Multi-objective particle swarm-differential evolution algorithm

A multi-objective particle swarm-differential evolution algorithm (MOPSDE) is proposed that combined a particle swarm optimization (PSO) with a differential evolution (DE). During consecutive generations, a scale factor is produced by using a proposed mechanism based on the simulated annealing method and is applied to dynamically adjust the percentage of use of PSO and DE. In addition, the mutation operation of DE is improved, to satisfy that the proposed algorithm has different mutation operation in different searching stage. As a result, the capability of the local searching is enhanced and the prematurity of the population is restrained. The effectiveness of the proposed method has been validated through comprehensive tests using benchmark test functions. The numerical results obtained by this algorithm are compared with those obtained by the improved non-dominated sorting genetic algorithm (NSGA-II) and the other algorithms mentioned in the literature. The results show the effectiveness of the proposed MOPSDE algorithm.

     

PSO优化在模糊联合补充问题中的应用

对用PSO算法解决需求为不确定的联合补充问题进行了研究。运用模糊规划方法处理需求为模糊变量的联合补充问题,得到了作为求解目标的模糊数学模型;采用PSO思想对该模型进行分析,转化为PSO问题模型,制定出算法流程,并用数值实例验证了提出的粒子群优化模型和求解算法的有效性;对随机生成的大量数据进行处理,结果证明问题规模相同时该算法较遗传算法具有更高的效率。     

Optimal short-term hydro-thermal scheduling using quasi-oppositional teaching learning based optimization

This paper presents a new approach for solving short-term hydrothermal scheduling (HTS) using an integrated algorithm based on teaching learning based optimization (TLBO) and oppositional based learning (OBL). The practical hydrothermal system is highly complex and possesses nonlinear relationship of the problem variables, cascading nature of hydro reservoirs, water transport delay and scheduling time linkage that make the problem of optimization difficult using standard optimization methods. To overcome these problems, the proposed quasi-oppositional teaching learning based optimization (QOTLBO) is employed. To show its efficiency and robustness, the proposed QOTLBO algorithm is applied on two test systems. Numerical results of QOTLBO are compared with those obtained by two phase neural network, augmented Lagrange method, particle swarm optimization (PSO), improved self-adaptive PSO (ISAPSO), improved PSO (IPSO), differential evolution (DE), modified DE (MDE), fuzzy based evolutionary programming (Fuzzy EP), clonal selection algorithm (CSA) and TLBO approaches. The simulation results reveal that the proposed algorithm appears to be the best in terms of convergence speed, solution time and minimum cost when compared with other established methods. This method is considered to be a promising alternative approach for solving the short-term HTS problems in practical power system.     

Applying modified NSGA-II for bi-objective supply chain problem

This paper minimizes the value of total cost and bullwhip effect in a supply chain. The objectives have been achieved through developing a new multi-objective formulation for minimizing the total cost and minimizing the bullwhip effect of a two-echelon serial supply chain. A new crossover algorithm for a fuzzy variable and a new mutation algorithm have also been proposed while applying Non-dominated Sorting Genetic Algorithm-II (NSGA-II) to the proposed problem. The formulated problem has been simulated by Matlab software and the results of the modified NSGA-II have been compared with those of original NSGA-II. It is found from the results that the modified NSGA-II algorithm performs better than the original NSGA-II algorithm since the minimum values for both total cost and the bullwhip effect are obtained in case of the modified NSGA-II. The formulated bi-objective problem is new to the research community. The minimization of bullwhip effect has never been considered in a multi-objective optimization before. Besides crossover operator applied to the fuzzy variable and the mutation operator are newly introduced operators.     

