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Artykuły w czasopismach na temat „Constrained Multi-Objective Optimization”

Autor: Grafiati

Data publikacji: 3 czerwca 2025

Data aktualizacji: 31 lipca 2025

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1

Adekoya, Adekunle Rotimi, and Mardé Helbig. "Decision-Maker’s Preference-Driven Dynamic Multi-Objective Optimization." Algorithms 16, no. 11 (2023): 504. http://dx.doi.org/10.3390/a16110504.

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DMOOP are optimization problems where elements of the problems, such as the objective functions and/or constraints, change with time. These problems are characterized by two or more objective functions, where at least two objective functions are in conflict with one another. When solving real-world problems, the incorporation of human DM’ preferences or expert knowledge into the optimization process and thereby restricting the search to a specific region of the POF may result in more preferred or suitable solutions. This study proposes approaches that enable DM to influence the search process

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Yang, Yufei, and Changsheng Zhang. "A Multi-Objective Carnivorous Plant Algorithm for Solving Constrained Multi-Objective Optimization Problems." Biomimetics 8, no. 2 (2023): 136. http://dx.doi.org/10.3390/biomimetics8020136.

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Satisfying various constraints and multiple objectives simultaneously is a significant challenge in solving constrained multi-objective optimization problems. To address this issue, a new approach is proposed in this paper that combines multi-population and multi-stage methods with a Carnivorous Plant Algorithm. The algorithm employs the ϵ-constraint handling method, with the ϵ value adjusted according to different stages to meet the algorithm’s requirements. To improve the search efficiency, a cross-pollination is designed based on the trapping mechanism and pollination behavior of carnivorou

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Zhang, Kai, Siyuan Zhao, Hui Zeng, and Junming Chen. "Two-Stage Archive Evolutionary Algorithm for Constrained Multi-Objective Optimization." Mathematics 13, no. 3 (2025): 470. https://doi.org/10.3390/math13030470.

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The core issue in handling constrained multi-objective optimization problems (CMOP) is how to maintain a balance between objectives and constraints. However, existing constrained multi-objective evolutionary algorithms (CMOEAs) often fail to achieve the desired performance when confronted with complex feasible regions. Building upon this theoretical foundation, a two-stage archive-based constrained multi-objective evolutionary algorithm (CMOEA-TA) based on genetic algorithms(GA) is proposed. In CMOEA-TA, First stage: The archive appropriately relaxes constraints based on the proportion of feas

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4

Wang, Qiuzhen, Zhibing Liang, Juan Zou, et al. "Dynamic Constrained Boundary Method for Constrained Multi-Objective Optimization." Mathematics 10, no. 23 (2022): 4459. http://dx.doi.org/10.3390/math10234459.

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When solving complex constrained problems, how to efficiently utilize promising infeasible solutions is an essential issue because these promising infeasible solutions can significantly improve the diversity of algorithms. However, most existing constrained multi-objective evolutionary algorithms (CMOEAs) do not fully exploit these promising infeasible solutions. In order to solve this problem, a constrained multi-objective optimization evolutionary algorithm based on the dynamic constraint boundary method is proposed (CDCBM). The proposed algorithm continuously searches for promising infeasib

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5

Zuo, Mingcheng, and Yuan Xue. "Population Feasibility State Guided Autonomous Constrained Multi-Objective Evolutionary Optimization." Mathematics 12, no. 6 (2024): 913. http://dx.doi.org/10.3390/math12060913.

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Many practical problems can be classified as constrained multi-objective optimization problems. Although various methods have been proposed for solving constrained multi-objective optimization problems, there is still a lack of research considering the integration of multiple constraint handling techniques. Given this, this paper combines the objective and constraint separation method with the multi-operator method, proposing a population feasibility state guided autonomous constrained evolutionary optimization method. This method first defines the feasibility state of the population based on

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6

Zhao, Tian Yang, Guo Bing Qiu, Ying Zhi Li, Wen Xia Liu, and Jian Hua Zhang. "Constrained Multi-Objective Differential Evolution for Security Constrained Economic/Environmental Dispatch." Applied Mechanics and Materials 291-294 (February 2013): 817–22. http://dx.doi.org/10.4028/www.scientific.net/amm.291-294.817.

