Expensive multiobjective optimization problems(EMOPs)are complex optimization problems exacted from realworld applications,where each objective function evaluation(FE)involves expensive computations or physical experi...Expensive multiobjective optimization problems(EMOPs)are complex optimization problems exacted from realworld applications,where each objective function evaluation(FE)involves expensive computations or physical experiments.Many surrogate-assisted evolutionary algorithms(SAEAs)have been designed to solve EMOPs.Nevertheless,EMOPs with large-scale decision variables remain challenging for existing SAEAs,leading to difficulties in maintaining convergence and diversity.To address this deficiency,we proposed a variable reconstructionbased SAEA(VREA)to balance convergence enhancement and diversity maintenance.Generally,a cluster-based variable reconstruction strategy reconstructs the original large-scale decision variables into low-dimensional weight variables.Thus,the population can be rapidly pushed towards the Pareto set(PS)by optimizing low-dimensional weight variables with the assistance of surrogate models.Population diversity is improved due to the cluster-based variable reconstruction strategy.An adaptive search step size strategy is proposed to balance exploration and exploitation further.Experimental comparisons with four state-of-the-art SAEAs are conducted on benchmark EMOPs with up to 1000 decision variables and an aerodynamic design task.Experimental results demonstrate that VREA obtains well-converged and diverse solutions with limited real FEs.展开更多
The paper addresses the constrained mean-semivariance portfolio optimization problem with the support of a novel multi-objective evolutionary algorithm (n-MOEA). The use of semivariance as the risk quantification meas...The paper addresses the constrained mean-semivariance portfolio optimization problem with the support of a novel multi-objective evolutionary algorithm (n-MOEA). The use of semivariance as the risk quantification measure and the real world constraints imposed to the model make the problem difficult to be solved with exact methods. Thanks to the exploratory mechanism, n-MOEA concentrates the search effort where is needed more and provides a well formed efficient frontier with the solutions spread across the whole frontier. We also provide evidence for the robustness of the produced non-dominated solutions by carrying out, out-of-sample testing during both bull and bear market conditions on FTSE-100.展开更多
Application of the multiobjective evolutionary algorithms to the aerodynamicoptimization design of a centrifugal impeller is presented. The aerodynamic performance of acentrifugal impeller is evaluated by using the th...Application of the multiobjective evolutionary algorithms to the aerodynamicoptimization design of a centrifugal impeller is presented. The aerodynamic performance of acentrifugal impeller is evaluated by using the three-dimensional Navier-Stokes solutions. Thetypical centrifugal impeller is redesigned for maximization of the pressure rise and blade load andminimization of the rotational total pressure loss at the given flow conditions. The Bezier curvesare used to parameterize the three-dimensional impeller blade shape. The present method obtains manyreasonable Pareto optimal designs that outperform the original centrifugal impeller. Detailedobservation of the certain Pareto optimal design demonstrates the feasibility of the presentmultiobjective optimization method tool for turbomachinery design.展开更多
In recent decades,great progress has been made in learnable multiobjective evolutionary algorithms(MOEAs)in the field of evolutionary computations.However,existing learnable MOEAs have not been equipped with powerful ...In recent decades,great progress has been made in learnable multiobjective evolutionary algorithms(MOEAs)in the field of evolutionary computations.However,existing learnable MOEAs have not been equipped with powerful strategies for addressing the grand series associated with sparse large-scale multiobjective optimization problems(sparse LSMOPs),which include the curse of dimensionality and unknown sparsity characteristics.This work proposes a generative adversarial network(GAN)-guided evolutionary algorithm for solving sparse LSMOPs.GAN-aided offspring generation is adopted at each generation to generate high-quality sparse offspring solutions to improve the search performance,owing to the GAN’s powerful learning and generative capabilities.Specifically,random interpolation and discretization strategies are utilized to prevent mode collapse and falling into local optima,thereby generating promising sparse offspring solutions.The experimental results on both benchmark and real-world problems verify the superior performance of the proposed algorithm compared with the state-of-the-art evolutionary algorithms.展开更多
