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A dueling double deep Q network assisted cooperative dual-population coevolutionary algorithm for multi-objective combined economic and emission dispatch problems

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SWARM AND EVOLUTIONARY COMPUTATION 2025年 95卷

作者： Yu, Xiaobing Wang, Yuan Zhang, Wen Nanjing Univ Informat Sci & Technol Collaborat Innovat Ctr Forecast & Evaluat Meteorol Nanjing 210044 Peoples R China Nanjing Univ Informat Sci & Technol Sch Management Sci & Engn Res Inst Risk Governance & Emergency Decis Making Nanjing 210044 Peoples R China

With the increasing demand for electricity and the awareness of environmental protection, requirements for economic efficiency and controlling environmental impact of the power system are increasing. However, traditional power system scheduling usually focuses on ensuring the stability of the power supply, which neglects the optimization of cost and emissions. Therefore, combined economic and emission dispatch (CEED) problem is proposed to overcome this challenge. Due to nonlinear and nonconvex objective functions and narrow feasible regions, the optimization of multi-objective CEED problem encounters many difficulties. A dueling double deep Q network-assisted cooperative dual-population coevolutionary algorithm (D3QN-CDCA) is developed to solve multi-objective CEED problems. The proposed algorithm utilizes D3QN to select operators dynamically and adaptively for two populations of coevolutionary algorithm, thus enhancing its adaptability to different practical constrained multi-objective problems and satisfying search needs of different iteration stages. The introduction of D3QN is to overcome the inherent overestimation of DQN and improve the learning efficiency of the network. To comprehensively evaluate its performance, we tested D3QN-CDCA on benchmark function sets and applied it to CEED problems in comparison with other competitive algorithms. Results demonstrate that D3QN-CDCA outperforms existing methods with an average IGD+ ranking of 1.4286 and an average HV ranking of 1.321 in benchmark function sets. Meanwhile, the proposed algorithm achieves an average improvement of 23.86 % in 6unit, 23.12 % in 11-unit and 13.51 % in 14-unit CEED problems. The improvement in solution quality demonstrates the effectiveness of D3QN-CDCA in solving high-dimensional multi-objective optimization problems, particularly in CEED, highlighting its potential for real-world energy management applications.

关键词： Combined economic and emission dispatch coevolutionary algorithm Deep Q learning Optimization algorithm

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Deep reinforcement learning-guided coevolutionary algorithm for constrained multiobjective optimization

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INFORMATION SCIENCES 2025年 692卷

作者： Luo, Wenguan Yu, Xiaobing Yen, Gary G. Wei, Yifan Nanjing Univ Informat Sci & Technol Sch Management Sci & Engn Nanjing Peoples R China Natl Univ Def Technol Coll Syst Engn Changsha Peoples R China Oklahoma State Univ Sch Elect & Comp Engn Stillwater OK 74078 USA

Effectively managing convergence, diversity, and feasibility constitutes a fundamental trinity of tasks in optimizing constrained multiobjective optimization problems (CMOPs). Nevertheless, contemporary constrained multiobjective evolutionary algorithms (CMOEAs) frequently encounter challenges in reconciling these imperatives simultaneously. Drawing inspiration from overwhelming success in artificial intelligence, we propose a deep reinforcement learning-guided coevolutionary algorithm (DRLCEA) to tackle this predicament. DRLCEA employs two populations to optimize the original and unconstrained versions of the CMOP, respectively and then fosters cooperation between them according to the guidance of DRL. The established DRL employs two evaluation metrics to appraise population convergence, diversity, and feasibility, thus remarkably proficient in reflecting and steering the coevolution. Therefore, the proposed DRLCEA could effectively locate the feasible regions and approximate the constrained Pareto front. We assess the proposed algorithm on 32 benchmark CMOPs and one real-world UAV emergency track planning (UETP) application. Experimental results undoubtedly demonstrate the superiority and robustness of the proposed DRLCEA.

