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Constrained optimization based on hybrid evolutionary algorithm and adaptive constraint-handling technique

STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION 2009年第4期37卷 395-413页

作者： Wang, Yong Cai, Zixing Zhou, Yuren Fan, Zhun Cent S Univ Sch Informat Sci & Engn Changsha 410083 Peoples R China S China Univ Technol Sch Engn & Comp Sci Guangzhou 516040 Guangdong Peoples R China Tech Univ Denmark Dept Engn Management DK-2800 Lyngby Denmark

A novel approach to deal with numerical and engineering constrained optimization problems, which incorporates a hybrid evolutionary algorithm and an adaptive constraint-handling technique, is presented in this paper. The hybrid evolutionary algorithm simultaneously uses simplex crossover and two mutation operators to generate the offspring population. Additionally, the adaptive constraint-handling technique consists of three main situations. In detail, at each situation, one constraint-handling mechanism is designed based on current population state. Experiments on 13 benchmark test functions and four well-known constrained design problems verify the effectiveness and efficiency of the proposed method. The experimental results show that integrating the hybrid evolutionary algorithm with the adaptive constraint-handling technique is beneficial, and the proposed method achieves competitive performance with respect to some other state-of-the-art approaches in constrained evolutionary optimization.

关键词： Constrained optimization Hybrid evolutionary algorithm constraint-handling technique

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Surrogate-Based constraint-handling technique for Multi-Area Combined Economic/Emission Dispatch Problems Within Bi-Level Programming Framework

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IEEE TRANSACTIONS ON EMERGING TOPICS IN COMPUTATIONAL INTELLIGENCE 2024年

作者： Liang, Huijun Lin, Chenhao Pang, Aokang Hubei Minzu Univ Coll Intelligent Syst Sci & Engn Enshi 445000 Peoples R China

Due to long optimization time and limited dispatching cycle, multi-area combined economic/emission dispatch (MACEED) problems are converted into computationally expensive MACEED (CEMACEED) problems. Existing centralized and distributed method for CEMACEED problems include time-consuming and inaccurate disadvantages. The drawbacks, i.e., low convergence rate and unaffordable computing time may make scheduling cycles can hardly be met. In this paper, a novel surrogate-based bi-level programming framework is proposed. CEMACEED problem is decoupled to obtain completely independent sub-area dispatching problems. Then, a novel surrogate-based constraint-handling technique is proposed to handle tie line constraint while realizing decoupling. Original tie line constraint is replaced by improved polynomial regression surrogate models to save more than 75% of operating time. Finally, a novel meta-heuristic algorithm named emotional accumulation game evolutionary algorithm (EAGEA) is proposed to execute CEMACEED problems. The proposed method obtains the minimum cost, emission, and operating time over all simulation cases.

关键词： Dispatching Optimization Costs Metaheuristics Programming Convergence Task analysis Bi-level programming constraint-handling technique game theory multi-area combined economic/emission dispatch surrogate model

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Surrogate-assisted constraint-handling technique for parametric multi-objective optimization

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STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION 2024年第9期67卷 167页

作者： Tsai, Ying-Kuan Malak Jr, Richard J. Northwestern Univ Dept Mech Engn Evanston IL 60208 USA Texas A&M Univ Dept Mech Engn College Stn TX 77843 USA

This work describes a new surrogate-assisted constraint-handling technique (CHT) for parametric multi-objective evolutionary algorithms, called Bayesian CHT. Parametric optimization finds optimal solutions as a function of one or more exogenous variables. The solution is a family of Pareto frontiers called the parameterized Pareto frontier (PPF). CHTs from non-parametric multi-objective evolutionary algorithms do not produce a good sampling of solutions on the PPF. The proposed CHT addresses this using Bayesian methods. A Gaussian process classifier serves as an uncertainty-quantified surrogate for problem constraints, enabling active learning and a novel repair mechanism that promotes sampling along the PPF. The new technique is evaluated on a suite of 36 test problems and two engineering cases of structural design. Quantitative results show that the proposed Bayesian CHT outperforms several state-of-the-art algorithms in most cases. From a qualitative perspective, the nondominated solutions are visualized to support the superiority of the new approach, which achieves a better spread of solutions on the PPF. The results of engineering studies also indicate that the new approach is computationally more efficient than the others.

关键词： Multi-objective Parametric optimization constraint-handling technique Evolutionary algorithms Surrogate modeling Bayesian active learning Test suite

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A novel constraint-handling technique based on dynamic weights for constrained optimization problems

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SOFT COMPUTING 2018年第12期22卷 3919-3935页

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

Bi-objective constraint-handling technique may be one of the most promising constraint techniques for constrained optimization problems. It regards the constraints as an extra objective and using Pareto ranking as selection operator. These algorithms achieve a good convergence by utilizing potential infeasible individuals, but not be good at maintaining the diversity of the population. It is significant to balance the diversity of the population and the convergence of the algorithm. This paper proposes a novel constraint-handling technique based on biased dynamic weights for constrained evolutionary algorithm. The biased weights are used to select different individuals with low objective values and low degree of constraint violations. Furthermore, along with the evolution, more emphasis is placed on the individuals with lower objective values and lower degree of constraint violations by adjusting the biased weights dynamically, which forces the search to a promising feasible region. Thus, the proposed algorithm can keep a good balance between the convergence and the diversity of the population. Moreover, we compared the proposed algorithm with other state-of-the-art algorithms on 42 benchmark problems. The experimental results showed the reliability and stabilization of the proposed algorithm.

