing system reliability and the need for improving the reliability of products and systems have become very important. Most solution methods for reliability optimization assume that systems have redundancy components in series and/or parallel systems and alternative designs are available. Reliability optimization problems concentrate on optimal allocation of redundancy components and optimal selection of alternative designs to meet system requirement. In the past two decades, numerous reliability optimization techniques have been proposed. Generally, these techniques can be classified as linear programming, dynamic programming, integer programming, geometric programming, heuristic method, Lagrangean multiplier method and so on. A Genetic Algorithm (GA), as a soft computing approach, is a powerful tool for solving various reliability optimization problems. In this paper, we briefly survey GA-based approach for various reliability optimization problems, such as reliability optimization of redundant system, reliability optimization with alternative design, reliability optimization with time-dependent reliability, reliability optimization with interval coefficients, bicriteria reliability optimization, and reliability optimization with fuzzy goals. We also introduce the hybrid approaches for combining GA with fuzzy logic, neural network and other conventional search techniques. Finally, we have some experiments with an example of various reliability optimization problems using hybrid GA approach.