Solving constrained multiobjective optimization problems(CMOPs) is a highly challenging work. Numerous complex nonlinear constraints significantly add to the complexity of CMOPs, resulting in an exceptionally intricat...Solving constrained multiobjective optimization problems(CMOPs) is a highly challenging work. Numerous complex nonlinear constraints significantly add to the complexity of CMOPs, resulting in an exceptionally intricate feasible region.Makes it difficult for the algorithm to search for the complete constraint PF. In addition, under the influence of multiple complex nonlinear constraints, the conventional calculation method of overall constraint violation is inefficient for assessing the quality of infeasible solutions, potentially misguiding the evolutionary direction of the population. In response to these challenges, this paper proposes the fuzzy constraint dominance strategy(FCDS).This novel approach facilitates nuanced comparisons of solutions to strike a better balance between objectives and constraints. The fuzzy constraint violation introduced in FCDS mitigates the misleading impact of complex nonlinear constraints. Moreover,FCDS divides the solution process of complex CMOP into multiple stages from easy to difficult, and uses adaptive methods to increase the difficulty level of the problem. Systematic experiments on four test suites and three real-world applications have conclusively demonstrated the superior competitiveness of FCDS against leading algorithms.展开更多
The binaphthol enantiomers separation process using simulation moving bed technology is simulated with the true moving bed approach (TMB). In order to systematically optimize the process with multiple productive obj...The binaphthol enantiomers separation process using simulation moving bed technology is simulated with the true moving bed approach (TMB). In order to systematically optimize the process with multiple productive objectives, this article develops a variant of tissue P system (TPS). Inspired by general tissue P systems, the special TPS has a tissue-like structure with several membranes. The key rules of each membrane are the communication rule and mutation rule. These characteristics contribute to the diversity of the population, the conquest of the multimodal of objective function, and the convergence of algorithm. The results of comparison with a popular algorithm——the non-dominated sorting genetic algorithm 2(NSGA-2) illustrate that the new algorithm has satisfactory performance. Using the algorithm, this study maximizes synchronously several conflicting objectives, purities of different products, and productivity.展开更多
In many real-world applications of evolutionary algorithms,the fitness of an individual requires a quantitative measure.This paper proposes a self-adaptive linear evolutionary algorithm (ALEA) in which we introduce ...In many real-world applications of evolutionary algorithms,the fitness of an individual requires a quantitative measure.This paper proposes a self-adaptive linear evolutionary algorithm (ALEA) in which we introduce a novel strategy for evaluating individual's relative strengths and weaknesses.Based on this strategy,searching space of constrained optimization problems with high dimensions for design variables is compressed into two-dimensional performance space in which it is possible to quickly identify 'good' individuals of the performance for a multiobjective optimization application,regardless of original space complexity.This is considered as our main contribution.In addition,the proposed new evolutionary algorithm combines two basic operators with modification in reproduction phase,namely,crossover and mutation.Simulation results over a comprehensive set of benchmark functions show that the proposed strategy is feasible and effective,and provides good performance in terms of uniformity and diversity of solutions.展开更多
For many real-world multiobjective optimization problems,the evaluations of the objective functions are computationally expensive.Such problems are usually called expensive multiobjective optimization problems(EMOPs)....For many real-world multiobjective optimization problems,the evaluations of the objective functions are computationally expensive.Such problems are usually called expensive multiobjective optimization problems(EMOPs).One type of feasible approaches for EMOPs is to introduce the computationally efficient surrogates for reducing the number of function evaluations.Inspired from ensemble learning,this paper proposes a multiobjective evolutionary algorithm with an ensemble classifier(MOEA-EC)for EMOPs.More specifically,multiple decision tree models are used as an ensemble classifier for the pre-selection,which is be more helpful for further reducing the function evaluations of the solutions than using single inaccurate model.The extensive experimental studies have been conducted to verify the efficiency of MOEA-EC by comparing it with several advanced multiobjective expensive optimization algorithms.The experimental results show that MOEA-EC outperforms the compared algorithms.展开更多
