面向梯级水库多目标优化调度的进化算法研究

实际工程中以梯级水库多目标优化调度为代表的大规模高维多目标优化问题,其优化难度是一般方法所难以应对的。为此本文提出一种新型的多目标粒子群算法LMPSO,其包含了基于超体积指标I_h^k的适应值分配方法与基于问题变换的搜索空间降维策略,以有效处理问题的高维目标向量与大规模决策变量。将该算法应用于溪洛渡-向家坝梯级水库的中长期多目标优化调度中,并与4种知名算法的计算结果进行对比分析,验证LMPSO在求解该类问题上的卓越性能。由此为多目标优化调度高质量非劣解集的获取提供一种可靠的方法,并为下一步的多目标调度决策提供有力的数据支持。     

Improving Optimization Efficiency for Reservoir Operation Using a Search Space Reduction Method

Reservoir operation problems are challenging to efficiently optimize because of their high-dimensionality, stochasticity, and non-linearity. To alleviate the computational burden involved in large-scale and stringent constraint reservoir operation problems, we propose a novel search space reduction method (SSRM) that considers the available equality (e.g., water balance equation) and inequality (e.g., firm output) constraints. The SSRM can effectively narrow down the feasible search space of the decision variables prior to the main optimization process, thus improving the computational efficiency. Based on a hydropower reservoir operation model, we formulate the SSRM for a single reservoir and a multi-reservoir system, respectively. To validate the efficiency of the proposed SSRM, it is individually integrated into two representative optimization techniques: discrete dynamic programming (DDP) and the cuckoo search (CS) algorithm. We use these coupled methods to optimize two real-world operation problems of the Shuibuya reservoir and the Shuibuya-Geheyan-Gaobazhou cascade reservoirs in China. Our results show that: (1) the average computational time of SSRM-DDP is 1.81, 2.50, and 3.07 times less than that of DDP when decision variables are discretized into 50, 100, and 500 intervals, respectively; and (2) SSRM-CS outperforms CS in terms of its capability of finding near-optimal solutions, convergence speed, and stability of optimization results. The SSRM significantly improves the search efficiency of the optimization techniques and can be integrated into almost any optimization or simulation method. Therefore, the proposed method is useful when dealing with large-scale and complex reservoir operation problems in water resources planning and management.     

An Efficient Optimization Method for Long-term Power Generation Scheduling of Hydropower Station: Improved Dynamic Programming with a Relaxation Strategy

Integrating the characteristics of hydropower reservoir operations into optimization methods is an effective approach. Based on the concavity and monotonicity of hydropower reservoir operation with dynamic programming (DP), improved DP (IDP) with monotonicity in optimal decision-making can quickly search for an approximate optimal solution. However, IDP may not converge to the optimal solution of the long-term power generation scheduling (LPGS) problem of hydropower station due to the analysis conclusion of approximate monotonicity. Therefore, the relaxation strategy for expanding the search space based on the monotonicity of optimal decisions is introduced into IDP, which is named DP with a relaxation strategy (DPRS). The experimental results of Xiluodu, Xiangjiaba, and Three Gorges Reservoir (TGR) show that 1) the time complexity of DPRS and IDP decreases from the quadratic growth of DP with an increasing number of discrete states to linear growth; 2) DPRS and DP can obtain the optimal solution of the long-term power generation scheduling (LPGS) problem of hydropower station under the given discrete precision, whereas IDP searches for only an approximate optimal solution. Combined with the discussion with other relevant literature, all these results indicate that the DPRS has the strongest competitiveness in solving the LPGS problem of hydropower station, both in convergence accuracy and in calculation speed.

     

Multi-Reservoir Operation Planning Using Hybrid Genetic Algorithm and Linear Programming (GA-LP): An Alternative Stochastic Approach

Many models have been suggested to deal with the multi-reservoir operation planning stochastic optimization problem involving decisions on water releases from various reservoirs in different time periods of the year. A new approach using genetic algorithm (GA) and linear programming (LP) is proposed here to determine operational decisions for reservoirs of a hydro system throughout a planning period, with the possibility of considering a variety of equally likely hydrologic sequences representing inflows. This approach permits the evaluation of a reduced number of parameters by GA and operational variables by LP. The proposed algorithm is a stochastic approximation to the hydro system operation problem, with advantages such as simple implementation and the possibility of extracting useful parameters for future operational decisions. Implementation of the method is demonstrated through a small hypothetical hydrothermal system used in literature as an example for stochastic dual dynamic programming (SDDP) method of Pereira and Pinto (Pereira, M. V. F. and Pinto, L. M. V. G.: 1985, Water Res. Res. 21(6), 779–792). The proposed GA-LP approach performed equally well as compared to the SDDP method.     

