The Enhanced Honey-Bee Mating Optimization Algorithm for Water Resources Optimization

Evolutionary and meta-heuristic algorithms are widely used to solve water resources optimization problems. In this context, the honey bee mating optimization (HBMO) algorithm, inspired by the mating ritual of honey bees, is a reliable and efficient algorithm. The HBMO algorithm is modified in this work leading to the Enhanced HBMO (EHBMO) algorithm. The EHBMO is then applied to solve several unconstrained/constrained mathematical benchmark functions and a multi-reservoir problem. The performance of the EHBMO is compared with those of the elitist genetic algorithm (EGA) and the HBMO algorithm. The results show that the EHBMO achieves a better solution in a smaller number of functional evaluations and with less variance of results about global optima in comparison with the EGA and the HBMO algorithm.     

Design-Operation of Multi-Hydropower Reservoirs: HBMO Approach

To illustrate and test the applicability and performance of the innovative honey-bee mating optimization (HBMO) algorithm in highly non-convex hydropower system design and operation, two problems are considered: single reservoir and multi-reservoir. Both hydropower problems are formulated to minimize the total present net cost of the system, while achieving the maximum possible ratio for generated power to installed capacity. The single hydropower reservoir problem is approached by the developed algorithm in 10 different runs. The first feasible solution was generated initially and later improved significantly and solutions converged to a near optimal solution very rapidly. In the application of the proposed algorithm to a five-reservoir hydropower system with 48 periods and a total of 230 decision variables, in early mating flights, the first feasible solution was identified and the results converged to a near optimal solution in later mating flights. In the case of the multi-reservoir problem, an efficient gradient-based nonlinear-programming solver (LINGO 8.0) failed to find a feasible solution and for the single hydropower reservoir design problem it performed much worse than the proposed algorithm.     

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.     

混沌粒子群优化算法在马斯京根模型参数优化中的应用

针对目前马斯京根模型参数率定中存在的求解复杂、精度不高等问题,本文将混沌搜索机制引入粒子群优化算法中,构建混沌粒子群优化算法对马斯京根模型参数进行率定。这种方法利用混沌运动的遍历性,改善了粒子群优化算法的全局寻优能力,避免算法陷入局部极值,使得粒子群体的进化速度加快,提高了算法的收敛速度和精度。通过实例应用表明,混沌粒子群优化算法可以有效地估算出马斯京根模型参数,优化效果明显优于粒子群优化算法及试错法,因此该算法具有很好的实用性。     

Effect of Breakage Level One in Design of Water Distribution Networks

Design of water distribution networks (WDNs) that do not consider performance criteria would possibly lead to less cost but it could also decrease water pressure reliability in abnormal conditions such as a breakage of pipes of the network. Thus, awareness of the situation of consumption nodes, by considering water pressures and the amount of water that is being supplied, could be an effective source of information for designing high performance WDNs. In this paper, Two-loop and Hanoi networks are selected for least-cost design, considering water pressures and the amount of water supplied on each consumption node under breakage level one, using the honey-bee mating optimization (HBMO) algorithm. In each state of design, a specific pressure is defined as the minimum expected pressure under breakage level one which holds the pressure reliability in the considered range. Also, variations of some criteria such as reliabilities of pressure and demand, vulnerability of the network, and flexibility of the design are analyzed as a tool for choosing the appropriate state of design. Results show that a minor increase in the cost of design could lead to a considerable improvement in reliabilities of pressure and demand under breakage level one.     

An Improved Continuous Ant Algorithm for Optimization of Water Resources Problems

Ant colony optimization was initially proposed for discrete search spaces while in continuous domains, discretization of the search space has been widely practiced. Attempts for direct extension of ant algorithms to continuous decision spaces are rapidly growing. This paper briefly reviews the central idea and mathematical representation of a recently proposed algorithm for continuous domains followed by further improvements in order to make the algorithm adaptive and more efficient in locating near optimal solutions. Performance of the proposed improved algorithm has been tested on few well-known benchmark problems as well as a real-world water resource optimization problem. The comparison of the results obtained by the present method with those of other ant-based algorithms emphasizes the robustness of the proposed algorithm in searching the continuous space more efficiently as locating the closest, among other ant methods, to the global optimal solution.     

Optimization of Hydropower Reservoir Using Evolutionary Algorithms Coupled with Chaos

Over the past decade, several conventional optimization techniques had been developed for the optimization of complex water resources system. To overcome some of the drawbacks of conventional techniques, soft computing techniques were developed based on the principles of natural evolution. The major difference between the conventional optimization techniques and soft computing is that in the former case, the optimal solution is derived where as in the soft computing techniques, it is searched from a randomly generated population of possible solutions. The results of the evolutionary algorithm mainly depend on the randomly generated initial population that is arrived based on the probabilistic theory. Recent research findings proved that most of the water resources variables exhibit chaotic behavior, which is a projection depends upon the initial condition. In the present study, the chaos algorithm is coupled with evolutionary optimization algorithms such as genetic algorithm (GA) and differential evolution (DE) algorithm for generating the initial population and applied for maximizing the hydropower production from a reservoir. The results are then compared with conventional genetic algorithm and differential evolution algorithm. The results show that the chaotic differential evolution (CDE) algorithm performs better than other techniques in terms of total annual power production. This study also shows that the chaos algorithm has enriched the search of general optimization algorithm and thus may be used for optimizing complex non-linear water resources systems.     

