Research papersMultiple hydropower reservoirs operation optimization by adaptive mutation sine cosine algorithm based on neighborhood search and simplex search strategies
Introduction
Over the past decades, the booming economic development has promoted the rapid increase of water and energy demands all over the world (Feng et al., 2019a, Wang et al., 2009, Yan et al., 2017). Reservoir is recognized as one of the most effective engineering measures to improve the utilization efficiency of water-energy resources (Yang et al., 2016, Feng et al., 2020a, Niu et al., 2018, Niu et al., 2020, Zhang et al., 2017, Yin et al., 2014). Thus far, a large number of hydropower projects have been put into operation (Hui et al., 2016, Pang et al., 2018a, Pang et al., 2018b, Xu et al., 2019). In China, the representatives are the world's biggest inter-basin water transfer project (South-North Water Transfer Project) and hydropower project (Three Gorges) (Liu et al., 2015, Wang et al., 2018, Xu et al., 2018, Zhao et al., 2015), and about a quarter of the total installed electricity capacity is provided by reservoirs equipped with huge hydropower turbines (Chen et al., 2013, Feng et al., 2020b, Ming et al., 2017). At the present stage, reservoirs are playing an increasingly important role in raising the people’s living standards by providing comprehensive benefits, like power generation, flood control, navigation, ecological protection and water supply. Thus, researchers and engineers are paying more and more attention to the reservoir operation problem (Bai et al., 2017, Li and Huang, 2008, Li et al., 2009a).
Mathematically, the reservoir operation problem is a complex constrained optimization problem involved numerous decision variables and physical constraints, like water balance equations and turbine discharge limits (Chen et al., 2014, Madani, 2010, Madani, 2011, Yang et al., 2017a). In order to effectively resolve this problem, various optimization methods have been successfully developed by scholars all over the world (He et al., 2004, Feng et al., 2019b, Ji et al., 2014, Li et al., 2010, Yang et al., 2017b), including linear programming, nonlinear programming, dynamic programming, network-based methods, swarm intelligence methods. However, some defects have greatly limited the widespread application of the above methods in practical engineering problems (Li et al., 2009b, Liu et al., 2019a, Zeng et al., 2013, Feng et al., 2018). For instance, linear programming cannot address the nonlinearity in both objective function and physical constraints (Cai et al., 2001, Xie et al., 2018); due to the expensive computational overhead, nonlinear programming may fail to produce the global optimal solution for non-differentiable or discontinuous optimization problems (Catalao et al., 2009, Catalão et al., 2012, Xu et al., 2014); the dynamic programming family methods often suffer from the severe curse of dimensionality in the multidimensional hydropower operation problem (Feng et al., 2020c, Li et al., 2014, Zeng et al., 2019, Jiang et al., 2018); for network-based methods, it is still difficult to determine the rational parameters and stopping criterion (Wen et al., 2019, Cao et al., 2019, Cao et al., 2020, Wang et al., 2020, Xiao et al., 2020); the swarm intelligence methods are usually limited by the premature convergence and unstable solution (Samadi-koucheksaraee et al., 2019, Wu and Chau, 2010, Zheng et al., 2017). Thus, scholars try to develop more effective optimization tools suitable for multiple hydropower reservoirs operation problem (Ahmadianfar et al., 2017, Ahmadianfar et al., 2019a, Ahmadianfar et al., 2019b, Azizi et al., 2019a, Taghian and Ahmadianfar, 2018, Duan, 2019).