Performance Assessment of a Coupled Particle Swarm Optimization and Network Flow Programming Model for Optimum Water Allocation

Water resources allocation problems are mainly categorized in two classes of simulation and optimization. In most cases, optimization problems due to the number of variables, constraints and nonlinear feasible search space are known as a challenging subject in the literature. In this research, by coupling particle swarm optimization (PSO) algorithm and a network flow programming (NFP) based river basin simulation model, a PSO-NFP hybrid structure is constructed for optimum water allocation planning. In the PSO-NFP model, the NFP core roles as the fast inner simulation engine for finding optimum values for a large number of water discharges in the network links (rivers and canals) and nodes (reservoirs and demands) while the heuristic PSO algorithm forms the outer optimization cover to search for the optimum values of reservoirs capacities and their storage priorities. In order to assess the performance of the PSO-NFP model, three hypothetical test problems are defined, and their equivalent nonlinear mathematical programs are developed in LINGO and the results are compared. Finally, the PSO-NFP model is applied in solving a real river basin water allocation problem. Results indicate that the applied method of coupling PSO and NFP has an efficient ability for handling river basin-scale water resources optimization problems.     

Water Supply Reservoir Operation by Combined Genetic Algorithm – Linear Programming (GA-LP) Approach

Multi-reservoir operation planning is a complex task involving many variables, objectives, and decisions. This paper applies a hybrid method using genetic algorithm (GA) and linear programming (LP) developed by the authors to determine operational decisions for a reservoir system over the optimization period. This method identifies part of the decision variables called cost reduction factors (CRFs) by GA and operational variables by LP. CRFs are introduced into the formulation to discourage reservoir depletion in the initial stages of the planning period. These factors are useful parameters that can be employed to determine operational decisions such as optimal releases and imports, in response to future inflow predictions. A part of the Roadford Water Supply System, UK, is used to demonstrate the performance of the GA-LP method in comparison to the RELAX algorithm. The proposed approach obtains comparable results ensuring non zero final storages in the larger reservoirs of the Roadford Hydrosystem. It shows potential for generating operating policy in the form of hegging rules without a priori imposition of their form.     

湖北汉江梯级水库群联合优化调度研究

湖北汉江流域已形成大规模梯级水库群,为了充分发挥梯级水库群联合补偿调节的优势,实现水电站最优经济运行,本文对湖北汉江流域水电站群运行特性进行分析研究。考虑各电站之间的水力和电力联系,在常规调度图模拟及传统优化调度的基础上,采用基于GAMS平台的非线性规划法以及基于可行空间搜索遗传算法,制定复杂混联水库群的发电优化调度规则。优化效果显著,充分体现水库群优化调度作用,为湖北汉江梯级水电站水库群的实际调度提供最佳的指导和方案。     

基于逐次逼近遗传算法的梯级水库优化调度

利用传统遗传算法求解水库优化调度问题时,经过遗传操作产生的新个体可能是不可行解,因此需要对其进行修正.但在梯级水库调度中,由于各时段间、水库间存在的水力电力联系,使这种修正变得复杂困难.鉴于此,提出了逐次逼近遗传算法(GASA),它可在包含不可行解的空间中寻优,并通过搜索空间的不断改变,逐渐逼近最优解.最后通过一个算例,并与离散微分动态规划法(DDDP)和逐步优化法(POA)的优化结果进行比较,说明了该方法的可行性与有效性.     