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A newly constrained multi-objective differential evolution optimization technique (CMODE) for security constrained economic/environmental dispatch (EED) was proposed. The proposed CMODE evolved a constrained multi-objective version of differential evolution (DE) by employing the traditional multi-objective differential evolution (DEMO) and constrain handle technique to balance the search between feasible region and infeasible region. The proposed CMODE method had been applied to solve the security constrained EED problem. Experiments had been carried on a standard test system. The results demo

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7

Ramirez-Atencia, Cristian, and David Camacho. "Constrained multi-objective optimization for multi-UAV planning." Journal of Ambient Intelligence and Humanized Computing 10, no. 6 (2018): 2467–84. http://dx.doi.org/10.1007/s12652-018-0930-0.

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8

Ramírez, Atencia Cristian, and David Camacho. "Constrained multi-objective optimization for multi-UAV planning." Journal of Ambient Intelligence and Humanized Computing 10 (June 1, 2019): 2467–84. https://doi.org/10.1007/s12652-018-0930-0.

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Over the last decade, developments in unmanned aerial vehicles (UAVs) has greatly increased, and they are being used in many fields including surveillance, crisis management or automated mission planning. This last field implies the search of plans for missions with multiple tasks, UAVs and ground control stations; and the optimization of several objectives, including makespan, fuel consumption or cost, among others. In this work, this problem has been solved using a multi-objective evolutionary algorithm combined with a constraint satisfaction problem model, which is used in the fitness funct

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9

Hamdy, A., and A. A. Mohamed. "Greedy Binary Particle Swarm Optimization for multi-Objective Constrained Next Release Problem." International Journal of Machine Learning and Computing 9, no. 5 (2019): 561–68. http://dx.doi.org/10.18178/ijmlc.2019.9.5.840.

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10

Xie, Shumin, Zhenjia Zhu, and Hui Wang. "An Improved Coevolutionary Algorithm for Constrained Multi-Objective Optimization Problems." International Journal of Cognitive Informatics and Natural Intelligence 18, no. 1 (2024): 1–16. http://dx.doi.org/10.4018/ijcini.355766.

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Constrained multi-objective optimization problems are ubiquitous in engineering applications. In recent years, constrained multi-objective optimization algorithms based on the dual population coevolutionary framework have been widely studied due to their excellent performance. However, when facing optimization problems with complex constraints, the performance of existing algorithms still needs further improvement. This paper proposes an improved constrained multi-objective coevolutionary algorithm (iCMOCA). The algorithm mainly includes two populations: One population takes into account const

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11

Park, Jeewon, Oladayo S. Ajani, and Rammohan Mallipeddi. "Optimization-Based Energy Disaggregation: A Constrained Multi-Objective Approach." Mathematics 11, no. 3 (2023): 563. http://dx.doi.org/10.3390/math11030563.

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Recently, optimization-based energy disaggregation (ED) algorithms have been gaining significance due to their capability to perform disaggregation with minimal information compared to the pattern-based ED algorithms, which demand large amounts of data for training. However, the performances of optimization-based ED algorithms depend on the problem formulation that includes an objective function(s) and/or constraints. In the literature, ED has been formulated as a constrained single-objective problem or an unconstrained multi-objective problem considering disaggregation error, sparsity of stat

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12

Chen, Gonggui, Xingting Yi, Zhizhong Zhang, and Hangtian Lei. "Solving the Multi-Objective Optimal Power Flow Problem Using the Multi-Objective Firefly Algorithm with a Constraints-Prior Pareto-Domination Approach." Energies 11, no. 12 (2018): 3438. http://dx.doi.org/10.3390/en11123438.