基于DE和PSO的混合智能算法及其在模糊EOQ模型中的应用*

设计了融合差分进化和PSO算法优点的混合智能优化算法DEPSO,通过在粒子迭代过程中,随机选择一定数量的粒子进行差分进化操作,增加粒子的多样性,使陷入局部极小的粒子逃出,以保证DEPSO的全局收敛性能,并采用典型测试函数验证了DEPSO的性能。针对模糊相关机会规划EOQ模型求解难题,设计了基于模糊模拟方法和DEPSO的智能求解算法来计算模糊事件的可信性,从而得到了使库存费用不超过预算水平的可信度最大的最优订货量,算例证实了此求解算法的有效性。     

不确定情形下在线多源多属性反向拍卖双边协商决策

针对现实中存在的带有协商交互的在线多源多属性反向拍卖(OMSMARA)情形,同时考虑到买卖(采供)双方面临的不同方面的不确定性,综合利用双层规划理论和模糊理论研究不确定情形下OMSMARA双边协商决策问题.首先,基于问题描述和适当假设,建立一个新的带有协商交互的模糊混合整数双层规划(FMIBLP)模型,并基于增广模糊最小最大决策方法进行模型的精确转化;其次,考虑到问题模型的特点以及粒子群算法(PSO)的优越性,提出基于修正PSO的双层分布迭代算法(PSO-BLDI)用于模型求解;然后,通过数值算例和对比分析展示所建模型的可行性以及所提出算法的有效性;最后,通过敏感性分析研究相关参数变化对模型求解结果的影响,进一步表明所提出模型的合理性与决策方法的有效性.     

Multi-objective node deployment in WSNs: In search of an optimal trade-off among coverage,lifetime, energy consumption,and connectivity

The increased demand of Wireless Sensor Networks (WSNs) in different areas of application have intensified studies dedicated to the deployment of sensor nodes in recent past. For deployment of sensor nodes some of the key objectives that need to be satisfied are coverage of the area to be monitored, net energy consumed by the WSN, lifetime of the network, and connectivity and number of deployed sensors. In this article the sensor node deployment task has been formulated as a constrained multi-objective optimization (MO) problem where the aim is to find a deployed sensor node arrangement to maximize the area of coverage, minimize the net energy consumption, maximize the network lifetime, and minimize the number of deployed sensor nodes while maintaining connectivity between each sensor node and the sink node for proper data transmission. We assume a tree structure between the deployed nodes and the sink node for data transmission. Our method employs a recently developed and very competitive multi-objective evolutionary algorithm (MOEA) known as MOEA/D-DE that uses a decomposition approach for converting the problem of approximation of the Pareto fronts (PF) into a number of single-objective optimization problems. This algorithm employs differential evolution (DE), one of the most powerful real parameter optimizers in current use, as its search method. The original MOEA/D has been modified by introducing a new fuzzy dominance based decomposition technique. The algorithm introduces a fuzzy Pareto dominance concept to compare two solutions and uses the scalar decomposition method only when one of the solutions fails to dominate the other in terms of a fuzzy dominance level. We have compared the performance of the resulting algorithm, called MOEA/DFD, with the original MOEA/D-DE and another very popular MOEA called Non-dominated Sorting Genetic Algorithm (NSGA-II). The best trade-off solutions from MOEA/DFD based node deployment scheme have also been compared with a few single-objective node deployment schemes based on the original DE, an adaptive DE-variant (JADE), original particle swarm optimization (PSO), and a state-of-the art variant of PSO (Comprehensive Learning PSO). In all the test instances, MOEA/DFD performs better than all other algorithms. Also the proposed multi-objective formulation of the problem adds more flexibility to the decision maker for choosing the necessary threshold of the objectives to be satisfied.     

Automatically extracting T–S fuzzy models using cooperative random learning particle swarm optimization

This paper proposes a methodology for automatically extracting T–S fuzzy models from data using particle swarm optimization (PSO). In the proposed method, the structures and parameters of the fuzzy models are encoded into a particle and evolve together so that the optimal structure and parameters can be achieved simultaneously. An improved version of the original PSO algorithm, the cooperative random learning particle swarm optimization (CRPSO), is put forward to enhance the performance of PSO. CRPSO employs several sub-swarms to search the space and the useful information is exchanged among them during the iteration process. Simulation results indicate that CRPSO outperforms the standard PSO algorithm, genetic algorithm (GA) and differential evolution (DE) on the functions optimization and benchmark modeling problems. Moreover, the proposed CRPSO-based method can extract accurate T–S fuzzy model with appropriate number of rules.     