粗粒度并行自适应混合粒子群算法及其在梯级水库群优化调度中的应用

为了充分利用现今普及的多核配置计算机,提高大规模梯级水库群优化调度问题的求解效率,提出了梯级水库群优化调度的粗粒度并行自适应混合粒子群算法。该方法以自适应混合粒子群算法为求解基础,采用粗粒度并行设计模式,利用Fork/Join多核并行框架的分治策略,将其初始种群递归划分为多个子种群,平均分配到不同的内核逻辑线程中实现并行计算,并在各子种群优化结束后,合并优化结果集从而输出全局最优解。以澜沧江下游梯级水库群发电优化调度为例,利用该方法进行计算。结果表明,该方法能充分发挥多核配置的计算性能,在4核环境下最大加速比达到3.97,缩短计算耗时1 787.2 s,计算效率显著提高,为我国不断扩张的大规模梯级水库群优化调度提供了一种切实可行的高效求解途径。     

Partially and Fully Constrained Ant Algorithms for the Optimal Solution of Large Scale Reservoir Operation Problems

This paper presents a constrained formulation of the ant colony optimization algorithm (ACOA) for the optimization of large scale reservoir operation problems. ACO algorithms enjoy a unique feature namely incremental solution building capability. In ACO algorithms, each ant is required to make a decision at some points of the search space called decision points. If the constraints of the problem are of explicit type, then ants may be forced to satisfy the constraints when making decisions. This could be done via the provision of a tabu list for each ant at each decision point of the problem. This is very useful when attempting large scale optimization problem as it would lead to a considerable reduction of the search space size. Two different formulations namely partially constrained and fully constrained version of the proposed method are outlined here using Max-Min Ant System for the solution of reservoir operation problems. Two cases of simple and hydropower reservoir operation problems are considered with the storage volumes taken as the decision variables of the problems. In the partially constrained version of the algorithm, knowing the value of the storage volume at an arbitrary decision point, the continuity equation is used to provide a tabu list for the feasible options at the next decision point. The tabu list is designed such that commonly used box constraints for the release and storage volumes are simultaneously satisfied. In the second and fully constrained algorithm, the box constraints of storage volumes at each period are modified prior to the main calculation such that ants will not have any chance of making infeasible decision in the search process. The proposed methods are used to optimally solve the problem of simple and hydropower operation of “Dez” reservoir in Iran and the results are presented and compared with the conventional unconstrained ACO algorithm. The results indicate the ability of the proposed methods to optimally solve large scale reservoir operation problems where the conventional heuristic methods fail to even find a feasible solution.     

梯级水库群优化调度精英集聚蛛群优化方法

将蛛群优化方法(SSO)这一新型群体智能寻优方法引入梯级水库群优化调度领域,并提出精英集聚蛛群优化方法(ESSO)进一步改善SSO的性能表现。ESSO在标准SSO方法寻优机制基础上,从精英个体动态更新策略与邻域变异搜索机制等两方面予以改进,提升蜘蛛群体的多样性与优秀个体领导能力,均衡方法的全局开采能力与局部勘探能力。澜沧江流域工程实例表明,所提ESSO方法能有效克服标准SSO的"早熟"缺陷,有效提升方法的搜索能力,可望为大规模梯级水库群优化调度提供一种新的高效求解思路。     

Multiple Hydropower Reservoirs Operation by Hyperbolic Grey Wolf Optimizer Based on Elitism Selection and Adaptive Mutation

Multiple hydropower reservoirs operation is an effective measure to rationally allocate the limited water resources under uncertainty. With the rapid expansion of water resources system, it becomes much more difficult for traditional methods to quickly yield the reasonable operational policy. Grey wolf optimizer, inspired by the wolves’ hunting behaviors, is a famous metaheuristic method to resolve engineering optimization problems, but still suffers from the local convergence and search stagnation defects. To alleviate this problem, this study proposes a hybrid grey wolf optimizer (HGWO) where the hyperbolic accelerating strategy is introduced to improve the local search ability; the adaptive mutation strategy is used to diversify the swarm; the elitism selection strategy is used to enhance the convergence speed. The experimental results show that the HGWO method can produce better solutions than its original version in several test functions. Then, the HGWO method is applied to resolve the optimal operation of a real-world hydropower system with the goal of maximizing the total generation benefit. The simulations indicate that the HGWO method produces satisfying scheduling schemes than several control methods in terms of all the statistical indicators. Hence, with the merits of superior search ability, rapid convergence rate and gradient information avoidance, HGWO proves to be a promising alternative optimization tool for the complex multireservoir system operation problem.