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Known as a multi-objective, large-scale, and complicated optimization problem, the multi-objective optimal power flow (MOOPF) problem tends to be introduced with many constraints. In this paper, compared with the frequently-used penalty function-based method (PFA), a novel constraint processing approach named the constraints-prior Pareto-domination approach (CPA) is proposed for ensuring non-violation of various inequality constraints on dependent variables by introducing the Pareto-domination principle based on the sum of constraint violations. Moreover, for solving the constrained MOOPF prob

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13

Lai, Yuling, Junming Chen, Yile Chen, Hui Zeng, and Jialin Cai. "Feedback Tracking Constraint Relaxation Algorithm for Constrained Multi-Objective Optimization." Mathematics 13, no. 4 (2025): 629. https://doi.org/10.3390/math13040629.

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In practical applications, constrained multi-objective optimization problems (CMOPs) often fail to achieve the desired results when dealing with CMOPs with different characteristics. Therefore, to address this drawback, we designed a constraint multi-objective evolutionary algorithm based on feedback tracking constraint relaxation, referred to as CMOEA-FTR. The entire search process of the algorithm is divided into two stages: In the first stage, the constraint boundaries are adaptively adjusted based on the feedback information from the population solutions, guiding the boundary solutions tow

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14

SHANG, Rong-Hua, Li-Cheng JIAO, and Wen-Ping MA. "Immune Clonal Multi-Objective Optimization Algorithm for Constrained Optimization." Journal of Software 19, no. 11 (2009): 2943–56. http://dx.doi.org/10.3724/sp.j.1001.2008.02943.

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15

Shi, Min, Tongqiang Shi, Lei Shi, Zhengrong Ouyang, and Junjie Li. "Constrained multi-objective optimization of helium liquefaction cycle." Thermal Science, no. 00 (2023): 278. http://dx.doi.org/10.2298/tsci230626278s.

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The helium cryo-plant is an indispensable subsystem for the application of low-temperature superconductors in large-scale scientific facilities. However, it is important to note that the cryo-plant requires stable operation and consumes a substantial amount of electrical power for its operation. Additionally, the construction of the cryo-plant incurs significant economic costs. To achieve the necessary cooling capacity while reducing power consumption and ensuring stability and economic feasibility, constrained multi-objective optimization is performed using the interior point method in this w

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16

Li, Huiting, Yaochu Jin, and Ran Cheng. "Multi-phase constrained multi-objective optimization via heterogeneous transfer." Information Sciences 700 (May 2025): 121836. https://doi.org/10.1016/j.ins.2024.121836.

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17

Liu, Chun-An, Yuping Wang, and Aihong Ren. "New Dynamic Multi-Objective Constrained Optimization Evolutionary Algorithm." Asia-Pacific Journal of Operational Research 32, no. 05 (2015): 1550036. http://dx.doi.org/10.1142/s0217595915500360.

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For dynamic multi-objective constrained optimization problem (DMCOP), it is important to find a sufficient number of uniformly distributed and representative dynamic Pareto optimal solutions. In this paper, the time period of the DMCOP is first divided into several random subperiods. In each random subperiod, the DMCOP is approximately regarded as a static optimization problem by taking the time subperiod fixed. Then, in order to decrease the amount of computation and improve the effectiveness of the algorithm, the dynamic multi-objective constrained optimization problem is further transformed

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18

Ahmadianshalchi, Alaleh, Syrine Belakaria, and Janardhan Rao Doppa. "Preference-Aware Constrained Multi-Objective Bayesian Optimization (Student Abstract)." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 21 (2024): 23436–38. http://dx.doi.org/10.1609/aaai.v38i21.30418.

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We consider the problem of constrained multi-objective optimization over black-box objectives, with user-defined preferences, with a largely infeasible input space. Our goal is to approximate the optimal Pareto set from the small fraction of feasible inputs. The main challenges include huge design space, multiple objectives, numerous constraints, and rare feasible inputs identified only through expensive experiments. We present PAC-MOO, a novel preference-aware multi-objective Bayesian optimization algorithm to solve this problem. It leverages surrogate models for objectives and constraints to

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19

Chen, Junming, Yanxiu Wang, Zichun Shao, Hui Zeng, and Siyuan Zhao. "Dual-Population Cooperative Correlation Evolutionary Algorithm for Constrained Multi-Objective Optimization." Mathematics 13, no. 9 (2025): 1441. https://doi.org/10.3390/math13091441.