Technical debt(TD)happens when project teams carry out technical decisions in favor of a short-term goal(s)in their projects,whether deliberately or unknowingly.TD must be properly managed to guarantee that its negati...Technical debt(TD)happens when project teams carry out technical decisions in favor of a short-term goal(s)in their projects,whether deliberately or unknowingly.TD must be properly managed to guarantee that its negative implications do not outweigh its advantages.A lot of research has been conducted to show that TD has evolved into a common problem with considerable financial burden.Test technical debt is the technical debt aspect of testing(or test debt).Test debt is a relatively new concept that has piqued the curiosity of the software industry in recent years.In this article,we assume that the organization selects the testing artifacts at the start of every sprint.Implementing the latest features in consideration of expected business value and repaying technical debt are among candidate tasks in terms of the testing process(test cases increments).To gain the maximum benefit for the organization in terms of software testing optimization,there is a need to select the artifacts(i.e.,test cases)with maximum feature coverage within the available resources.The management of testing optimization for large projects is complicated and can also be treated as a multi-objective problem that entails a trade-off between the agile software’s short-term and long-term value.In this article,we implement a multi-objective indicatorbased evolutionary algorithm(IBEA)for fixing such optimization issues.The capability of the algorithm is evidenced by adding it to a real case study of a university registration process.展开更多
This paper presents an optimization technique coupling two optimization techniques for solving Economic Emission Load Dispatch Optimization Problem EELD. The proposed approach integrates the merits of both genetic alg...This paper presents an optimization technique coupling two optimization techniques for solving Economic Emission Load Dispatch Optimization Problem EELD. The proposed approach integrates the merits of both genetic algorithm (GA) and local search (LS), where it maintains a finite-sized archive of non-dominated solutions which gets iteratively updated in the presence of new solutions based on the concept of ε-dominance. To improve the solution quality, local search technique was applied as neighborhood search engine, where it intends to explore the less-crowded area in the current archive to possibly obtain more non-dominated solutions. TOPSIS technique can incorporate relative weights of criterion importance, which has been implemented to identify best compromise solution, which will satisfy the different goals to some extent. Several optimization runs of the proposed approach are carried out on the standard IEEE 30-bus 6-genrator test system. The comparison demonstrates the superiority of the proposed approach and confirms its potential to solve the multiobjective EELD problem.展开更多
动态约束多目标优化问题存在时变目标函数和约束条件,导致现有方法无法有效平衡变化响应的性能和效率。鉴于此,提出一种基于多源知识迁移策略的动态约束多目标进化算法(multi-source knowledge transfer based dynamic constrained mult...动态约束多目标优化问题存在时变目标函数和约束条件,导致现有方法无法有效平衡变化响应的性能和效率。鉴于此,提出一种基于多源知识迁移策略的动态约束多目标进化算法(multi-source knowledge transfer based dynamic constrained multiobjective evolutionary algorithm,MSKTEA)。该算法设计知识提取策略,利用预测方法分别估计新环境帕累托解集和帕累托前沿,并进一步建立外部存档,以存储多样性的历史解集。随后,设计多源知识迁移策略,利用预测方法得到的时序知识,并基于时序知识在外部存档中提取的相似环境知识,进行知识迁移以生成新环境初始种群。实验结果表明,MSKTEA相较于多个当前较优的算法在处理动态约束多目标优化问题时具有较强的竞争力,能够有效平衡算法追踪动态帕累托最优的性能和效率。展开更多
实数编码的多目标进化算法常使用模拟二进制交叉(simulated binary crossover,称SBX)算子.通过对SBX以及进化策略中变异算子进行对比分析,并引入进化策略中的离散重组算子,提出了一种正态分布交叉(normal distribution crossover,称NDX...实数编码的多目标进化算法常使用模拟二进制交叉(simulated binary crossover,称SBX)算子.通过对SBX以及进化策略中变异算子进行对比分析,并引入进化策略中的离散重组算子,提出了一种正态分布交叉(normal distribution crossover,称NDX)算子.首先在一维搜索空间实例中对NDX与SBX算子进行比较和分析,然后将NDX算子应用于Deb等人提出的稳态多目标进化算法ε-MOEA(ε-dominance based multiobjective evolutionary algorithm)中.采用NDX算子的ε-MOEA(记为ε-MOEA/NDX)算法在多目标优化标准测试集ZDT和DTLZ的10个函数上进行了实验比较.实验结果和分析表明,采用NDX的ε-MOEA所求得的Pareto最优解集质量明显优于经典算法ε-MOEA/SBX和NSGA-Ⅱ.展开更多
为了准确地求解组合权重的组合系数,将基于分解的多目标进化算法(multi-objective evolutionary algorithm based on decomposition,MOEA/D)思想引入评估领域,提出一种基于MOEA/D的组合权重方法.通常,利用加权和法将组合权重模型转化为...为了准确地求解组合权重的组合系数,将基于分解的多目标进化算法(multi-objective evolutionary algorithm based on decomposition,MOEA/D)思想引入评估领域,提出一种基于MOEA/D的组合权重方法.通常,利用加权和法将组合权重模型转化为单目标模型时,模型加权系数难以准确确定.对此,引入MOEA/D算法的分解思想,将组合权重模型转化为多个单目标子模型.MOEA/D算法仅适用于无约束优化问题,而较为常用的惩罚函数法难以表达进化初期无可行解的情况,因而提出改进自适应惩罚函数(improved adaptive penalty function,IAPF),将组合权重模型转化为无约束优化模型.应用所提出方法与其他方法进行仿真实验,实验结果表明,所提出算法具有有效性.展开更多
基金supported by the National Natural Science Foundation of China(U20A20306,62276191)the Fundamental Research Funds for the Central Universities(HUST2023JYCXJJ011).