     

引江济淮工程（河南段）多目标水量优化调度

引江济淮工程（河南段）涉及河道、闸泵、管道和调蓄水库,约束条件复杂,常规的优化调度算法难以搜索可行解,求解效率低。选用受水区缺水率平均值最小、泵站总抽水量最小和受水区缺水率标准差最小作为目标函数,从供水保障、供水成本和公平性角度构建多目标水量优化调度模型。基于可行搜索思路,结合逆序演算和顺序演算过程对约束条件进行处理,引入决策系数,通过映射关系使搜索空间保持在可行域中,结合多目标非支配排序遗传算法（non-dominated sorting genetic algorithms,NSGA-II）进行求解,得到Pareto最优解集,并采用熵权法进行方案优选。结果表明,基于可行搜索的NSGA-II算法能够有效求解复杂调度系统的多目标优化问题,综合考虑多个目标的最优方案相对单目标方案更加合理,结果可为引江济淮工程（河南段）运行管理提供决策支撑。     

Adaptive Genetic Algorithm for Daily Optimal Operation of Cascade Reservoirs and its Improvement Strategy

For the specialty of cascade reservoirs optimization and the premature convergence of GA, several improvement strategies are presented in this paper. Firstly, solution space generation method is found application to generate feasible initial population. Secondly, chaos optimization is adopted to optimize initial population. Thirdly, new selective operators, trigonometric selective operators, are proposed to overcome the fitness requirement of non-negative and to maintain the diversity of population. Fourthly, adaptive probabilities of crossing and mutation are adopted in order to improve the convergence speed of GA. Besides, elitist strategy is used to ensure that the best individual can be remained in each generation. Furthermore, the performance of these proposed improvement strategies was checked against the historical improvement strategies by simulating optimal operation of Three Gorges cascade reservoirs premised on historical hourly inflows, and the comparison yields indications of superior performance. In these proposed improvement strategies, trigonometric selective operators are feasible and effective for optimizing operation of cascade reservoirs. These new selective operators could help GA to find a more excellent solution in the same algebra, and the performance of convergence speed is advanced. Adaptive probabilities of crossing and mutation have better performance than other improvement strategies, such as annealing chaotic mutation and simulated annealing of large probability of mutation, because this method realizes the twin goals of maintaining diversity in the population and advancing the convergence speed of GA.     

An Efficient Linearization Method for Long-Term Operation of Cascaded Hydropower Reservoirs

The hydropower reservoir operation is a challenging optimization problem due to the nonlinear factors, where the water head, reservoir storage, release, generating capacity, and water rate are interconnected. To solve such a difficult problem in an efficient and stable way based on mathematical programming, efficient linearization method with high accuracy is of vital importance. This paper simplifies the hydropower output as the function of average reservoir storage and release, and presents an efficient piecewise linearization method that concaves the hydropower output function with a series of planes, which transforms the original nonlinear problem into a linear programming one without introducing any integer variables. The presented method is applied to a long-term hydropower scheduling (LHS) problem with 7 cascaded reservoirs, and a nonlinear direct search procedure is then employed to search further. The performance is compared with that of another linearization method that uses special ordered sets of type two, case study shows that LHS using the presented linearization method runs much faster and obtains results very close to that of the latter one. The presented method, as a high performance exact algorithm, should be very promising in solving the real-world hydropower operation problems.     

鲸鱼优化算法在水库优化调度中的应用

为验证鲸鱼优化算法在水库优化调度求解中的可行性和有效性,采用4个典型测试函数对鲸鱼优化算法进行仿真验证,并与布谷鸟搜索算法、差分进化算法、混合蛙跳算法、粒子群优化算法、萤火虫算法和SCE-UA算法共6种算法的仿真结果进行对比分析;将鲸鱼优化算法与6种对比算法应用于某单一水库和某梯级水库中长期优化调度求解。结果表明:鲸鱼优化算法寻优精度高于其他6种算法8个数量级以上,具有收敛速度快、收敛精度高和极值寻优能力强等特点;鲸鱼优化算法单一水库和梯级水库优化调度结果均优于其他6种算法;鲸鱼优化算法应用于水库优化调度求解是可行和有效的。     