关键词： constraint-handling technique Evolutionary algorithm Tchebycheff approach Constrained optimization

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A comprehensive opposition Multi-Verse Optimizer ensemble coordination constraint handling technique for hybrid hydro-thermal-wind problem

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EXPERT SYSTEMS WITH APPLICATIONS 2024年 245卷

作者： Liu, Shuai Qin, Hui Liu, Guanjun Qu, Yuhua Tang, Yi Jiang, Zhiqiang Huazhong Univ Sci & Technol Sch Civil & Hydraul Engn Wuhan 430074 Peoples R China Huazhong Univ Sci & Technol Hubei Key Lab Digital Valley Sci & Technol Wuhan 430074 Peoples R China

In this paper, a Comprehensive Opposition Multi-Verse Optimizer (COMVO) is proposed to find the optimal solution to the scheduling problem of hybrid hydro-thermal-wind systems. In COMVO, three improvement mechanisms are introduced to enhance the search performance of the original MVO. The proposed method is analyzed and statistically tested against existing state-of-the-art methods in 23 classic benchmark problems and CEC2009 test suite, which demonstrate the superiority of the proposed method. Meanwhile, a constrainthandling technique is developed to solve the complex coupling constraints in the HTW problem and is finally evaluated on a 4 hydro-3 thermal-2 wind system. The results of the comparative analyses show that the proposed method is able to achieve lower costs and fewer emissions than the existing popular methods. In addition, the proposed method reduces emissions by 54%, 81%, 3%, 44%, 17% and 5% in the mean value metrics compared to DA, FFA, GWO, HS, MFO and MVO at 2% wind penetration rate, which fully demonstrates the practicability of the proposed methodology and constraint-handling technique.

关键词： Multi-verse optimizer constraint-handling technique Hybrid hydro-thermal-wind problem

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An adaptive coordinate systems for constrained differential evolution

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CLUSTER COMPUTING-THE JOURNAL OF NETWORKS SOFTWARE TOOLS AND APPLICATIONS 2025年第1期28卷 1-24页

作者： Boualem, Sid Ahmed El Mahdi Meftah, Boudjelal Debbat, Fatima Univ Mascara Comp Sci Dept Mascara Algeria

Constrained optimization problems (COPs) are essential in many real-world applications. Existing methods often rely on a fixed coordinate system to explore the solution space of COPs, limiting their adaptability to complex and varying landscapes, particularly when constraints are involved. Solving COPs using evolutionary algorithms remains challenging due to the need to balance objective optimization and constraint satisfaction. To overcome these limitations, this paper proposes an Adaptive Coordinate System for Constrained Differential Evolution (ACSCDE). ACSCDE introduces two specialized coordinate systems: one focuses on guiding the search to the objective space, while the other directs the search toward feasible solutions. These coordinate systems are built using an archive-based covariance matrix that captures the characteristics of the fitness landscape and constraints. An adaptive selection process dynamically chooses the most suitable coordinate system based on feedback from the evolutionary process. Additionally, the original coordinate system is retained to enhance population diversity, and a tailored mutation strategy is applied to each system. The proposed method was tested on benchmark suites CEC2010 and CEC2017, designed to challenge state-of-the-art algorithms. The results demonstrate that ACSCDE achieves competitive performance, outperforming advanced techniques in complex constrained optimization scenarios. These findings highlight ACSCDE as a promising approach for improving the performance of evolutionary algorithms in constrained optimization tasks.

关键词： Constrained optimization Differential evolution Eigen coordinate system constraint-handling technique

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Comparative study of four penalty-free constraint-handling techniques in structural optimization using harmony search

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ENGINEERING WITH COMPUTERS 2022年第SUPPL 1期38卷 561-581页

作者： Cao, Hongyou Chen, Yupeng Zhou, Yunlai Liu, Shuang Qin, Shiqiang Wuhan Univ Technol Sch Civil Engn & Architecture Wuhan 430074 Peoples R China Xi An Jiao Tong Univ Sch Aerosp Engn State Key Lab Strength & Vibrat Mech Struct Xian 710049 Peoples R China Huazhong Univ Sci & Technol Sch Civil Engn & Mech Wuhan 430074 Peoples R China

This study investigates the search capability, stability, and computational efficiency of four improved penalty-free constraint-handling techniques (CHTs), including the death penalty, the Deb rule, the filter method, and the mapping strategy, in structural optimization using harmony search (HS). The first three general-purpose CHTs have been improved by hybridizing with a structural analysis filter strategy to enhance their computational efficiency based on the characteristics of structural optimization and the solution updating rule of the HS. This study also has modified the mapping operator of the mapping strategy to handle size and shape optimization with Euler buckling constraints. Four numerical examples examine the performances of these CHTs. The comparative results show that the mapping strategy exhibits apparent superiority both in search capability and stability among the four. However, it also demands the most computational cost, and the improved Deb rule becomes the most competitive method while considering computational efficiency. The difference between the death penalty and the Deb rule method is that the feasible solution initialization process required by the death penalty method will deteriorate its computational efficiency in problems with small feasible space. The filter method always reserves some infeasible solutions to guide the search in the iteration process. However, its performances are inferior to the other three approaches in four benchmark problems.