基于扩展T-S模型的PSO神经网络在故障诊断中的应用

针对现实故障现象具有模糊性和非线性的特点,提出了一种利用自适应扩展T-S(Takagi-Sugeno)模糊模型的PSO(Particle Swarm Optimization)算法和神经网络相结合的新型智能结构化算法来进行故障诊断的新方法.首先通过自适应的高斯函数来更改基本T-S模糊模型中的隶属度函数,进而使用扩展的T-S模糊模型来调整PSO算法的参数.然后使用该PSO算法作为神经网络的学习训练算法来进行训练.最后将此算法用于齿轮箱实测故障诊断.诊断结果显示均方误差提高了0.1981%.通过不同模型的诊断结果比较,表明本方法便捷、高效,为解决故障诊断问题提供了一条新途径.     

Bi-level programming modeling and hierarchical hybrid algorithm for antimissile dynamic firepower allocation problem with uncertain environment

Aiming at the shortcomings of antimissile dynamic firepower allocation (ADFA) researches under uncertain environment, the fuzzy chance-constrained bi-level programming model with complex constraints is proposed by introducing the uncertain programming theory. Firstly, maximization cost-effectiveness ratio and earliest interception time as the upper and the lower objective functions of the model, respectively, are used. In order to close to the battlefield environment, the model constraint includes interception time window, effective damage lower bound and intercept strategy, etc. Secondly, a particle coding scheme and repairing scheme are given with hierarchical structure for multi-constrained bi-level ADFA problem. Furthermore, the improved variable neighborhood PSO algorithm with convergence criterions and the PSO algorithm with doubt and repulsion factor (PSO-DR) are effectively combined. On these bases, the hierarchical hybrid fuzzy particle swarm optimization algorithm is presented with fuzzy simulation technique. Finally, the results of comparison show the proposed algorithm has stronger global searching ability and faster convergence speed, which can effectively solve large-scale ADFA problem and adapt to the requirements of real-time decision.     

差分进化粒子群混合优化算法的研究与应用

对基本粒子群算法（PSO）和差分进化算法（DE）进行了分析,有机结合两种进化算法提出了一种新型差分进化粒子群混合优化算法,该算法将优化过程分成两阶段,两分群分别采用PSO算法和DE算法同时进行。迭代过程中引入进化速度因子并通过群体间的信息交流阻止算法陷入局部最优。对4个高维复杂函数寻优测试表明算法的鲁棒性、收敛速度和精度,全局搜索能力均优于常规PSO和DE。将提出的改进算法用于乙烯收率软测量建模,应用结果表明模型精度较高、泛化性能较好。     

A modular Decision Support System for optimum investment selection in presence of uncertainty: Combination of fuzzy mathematical programming and fuzzy rule based system

In this paper, we have developed a modular Decision Support System (DSS) in order to select an optimum portfolio of several chances for investments in presence of uncertainty. The investments are considered as the projects so as their initial investment costs, profits, resource requirement, and total available budget are assumed to be uncertain. This uncertainty has been modeled using fuzzy concepts. The proposed DSS has two main modules. The first one is a fuzzy binary programming model which represents the mathematical model of the associated fuzzy capital-budgeting problem. It involves finding optimum combination of investment portfolio considering a multi-objective measurement function and subject to several set of constraints. The results of optimistic and pessimistic analysis of the aforementioned fuzzy binary programming model plus a managerial Confidence Level (CL) value are treated as input of a fuzzy rule based system which is the second module of the proposed DSS. Although some projects are simple to make a decision about at the final step of the first module but the unique output of the second module of the proposed DSS is Risk of Investment (ROI) for all remained project. The logic relations between precedence parts of the rules as well as CL value will work in favor of computational efforts in second module through diminishing some unessential rules. This will help to define a complete set of fuzzy IF-THEN rules more efficiently. The proposed DSS can help the decision makers to select an optimum investment portfolio with minimum risk in a complete ambiguous condition.     