确定越流含水层参数的混沌序列优化算法

将混沌序列优化算法应用在第一类越流系统含水层非稳定流井流问题上,进行抽水试验数据的分析、含水层参数的求解,并就算法的搜索能力和结果与给定含水层各参数取值范围的关系进行探讨。结果表明:(1)求解越流条件下含水层参数的计算问题能用混沌序列优化算法得到很好的解决;(2)除越流因数上限取值会降低越流因数搜索结果的准确性外,储水系数、导水系数、越流因数上限取值对算法的搜索能力和搜索结果没有太明显的影响。相较于其他方法,混沌序列优化算法易于编程、运算简单、运算结果不被人为因素干扰等特点更为突出。     

树状给水管网布置形式优化设计

以管网年费用折算值作为管段的权值建立目标函数,以基于破圈法及Mayeda-Seshu算法的列队竞争算法作为求解方法,用于进行树状给水管网系统的优化,并将该方法用于实例研究。结果表明:该算法既可以完全避免以往各种优化算法在进化过程中产生不可行解的弊端,又继承了普通列队竞争算法寻优速度快的优点,使得算法的计算效率显著提高,计算结果的准确性也得以保证。该优化算法的提出对树状给水管网布置形式优化设计具有重要意义。     

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.     

混沌粒子群优化算法在确定含水层参数中的应用

以泰斯公式为例,将混沌粒子群优化算法应用于求解分析抽水试验数据,解决含水层参数的函数优化问题.通过在粒子群算法的初始化粒子位置及后续的细搜索过程中加入混沌序列,提高了算法的收敛速度和精度.数值实验结果表明:混沌粒子群算法能够有效地应用于求解含水层参数计算问题;粒子数的增多对混沌粒子群算法收敛性的影响不明显;待估导水系数选取不同的倍数均体现出混沌粒子群算法的收敛性明显优于粒子群优化算法.混沌粒子群算法应用于确定含水层参数是可行的.     

Chaotic Evolutionary Algorithms for Multi-Reservoir Optimization

The water sharing dispute in a multi-reservoir river basin forces the water resources planners to have an integrated operation of multi-reservoir system rather than considering them as a single reservoir system. Thus, optimizing the operations of a multi-reservoir system for an integrated operation is gaining importance, especially in India. Recently, evolutionary algorithms have been successfully applied for optimizing the multi-reservoir system operations. The evolutionary optimization algorithms start its search from a randomly generated initial population to attain the global optimal solution. However, simple evolutionary algorithms are slower in convergence and also results in sub-optimal solutions for complex problems with hardbound variables. Hence, in the present study, chaotic technique is introduced to generate the initial population and also in other search steps to enhance the performance of the evolutionary algorithms and applied for the optimization of a multi-reservoir system. The results are compared with that of a simple GA and DE algorithm. From the study, it is found that the chaotic algorithm with the general optimizer has produced the global optimal solution (optimal hydropower production in the present case) within lesser generations. This shows that coupling the chaotic algorithm with evolutionary algorithm will enrich the search technique by having better initial population and also converges quickly. Further, the performances of the developed policies are evaluated for longer run using a simulation model to assess the irrigation deficits. The simulation results show that the model satisfactorily meets the irrigation demand in most of the time periods and the deficit is very less.     

基于C-PSO算法的混凝土面板堆石坝断面优化设计

针对基本粒子群算法(PSO)寻优过程中存在收敛速度慢、易陷入局部最优和计算精度差等缺陷,采用分簇思想和碰撞策略,提出了一种改进的粒子群算法(C-PSO),在该算法中,粒子通过分簇并行搜索,有效避免了群体过度集中现象,极大地增强粒子全局搜索能力。将C-PSO算法应用于混凝土面板堆石坝断面优化设计中,优化结果表明,该算法对解决复杂的多变量多约束非线性问题具有较好的适应性,为复杂的混凝土面板堆石坝断面优化设计问题提供了新的解决思路。     

