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Hydrothermal coordination by bi-level optimization and composite constraint handling method

INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2014年 62卷 476-489页

作者： Hajinassiry, Mojtaba Amjady, Nima Sharifzadeh, Hossein Semnan Univ Dept Elect Engn Semnan Iran

This paper presents a new adaptive bi-level optimization approach to solve short-term hydrothermal coordination (STHTC) problem with AC network constraints. The proposed bi-level approach is composed of an integer coded genetic algorithm (ICGA) to solve unit commitment (UC) in the upper level and a new modified chaotic simulated annealing (MCSA) technique to determine economic dispatch (ED) for each time interval in the lower level. Moreover, a new composite constraint handling method is also presented, which enhances the efficiency of the proposed approach to solve STHTC problem with AC constraints. The proposed methodology is tested on the 9-bus and IEEE 118-bus test systems. The obtained results confirm the validity of the developed approach. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Short-term hydrothermal coordination Bi-level optimization approach ICGA MCSA constraint handling method

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Optimizing reserve-constrained economic dispatch: Cheetah optimizer with constraint handling method in static/dynamic/single/multi-area systems

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ENERGY 2024年 313卷

作者： Zare, Mohsen Farhang, Saman Akbari, Mohammad Amin Azizipanah-Abarghooee, Rasoul Trojovsky, Pavel Jahrom Univ Fac Engn Dept Elect Engn Jahrom Iran Proximus Luxembourg Luxembourg Shiraz Univ Technol Dept Elect & Elect Engn Shiraz Iran WSP Energy Advisory Dept Manchester England Univ Hradec Kralove Fac Sci Dept Math Hradec Kralove 50003 Czech Republic

Managing the power-generating units on the horizon of one-day scheduling considering all practical equality, inequality, and realistic constraints has always been a significant challenge in power systems. The constraints, such as valve-point effects, prohibited operation zones, transmission losses, and ramp rate limits corresponding to dynamic economic dispatch, change the optimization problem to a complex, nonlinear, non-smooth, high- dimensional, and non-convex one. Therefore, an efficient algorithm and a suitable constraint handling method are needed to solve practical constrained dynamic economic dispatch (DED). This paper proposes a newly developed Cheetah optimizer (CO) that coincides with a backward-forward constraint handling method to tackle the optimum operational cost. The CO algorithm's performance is verified using eight DED and ED test cases from five different systems. The suggested technique is compared with several state-of-theart optimization algorithms regarding the effectiveness of achieved results. Numerical results evaluate the performances of the CO advantages on the benchmarks and the DED cases where the results of 5-,10- and 30-unit systems are enhanced in different cases. To achieve a higher level of realism in modeling the ED and DED problem, adopting a multi-area DED (MADED) approach has emerged as a promising strategy. In this paper, three distinct cases of MAED and MADED problems are investigated to demonstrate the effectiveness of the proposed method. Specifically, incases involving DED-10 and 30 units, two-area 40 units ED, and four-area 40 units DED, significantly improved solutions were obtained compared to previous studies.

关键词： Cheetah optimizer constraint handling method Multi-area dynamic economic dispatch Reserve-constrained dynamic economic dispatch Spinning reserve requirement Valve point effect

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Study on the constraint handling method for high-dimensional optimization of cascade reservoirs

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JOURNAL OF CLEANER PRODUCTION 2024年 449卷

作者： Li, Shuliang He, Zhongzheng Huang, Wei Wei, Bowen Yan, Feng Fu, Jisi Xiong, Bin Nanchang Univ Sch Infrastruct Engn Nanchang 330031 Peoples R China Nanchang Univ Key Lab Poyang Lake Environm & Resource Utilizat Minist Educ Nanchang 330031 Peoples R China