基于多元模糊规划的微粒群优化算法

在微粒群的静态多元规划模式的基础上,考虑到多元最优值对群体寻优的引导因子间的比例在寻优过程中不能进行动态自适应调整,因而将模糊逻辑引入对微粒群的多元规划引导,提出了一种用于自适应动态规划的模糊微粒群算法模式,并以最优和次最优分布信息的模糊规划为例,进行了微粒群多元模糊规划模式的设计和数值仿真.仿真结果表明,该算法模式较静态多元规划模式具有更好的总体收敛性能.     

Credibilistic multi-period portfolio optimization model with bankruptcy control and affine recourse

Avoiding the possibility of bankruptcy during the investment horizon is very important to multi-period portfolio management. This paper considers a multi-period fuzzy portfolio selection problem with bankruptcy control. A multi-period portfolio optimization model imposed by a bankruptcy control constraint in fuzzy environment is proposed on the basis of credibility theory. In the proposed model, a linearly recourse policy is used to reflect the influence of historical predication basis on current portfolio decision. Three optimization objectives, viz., maximizing the terminal wealth and minimizing the cumulative risk and the cumulative uncertainty of the returns of portfolios over the whole investment horizon, are taken into consideration. For solving the proposed model, a fuzzy programming approach is applied to transform it into a single objective programming model. Then, a hybrid particle swarm optimization algorithm is designed for solution. Finally, an empirical example is presented to illustrate the application of the proposed model and solution comparisons are also given to demonstrate the effectiveness of the designed algorithm.     

Multi-objective optimization of TSK fuzzy models

In this paper we propose a hybrid algorithm to optimize the structure of TSK type fuzzy model using backpropagation (BP) learning algorithm and non-dominated sorting genetic algorithm (NSGA-II). In a first step, BP algorithm is used to optimize the parameters of the model (parameters of membership functions and fuzzy rules). NSGA-II is used in a second phase, to optimize the number of fuzzy rules and to fine tune the parameters. A well known benchmark is used to evaluate performances of the proposed modelling approach, and compare it with other modelling approaches.     

A group decision-making model based on incomplete comparative expressions with hesitant linguistic terms

As a result of uncertainty and complexity for environments of decision-making, it is more suitable for decision makers to use hesitant fuzzy linguistic information. In this paper, a novel group decision making (GDM) model based on fuzzy linear programming is proposed for incomplete comparative expressions with hesitant fuzzy linguistic term set (HFLTSs). We establish an equivalence theorem of additive consistency between 2-tuple fuzzy linguistic preference relation (FLPR) and corresponding fuzzy preference relation. Based on this framework, a fuzzy linear programming is established to address incomplete comparative expressions with HFLTSs. It is more important that the proposed fuzzy linear programming has a double action, finding the highest consistent incomplete 2-tuple FLPR and increasing inconsistent 2-tuple FLPR to the additive consistent 2-tuple FLPR based on given incomplete comparative expressions with HFLTSs. By this means, a novel GDM model is constructed based on importance induced ordered weighted averaging operator. Finally, an investment decision-making in real-world is solved by the proposed model, which shows the result of GDM is effectiveness.     