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When addressing constrained multi-objective optimization problems (CMOPs), the key challenge lies in achieving a balance between the objective functions and the constraint conditions. However, existing evolutionary algorithms exhibit certain limitations when tackling CMOPs with complex feasible regions. To address this issue, this paper proposes a constrained multi-objective evolutionary algorithm based on a dual-population cooperative correlation (CMOEA-DCC). Under the CMOEA-DDC framework, the system maintains two independently evolving populations: the driving population and the conventional

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20

Yi, Wenchao, Zhilei Lin, Youbin Lin, Shusheng Xiong, Zitao Yu, and Yong Chen. "Solving Optimal Power Flow Problem via Improved Constrained Adaptive Differential Evolution." Mathematics 11, no. 5 (2023): 1250. http://dx.doi.org/10.3390/math11051250.

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The optimal power flow problem is one of the most widely used problems in power system optimizations, which are multi-modal, non-linear, and constrained optimization problems. Effective constrained optimization methods can be considered in tackling the optimal power flow problems. In this paper, an ϵ-constrained method-based adaptive differential evolution is proposed to solve the optimal power flow problems. The ϵ-constrained method is improved to tackle the constraints, and a p-best selection method based on the constraint violation is implemented in the adaptive differential evolution. The

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21

Chen, Junming, Kai Zhang, Hui Zeng, Jin Yan, Jin Dai, and Zhidong Dai. "Adaptive Constraint Relaxation-Based Evolutionary Algorithm for Constrained Multi-Objective Optimization." Mathematics 12, no. 19 (2024): 3075. http://dx.doi.org/10.3390/math12193075.

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The key problem to solving constrained multi-objective optimization problems (CMOPs) is how to achieve a balance between objectives and constraints. Unfortunately, most existing methods for CMOPs still cannot achieve the above balance. To this end, this paper proposes an adaptive constraint relaxation-based evolutionary algorithm (ACREA) for CMOPs. ACREA adaptively relaxes the constraints according to the iteration information of population, whose purpose is to induce infeasible solutions to transform into feasible ones and thus improve the ability to explore the unknown regions. Completely ig

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22

Qiao, Kangjia, Jing Liang, Kunjie Yu, et al. "Constraints Separation Based Evolutionary Multitasking for Constrained Multi-Objective Optimization Problems." IEEE/CAA Journal of Automatica Sinica 11, no. 8 (2024): 1819–35. http://dx.doi.org/10.1109/jas.2024.124545.

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23

Qian, Xue Yi. "The Multi-Objective Optimization for Cycloidal Gear Drive Based on the Elastohydrodynamic Lubrication Theory." Advanced Materials Research 591-593 (November 2012): 697–703. http://dx.doi.org/10.4028/www.scientific.net/amr.591-593.697.

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For improving the designed quality of the cycloidal gear planetary drive, the paper derives a calculation formula of the minimum film thickness, which is between cycloidal gear teeth, based on elastohydrodynamic lubrication theory and gear geometry. A mathematical model for constrained multi-objective optimization is established and the model satisfies three constrains:maximize minimum film thickness between gear teeth( minimize the reciprocal ), minimize average value of m points’s absolute error value on active section that is between the tooth curves of positive shift optimal combination an

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24

LING, Hai-feng, Xian-zhong ZHOU, Xun-lin JIANG, and Yi-hong XIAO. "Improved constrained multi-objective particle swarm optimization algorithm." Journal of Computer Applications 32, no. 5 (2013): 1320–24. http://dx.doi.org/10.3724/sp.j.1087.2012.01320.

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SHANG, Rong-Hua, Li-Cheng JIAO, Chao-Xu HU, and Jing-Jing MA. "Modified Immune Clonal Constrained Multi-Objective Optimization Algorithm." Journal of Software 23, no. 7 (2012): 1773–86. http://dx.doi.org/10.3724/sp.j.1001.2012.04108.

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Cuate, Oliver, Lourdes Uribe, Adriana Lara, and Oliver Schütze. "A benchmark for equality constrained multi-objective optimization." Swarm and Evolutionary Computation 52 (February 2020): 100619. http://dx.doi.org/10.1016/j.swevo.2019.100619.

