检索结果-内蒙古大学图书馆

handling Constrained Multiobjective Optimization Problems With constraints in Both the Decision and Objective Spaces

引用

IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION 2019年第5期23卷 870-884页

作者： Liu, Zhi-Zhong Wang, Yong Cent South Univ Sch Automat Changsha 410083 Hunan Peoples R China

Constrained multiobjective optimization problems (CMOPs) are frequently encountered in real-world applications, which usually involve constraints in both the decision and objective spaces. However, current artificial CMOPs never consider constraints in the decision space (i.e., decision constraints) and constraints in the objective space (i.e., objective constraints) at the same time. As a result, they have a limited capability to simulate practical scenes. To remedy this issue, a set of CMOPs, named DOC, is constructed in this paper. It is the first attempt to consider both the decision and objective constraints simultaneously in the design of artificial CMOPs. Specifically, in DOC, various decision constraints (e.g., inequality constraints, equality constraints, linear constraints, and nonlinear constraints) are collected from real-world applications, thus making the feasible region in the decision space have different properties (e.g., nonlinear, extremely small, and multimodal). On the other hand, some simple and controllable objective constraints are devised to reduce the feasible region in the objective space and to make the Pareto front have diverse characteristics (e.g., continuous, discrete, mixed, and degenerate). As a whole, DOC poses a great challenge for a constrained multiobjective evolutionary algorithm (CMOEA) to obtain a set of well-distributed and well-converged feasible solutions. In order to enhance current CMOEAs' performance on DOC, a simple and efficient two-phase framework, named ToP, is proposed in this paper. In ToP, the first phase is implemented to find the promising feasible area by transforming a CMOP into a constrained single-objective optimization problem. Then in the second phase, a specific CMOEA is executed to obtain the final solutions. ToP is applied to four state-of-the-art CMOEAs, and the experimental results suggest that it is quite effective.

关键词： Pareto optimization Linear programming Automobiles Aerospace electronics Evolutionary computation Decision feedback equalizers Constrained multiobjective optimization problems (CMOPs) constraint-handling technique decision space evolutionary algorithms objective space

来源：评论

学校读者我要写书评

暂无评论

Composite Differential Evolution for Constrained Evolutionary Optimization

引用

IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS 2019年第7期49卷 1482-1495页

作者： Wang, Bing-Chuan Li, Han-Xiong Li, Jia-Peng Wang, Yong City Univ Hong Kong Dept Syst Engn & Engn Management Hong Kong Peoples R China Cent South Univ State Key Lab High Performance Complex Mfg Changsha 410083 Hunan Peoples R China Cent South Univ Sch Informat Sci & Engn Changsha 410083 Hunan Peoples R China Univ Essex Sch Comp Sci & Elect Engn Colchester CO4 3SQ Essex England

When solving constrained optimization problems (COPs) by evolutionary algorithms, the search algorithm plays a crucial role. In general, we expect that the search algorithm has the capability to balance not only diversity and convergence but also constraints and objective function during the evolution. For this purpose, this paper proposes a composite differential evolution (DE) for constrained optimization, which includes three different trial vector generation strategies with distinct advantages. In order to strike a balance between diversity and convergence, one of these three trial vector generation strategies is able to increase diversity, and the other two exhibit the property of convergence. In addition, to accomplish the tradeoff between constraints and objective function, one of the two trial vector generation strategies for convergence is guided by the individual with the least degree of constraint violation in the population, and the other is guided by the individual with the best objective function value in the population. After producing offspring by the proposed composite DE, the feasibility rule and the e constrained method are combined elaborately for selection in this paper. Moreover, a restart scheme is proposed to help the population jump out of a local optimum in the infeasible region for some extremely complicated COPs. By assembling the above techniques together, a constrained composite DE is proposed. The experiments on two sets of benchmark test functions with various features, i.e., 24 test functions from IEEE CEC2006 and 18 test functions with 10 dimensions and 30 dimensions from IEEE CEC2010, have demonstrated that the proposed method shows better or at least competitive performance against other state-of-the-art methods.