Multicomplex constraints often need to be considered in the optimal operation of cascade reservoirs with highdimensional decision variables, making it difficult for traditional optimization methods and modern intelligent algorithms to solve such problems. Therefore, this study proposes a constraint handling method combining a penalty function nested DPSA-POA and an intelligent algorithm, to determine the optimal flood control operation of cascade reservoirs in the middle reaches of the Ganjiang River, a problem with decision variables of up to 2196 dimensions. The results indicate that the constraint handling method proposed in this paper can solve highdimensional optimization problems in three modes: continuous nesting (Mode 1), optimization with intelligence after obtaining a feasible solution (Mode 2), and optimization with the DPSA-POA after obtaining a feasible solution (Mode 3). Of the three modes, Mode 2 has the highest accuracy, but its calculation time is approximately 10 h. Although the accuracy of Mode 3 is slightly worse, can only achieve 98% - 99% of Mode 2, its calculation time is only approximately 1 - 3 h. The comprehensive performance of Mode 1 is poor, the convergence accuracy can only reach 97% of Mode 2, which corresponds to a calculation time of approximately 4 - 6 h. The existing superiority of feasibility (SF), stochastic ranking (SR), penalty function (PF), epsilon -constraint (EC) and adaptive epsilon -constraint (Adaptive EC) methods cannot converge to a feasible solution stably, and the accuracy of the results of these methods under the condition of obtaining a feasible solution is significantly lower than that of Mode 2 and Mode 3, reaching only 95%.

关键词： High -dimensional optimization problem constraint handling method DPSA-POA Cascade reservoirs Multiple objectives

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An efficient geometric constraint handling method for surrogate-based aerodynamic shape optimization

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ENGINEERING APPLICATIONS OF COMPUTATIONAL FLUID MECHANICS 2023年第1期17卷 Article: e2153173页

作者： Wang, Kai Han, Zhong-Hua Zhang, Ke-Shi Song, Wen-Ping Natl Key Lab Sci & Technol Aerodynam Design & Res Xian Peoples R China Northwestern Polytech Univ Inst Aerodynam & Multidisciplinary Design Optimiza Sch Aeronaut Xian Peoples R China

handling a large number of geometric constraints brings a big challenge to the surrogate-based aerodynamic shape optimization (ASO) driven by computational fluid dynamics (CFD). It is not feasible to calculate the geometric constraint functions directly during the sub-optimization of a surrogate-based optimization, as the geometric constraint functions are to be evaluated thousands of times for each updating cycle and the total cost of a number of cycles can be prohibitive. This article proposes an efficient method of handling geometric constraints within the framework of a surrogate-based optimization to address this problem. The core idea is to use the Kreisselmeier-Steinhauser (KS) method to aggregate all geometric constraints into one that can be approximated by a cheap surrogate model, in order to avoid the large computational cost associated with tremendous calculation of geometric constraint values. The proposed method is verified by an analytical test case. Then, the proposed method is demonstrated and compared with the methods of building surrogate models of all geometric constraints and calculating all geometric constraints directly during each sub-optimization by drag minimizations of NACA0012 air foil and ONERA M6 wing in transonic flows. To investigate the ability of the proposed method for handling various geometric constraints, drag minimization of CRM wing in viscous transonic flow driven by CFD is performed. Results show that the proposed method can dramatically improve the optimization efficiency of ASO with the number of geometric constraints ranging from 15 to 1429 and the number of types of geometric constraints up to 3, which offers great potential for handling a larger number and more types of geometric constraints.

关键词： Surrogate-based optimization aerodynamic shape optimization constraint handling method constrained optimization

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Voting enabled dynamic constraint handling portfolios for evolutionary multi/many-objective optimization

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INFORMATION SCIENCES 2025年 694卷

作者： Zhou, Jiajun Liu, Zhao Li, Yongxiang Lu, Chao Gao, Liang China Univ Geosci Sch Comp Sci Wuhan 430074 Peoples R China Guizhou Univ Engn Sci Sch Mech Engn Bijie 551700 Peoples R China Huazhong Univ Sci & Technol State Key Lab Intelligent Mfg Equipment & Technol Wuhan 430074 Peoples R China

constraint handling technique (CHT) plays a key role in handling constrained multi-objective optimization problems (CMOPs). In general, CHTs are associated with their own pros and cons under different scenarios, giving rise to an inherent risk in the selection of appropriate CHTs. To take advantages of diverse CHTs, we design a novel competitive co-evolution scheme for CHT portfolios in which multiple complementary CHTs are synergized via a single-population competitive ensemble framework. A self-organizing voting strategy is developed to allocate restrictive resources to constituent CHTs adaptively according to the feedbacks of CHTs as the search proceeds. In addition, an archive update strategy is designed to facilitate effective usage of potential solutions and achieve better compromise between convergence and diversity. Then the concrete algorithm, namely, VP-CMOEA, is presented. We have comprehensively evaluated our proposal on diverse benchmark functions and real-world applications. Empirical results demonstrate the better generality of VP-CMOEA compared with state-of-the-art peers.