摘要Expensive multiobjective optimization problems(EMOPs)are complex optimization problems exacted from realworld applications,where each objective function evaluation(FE)involves expensive computations or physical experiments.Many surrogate-assisted evolutionary algorithms(SAEAs)have been designed to solve EMOPs.Nevertheless,EMOPs with large-scale decision variables remain challenging for existing SAEAs,leading to difficulties in maintaining convergence and diversity.To address this deficiency,we proposed a variable reconstructionbased SAEA(VREA)to balance convergence enhancement and diversity maintenance.Generally,a cluster-based variable reconstruction strategy reconstructs the original large-scale decision variables into low-dimensional weight variables.Thus,the population can be rapidly pushed towards the Pareto set(PS)by optimizing low-dimensional weight variables with the assistance of surrogate models.Population diversity is improved due to the cluster-based variable reconstruction strategy.An adaptive search step size strategy is proposed to balance exploration and exploitation further.Experimental comparisons with four state-of-the-art SAEAs are conducted on benchmark EMOPs with up to 1000 decision variables and an aerodynamic design task.Experimental results demonstrate that VREA obtains well-converged and diverse solutions with limited real FEs.
摘要The paper addresses the constrained mean-semivariance portfolio optimization problem with the support of a novel multi-objective evolutionary algorithm (n-MOEA). The use of semivariance as the risk quantification measure and the real world constraints imposed to the model make the problem difficult to be solved with exact methods. Thanks to the exploratory mechanism, n-MOEA concentrates the search effort where is needed more and provides a well formed efficient frontier with the solutions spread across the whole frontier. We also provide evidence for the robustness of the produced non-dominated solutions by carrying out, out-of-sample testing during both bull and bear market conditions on FTSE-100.
摘要Application of the multiobjective evolutionary algorithms to the aerodynamicoptimization design of a centrifugal impeller is presented. The aerodynamic performance of acentrifugal impeller is evaluated by using the three-dimensional Navier-Stokes solutions. Thetypical centrifugal impeller is redesigned for maximization of the pressure rise and blade load andminimization of the rotational total pressure loss at the given flow conditions. The Bezier curvesare used to parameterize the three-dimensional impeller blade shape. The present method obtains manyreasonable Pareto optimal designs that outperform the original centrifugal impeller. Detailedobservation of the certain Pareto optimal design demonstrates the feasibility of the presentmultiobjective optimization method tool for turbomachinery design.
基金supported in part by National Natural Science Foundation of China(Nos.61906002,62076005,and U20A20398)the Natural Science Foundation of Anhui Province,China(Nos.2008085MF191 and 2508085 MF157)the University Synergy Innovation Program of Anhui Province,China(No.GXXT-2021-002).
摘要In recent decades,great progress has been made in learnable multiobjective evolutionary algorithms(MOEAs)in the field of evolutionary computations.However,existing learnable MOEAs have not been equipped with powerful strategies for addressing the grand series associated with sparse large-scale multiobjective optimization problems(sparse LSMOPs),which include the curse of dimensionality and unknown sparsity characteristics.This work proposes a generative adversarial network(GAN)-guided evolutionary algorithm for solving sparse LSMOPs.GAN-aided offspring generation is adopted at each generation to generate high-quality sparse offspring solutions to improve the search performance,owing to the GAN’s powerful learning and generative capabilities.Specifically,random interpolation and discretization strategies are utilized to prevent mode collapse and falling into local optima,thereby generating promising sparse offspring solutions.The experimental results on both benchmark and real-world problems verify the superior performance of the proposed algorithm compared with the state-of-the-art evolutionary algorithms.