关键词： Composite differential evolution (DE) constrained optimization constraint-handling technique evolutionary algorithm (EA)

来源：评论

学校读者我要写书评

暂无评论

Combining Multiobjective Optimization with Differential Evolution to Solve Constrained Optimization Problems

引用

IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION 2012年第1期16卷 117-134页

作者： Wang, Yong Cai, Zixing Cent S Univ Sch Informat Sci & Engn Changsha 410083 Hunan Peoples R China

During the past decade, solving constrained optimization problems with evolutionary algorithms has received considerable attention among researchers and practitioners. Cai and Wang's method (abbreviated as CW method) is a recent constrained optimization evolutionary algorithm proposed by the authors. However, its main shortcoming is that a trial-and-error process has to be used to choose suitable parameters. To overcome the above shortcoming, this paper proposes an improved version of the CW method, called CMODE, which combines multiobjective optimization with differential evolution to deal with constrained optimization problems. Like its predecessor CW, the comparison of individuals in CMODE is also based on multiobjective optimization. In CMODE, however, differential evolution serves as the search engine. In addition, a novel infeasible solution replacement mechanism based on multiobjective optimization is proposed, with the purpose of guiding the population toward promising solutions and the feasible region simultaneously. The performance of CMODE is evaluated on 24 benchmark test functions. It is shown empirically that CMODE is capable of producing highly competitive results compared with some other state-of-the-art approaches in the community of constrained evolutionary optimization.

关键词： Constrained optimization problems constraint-handling technique differential evolution multiobjective optimization

来源：评论

学校读者我要写书评

暂无评论

A constrained multi-objective optimization algorithm with two cooperative populations

引用

MEMETIC COMPUTING 2022年第1期14卷 95-113页

作者： Zhang, Jianlin Cao, Jie Zhao, Fuqing Chen, Zuohan Lanzhou Univ Technol Sch Comp & Commun Technol Lanzhou 730050 Peoples R China Gansu Engn Res Ctr Mfg Informat Lanzhou 730050 Peoples R China

Constrained multi-objective problems (CMOPs) require balancing convergence, diversity, and feasibility of solutions. Unfortunately, the existing constrained multi-objective optimization algorithms (CMOEAs) exhibit poor performance when solving the CMOPs with complex feasible regions. To solve this shortcoming, this work proposes an improved algorithm named the CMOEA-TCP, which maintains two populations cooperating to push the solutions to approximate the constrained Pareto front. Specifically, one population is obtained by the Pareto-based method and aims to strengthen the algorithm's convergence ability. Meanwhile, another population is maintained by decomposition-based method and devoted to improving its diversity. The two populations work cooperatively during the entire evolution process with the constraint-handling technique. The performance of the CMOEA- TCP is verified on three benchmark suites with 34 problems. The experimental results demonstrate that the CMOEA-TCP can achieve performance comparable to or better than the other six state-of-the-art CMOEAs on the majority of considered problems.

关键词： Constrained multi-objective optimization problem Constrained multi-objective algorithm Cooperative population constraint-handling technique

来源：评论

学校读者我要写书评

暂无评论

A fast constrained state transition algorithm

引用

NEUROCOMPUTING 2021年 455卷 202-214页

作者： Zhou, Xiaojun Tian, Jituo Long, Jianpeng Jin, Yaochu Yu, Guo Yang, Chunhua Cent South Univ Sch Automat Changsha 410083 Peoples R China Univ Surrey Dept Comp Sci Guildford GU2 7XH Surrey England

When solving constrained optimization problems in real industrial processes, both optimality and computational efficiency need to be considered. However, most existing meta-heuristic algorithms are slow to find the global optimum. The first reason is that the way to generate and select candidate solutions is time-consuming. The low probability to generate and select potential solutions in assisting the computational efficiency is another reason. In this paper, a simplified state transition algorithm (STA) and a novel constraint-handling technique are proposed to address the above issues for small size constrained optimization problems. Firstly, three out of four operators in basic STA to produce candidate solutions are selected and two operators are modified with adaptive parameter tuning, which have a large probability to generate potential solutions, but consumes less time. Secondly, the constraint-handling technique considers not only the objective function value and the constraint violation but also the difference among candidate solutions. Thirdly, the sequential quadratic programming embedded into the simplified STA can further speed up the convergence. Experiments are conducted on 22 well-known test functions from IEEE CEC2006 and 4 engineering constrained optimization problems, in comparison with state-of-the-art algorithms. The experimental results show that the proposed method is competitive in finding the optimum faster. (c) 2021 Elsevier B.V. All rights reserved.