关键词： Constrained multiobjective optimization Evolutionary algorithm Deep reinforcement learning coevolutionary algorithm UAV path planning

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A double decomposition based coevolutionary algorithm for distributed multi-objective OPF solution

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2024年第PartB期155卷

作者： Zeng, Cong Chen, Ziyu Zhu, Jizhong Ieee, Fellew South China Univ Technol Sch Elect Power Guangzhou 510630 Peoples R China

Due to the vast and complex nature of the power systems, the study of distributed solution to multi-objective OPF (MO-OPF) problem is vital. However, the existing distributed MO-OPF approaches are based on mathematical programming techniques. The tedious repetition of algorithmic executions is inevitable. Moreover, they can hardly solve the non-differential problem. In this paper, the coevolutionary multi-objective evolutionary algorithm (MOEA), combining the idea of decomposition, is introduced to solve the distributed MO-OPF problem. The decomposition first occurs on decision variables. After segmenting, multiple subpopulations can coevolve in a distributed manner under the support of a new proposed distributed fitness evaluation method. Further, an objective decomposition (OBD) method is applied to the proposed distributed MO-OPF approach. The problem is decomposed again based on objective functions. By this OBD method, the fitness assignment problem is effectively alleviated and a more extensively covered pareto front can be obtained. The experimental results on two systems of different scales first show the effectiveness of the proposed distributed approach and then demonstrate the excellence of the OBD method in large-scale system.

关键词： Multi-objective OPF Pareto front Multi-area power systems Distributed optimization coevolutionary algorithm

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A dual-population auxiliary multiobjective coevolutionary algorithm for constrained multiobjective optimization problems

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APPLIED SOFT COMPUTING 2024年 162卷

作者： He, Zhao Liu, Hui Cent South Univ Inst Artificial Intelligence & Robot IAIR Sch Traff & Transportat Engn Key Lab Traff Safety TrackMinist Educ Changsha 410075 Hunan Peoples R China

The key to solving constrained multiobjective optimization problems (CMOPs) lies in maintaining the feasibility, convergence, and diversity of the population. In recent years, various constraint handling techniques (CHTs) and strategies have been proposed to enhance the performance of constrained multiobjective evolutionary algorithms (CMOEAs). However, most of these algorithms face difficulties in dealing with problems that have large infeasible regions and discontinuous small feasible regions, as they have trouble crossing large infeasible regions while simultaneously maintaining the convergence and diversity of the population. To tackle this issue, this paper proposes a dual-population auxiliary coevolutionary algorithm with an enhanced operator, denoted as DAEAEO. Auxiliary population 1 employs an improved epsilon-constraint handling technique to provide high-quality feasible solutions for the main population. Auxiliary population 2 adopts the non-dominated sorting method to provide favorable objective information for the main population to help it cross the infeasible region. In addition, to further improve diversity, each population adopts an enhanced operator and a genetic operator to generate offspring, respectively. Finally, knowledge transfer between offspring is realized. Compared to six state-of-the-art CMOEAs on DASCMOPs, LIR-CMOPs, DOC test suites, and two real-world problems, the proposed DAEAEO achieved superior performance, especially for CMOPs with large infeasible regions and discontinuous small feasible regions.

关键词： Dual-population auxiliary Enhanced operator Knowledge transfer Constrained multiobjective optimization problems coevolutionary algorithm

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A coevolutionary algorithm for constrained multi-objective optimization with dynamic relaxation

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SWARM AND EVOLUTIONARY COMPUTATION 2025年 95卷

作者： Li, Yongchao Jia, Heming Li, Hongguang Heilongjiang Bayi Agr Univ Sch Informat & Elect Engn Daqing 163000 Heilongjiang Peoples R China Sanming Univ Sch Informat Engn Sanming 365000 Fujian Peoples R China Harbin Normal Univ Sch Math Sci Harbin 150001 Heilongjiang Peoples R China