Fuzzy particle swarm optimization algorithms for the open shortest path first weight setting problem

The open shortest path first (OSPF) routing protocol is a well-known approach for routing packets from a source node to a destination node. The protocol assigns weights (or costs) to the links of a network. These weights are used to determine the shortest paths between all sources to all destination nodes. Assignment of these weights to the links is classified as an NP-hard problem. The aim behind the solution to the OSPF weight setting problem is to obtain optimized routing paths to enhance the utilization of the network. This paper formulates the above problem as a multi-objective optimization problem. The optimization metrics are maximum utilization, number of congested links, and number of unused links. These metrics are conflicting in nature, which motivates the use of fuzzy logic to be employed as a tool to aggregate these metrics into a scalar cost function. This scalar cost function is then optimized using a fuzzy particle swarm optimization (FPSO) algorithm developed in this paper. A modified variant of the proposed PSO, namely, fuzzy evolutionary PSO (FEPSO), is also developed. FEPSO incorporates the characteristics of the simulated evolution heuristic into FPSO. Experimentation is done using 12 test cases reported in literature. These test cases consist of 50 and 100 nodes, with the number of arcs ranging from 148 to 503. Empirical results have been obtained and analyzed for different values of FPSO parameters. Results also suggest that FEPSO outperformed FPSO in terms of quality of solution by achieving improvements between 7 and 31 %. Furthermore, comparison of FEPSO with various other algorithms such as Pareto-dominance PSO, weighted aggregation PSO, NSGA-II, simulated evolution, and simulated annealing algorithms revealed that FEPSO performed better than all of them by achieving best results for two or all three objectives.     

基于改进粒子群优化的模糊熵煤尘图像分割

针对基本粒子群算法易陷入局部最优和过早收敛的缺陷,提出权重因子自适应的粒子群算法,并对部分粒子进行Morlet变异操作,由此得到改进粒子群优化算法.将该算法和模糊熵相结合并用于图像分割,利用改进粒子群优化算法来搜索使模糊熵最大的参数值,得到模糊参数的最优组合,进而确定图像的分割阈值.通过与其他两种粒子群算法的分割结果进行比较,该算法取得了令人满意的分割结果,且算法运算时间较小,满足煤尘浓度实时精确测量的要求.     

模糊时间窗VRP的动态规划和禁忌搜索混合算法

为优化具有模糊时间窗的车辆路径问题,以物流配送成本和顾客平均满意度为目标,建立了多目标数学规划模型。基于Pareto占优的理论给出了求解多目标优化问题的并行多目标禁忌搜索算法,算法中嵌入同时优化顾客满意度的动态规划方法,运用阶段划分,把原问题分解为关于紧路径的优化子问题。对模糊时间窗为线性分段函数形式和非线性凹函数形式的隶属度函数,分别提出了次梯度有限迭代算法和次梯度中值迭代算法来优化顾客的最优开始服务时间。通过Solomon的标准算例,与次梯度投影算法的比较验证了动态规划方法优化服务水平的有效性,与主流的NSGA-II算法的对比实验表明了该研究提出的多目标禁忌搜索算法的优越性。     

Forecasting of Software Reliability Using Neighborhood Fuzzy Particle Swarm Optimization Based Novel Neural Network

This paper proposes an artificial neural network (ANN) based software reliability model trained by novel particle swarm optimization (PSO) algorithm for enhanced forecasting of the reliability of software. The proposed ANN is developed considering the fault generation phenomenon during software testing with the fault complexity of different levels. We demonstrate the proposed model considering three types of faults residing in the software. We propose a neighborhood based fuzzy PSO algorithm for competent learning of the proposed ANN using software failure data. Fitting and prediction performances of the neighborhood fuzzy PSO based proposed neural network model are compared with the standard PSO based proposed neural network model and existing ANN based software reliability models in the literature through three real software failure data sets. We also compare the performance of the proposed PSO algorithm with the standard PSO algorithm through learning of the proposed ANN. Statistical analysis shows that the neighborhood fuzzy PSO based proposed neural network model has comparatively better fitting and predictive ability than the standard PSO based proposed neural network model and other ANN based software reliability models. Faster release of software is achievable by applying the proposed PSO based neural network model during the testing period.