关键词： Constrained optimization Fast state transition algorithm Sequential quadratic programming constraint-handling technique

来源：评论

学校读者我要写书评

暂无评论

Two cooperative constraint handling techniques with an external archive for constrained multi-objective optimization

引用

MEMETIC COMPUTING 2024年第2期16卷 115-137页

Constrained multi-objective problems are difficult for researchers to solve because they contain infeasible regions. To address this issue, this paper proposes two cooperative constraint handling techniques that use an external archive. First, two constraint handling techniques, i.e., the penalty function and the constrained dominance principle, are embedded in multi-objective optimization algorithms and work cooperatively on two populations to increase population diversity. Then, an external archive is designed to preserve high-quality solutions that strike a good balance between objectives, values, and constraints throughout the evolution process. Finally, comprehensive experiments are conducted to validate the performance of the proposed algorithm, and seven state-of-the-art constrained multi-objective optimization algorithms are used to compare three test suites and ten real-world problems. The experimental results demonstrate that the proposed algorithm can achieve competitive performance in solving various constrained multi-objective problems. Additionally, the results show that cooperative constraint handling techniques are more robust than single constraint handling methods.

关键词： Constrained multi-objective optimization problems Constrained multi-objective algorithms constraint-handling technique Penalty function Constrained dominance principle

来源：评论

学校读者我要写书评

暂无评论

A Biobjective Perspective for Mixed-Integer Programming

引用

IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS 2022年第4期52卷 2374-2385页

作者： Liu, Jiao Wang, Yong Xin, Bin Wang, Ling Cent South Univ Sch Automat Changsha 410083 Peoples R China Hunan Xiangjiang Artificial Intelligence Acad Changsha 410083 Peoples R China Beijing Inst Technol Sch Automat Beijing 100081 Peoples R China Beijing Inst Technol Key Lab Intelligent Control & Decis Complex Syst Beijing 100081 Peoples R China Beijing Inst Technol Beijing Adv Innovat Ctr Intelligent Robots & Syst Beijing 100081 Peoples R China Tsinghua Univ Dept Automat Beijing 100084 Peoples R China

A mixed-integer programming (MIP) problem contains not only constraints but also integer restrictions. Integer restrictions divide the feasible region defined by constraints into multiple discontinuous feasible parts with different sizes. Several popular methods (e.g., rounding and truncation) have been proposed to deal with integer restrictions. Although it is easy for these methods to generate an integer, they tend to converge to an integer which is located in a feasible part with a big size. If the optimal solution is not in this feasible part, they are very likely to converge to a local optimal solution due to the loss of diversity of the population. To overcome this shortcoming, a biobjective optimization-based two-phase method is proposed in this article. In the first phase, a measure function is designed to compute the degree that a solution violates integer restrictions. By employing this measure function as the second objective function and removing integer restrictions, a MIP problem is transformed into a constrained biobjective optimization problem (CBOP). It can be proven that the Pareto optimal solution of the transformed CBOP which satisfies integer restrictions is the optimal solution of the original MIP problem. To solve the transformed CBOP, a new comparison rule is designed. After the first phase, the population can approach the Pareto optimal solution which satisfies integer restrictions. Then, the second phase is implemented to enhance the convergence precision and obtain the optimal solution. In addition, we design 12 test problems to verify the effectiveness of the proposed method. The results demonstrate that the proposed method shows better performance against five state-of-the-art evolutionary algorithms for MIP.

关键词： Optimization Statistics Sociology Pareto optimization Linear programming Programming Phase measurement Biobjective optimization constraint-handling technique evolutionary algorithms (EAs) integer-restriction-handling (IRH) technique mixed-integer programming (MIP)

来源：评论

学校读者我要写书评

暂无评论

Constrained Evolutionary Optimization by Means of (μ plus λ)-Differential Evolution and Improved Adaptive Trade-Off Model

引用

EVOLUTIONARY COMPUTATION 2011年第2期19卷 249-285页

作者： Wang, Yong Cai, Zixing Cent S Univ Sch Informat Sci & Engn Changsha 410083 Hunan Peoples R China