To effectively address constrained multi-objective problems, algorithms need to strike a balance between objectives and constraints. This article introduces a method that utilizes two separate populations to investigate the exploration of the constrained Pareto front (CPF) and the unconstrained Pareto front (UPF). The fitness of each population is evaluated based on the information entropy of their positions, and suitable evolutionary operators are employed to improve solution quality in terms of convergence and diversity. Moreover, by adaptively relaxing constraint conditions, the auxiliary population can traverse large infeasible domains, thereby enhancing solution diversity. In the initial stages, the auxiliary population evolves alongside the main population, bringing it close to the CPF and minimizing computational resource wastage. A tournament environment selection model based on a dynamic relaxation (DR) function is utilized in the later stages, helping the auxiliary population relax constraints, retain promising solutions, and augment diversity. In addition, an entropy selection evolutionary strategy was designed to address the problem of populations easily falling into local optima during the evolution process. By calculating the entropy information of the population, the current state of the population can be determined, and then appropriate operators can be selected to enable the population to effectively escape from local optimal solutions. Compared against seven state-of-theart algorithms, demonstrate that the proposed constrained multi-objective optimization evolutionary algorithm (CMOEA) surpasses the performance of existing CMOEAs.

关键词： Constrained multi-objective optimization coevolutionary algorithm DR tournament selection model Entropy selection evolution strategy

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BC-PINN: an adaptive physics informed neural network based on biased multiobjective coevolutionary algorithm

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NEURAL COMPUTING & APPLICATIONS 2023年第28期35卷 21093-21113页

作者： Zhu, Zhicheng Hao, Jia Huang, Jin Huang, Biao Beijing Inst Technol 5 South St Zhongguancun Beijing 100081 Peoples R China

Physics informed neural network (PINN) has become a promising method for solving partial differential equations (PDEs). The loss function of PINN is a weighted sum of multiple items. This makes it easy to fall into local optima, especially the gradient pathologies when solving high frequency problems. The value of penalty coefficients has a crucial impact on the prediction results. Therefore, a new PINN with adaptive penalty coefficients iteratively optimized by biased multiobjective coevolutionary algorithm (BC-PINN) is presented. In BC-PINN, a two-stage optimization mechanism is used to search for parameters of neural network and penalty coefficients respectively. This method involves constructing the fitness function of penalty coefficients based on the biased dominance ranking by data item and regularization item. Compared with the previous works of others, the accuracy of fitting the initial conditions and boundary conditions is considered to be given priority, which is more conducive to PINN converging to the particular solution of PDE. In addition, the set of penalty coefficients is divided into multiple populations to improve the optimization efficiency through coevolutionary algorithm. The empirical results show that: (1) Our method can improve the gradient pathologies and effectively capture the high-frequency features. (2) Compared to the original PINN, it reduces the MSE by 1-6 orders of magnitude in our benchmark functions.

关键词： Physics informed neural network Gradient pathologies coevolutionary algorithm Biased multiobjective optimization

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A coevolutionary algorithm based on the auxiliary population for constrained large-scale multi-objective supply chain network

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MATHEMATICAL BIOSCIENCES AND ENGINEERING 2022年第1期19卷 271-286页

作者： Zhang, Xin Ma, Zhaobin Ding, Bowen Fang, Wei Qian, Pengjiang Jiangnan Univ Sch Artificial Intelligence & Comp Sci Wuxi 214122 Jiangsu Peoples R China Jiangnan Univ Jiangsu Key Lab Media Design & Software Technol Wuxi 214122 Jiangsu Peoples R China Jilin Univ Minist Educ Key Lab Symbol Computat & Knowledge Engn Changchun 130012 Peoples R China

Supply chain network is important for the enterprise to improve the operation and management, but has become more complicated to optimize in reality. With the consideration of multiple objectives and constraints, this paper proposes a constrained large-scale multi-objective supply chain network (CLMSCN) optimization model. This model is to minimize the total operation cost (including the costs of production, transportation, and inventory) and to maximize the customer satisfaction under the capacity constraints. Besides, a coevolutionary algorithm based on the auxiliary population (CAAP) is proposed, which uses two populations to solve the CLMSCN problem. One population is to solve the original complex problem, and the other population is to solve the problem without any constraints. If the infeasible solutions are generated in the first population, a linear repair operator will be used to improve the feasibility of these solutions. To validate the effectivity of the CAAP algorithm, the experiment is conducted on the randomly generated instances with three different problem scales. The results show that the CAAP algorithm can outperform other compared algorithms, especially on the large-scale instances.