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Husain, Riyasat, and A. D. Ghodke. "Constrained multi-objective optimization of storage ring lattices." Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 883 (March 2018): 151–58. http://dx.doi.org/10.1016/j.nima.2017.11.077.

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Singh, Prashant, Marco Rossi, Ivo Couckuyt, Dirk Deschrijver, Hendrik Rogier, and Tom Dhaene. "Constrained multi-objective antenna design optimization using surrogates." International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 30, no. 6 (2017): e2248. http://dx.doi.org/10.1002/jnm.2248.

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Yang, Ning, and Hai-Lin Liu. "Adaptively Allocating Constraint-Handling Techniques for Constrained Multi-objective Optimization Problems." International Journal of Pattern Recognition and Artificial Intelligence 35, no. 08 (2021): 2159032. http://dx.doi.org/10.1142/s0218001421590321.

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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

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30

Huang, Gang, Min Hu, Xueying Yang, Xun Wang, Yijun Wang, and Feiyao Huang. "A Review of Constrained Multi-Objective Evolutionary Algorithm-Based Unmanned Aerial Vehicle Mission Planning: Key Techniques and Challenges." Drones 8, no. 7 (2024): 316. http://dx.doi.org/10.3390/drones8070316.

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UAV mission planning is one of the core problems in the field of UAV applications. Currently, mission planning needs to simultaneously optimize multiple conflicting objectives and take into account multiple mutually coupled constraints, and traditional optimization algorithms struggle to effectively address these difficulties. Constrained multi-objective evolutionary algorithms have been proven to be effective methods for solving complex constrained multi-objective optimization problems and have been gradually applied to UAV mission planning. However, recent advances in this area have not been

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31

Liu, Hai-Lin, Chaoda Peng, Fangqing Gu, and Jiechang Wen. "A Constrained Multi-Objective Evolutionary Algorithm Based on Boundary Search and Archive." International Journal of Pattern Recognition and Artificial Intelligence 30, no. 01 (2015): 1659002. http://dx.doi.org/10.1142/s0218001416590023.

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In this paper, we propose a decomposition-based evolutionary algorithm with boundary search and archive for constrained multi-objective optimization problems (CMOPs), named CM2M. It decomposes a CMOP into a number of optimization subproblems and optimizes them simultaneously. Moreover, a novel constraint handling scheme based on the boundary search and archive is proposed. Each subproblem has one archive, including a subpopulation and a temporary register. Those individuals with better objective values and lower constraint violations are recorded in the subpopulation, while the temporary regis

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32

Zhao, Shaoyu, Heming Jia, Yongchao Li, and Qian Shi. "A Constrained Multi-Objective Optimization Algorithm with a Population State Discrimination Model." Mathematics 13, no. 5 (2025): 688. https://doi.org/10.3390/math13050688.

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The solution to constrained multi-objective optimization problems (CMOPs) requires optimizing the objective functions while satisfying the constraint conditions. To effectively address CMOPs, algorithms must balance objectives and constraints. However, the limited adaptability of specific constraint-handling techniques (CHTs) has hindered the widespread applicability of constrained multi-objective evolutionary algorithms (CMOEAs). To overcome this limitation, this article proposes a population state-based CMOEA. First, a model is developed to identify population states based on the positions o

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Lv, Yongjing, Kaiwen Li, Hong Zhao, and Hongtao Lei. "A Multi-Stage Constraint-Handling Multi-Objective Optimization Method for Resilient Microgrid Energy Management." Applied Sciences 14, no. 8 (2024): 3253. http://dx.doi.org/10.3390/app14083253.

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In recent years, renewable energy has seen widespread application. However, due to its intermittent nature, there is a need to develop energy management systems for its scheduling and control. This paper introduces a multi-stage constraint-handling multi-objective optimization method tailored for resilient microgrid energy management. The microgrid encompasses diesel generators, energy storage systems, renewable energy sources, and various load types. The intelligent management of generators, batteries, switchable loads, and controllable loads ensures a reliable power supply for the critical l

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Singh, Hemant Kumar, Tapabrata Ray, and Warren Smith. "C-PSA: Constrained Pareto simulated annealing for constrained multi-objective optimization." Information Sciences 180, no. 13 (2010): 2499–513. http://dx.doi.org/10.1016/j.ins.2010.03.021.