Sine cosine algorithm (SCA) is a brand-new swarm intelligence method inspired by both sine and cosine functions (Mirjalili, 2016). In SCA, a set of solutions are randomly produced in the problem space, and then iteratively update their positions from generation to generation. During the evolutionary process, the sine and cosine functions are adopted to achieve a balance between global exploration and local exploitation, and thereby the probability of capturing the global optima will be increased when the amount of iterations becomes sufficient (Gupta and Deep, 2019, Nenavath et al., 2018, Fu et al., 2019). With the merits of simple evolutionary mode and easy implementation, SCA has been widely used to solve various real-world application cases (like wind speeding forecasting and optimal power flow) (Long et al., 2018). However, for all we know, there are still a few reports about using SCA to address the power generation operation of multiple hydropower reservoirs. In order to fill this research gap, this paper tries to verify the feasibility of SCA in the reservoir operation field. From the experimental analysis, it is unfortunately observed that like other swarm-based methods, SCA usually falls into local optima with a high probability due to the loss of swarm diversity. Therefore, this paper aims at developing a SCA variant named as adaptive sine cosine algorithm (ASCA) to resolve the reservoir operation problem. In ASCA, three modified strategies are incorporated into the standard SCA approach, including the elite mutation strategy for increasing the individual diversity, the simplex dynamic search strategy for enhancing the solution quality and the neighborhood search strategy for improving the search rate. The results from numerical experiments and real-world simulations demonstrate the effectiveness and robustness of the proposed method.
To sum up, the main contributions of this research lie in: (1) a practical optimization model is developed for power generation of multiple hydropower reservoirs; (2) the ASCA algorithm based on mutation operator, neighborhood and simplex search strategies are presented to effectively improve the SCA performance; (3) the developed method can produce better results as compared with several existing methods in numerical experiments and real-world simulations, providing a practical method for the complicated engineering optimization problems.
The rest of this paper is organized as below. Section 2 gives the optimization model for multiple hydropower reservoirs operation. Section 3 presents the ASCA method. Section 4 tests the ASCA feasibility in 25 numerical functions. Section 5 gives the technical details of ASCA for reservoir operation problem. Section 6 testifies the ASCA performances in a real-world hydropower system. The conclusions are summarized in the end.
Section snippets
Objective function
Here, the maximization of the total power generation is chosen as the objective function and the mathematical formula can be established as below:where E is the total generation of hydropower system. N is the number of reservoirs. T is the number of periods. is the number of hours at the tth period. is the power output of the nth hydropower reservoir at the tth period.
Operation constraints
(1) Water balance equation:where ,
Overview of sine cosine algorithm (SCA)
With the rapid development of computer technology, the swarm-based approaches simulating the biological evolution in nature have been successfully proposed by scholars in recent years. As a brand-new swarm evolutionary algorithm, SCA can dynamically adjust the search range of the population to achieve the desired optimization effect (Rizk-Allah, 2018, Liu et al., 2019b, Fu et al., 2018). Generally, SCA starts from a set of solutions randomly placed in the decision space, and then uses the
Benchmark functions
Generally, 25 test functions listed in Table 1, Table 2 can be roughly divided into two different kinds of groups: unimodal functions (F1-F11) with one global optimal solution and multimodal functions (F12-F25) with multiple local optimal solution. The unimodal function can test the search speed of the evolutionary algorithm, while the multimodal function can prove the robust ability of avoiding local minimum. In the following sections, the ASCA performance in two kinds of test functions will
ASCA for solving multiple hydropower reservoirs operation optimization problem
Due to the complexity of practical engineering problems, it is often difficult to directly use the ASCA approach to solve the optimal operation of multiple hydropower reservoirs problem. Hence, the information of the ASCA method for hydropower operation is given in detail.