关键词： supply chain network large-scale optimization multi-objective optimization constrained optimization coevolutionary algorithm

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An Improved coevolutionary algorithm for Constrained Multi-Objective Optimization Problems

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INTERNATIONAL JOURNAL OF COGNITIVE INFORMATICS AND NATURAL INTELLIGENCE 2024年第1期18卷 1页

作者： Xie, Shumin Zhu, Zhenjia Wang, Hui Shenzhen Inst Informat Technol Shenzhen Peoples R China

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 constraints, while the other population disregards them. Meanwhile, the iCMOCA employs effective collaboration between two populations during the process of offspring generation and environmental selection, and it utilizes an environmental selection strategy based on multi-objective to multi-objective decomposition to improve the performance. Comparative analysis conducted on the DAS-CMOP and MW test suites provides empirical evidence that iCMOCA outperforms five state-of-the-art algorithms.

关键词： Constrained Multi-Objective Optimization Dual-Population coevolutionary algorithm

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A bi-subpopulation coevolutionary immune algorithm for multi-objective combinatorial optimization in multi-UAV task allocation

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COMPLEX & INTELLIGENT SYSTEMS 2025年第2期11卷 1-19页

作者： Chen, Xi Wan, Yu Qi, Jingtao Zhao, Zipeng Ruan, Yirun Tang, Jun Natl Univ Def Technol Lab big data & decis Changsha 410073 Peoples R China

With the development of Unmanned Aerial Vehicle (UAV) technology towards multi-UAV and UAV swarm, multi-UAV cooperative task allocation has more and more influence on the success or failure of UAV missions. From the operational research point of view, such problems belong to high-dimensional combinatorial optimization problems, which makes the solving process face many challenges. One is that the discrete and high-dimensional decision variables make the quality of the solution obtained with acceptable time not guaranteed. Second, the desired solution of real missions often needs to satisfy multiple objective functions, or a set of solutions for decision-making. Therefore, this paper constructs a Multi-objective Combinatorial Optimization in Multi-UAV Task Allocation Problem (MCOTAP) model, and proposes a Bi-subpopulation coevolutionary Immune algorithm (BCIA). The two coevolutionary mechanisms improve the lower limit of population diversity, and the evolutionary strategy pool integrating multiple strategies and the adaptive strategy selection mechanism enhance the local search ability in the late evolution. In the experiments, BCIA competes fairly with the mainstream multi-objective evolutionary algorithms (MOEAs), multi-objective immune algorithms (MOIAs) and the recently proposed multi-UAV mission planning algorithms. The experimental results on different test problems (including several multi-objective combinatorial optimization benchmark problems and the proposed MCOTAP model) show that BCIA has superior performance in solving multi-objective combinatorial optimization problems (MCOPs). At the same time, the effectiveness of each design component of BCIA has been comprehensively verified in the ablation study.

关键词： coevolutionary algorithm Multi-objective combinatorial optimization Multi-objective immune algorithm Multi-UAV Task allocation problem

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Two Player Zero Sum Multi-Stage Game Analysis Using coevolutionary algorithm

Two Player Zero Sum Multi-Stage Game Analysis Using Coevolut...

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作者： Sumedh Sopan Nagrale Wright State University

学位级别：硕士

A New Two player zero sum multistage simultaneous Game has been developed from a real-life situation of dispute between two individual. Research identifies a multistage game as a multi-objective optimization problem and solves it using coevolutionary algorithm which converges to a solution from pareto optimal solution. A comparison is done between individual stage behaviour and multistage behaviour. Further, simulations over a range for Crossover rate, Mutation rate and Number of interaction is done to narrow down the range for a range with optimal computation speed. A relationship has been observed which identifies a relationship between population size, number of interactions, crossover rate, mutation rate and computational time. A point from the obtained range is then selected and applied to a new game to see if the point from the narrowed range works.

关键词： Electrical Engineering coevolutionary algorithm Parameters Game Theory Multistage Game computation speed population size Mutation rate Crossover rate Parameters relations equation

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