关键词： constraint-handling technique Structural optimization Metaheuristic algorithm Harmony search Computational efficiency

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A survey and numerical comparison of factor-free penalty function constraint-handling techniques in genetic algorithms

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JOURNAL OF INDUSTRIAL AND PRODUCTION ENGINEERING 2012年第1期29卷 61-86页

作者： Lee, Jung-Hua Chang, Ping-Teng Tunghai Univ Dept Ind Engn & Enterprise Informat Box 985 Taichung 407 Taiwan

Numerous techniques have been proposed for handling almost all kinds of constraints in searching for solutions to constrained optimization problems. Among these methods, penalty function has been the most commonly used approach. However, a drawback of the penalty function method lies in the difficulty of setting adequate penalty factors. Thus, due to the unavailability of appropriate penalty factors, the factor-free penalty function is created to decide penalties directly by the severities of constraint violations, and is expected to capture the distance to feasibility without any user-defined factors. However, although various factor-free penalty functions have been developed, a formal comparison of these functions is short. Therefore, in order to have a clearer picture of the factor-free penalty functions and their performances, this article surveys and compares the factor-free penalty functions proposed in prior literature, and performs a numerical comparison of these (nine) functions by applying the genetic algorithm on a collection of 37 popular test problems.

关键词： factor-free penalty function constraint-handling technique numerical comparison constrained optimization problem genetic algorithm

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Adaptively Allocating constraint-handling techniques for Constrained Multi-objective Optimization Problems

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INTERNATIONAL JOURNAL OF PATTERN RECOGNITION AND ARTIFICIAL INTELLIGENCE 2021年第8期35卷 2159032-2159032页

作者： Yang, Ning Liu, Hai-Lin Guangdong Univ Technol Sch Automat Guangzhou Peoples R China Guangdong Univ Technol Sch Appl Math Guangzhou Peoples R China

For solving constrained multi-objective optimization problems (CMOPs), an effective constraint-handling technique (CHT) is of great importance. Recently, many CHTs have been proposed for solving CMOPs. However, no single CHT can outperform all kinds of CMOPs. This paper proposes an algorithm, namely, ACHT-M2M, which adaptively allocates the existing CHTs in an M2M framework for solving CMOPs. To be more specific, a CMOP is first decomposed into several constrained multi-objective optimization subproblems by ACHT-M2M. Each subproblem has a subpopulation in a subregion. CHT for each subregion is adaptively allocated according to a proposed composite performance measure. Population for the next generation is selected from subregions by selection operators with different CHTs and the obtained nondominated feasible solutions in each generation are used to update a predefined archive. ACHT-M2M assembles the advantages of different CHTs and makes them cooperate with each other. The proposed ACHT-M2M is finally compared with the other 12 representative algorithms on benchmark CMOPs and the experimental results further confirm the effectiveness of ACHT-M2M for solving CMOPs.

关键词： Adaptive allocation constraint-handling technique constrained multi-objective optimization evolutionary algorithm M2M

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handling multi-objective optimization problems with unbalanced constraints and their effects on evolutionary algorithm performance

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SWARM AND EVOLUTIONARY COMPUTATION 2020年 55卷 100676-100676页

作者： Peng, Chaoda Liu, Hai-Lin Goodman, Erik D. Guangdong Univ Technol Guangzhou Guangdong Peoples R China Michigan State Univ BEACON Ctr Study Evolut Act E Lansing MI 48824 USA

Despite the successful application of an extension of the Multi-Objective Evolution Algorithm based on Decomposition (MOEA/D-M2M) to solve unbalanced multi-objective optimization problems (UMOPs), its use in eonstrained unbalanced multi-objective optimization problems has not been fully explored. In an earlier paper, a definition of UMOPs was suggested that had two necessary conditions: 1) finding a favored subset of the Pareto set is easier than finding an unfavored subset, and 2) the favored subset of the Pareto set dominates a large part of the feasible space. The second condition strongly reduces the fraction of MOPs that are considered UMOPs. In this paper, we eliminate that second condition and consider a broader class of UMOPs. We design an unbalanced constrained multi-objective test suite with three different types of biased constraints, yielding three different types of constrained test problems in which the degree of imbalance is scalable via a set of parameters introduced for each problem. We analyse the characteristics of three types of constraints and the difficulties they present for potential solution algorithms-i.e., NSGA-II, MOEA/D and MOEA/D-M2M, with four constraint-handling techniques. MOEA/D-M2M is shown to significantly outperform the other algorithms on these problems due to its decomposition strategy.

关键词： Multi-objective Evolutionary algorithm MOEA/D-M2M Unbalanced constraints constraint-handling technique

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