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.     

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.     

An Effective Approach to Long-Term Optimal Operation of Large-Scale Reservoir Systems: Case Study of the Three Gorges System

A new approach for optimization of long-term operation of large-scale reservoirs is presented, incorporating Incremental Dynamic Programming (IDP) and Genetic algorithm (GA) . The immense storage capacity of the large scale reservoirs enlarges feasible region of the operational decision variables, which leads to invalidation of traditional random heuristic optimization algorithms. Besides, long term raised problem dimension, which has a negative impact on reservoir operational optimization because of its non-linearity and non-convexity. The hybrid IDP-GA approach proposed exploits the validity of IDP for high dimensional problem with large feasible domain by narrowing the search space with iterations, and also takes the advantage of the efficiency of GA in solving highly non-linear, non-convex problems. IDP is firstly used to narrow down the search space with discrete d variables. Within the sub search space provided by IDP, GA searches the optimal operation scheme with continuous variables to improve the optimization precision. This hybrid IDP-GA approach was applied to daily optimization of the Three Gorges Project-Gezhouba cascaded hydropower system for annual evaluation from the year of 2004 to 2008. Contrast test shows hybrid IDP-GA approach outperforms both the univocal IDP and the classical GA. Another sub search space determined by actual operational data is also compared, and the hybrid IDP-GA approach saves about 10 times of computing resources to obtain similar increments. It is shown that the hybrid IDP GA approach would be a promising approach to dealing with long-term optimization problems of large-scale reservoirs.     

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.     

Application of Intelligent Water Drops Algorithm in Reservoir Operation

Optimum reservoir operation is a challenging problem in water resources systems. In this paper, Intelligent Water Drops (IWD) algorithm is applied in a reservoir operation problem. IWD is a population based algorithm and is initially proposed for solving combinatorial problems. The algorithm mimics the dynamics of river system and the behavior of water drops in the rivers. For this purpose data from Dez reservoir, located in southwestern Iran, has been used to examine the performance of the model. Moreover, due to similarities between IWD and the Ant Colony Optimization (ACO) algorithms, the results are compared with those of the ACO algorithm. Comparison of the results shows that while the IWD algorithm finds relatively better solutions, it is able to overcome the computational time consumption deficiencies inherited in the ACO methods. This is very important in large models with too many decision variables where run time becomes a limiting factor for optimization model applications.     

Multi Objective Optimization with a New Evolutionary Algorithm

Various objectives are mainly met through decision making in real world. Achieving desirable condition for all objectives simultaneously is a necessity for conflicting objectives. This concept is called multi objective optimization widely used nowadays. In this study, a new algorithm, comprehensive evolutionary algorithm (CEA), is developed based on general concepts of evolutionary algorithms that can be applied for single or multi objective problems with a fixed structure. CEA is validated through solving several mathematical multi objective problems and the obtained results are compared with the results of the non-dominated sorting genetic algorithm II (NSGA-II). Also, CEA is applied for solving a reservoir operation management problem. Comparisons show that CEA has a desirable performance in multi objective problems. The decision space is accurately assessed by CEA in considered problems and the obtained solutions’ set has a great extent in the objective space of each problem. Also, CEA obtains more number of solutions on the Pareto than NSGA-II for each considered problem. Although the total run time of CEA is longer than NSGA-II, solution set obtained by CEA is about 32, 4.4 and 1.6% closer to the optimum results in comparison with NSGA-II in the first, second and third mathematical problem, respectively. It shows the high reliability of CEA’s results in solving multi objective problems.     

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.     

改进蚁群算法及其在水利工程项目管理中的应用

为了更加有效解决水利工程项目管理中的多目标决策问题,提出了一种改进蚁群算法。该算法首先利用遗传算法的全局搜索能力将信息素初始化,然后在算法进行遍历过程中引入变异操作和交叉操作,提高算法的鲁棒性和有效性。水利工程项目多目标优化案例分析表明,较传统遗传算法和蚁群算法,本文提出的方法对于解的寻找速度更快,解的质量更高,该算法具有较高的全局寻优能力。该研究为水利工程项目管理多目标决策问题的解决提供了一种新的思路和方法。     

基于GACO-BP-MC的大坝变形监控模型

建立相应的安全监控模型来分析大坝变形监测资料对保障大坝服役安全意义重大。BP神经网络模型在此方面得到了广泛应用,但采用蚁群算法(ACO)对BP神经网络参数寻优时存在因初期搜索完全随机导致收敛速度慢的问题。将具有快速随机的全局搜索能力的遗传算法(GA)引入蚁群算法中,利用遗传算法指导生成初始信息素分布,再由蚁群算法正反馈寻得最优解来训练BP神经网络,从而得到大坝变形预测值,2种算法优势互补,缩短了蚁群算法的搜索时间并避免陷入局部最优点。在此基础上,为进一步提高预测精度,采用马尔科夫链(MC)对预测结果进行改进,由此建立了应用于大坝变形监控的GACO-BP-MC模型。工程实例分析表明,该模型在参数优化方面具有较快的寻优速率,且具有较高的拟合和预报能力。     