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Zeltni, Kamel, Souham Meshoul, and Heyam H. Al-Baity. "On the Convergence and Diversity of Pareto Fronts Using Swarm Intelligence Metaheuristics for Constrained Search Space." International Journal of Swarm Intelligence Research 9, no. 1 (2018): 20–38. http://dx.doi.org/10.4018/ijsir.2018010102.

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This article reviews existing constraint-handling techniques then presents a new design for Swarm Intelligence Metaheuristics (SIM) to deal with constrained multi-objective optimization problems (CMOPs). This new design aims to investigate potential effects of leader concepts that characterize the dynamic of SIM in the hope to help the population to reach Pareto optimal solutions in a constrained search space. The new leader-based constraint handling mechanism is incorporated in Constrained Multi-Objective Cuckoo Search (C-MOCS) and Constrained Multi-Objective Particle Swarm Optimization (C-MO

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Yang, Yongkuan, Jianchang Liu, and Shubin Tan. "A multi-objective evolutionary algorithm for steady-state constrained multi-objective optimization problems." Applied Soft Computing 101 (March 2021): 107042. http://dx.doi.org/10.1016/j.asoc.2020.107042.

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Premkumar, M., Pradeep Jangir, R. Sowmya, Hassan Haes Alhelou, Seyedali Mirjalili, and B. Santhosh Kumar. "Multi-objective equilibrium optimizer: framework and development for solving multi-objective optimization problems." Journal of Computational Design and Engineering 9, no. 1 (2021): 24–50. http://dx.doi.org/10.1093/jcde/qwab065.

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ABSTRACT This paper proposes a new Multi-Objective Equilibrium Optimizer (MOEO) to handle complex optimization problems, including real-world engineering design optimization problems. The Equilibrium Optimizer (EO) is a recently reported physics-based metaheuristic algorithm, and it has been inspired by the models used to predict equilibrium state and dynamic state. A similar procedure is utilized in MOEO by combining models in a different target search space. The crowding distance mechanism is employed in the MOEO algorithm to balance exploitation and exploration phases as the search progress

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Wang, Hui, Tie Cai, Dongsheng Cheng, Kangshun Li, Guangming Lin, and Zhijian Wu. "A Web Data Mining Algorithm Based on Manifold Distance for Mixed Data in Cloud Service Architecture." International Journal of Cognitive Informatics and Natural Intelligence 18, no. 1 (2024): 1–7. http://dx.doi.org/10.4018/ijcini.344021.

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Due to the complex distribution of web data and frequent updates under the cloud service architecture, the existing methods for global consistency of data ignore the global consistency of distance measurement and the inability to obtain neighborhood information of data. To overcome these problems, we transform the multi-information goal and multi-user demand (constraint conditions) in web data mining into a constrained multi-objective optimization model and solve it by a constrained particle swarm multi-objective optimization algorithm. While we measure the distance between data by manifold di

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Zhang, Lei, and Jun Liu. "Dynamic Economic Emission Dispatch Using Multi-Objective Hybrid Evolutionary Algorithm." Applied Mechanics and Materials 291-294 (February 2013): 2154–58. http://dx.doi.org/10.4028/www.scientific.net/amm.291-294.2154.

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Dynamic economic emission dispatch (DEED) is an important optimization task for power plants. The problem is a highly constrained multi-objective optimization problem involving conflicting objectives with both equality and inequality constraints. This paper introduces two objective functions of DEED model: the lowest generation cost and the smallest carbon emissions with power balance constraints, unit output constraints and unit ramp rate limits. Then the paper presents a multi-objective hybrid evolutionary algorithm (MHEA) to solve the DEED model. The MHEA is a hybrid optimization algorithm

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Luo, Qi Fang, Qiao Qiao Gong, and Yong Quan Zhou. "Artificial Glowworm Swarm Optimization Algorithm for Solving Multi-Objective Constrained Optimization." Applied Mechanics and Materials 220-223 (November 2012): 2393–97. http://dx.doi.org/10.4028/www.scientific.net/amm.220-223.2393.