Study area
The Wu River cascade hydropower system in southwest China is chosen to test the performance of the ASCA method. As the largest tributary on the right bank of the Upper Yangtze River, this river is originated from the eastern part of the Censer mountain and flows through four provinces before injecting into the Yangtze River. With enormous hydropower potential and huge head drop, the Wu River has become one of the largest hydropower bases in China. Here, five reservoirs on the Wu River’s
Conclusion
In this study, a practical population-based method called adaptive sine cosine algorithm (ASCA) is developed to address the numerical optimization and multiple hydropower reservoirs operation optimization problem. In ASCA, three modified strategies are used to improve the performances of the standard sine cosine algorithm (SCA), including elite mutation strategy, simplex dynamic search strategy and neighborhood search strategy. The results of 25 famous test functions show that the presented
Author contribution
All authors contributed extensively to the work presented in this paper. Zhong-kai Feng and Wen-jing Niu contributed to model development and finalized the manuscripts. Shuai Liu contributed to programming implementation and data analysis. Bin Luo and Shu-min Miao; contributed to manuscripts revision and supervision. Kang Liu contributed to the literature review.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This paper is supported by the National Natural Science Foundation of China (51709119), Natural Science Foundation of Hubei Province (2018CFB573), National Natural Science Foundation of China (U1865202 and 51909133) and the Fundamental Research Funds for the Central Universities (HUST: 2017KFYXJJ193). The writers would like to thank editors and reviewers for their valuable comments and suggestions.
References (86)
- et al.
Developing optimal policies for reservoir systems using a multi-strategy optimization algorithm
Appl. Soft Comput. J.
(2019) - et al.
Upgraded Whale Optimization Algorithm for fuzzy logic based vibration control of nonlinear steel structure
Eng. Struct.
(2019) - et al.
Fusing feasible search space into PSO for multi-objective cascade reservoir optimization
Appl. Soft Comput. J.
(2017) - et al.
Solving nonlinear water management models using a combined genetic algorithm and linear programming approach
Adv. Water Resour.
(2001) - et al.
Synchronization of memristive neural networks with leakage delay and parameters mismatch via event-triggered control
Neural Networks
(2019) - et al.
Global exponential synchronization of delayed memristive neural networks with reaction–diffusion terms
Neural Networks
(2020) - et al.
Optimal hydro scheduling and offering strategies considering price uncertainty and risk management
Energy
(2012) - et al.
A comparative study of population-based optimization algorithms for downstream river flow forecasting by a hybrid neural network model
Eng. Appl. Artif. Intel.
(2015) - et al.
Nonlinear dynamical analysis of hydro-turbine governing system with a surge tank
Appl. Math. Model.
(2013) - et al.
An opposition-based sine cosine approach with local search for parameter estimation of photovoltaic models
Energy Convers Manage.
(2019)
Research on a layered coupling optimal operation model of the Three Gorges and Gezhouba cascade hydropower stations
Energ Convers. Manage.
Identifying changing patterns of reservoir operating rules under various inflow alteration scenarios
Adv. Water Resour.
Ecological operation of cascade hydropower reservoirs by elite-guide gravitational search algorithm with Lévy flight local search and mutation
J. Hydrol.
Optimizing electrical power production of hydropower system by uniform progressive optimality algorithm based on two-stage search mechanism and uniform design
J. Clean Prod.
Operation rule derivation of hydropower reservoir by k-means clustering method and extreme learning machine based on particle swarm optimization
J. Hydrol.
A mixed integer linear programming model for unit commitment of thermal plants with peak shaving operation aspect in regional power grid lack of flexible hydropower energy
Energy
An effective three-stage hybrid optimization method for source-network-load power generation of cascade hydropower reservoirs serving multiple interconnected power grids
J. Clean Prod.
A hybrid self-adaptive sine cosine algorithm with opposition based learning
Expert Syst. Appl.
Multi-stage progressive optimality algorithm and its application in energy storage operation chart optimization of cascade reservoirs
Energy
Structural inverse analysis by hybrid simplex artificial bee colony algorithms
Comput Struct.
Artificial bee colony algorithm and pattern search hybridized for global optimization
Appl. Soft Comput.
Deriving mixed reservoir operating rules for flood control based on weighted non-dominated sorting genetic algorithm II
J. Hydrol.
Dynamic control of flood limited water level for reservoir operation by considering inflow uncertainty
J. Hydrol.
A parallel dynamic programming algorithm for multi-reservoir system optimization
Adv. Water Resour.