关键词： Algorithm configuration Multi-objective optimization Evolutionary algorithm constraint handling method Dynamic resource allocation

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A Novel Adaptive Multi-Objective Particle Swarm Optimization Based on Decomposition and Dominance for Long-term Generation Scheduling of Cascade Hydropower System

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WATER RESOURCES MANAGEMENT 2019年第11期33卷 4007-4026页

作者： Hu, Hu Yang, Kan Su, Lyuwen Yang, Zhe Hohai Univ Coll Hydrol & Water Resources Nanjing 210098 Jiangsu Peoples R China

Multi-objective long-term generation scheduling (MLGS) considering ecological flow demands is important for comprehensive utilization of water resources in cascade hydropower system (CHS). A novel adaptive multi-objective particle swarm optimization based on decomposition and dominance (D(2)AMOPSO) is developed in this paper to solve the MLGS problem. In D(2)AMOPSO, a constraint handling method based on repair strategy and individualconstraints and group constraints (ICGC) technique is embedded to address various constraints. An improved logistic map is adopted to initialize the population. During the evolutionary process, an improved Tchebycheff decomposition is introduced to select personal best and global best for each particle, and the non-dominated solutions found so far are stored in an external archive where crowding distance and elitist learning strategy are performed to improve its diversity. Meanwhile, an adaptive flight parameter adjustment mechanism based on Pareto entropy is adopted to balance the global exploration and local exploitation abilities of the population. A normal cloud mutation operator is used to keep the population diversity and escape local minima. In the case study of the Three Gorges Cascade hydropower system (TGC) under three typical years, the results of the proposed method and other four competitors show that D(2)AMOPSO can obtain better diversity and faster convergence solutions for the MLGS problem in less time.

关键词： Multi-objective long-term generation scheduling Ecological flow Cascade hydropower system Particle swarm optimization constraint handling method

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Optimal Operation of Hydropower System by Improved Grey Wolf Optimizer Based on Elite Mutation and Quasi-Oppositional Learning

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IEEE ACCESS 2019年 7卷 155513-155529页

作者： Feng, Zhong-Kai Liu, Shuai Niu, Wen-Jing Liu, Yi Luo, Bin Miao, Shu-Min Wang, Sen Huazhong Univ Sci & Technol Sch Hydropower & Informat Engn Wuhan 430074 Peoples R China Changjiang Water Resources Commiss Bur Hydrol Wuhan 430010 Peoples R China Tsinghua Sichuan Energy Internet Res Inst Chengdu 610200 Peoples R China State Grid Sichuan Elect Power Res Inst Chengdu 610072 Peoples R China Minist Water Resources Key Lab Pearl River Estuarine Dynam & Associated Guangzhou 510611 Peoples R China

As one of the most important renewable energy, hydropower is often asked to satisfy the load demand of power system at peak periods. Thus, the optimal operation of hydropower system is modelled to minimize the standard deviation of the residual load series obtained by subtracting the total power outputs of all the involved hydropower plants from the original load curve. Hence, this paper develops an improved grey wolf optimizer (IGWO) to effectively address the complex constrained optimization problem. In the proposed method, the quasi-oppositional learning is used to enhance the convergence rate of the swarm;the elite mutation operator is used to increase the probability of escaping from local optima;the elastic-ball strategy and heuristic constraint handling method are used to help infeasible individuals rebound to feasible space. Numerical experiments of 12 classical test functions demonstrate the feasibility of the IGWO method in the global optimization problems. Then, the developed method is applied to solve the optimal operation of two cascade hydropower systems. The results indicate that the proposed method outperforms several traditional methods in smoothing the peak loads of power system. To sum up, an effective solution tool is provided for the hydropower system operation optimization problem.

关键词： Hydropower system grey wolf optimizer quasi-oppositional learning elite mutation elastic-ball strategy constraint handling method

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Multi-objective quantum-behaved particle swarm optimization for economic environmental hydrothermal energy system scheduling

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ENERGY 2017年 131卷 165-178页

作者： Feng, Zhong-kai Niu, Wen-jing Cheng, Chun-tian Huazhong Univ Sci & Technol Sch Hydropower & Informat Engn Wuhan 430074 Peoples R China Dalian Univ Technol Inst Hydropower & Hydroinformat Dalian 116024 Peoples R China