This paper proposes a (mu + lambda)-differential evolution and an improved adaptive trade-off model for solving constrained optimization problems. The proposed (mu + lambda)-differential evolution adopts three mutation strategies (i.e., rand/1 strategy, current-to-best/1 strategy, and rand/2 strategy) and binomial crossover to generate the offspring population. Moreover, the current-to-best/1 strategy has been improved in this paper to further enhance the global exploration ability by exploiting the feasibility proportion of the last population. Additionally, the improved adaptive trade-off model includes three main situations: the infeasible situation, the semi-feasible situation, and the feasible situation. En each situation, a constraint-handling mechanism is designed based on the characteristics of the current population. By combining the (mu + lambda)-differential evolution with the improved adaptive trade-off model, a generic method named (mu + lambda)-constrained differential evolution ((mu + lambda)-CDE) is developed. The (mu + lambda)-CDE is utilized to solve 24 well-known benchmark test functions provided for the special session on constrained real-parameter optimization of the 2006 IEEE Congress on Evolutionary Computation (CEC2006). Experimental results suggest that the (mu + lambda)-CDE is very promising for constrained optimization, since it can reach the best known solutions for 23 test functions and is able to successfully solve 21 test functions in all runs. Moreover, in this paper, a self-adaptive version of (mu + lambda)-CDE is proposed which is the most competitive algorithm so far among the CEC2006 entries.

关键词： Constrained optimization problems constraint-handling technique evolutionary algorithm differential evolution adaptive trade-off model

来源：评论

学校读者我要写书评

暂无评论

An evolutionary algorithm with directed weights for constrained multi-objective optimization

引用

APPLIED SOFT COMPUTING 2017年 60卷 613-622页

作者： Peng, Chaoda Liu, Hai-Lin Gu, Fangqing Guangdong Univ Technol Guangzhou Guangdong Peoples R China

When solving constrained multi-objective optimization problems (CMOPs), keeping infeasible individuals with good objective values and small constraint violations in the population can improve the performance of the algorithms, since they provide the information about the optimal direction towards Pareto front. By taking the constraint violation as an objective, we propose a novel constraint-handling technique based on directed weights to deal with CMOPs. This paper adopts two types of weights, i.e. feasible and infeasible weights distributing on feasible and infeasible regions respectively, to guide the search to the promising region. To utilize the useful information contained in infeasible individuals, this paper uses infeasible weights to maintain a number of well-diversified infeasible individuals. Meanwhile, they are dynamically changed along with the evolution to prefer infeasible individuals with better objective values and smaller constraint violations. Furthermore, 18 test instances and 2 engineering design problems are used to evaluate the effectiveness of the proposed algorithm. Several numerical experiments indicate that the proposed algorithm outperforms four compared algorithms in terms of finding a set of well-distributed non-domination solutions. (C) 2017 Elsevier B.V. All rights reserved.

关键词： constraint-handling technique Constrained multi-objective optimization Decomposition Evolutionary algorithm

来源：评论

学校读者我要写书评

暂无评论

An interactive approach based on a discrete differential evolution algorithm for a class of integer bilevel programming problems

引用

INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE 2016年第10期47卷 2330-2341页

作者： Li, Hong Zhang, Li Jiao, Yong-Chang Xidian Univ Sch Math & Stat Xian Peoples R China Xidian Univ Sch Elect Engn Xian Peoples R China

This paper presents an interactive approach based on a discrete differential evolution algorithm to solve a class of integer bilevel programming problems, in which integer decision variables are controlled by an upper-level decision maker and real-value or continuous decision variables are controlled by a lower-level decision maker. Using the Karush--Kuhn-Tucker optimality conditions in the lower-level programming, the original discrete bilevel formulation can be converted into a discrete single-level nonlinear programming problem with the complementarity constraints, and then the smoothing technique is applied to deal with the complementarity constraints. Finally, a discrete single-level nonlinear programming problem is obtained, and solved by an interactive approach. In each iteration, for each given upper-level discrete variable, a system of nonlinear equations including the lower-level variables and Lagrange multipliers is solved first, and then a discrete nonlinear programming problem only with inequality constraints is handled by using a discrete differential evolution algorithm. Simulation results show the effectiveness of the proposed approach.

关键词： interactive approach discrete differential evolution algorithm discrete bilevel programming problem smoothing function constraint-handling technique

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：