An adaptive chaotic artificial bee colony algorithm for short-term hydrothermal generation scheduling
Int. J. Elec. Power
Optimal design of seasonal flood limited water levels and its application for the Three Gorges Reservoir
J. Hydrol.
Short-term optimal operation of Three-gorge and Gezhouba cascade hydropower stations in non-flood season with operation rules from data mining
Energy Convers. Manage.
Game theory and water resources
J. Hydrol.
Hydropower licensing and climate change: Insights from cooperative game theory
Adv. Water Resour.
Robust hydroelectric unit commitment considering integration of large-scale photovoltaic power: A case study in China
Appl. Energy
SCA: A sine cosine algorithm for solving optimization problems
Knowl.-Based Syst.
A synergy of the sine-cosine algorithm and particle swarm optimizer for improved global optimization and object tracking
Swarm Evol. Comput.
Seismic fragility for high CFRDs based on deformation and damage index through incremental dynamic analysis
Soil Dyn. Earthq. Eng.
Seismic reliability assessment of earth-rockfill dam slopes considering strain-softening of rockfill based on generalized probability density evolution method
Soil Dyn. Earthq. Eng.
Economic emission dispatch problems with stochastic wind power using summation based multi-objective evolutionary algorithm
Inf. Sci.
Hybridizing sine cosine algorithm with multi-orthogonal search strategy for engineering design problems
J Comput. Des. Eng.
Event-triggered distributed control for synchronization of multiple memristive neural networks under cyber-physical attacks
Inf. Sci.
A comparison of performance of several artificial intelligence methods for forecasting monthly discharge time series
J. Hydrol.
An ecologically oriented operation strategy for a Multi-Reservoir system: A case study of the middle and lower han river basin, China
Eng. -Prc.
Data-driven models for monthly streamflow time series prediction
Eng. Appl. Artif. Intel.
Simplex quantum-behaved particle swarm optimization algorithm with application to ecological operation of cascade hydropower reservoirs
Appl. Soft Comput.
New approach to global Mittag-Leffler synchronization problem of fractional-order quaternion-valued BAM neural networks based on a new inequality
Neural Networks
Improving the multi-objective evolutionary optimization algorithm for hydropower reservoir operations in the California Oroville-Thermalito complex
Environ. Model. Softw.
Cited by (37)
Efficient scheduling of jobs on dissimilar parallel machines using heuristic assisted metaheuristic techniques
2022, Chemical Engineering Research and DesignRanked-based mechanism-assisted Biogeography optimization: Application of global optimization problems
2022, Advances in Engineering SoftwareCitation Excerpt :According to the findings of an experiment in China's Wu hydroelectric system, the proposed method had acceptable results in decreasing ecological water scarcity. Feng et al. (2020) proposed an adaptive sine and cosine optimization algorithm (ASCA) with several efficient strategies and assessed it on 25 benchmark test functions [35]. In addition, the authors evaluated the ASCA to optimize a multi-reservoir system for hydropower purposes.
Energy conversion path improvement by optimizing motion profile on a two-stroke rod-less opposed pistons engine
2022, Energy Conversion and ManagementCitation Excerpt :The driving cam profile on both sides of the intake and exhaust is always the same, and the cylinder volume change rate is dominated by the synthetic cam profile on both sides. In the present research, the Simplex search optimization algorithm [31,32], a direct search algorithm, is used to optimize the driving cam profile, through which it does not need to calculate the derivative of the objective equation, but only the function value of each parameter design scheme is needed. This makes it possible for highly-nonlinear equations like the cam profile control equation and the thermodynamic model of engine mentioned above to be used in the present research.
Multi-strategy Slime Mould Algorithm for hydropower multi-reservoir systems optimization
2022, Knowledge-Based SystemsCitation Excerpt :The results of their study showed that the raised method was a good way to solve difficult reservoir problems. In another research, experts came up with a new version of a sine and cosine algorithm called (MSCA) in order to improve the multiplex hydropower reservoirs in China [1]. The simulation results showed that the proposed approach could help establish more accurate estimates than some of the other optimization algorithms.