With increasing attention paid to energy and environment in recent years, the hydrothermal scheduling considering economic and environmental objectives is becoming one of the most important optimization problems in power system. With two competing objectives and a set of operation constraints, the economic environmental hydrothermal scheduling problem is classified as a typical multi-objective nonlinear constrained optimization problem. Thus, in order to efficiently resolve this problem, the multi-objective quantum-behaved particle swarm optimization (MOQPSO) is presented in this paper. In MOQPSO, the elite archive set is adopted to conserve Pareto optimal solutions and provide multiple evolutionary directions for individuals, while the neighborhood searching and chaotic mutation strategies are used to enhance the search capability and diversity of population. Furthermore, a novel constraint handling method is designed to adjust the constraint violation of hydro and thermal plants, respectively. In order to verify its effectiveness, the MOQPSO is applied to a classical hydrothermal system with four hydropower plants and three thermal plants. The simulations show that the proposed method has competitive performance compared with several traditional methods. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Multi-objective optimization Hydrothermal scheduling Quantum-behaved particle swarm optimization Chaotic mutation constraint handling method

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Economic emission dispatch problems with stochastic wind power using summation based multi-objective evolutionary algorithm

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INFORMATION SCIENCES 2016年 351卷 48-66页

作者： Qu, B. Y. Liang, J. J. Zhu, Y. S. Wang, Z. Y. Suganthan, P. N. Zhongyuan Univ Technol Sch Elect & Informat Engn Zhongyuan 450007 Peoples R China Zhengzhou Univ Sch Informat Engn Zhengzhou 450001 Peoples R China Zhengzhou Univ Sch Elect Engn Zhengzhou 450001 Peoples R China Nanyang Technol Univ Sch Elect & Elect Engn Singapore 639798 Singapore

In recent years, renewable energy sources such as wind energy have been used as one of the most effective ways to reduce pollution emissions. In this paper, a summation based multi-objective differential evolution (SMODE) algorithm is used to optimize the economic emission dispatch problem with stochastic wind power. The Weibull probability distribution function is used to model the stochastic nature of the wind power and the uncertainty is treated as the system constraints with stochastic variables. The algorithm is integrated with the superiority of feasible solution constraint handling technique. To validate the effectiveness of the proposed method, the standard IEEE 30-bus 6-generator test system with wind power (with/without considering losses) is studied with fuel cost and emission as two conflicting objectives to be optimized at the same time. Besides, a larger 40-generator system with wind farms is also solved by the proposed method. The results generated by SMODE are compared with those obtained using NSGAII as well as a number of techniques reported in literature. The results reveal that SMODE generates superior and consistent solutions. (C) 2016 Published by Elsevier Inc.

关键词： Environmental/Economic dispatch Wind power Multi-objective optimization Differential evolution constraint handling method

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Scheduling of short-term hydrothermal energy system by parallel multi-objective differential evolution

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APPLIED SOFT COMPUTING 2017年 61卷 58-71页

作者： Feng, Zhong-kai Niu, Wen-jing Zhou, Jian-zhong Cheng, Chun-tian Zhang, Yong-chuan Huazhong Univ Sci & Technol Sch Hydropower & Informat Engn Wuhan 430074 Hubei Peoples R China ChangJiang Water Resources Commiss Bur Hydrol Wuhan 430010 Hubei Peoples R China Dalian Univ Technol Inst Hydropower & Hydroinformat Dalian 116024 Peoples R China

With the growing concerns on energy and environment, the short-term hydrothermal scheduling (SHTS) which minimizes the fuel cost and pollutant emission simultaneously is playing an increasing important role in the modern electric power system. Due to the complicated operation constraints and objectives, SHTS is classified as a multi-objective optimization problem. Thus, to efficiently resolve this problem, this paper develops a novel parallel multi-objective differential evolution (PMODE) combining the merits of parallel technology and multi-objective differential evolution. In PMODE, the population with larger size is first divided into several smaller subtasks to be concurrently executed in different computing units, and then the main thread collects the results of each subpopulation to form the final Pareto solutions set for the SHTS problem. During the evolutionary process of each subpopulation, the mutation crossover and selection operators are modified to enhance the performance of population. Besides, an external archive set is used to conserve the Pareto solutions and provide multiple evolutionary directions for individuals, while the constraint handling method is introduced to address the complicated operational constraints. The results from a mature hydrothermal system indicate that when compared with several existing methods, PMODE can obtain satisfactory solutions in both fuel cost and environmental pollutant, which is an effective tool to generate trade-off schemes for the hydrothermal scheduling problem. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Hydrothermal scheduling Multi-objective differential evolution Parallel computing Fork/Join framework constraint handling method

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