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Focused on the disadvantages of some current constrained optimization algorithm, glowworm swarm multi-objective optimization algorithm ( GSMOA） is proposed in this paper. The main character of this algorithm conforms to feasibility rules and adapts self- adaptive penalty function to search feasible solutions. This algorithm has been tested on 4 standard functions and it shows that the proposed algorithm has more advantage in the convergence rate and the solution precision.

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Zhang, Zhuhong, Min Liao, and Lei Wang. "Immune Optimization Approach for Dynamic Constrained Multi-Objective Multimodal Optimization Problems." American Journal of Operations Research 02, no. 02 (2012): 193–202. http://dx.doi.org/10.4236/ajor.2012.22022.

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Ning, Weikang, Baolong Guo, Yunyi Yan, Xianxiang Wu, Jinfu Wu, and Dan Zhao. "Constrained multi-objective optimization using constrained non-dominated sorting combined with an improved hybrid multi-objective evolutionary algorithm." Engineering Optimization 49, no. 10 (2017): 1645–64. http://dx.doi.org/10.1080/0305215x.2016.1271661.

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Qu, B. Y., and P. N. Suganthan. "Constrained multi-objective optimization algorithm with an ensemble of constraint handling methods." Engineering Optimization 43, no. 4 (2011): 403–16. http://dx.doi.org/10.1080/0305215x.2010.493937.

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Osiadacz, Andrzej J., and Niccolo Isoli. "Multi-Objective Optimization of Gas Pipeline Networks." Energies 13, no. 19 (2020): 5141. http://dx.doi.org/10.3390/en13195141.

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The main goal of this paper is to prove that bi-objective optimization of high-pressure gas networks ensures grater system efficiency than scalar optimization. The proposed algorithm searches for a trade-off between minimization of the running costs of compressors and maximization of gas networks capacity (security of gas supply to customers). The bi-criteria algorithm was developed using a gradient projection method to solve the nonlinear constrained optimization problem, and a hierarchical vector optimization method. To prove the correctness of the algorithm, three existing networks have bee

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Ye, Qianlin, Wanliang Wang, Guoqing Li, and Zheng Wang. "Dynamic-multi-task-assisted evolutionary algorithm for constrained multi-objective optimization." Swarm and Evolutionary Computation 90 (October 2024): 101683. http://dx.doi.org/10.1016/j.swevo.2024.101683.

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Feng, Xue, Anqi Pan, Zhengyun Ren, and Zhiping Fan. "Hybrid driven strategy for constrained evolutionary multi-objective optimization." Information Sciences 585 (March 2022): 344–65. http://dx.doi.org/10.1016/j.ins.2021.11.062.

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TANABE, Ryoji, and Akira OYAMA. "On Benchmark Problems for Constrained Multi-Objective Optimization Problems." Proceedings of OPTIS 2016.12 (2016): 2105. http://dx.doi.org/10.1299/jsmeoptis.2016.12.2105.

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Bhuvaraghan, Baskaran, Sivakumar M. Srinivasan, Bob Maffeo, and Om Prakash. "Constrained probabilistic multi-objective optimization of shot peening process." Engineering Optimization 43, no. 6 (2011): 657–73. http://dx.doi.org/10.1080/0305215x.2010.508523.

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Zhang, Weiwei, Jiaxin Yang, Guoqing Li, Weizheng Zhang, and Gary G. Yen. "Manifold-assisted coevolutionary algorithm for constrained multi-objective optimization." Swarm and Evolutionary Computation 91 (December 2024): 101717. http://dx.doi.org/10.1016/j.swevo.2024.101717.

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Yu, Xiaobing, Xianrui Yu, Yiqun Lu, Gary G. Yen, and Mei Cai. "Differential evolution mutation operators for constrained multi-objective optimization." Applied Soft Computing 67 (June 2018): 452–66. http://dx.doi.org/10.1016/j.asoc.2018.03.028.

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