基金supported by the Scientific Research Project of Xiang Jiang Lab(22XJ02003)the University Fundamental Research Fund(23-ZZCX-JDZ-28)+3 种基金the National Science Fund for Outstanding Young Scholars(62122093)the National Natural Science Foundation of China(72421002,62403477)the Science and Technology Innovation Program of Hunan Province(ZC23112101-10)the Hunan Natural Science Foundation Regional Joint Project(2023JJ50490)
摘要Solving constrained multiobjective optimization problems(CMOPs) is a highly challenging work. Numerous complex nonlinear constraints significantly add to the complexity of CMOPs, resulting in an exceptionally intricate feasible region.Makes it difficult for the algorithm to search for the complete constraint PF. In addition, under the influence of multiple complex nonlinear constraints, the conventional calculation method of overall constraint violation is inefficient for assessing the quality of infeasible solutions, potentially misguiding the evolutionary direction of the population. In response to these challenges, this paper proposes the fuzzy constraint dominance strategy(FCDS).This novel approach facilitates nuanced comparisons of solutions to strike a better balance between objectives and constraints. The fuzzy constraint violation introduced in FCDS mitigates the misleading impact of complex nonlinear constraints. Moreover,FCDS divides the solution process of complex CMOP into multiple stages from easy to difficult, and uses adaptive methods to increase the difficulty level of the problem. Systematic experiments on four test suites and three real-world applications have conclusively demonstrated the superior competitiveness of FCDS against leading algorithms.
基金Supported by the National Natural Science Foundation of China (No.60421002)
摘要The binaphthol enantiomers separation process using simulation moving bed technology is simulated with the true moving bed approach (TMB). In order to systematically optimize the process with multiple productive objectives, this article develops a variant of tissue P system (TPS). Inspired by general tissue P systems, the special TPS has a tissue-like structure with several membranes. The key rules of each membrane are the communication rule and mutation rule. These characteristics contribute to the diversity of the population, the conquest of the multimodal of objective function, and the convergence of algorithm. The results of comparison with a popular algorithm——the non-dominated sorting genetic algorithm 2(NSGA-2) illustrate that the new algorithm has satisfactory performance. Using the algorithm, this study maximizes synchronously several conflicting objectives, purities of different products, and productivity.
基金supported by the National Natural Science Foundation of China(No.60803049,60472060)
摘要In many real-world applications of evolutionary algorithms,the fitness of an individual requires a quantitative measure.This paper proposes a self-adaptive linear evolutionary algorithm (ALEA) in which we introduce a novel strategy for evaluating individual's relative strengths and weaknesses.Based on this strategy,searching space of constrained optimization problems with high dimensions for design variables is compressed into two-dimensional performance space in which it is possible to quickly identify 'good' individuals of the performance for a multiobjective optimization application,regardless of original space complexity.This is considered as our main contribution.In addition,the proposed new evolutionary algorithm combines two basic operators with modification in reproduction phase,namely,crossover and mutation.Simulation results over a comprehensive set of benchmark functions show that the proposed strategy is feasible and effective,and provides good performance in terms of uniformity and diversity of solutions.
摘要For many real-world multiobjective optimization problems,the evaluations of the objective functions are computationally expensive.Such problems are usually called expensive multiobjective optimization problems(EMOPs).One type of feasible approaches for EMOPs is to introduce the computationally efficient surrogates for reducing the number of function evaluations.Inspired from ensemble learning,this paper proposes a multiobjective evolutionary algorithm with an ensemble classifier(MOEA-EC)for EMOPs.More specifically,multiple decision tree models are used as an ensemble classifier for the pre-selection,which is be more helpful for further reducing the function evaluations of the solutions than using single inaccurate model.The extensive experimental studies have been conducted to verify the efficiency of MOEA-EC by comparing it with several advanced multiobjective expensive optimization algorithms.The experimental results show that MOEA-EC outperforms the compared algorithms.
基金The authors would like to thank the Deanship of Scientific Research at Umm Al-Qura University for supporting this work by Grant Code:(22UQUyouracademicnumberDSRxx).