基于二进制和声粒子群算法的电站经济运行问题研究

机组组合是电站经济运行问题中典型的复杂非线性优化问题,其求解难度随系统规模增大呈非线性增长,如何对其进行高效求解一直是电力系统研究领域的热点和难点问题。为此,提出一种适用于电站经济运行中机组组合问题的二进制和声粒子群算法(BHSPSO):首先将粒子群算法的信息共享机制纳入到和声搜索算法的和声记忆库考虑操作中,并利用全局极值实现音调微调;然后采用启发式智能调整策略处理时段关联型约束条件,即根据机组优先顺序修复旋转备用约束,在此基础上,设计了一种“开-停-开”的修复策略处理最小开停机时间约束,有效改善了优化计算结果质量。将该方法分别应用于电站10台机组(简称10机)至电站100台机组(简称100机)系统标准算例,仿真结果表明:所提算法具有简单高效、收敛速度快、鲁棒性强等优点,为水、火电机组组合优化运行问题的高效求解提供一种新的途径。     

飞蛾火焰优化算法在承压含水层参数反演中的应用

通过10个典型低维函数对一种新型群体智能仿生算法——飞蛾火焰优化(MFO)算法进行仿真验证,并与粒子群优化(PSO)算法的寻优结果进行对比。以无界井流问题及直线隔水边界附近井流问题的解析解为基础,将MFO算法应用于分析抽水试验数据,进行反演承压含水层参数,并以2个实例对MFO算法进行验证。结果表明:MFO算法在低维函数极值寻优问题上具有较好的收敛精度和全局寻优能力,寻优精度较PSO算法提高了7个数量级以上。MFO算法对2个实例的反演精度较文献改进SA算法等提高了56.5%以上,具有较好的稳健性能、收敛速度和全局寻优能力。利用MFO算法对承压含水层参数进行反演,可获得比相关文献更高的反演精度,不但为精确估计承压含水层参数提供了有效方法,而且拓展了MFO算法在地下水模型参数反演中的应用,具有良好的应用价值和前景。     

基坑变形预测的改进供需优化算法-指数幂乘积模型

为提高基坑变形预测精度,提出改进供需优化算法-指数幂乘积基坑变形预测模型(ISDO-EPP模型)。通过6个标准测试函数和3个应用实例对ISDO算法的寻优能力进行验证,并与基本供需优化(SDO)算法、鲸鱼优化算法(WOA)、灰狼优化(GWO)算法、蛾群算法(MSA)、粒子群优化(PSO)算法的寻优结果进行比较。以3个基坑沉降预测为例,通过自相关函数法和虚假最邻近法确定各实例延迟时间和嵌入维数,构造输入、输出向量对各模型进行训练和预测。结果表明,ISDO算法搜索能力优于SDO等5种算法,具有较好的寻优精度、全局搜索能力和稳健性能。ISDO-EPP模型对3个实例预测的平均相对误差绝对值分别为0.73%、3.36%和1.33%,均优于ISDO-SVM、ISDO-BP模型,表明ISDO算法能有效优化EPP模型参数,ISDO-EPP模型用于变形预测是可行和有效的。     

改进粒子群算法求解水火电系统短期负荷分配问题

粒子群优化（PSO）算法是一种基于群体智能的启发式搜索方法，应用领域很广。文中将PSO算法用于求解水火电系统短期负荷的经济分配，属于高维、强约束工程问题。分析了算法参数设置对解的影响，发现算法的局部开发能力和粒子的多样性是影响解的优劣的关键因素;提出多子群辅助的PSO算法，兼顾了对解空间的全局搜索和局部开发。实际算例证明，改进的算法是有效的。     

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。     

改进粒子群优化算法在水文模型参数优化中的应用研究

引入改进的粒子群优化算法,对垂向混合产流模型计算参数进行优化,并对比参数优化前后水文模拟精度。研究结果表明：改进的粒子群优化算法模型可较快完成参数优化,相比于参数优化前,垂向混合产流模型年尺度模拟相对误差减少6.15%,模拟的过程确定性系数平均提高0.11;在次洪模拟中,模拟相对误差平均减少3.03%,模拟的洪水过程确定性系数平均提高0.19,水文模拟精度得到较大程度提高。研究成果对于区域水文模型参数优化提供参考价值。     

边坡稳定极限分析斜条分上限法的全局优化方法

边坡稳定极限分析斜条分上限法需要寻求最小安全系数对应的临界滑动模式。由于待优化变量中包含了滑裂面位置与条块界面倾角,问题的自由度与非线性程度明显增加,寻找安全系数的整体极值变得十分困难。本文建立了任意形状滑裂面通过与不通过软弱夹层两种情况下斜条分上限法滑动模式优化的数学模型。为保证在随机搜索过程中生成合理的滑动模式,引入一系列约束条件,将临界滑动模式的搜索问题转化为一个有界约束的数学极小值问题,并结合遗传算法和粒子群算法两种全局优化方法,对多个典型算例进行对比分析。研究表明,提出的模型可以解决优化过程中生成不合理滑动模式的问题,不仅极大地提高了优化效率,而且可以避免数值计算不收敛的麻烦;将模型与全局优化算法相结合,在大多数情况下能够得到一个合理的、与极限平衡解十分接近的上限解,具有较好的全局收敛性。