遗传算法在水库调度中的应用综述

简要回顾了遗传算法在水库调度中的应用概况,对遗传算法用于水库调度优化时的编码、约束条件处理、早熟与全局收敛性、参数设置、混合遗传算法、多目标遗传算法以及效率评定准则等问题进行了综述。分析遗传算法耗时与全局收敛之间的矛盾后认为,遗传算法适用于传统方法难以求解的优化问题,以及对计算时效性要求不高或者目标函数计算复杂度不高的实时水库调度问题,特别是水库中长期调度以及水资源规划问题。     

Multi-Colony Ant Algorithm for Continuous Multi-Reservoir Operation Optimization Problem

Ant Colony Optimization (ACO) algorithms are basically developed for discrete optimization and hence their application to continuous optimization problems require the transformation of a continuous search space to a discrete one by discretization of the continuous decision variables. Thus, the allowable continuous range of decision variables is usually discretized into a discrete set of allowable values and a search is then conducted over the resulting discrete search space for the optimum solution. Due to the discretization of the search space on the decision variable, the performance of the ACO algorithms in continuous problems is poor. In this paper a special version of multi-colony algorithm is proposed which helps to generate a non-homogeneous and more or less random mesh in entire search space to minimize the possibility of loosing global optimum domain. The proposed multi-colony algorithm presents a new scheme which is quite different from those used in multi criteria and multi objective problems and parallelization schemes. The proposed algorithm can efficiently handle the combination of discrete and continuous decision variables. To investigate the performance of the proposed algorithm, the well-known multimodal, continuous, nonseparable, nonlinear, and illegal (CNNI) Fletcher–Powell function and complex 10-reservoir problem operation optimization have been considered. It is concluded that the proposed algorithm provides promising and comparable solutions with known global optimum results.     

A Memetic Multi-objective Immune Algorithm for Reservoir Flood Control Operation

Reservoir flood control operation (RFCO) is a challenging optimization problem with multiple conflicting decision goals and interdependent decision variables. With the rapid development of multi-objective optimization techniques in recent years, more and more research efforts have been devoted to optimize the conflicting decision goals in RFCO problems simultaneously. However, most of these research works simply employ some existing multi-objective optimization algorithms for solving RFCO problem, few of them considers the characteristics of the RFCO problem itself. In this work, we consider the complexity of the RFCO problem in both objective space and decision space, and develop an immune inspired memetic algorithm, named M-NNIA2, to solve the multi-objective RFCO problem. In the proposed M-NNIA2, a Pareto dominance based local search operator and a differential evolution inspired local search operator are designed for the RFCO problem to guide the search towards the and along the Pareto set respectively. On the basis of inheriting the good diversity preserving in immune inspired optimization algorithm, M-NNIA2 can obtain a representative set of best trade-off scheduling plans that covers the whole Pareto front of the RFCO problem in the objective space. Experimental studies on benchmark problems and RFCO problem instances have illustrated the superiority of the proposed algorithm.     

Optimizing Hydropower Reservoir Operation Using Hybrid Genetic Algorithm and Chaos

Genetic algorithms (GA) have been widely applied to solve water resources system optimization. With the increase of the complexity and the larger problem scale of water resources system, GAs are most frequently faced with the problems of premature convergence, slow iterations to reach the global optimal solution and getting stuck at a local optimum. A novel chaos genetic algorithm (CGA) based on the chaos optimization algorithm (COA) and genetic algorithm (GA), which makes use of the ergodicity and internal randomness of chaos iterations, is presented to overcome premature local optimum and increase the convergence speed of genetic algorithm. CGA integrates powerful global searching capability of the GA with that of powerful local searching capability of the COA. Two measures are adopted in order to improve the performance of the GA. The first one is the adoption of chaos optimization of the initialization to improve species quality and to maintain the population diversity. The second is the utilization of annealing chaotic mutation operation to replace standard mutation operator in order to avoid the search being trapped in local optimum. The Rosenbrock function and Schaffer function, which are complex and global optimum functions and often used as benchmarks for contemporary optimization algorithms for GAs and Evolutionary computation, are first employed to examine the performance of the GA and CGA. The test results indicate that CGA can improve convergence speed and solution accuracy. Furthermore, the developed model is applied for the monthly operation of a hydropower reservoir with a series of monthly inflow of 38 years. The results show that the long term average annual energy based CGA is the best and its convergent speed not only is faster than dynamic programming largely, but also overpasses the standard GA. Thus, the proposed approach is feasible and effective in optimal operations of complex reservoir systems.