摘要Technical debt(TD)happens when project teams carry out technical decisions in favor of a short-term goal(s)in their projects,whether deliberately or unknowingly.TD must be properly managed to guarantee that its negative implications do not outweigh its advantages.A lot of research has been conducted to show that TD has evolved into a common problem with considerable financial burden.Test technical debt is the technical debt aspect of testing(or test debt).Test debt is a relatively new concept that has piqued the curiosity of the software industry in recent years.In this article,we assume that the organization selects the testing artifacts at the start of every sprint.Implementing the latest features in consideration of expected business value and repaying technical debt are among candidate tasks in terms of the testing process(test cases increments).To gain the maximum benefit for the organization in terms of software testing optimization,there is a need to select the artifacts(i.e.,test cases)with maximum feature coverage within the available resources.The management of testing optimization for large projects is complicated and can also be treated as a multi-objective problem that entails a trade-off between the agile software’s short-term and long-term value.In this article,we implement a multi-objective indicatorbased evolutionary algorithm(IBEA)for fixing such optimization issues.The capability of the algorithm is evidenced by adding it to a real case study of a university registration process.
摘要This paper presents an optimization technique coupling two optimization techniques for solving Economic Emission Load Dispatch Optimization Problem EELD. The proposed approach integrates the merits of both genetic algorithm (GA) and local search (LS), where it maintains a finite-sized archive of non-dominated solutions which gets iteratively updated in the presence of new solutions based on the concept of ε-dominance. To improve the solution quality, local search technique was applied as neighborhood search engine, where it intends to explore the less-crowded area in the current archive to possibly obtain more non-dominated solutions. TOPSIS technique can incorporate relative weights of criterion importance, which has been implemented to identify best compromise solution, which will satisfy the different goals to some extent. Several optimization runs of the proposed approach are carried out on the standard IEEE 30-bus 6-genrator test system. The comparison demonstrates the superiority of the proposed approach and confirms its potential to solve the multiobjective EELD problem.
摘要动态约束多目标优化问题存在时变目标函数和约束条件,导致现有方法无法有效平衡变化响应的性能和效率。鉴于此,提出一种基于多源知识迁移策略的动态约束多目标进化算法(multi-source knowledge transfer based dynamic constrained multiobjective evolutionary algorithm,MSKTEA)。该算法设计知识提取策略,利用预测方法分别估计新环境帕累托解集和帕累托前沿,并进一步建立外部存档,以存储多样性的历史解集。随后,设计多源知识迁移策略,利用预测方法得到的时序知识,并基于时序知识在外部存档中提取的相似环境知识,进行知识迁移以生成新环境初始种群。实验结果表明,MSKTEA相较于多个当前较优的算法在处理动态约束多目标优化问题时具有较强的竞争力,能够有效平衡算法追踪动态帕累托最优的性能和效率。
摘要实数编码的多目标进化算法常使用模拟二进制交叉(simulated binary crossover,称SBX)算子.通过对SBX以及进化策略中变异算子进行对比分析,并引入进化策略中的离散重组算子,提出了一种正态分布交叉(normal distribution crossover,称NDX)算子.首先在一维搜索空间实例中对NDX与SBX算子进行比较和分析,然后将NDX算子应用于Deb等人提出的稳态多目标进化算法ε-MOEA(ε-dominance based multiobjective evolutionary algorithm)中.采用NDX算子的ε-MOEA(记为ε-MOEA/NDX)算法在多目标优化标准测试集ZDT和DTLZ的10个函数上进行了实验比较.实验结果和分析表明,采用NDX的ε-MOEA所求得的Pareto最优解集质量明显优于经典算法ε-MOEA/SBX和NSGA-Ⅱ.
摘要为了准确地求解组合权重的组合系数,将基于分解的多目标进化算法(multi-objective evolutionary algorithm based on decomposition,MOEA/D)思想引入评估领域,提出一种基于MOEA/D的组合权重方法.通常,利用加权和法将组合权重模型转化为单目标模型时,模型加权系数难以准确确定.对此,引入MOEA/D算法的分解思想,将组合权重模型转化为多个单目标子模型.MOEA/D算法仅适用于无约束优化问题,而较为常用的惩罚函数法难以表达进化初期无可行解的情况,因而提出改进自适应惩罚函数(improved adaptive penalty function,IAPF),将组合权重模型转化为无约束优化模型.应用所提出方法与其他方法进行仿真实验,实验结果表明,所提出算法具有有效性.