A quadratic bilevel programming problem is transformed into a single level complementarity slackness problem by applying Karush-Kuhn-Tucker（KKT） conditions.To cope with the complementarity constraints,a binary encod...A quadratic bilevel programming problem is transformed into a single level complementarity slackness problem by applying Karush-Kuhn-Tucker（KKT） conditions.To cope with the complementarity constraints,a binary encoding scheme is adopted for KKT multipliers,and then the complementarity slackness problem is simplified to successive quadratic programming problems,which can be solved by many algorithms available.Based on 0-1 binary encoding,an orthogonal genetic algorithm,in which the orthogonal experimental design with both two-level orthogonal array and factor analysis is used as crossover operator,is proposed.Numerical experiments on 10 benchmark examples show that the orthogonal genetic algorithm can find global optimal solutions of quadratic bilevel programming problems with high accuracy in a small number of iterations.展开更多
Radial Basis Function Neural Network(RBFNN)ensembles have long suffered from non-efficient training,where incorrect parameter settings can be computationally disastrous.This paper examines different evolutionary algor...Radial Basis Function Neural Network(RBFNN)ensembles have long suffered from non-efficient training,where incorrect parameter settings can be computationally disastrous.This paper examines different evolutionary algorithms for training the Symbolic Radial Basis Function Neural Network(SRBFNN)through the behavior’s integration of satisfiability programming.Inspired by evolutionary algorithms,which can iteratively find the nearoptimal solution,different Evolutionary Algorithms(EAs)were designed to optimize the producer output weight of the SRBFNN that corresponds to the embedded logic programming 2Satisfiability representation(SRBFNN-2SAT).The SRBFNN’s objective function that corresponds to Satisfiability logic programming can be minimized by different algorithms,including Genetic Algorithm(GA),Evolution Strategy Algorithm(ES),Differential Evolution Algorithm(DE),and Evolutionary Programming Algorithm(EP).Each of these methods is presented in the steps in the flowchart form which can be used for its straightforward implementation in any programming language.With the use of SRBFNN-2SAT,a training method based on these algorithms has been presented,then training has been compared among algorithms,which were applied in Microsoft Visual C++software using multiple metrics of performance,including Mean Absolute Relative Error(MARE),Root Mean Square Error(RMSE),Mean Absolute Percentage Error(MAPE),Mean Bias Error(MBE),Systematic Error(SD),Schwarz Bayesian Criterion(SBC),and Central Process Unit time(CPU time).Based on the results,the EP algorithm achieved a higher training rate and simple structure compared with the rest of the algorithms.It has been confirmed that the EP algorithm is quite effective in training and obtaining the best output weight,accompanied by the slightest iteration error,which minimizes the objective function of SRBFNN-2SAT.展开更多
基金supported by the National Natural Science Foundation of China (60873099)
文摘A quadratic bilevel programming problem is transformed into a single level complementarity slackness problem by applying Karush-Kuhn-Tucker（KKT） conditions.To cope with the complementarity constraints,a binary encoding scheme is adopted for KKT multipliers,and then the complementarity slackness problem is simplified to successive quadratic programming problems,which can be solved by many algorithms available.Based on 0-1 binary encoding,an orthogonal genetic algorithm,in which the orthogonal experimental design with both two-level orthogonal array and factor analysis is used as crossover operator,is proposed.Numerical experiments on 10 benchmark examples show that the orthogonal genetic algorithm can find global optimal solutions of quadratic bilevel programming problems with high accuracy in a small number of iterations.
基金This work is supported by Ministry of Higher Education(MOHE)through Fundamental Research Grant Scheme(FRGS)(FRGS/1/2020/STG06/UTHM/03/7).
文摘Radial Basis Function Neural Network(RBFNN)ensembles have long suffered from non-efficient training,where incorrect parameter settings can be computationally disastrous.This paper examines different evolutionary algorithms for training the Symbolic Radial Basis Function Neural Network(SRBFNN)through the behavior’s integration of satisfiability programming.Inspired by evolutionary algorithms,which can iteratively find the nearoptimal solution,different Evolutionary Algorithms(EAs)were designed to optimize the producer output weight of the SRBFNN that corresponds to the embedded logic programming 2Satisfiability representation(SRBFNN-2SAT).The SRBFNN’s objective function that corresponds to Satisfiability logic programming can be minimized by different algorithms,including Genetic Algorithm(GA),Evolution Strategy Algorithm(ES),Differential Evolution Algorithm(DE),and Evolutionary Programming Algorithm(EP).Each of these methods is presented in the steps in the flowchart form which can be used for its straightforward implementation in any programming language.With the use of SRBFNN-2SAT,a training method based on these algorithms has been presented,then training has been compared among algorithms,which were applied in Microsoft Visual C++software using multiple metrics of performance,including Mean Absolute Relative Error(MARE),Root Mean Square Error(RMSE),Mean Absolute Percentage Error(MAPE),Mean Bias Error(MBE),Systematic Error(SD),Schwarz Bayesian Criterion(SBC),and Central Process Unit time(CPU time).Based on the results,the EP algorithm achieved a higher training rate and simple structure compared with the rest of the algorithms.It has been confirmed that the EP algorithm is quite effective in training and obtaining the best output weight,accompanied by the slightest iteration error,which minimizes the objective function of SRBFNN-2SAT.
文摘粒子群优化(particle swarm optimization,PSO)算法是一种在机器人运动规划、信号处理等领域有广泛应用的优化算法。然而该算法易陷入局部最优解,从而导致早熟问题。出现早熟问题的原因之一是粒子群仅依靠适应度值选择学习范例。为了克服上述问题,提出了一种基于适应度值、改进率和新颖性混合驱动的PSO算法(particle swarm optimization algorithm based on hybrid driven by fitness values,improvement rate,and novelty,FINPSO)。在该算法中,引入的新指标和遗传算法会平衡种群的探索与开发,降低粒子群早熟的可能性。适应度值、改进率和新颖性会作为粒子的评价指标。各指标独立地选择学习范例并保存到不同的档案中。粒子每一次速度更新都要确定各个指标的权重,并从每个档案中选择一个范例学习。该算法采用了遗传算法进行粒子间的信息交流。遗传算法中的交叉互换和突变会给种群带来更多的随机性,提升种群的全局搜索能力。以八个PSO算法变体作为对比算法,两个CEC测试套件作为基准函数进行实验。实验结果表明,FINPSO算法优于已有的PSO算法变体达到最先进水平。
文摘以一款混联插电式混合动力汽车(Plug-in hybrid electric vehicle,PHEV)的燃油经济性为研究目标,为改善以等效因子为核心的等效燃油瞬时消耗最小策略(Equivalent fuel consumption minimization strategy,ECMS)的控制效果,考虑电池荷电状态(State of charge,SOC)、等效因子与燃油消耗的关系,构建等效因子全局优化模型;利用遗传算法离线优化一定工况下的等效因子S,得到不同电消耗续航行驶里程与电池SOC初始值的最佳等效因子MAP图,建立基于等效因子优化的ECMS能量管理策略,并考虑动力电池、电动机等部件的效率,获得最佳等效因子下的发动机、ISG电机、驱动电机的功率分配,并进行仿真与硬件在环试验,其中仿真结果表明,与未优化的等效因子相比,燃油经济性提高20.81%,硬件在环试验结果与仿真结果基本一致,表明所制定能量管理策略的有效性和可行性,进而为解决不同的行驶里程PHEV功率分配策略提供理论基础。