基于和声搜索算法的地下水污染源与未知含水层参数的同步反演研究

地下水污染源反演问题和含水层参数反演问题都是典型的地下水逆问题。在未知含水层参数(渗透系数、弥散度等)等先决信息的情况下进行地下水污染源反演计算时,需要根据已有的监测数据(水位和浓度等)对地下水污染源和未知含水层参数进行同步反演。在同步反演优化问题中,决策变量包括污染源位置、强度以及待求的含水层参数。论文首先介绍同步反演模型的框架组成(包括污染物迁移模型和反演优化模型),然后在对已有的各种和声搜索改进算法进行研究的基础上结合同步反演模型提出一种改进的和声搜索算法,最后将同步反演模型和改进的和声搜索算法应用于具体的算例研究。研究表明,改进的和声搜索算法具有算法稳定高效、求解精度高等特点,能够广泛应用于复杂的地下水污染源和含水层参数反演问题。     

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.     

基于系统微分响应的暴雨强度公式参数优化

暴雨强度公式参数的优化求解本质是一个高维非线性优化问题,目前常采用的优化求解方法是在以误差平方和为目标函数的基础上通过智能算法优化求解参数。为研究这类方法的合理性,通过随机抽样、参数空间网格化方法分析了常用暴雨强度公式参数求解方法的局限性,评价了常用智能算法的参数优化能力,进而提出了基于系统微分响应的暴雨强度公式参数优化方法。结果表明:以均方误差作为目标函数对非线性函数求解参数会增加额外参数解;在没有有效确定参数范围的情况下,随机抽样很难获得满足精度要求的参数样本,在有效确定参数范围后,目标函数的响应面上仍会存在无穷多个局部最优值,且很多局部最优的目标函数与全局最优近乎相同;以粒子群算法、SCE-UA算法为代表的随机搜索优化算法会因为参数初始取值范围过大、目标函数响应面局部最优参数解数量过多等问题而难以获得参数真值;提出的基于系统微分响应的暴雨强度公式参数优化方法能够快速寻找到参数真值,不仅效率高且能够避免陷入局部最优。     

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。     

基于模拟退火遗传算法的自压树状管网优化

将遗传算法全局优化和模拟退火的良好局部搜索能力有机结合,构造出一种退火遗传算法用于自压树状管网的优化设计方法。假定管网中每一管段最多只能由两种管径的管道组成,建立了以管网造价为目标函数,以管长、标准管径为决策变量的自压树状管网优化数学模型。采用基于不可行度的退火算法处理约束条件,应用遗传算法进行优化计算。仿真实例结果表明,该模型与算法在求解自压树状管网优化问题上,具有良好的优化性能和求解效率。     

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.     

基于粒子群优化BP神经网络的隧道围岩位移反演分析

针对无锡惠山隧道岩体破碎、围岩稳定性差等特点,基于长期现场监测变形位移数据,借助粒子群算法的参数优化功能,利用Matlab神经网络工具箱编制了优化PSO—BP隧道位移反分析系统。PSO—BP系统利用正交试验设计和有限元方法获得学习样本,再通过粒子群算法搜索最优的神经网络模型参数。用BP神经网络模型建立待反参数与实测位移之间的非线性映射关系,最后用粒子群算法从全局空间上搜索最优反演参数。克服了普通智能优化算法收敛速度慢、正分析计算量大等缺陷,具有全局优化特性。将模型应用于惠山隧道Ⅳ级围岩断面ZK6+485的反分析中,计算结果与实测值对比表明采用PSO—BP预测模型进行隧道位移预测是可行的。     

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。     

正弦余弦算法-投影寻踪水污染物总量分配模型

基于水资源禀赋条件、效率原则和尊重现状的原则,构建水污染物总量分配指标体系和水污染物分配投影寻踪(PP)模型。针对PP模型最佳投影方向难以确定的不足,利用正弦余弦算法(SCA)搜寻PP模型最佳投影方向,构建SCA-PP模型对云南省文山州壮族苗族自治州8县(市)水污染物控制总量进行分配。并通过6个典型测试函数对SCA算法进行仿真验证,仿真结果与蚁群优化(ACO)算法、模拟退火算法(SA)、文化算法(CA)、布谷鸟搜索(CS)算法和人工蜂群(ABC)算法进行对比。结果表明:(1)SCA算法寻优效果明显优于ACO、SA、CA、CS和ABC算法,具有模型简单、调节参数少、收敛速度快、寻优精度高、全局寻优能力强以及收敛稳定性与收敛可靠性好等特点。(2)SCA-PP模型水污染物控制总量分配结果符合区域经济社会发展和水污物染削减客观要求。模型及方法具有一定的可操作性和有效性,可为水污染物分配提供新的途径和方法。     

基于改进萤火虫算法的梯级水库优化调度研究

梯级水电站水库群联合调度问题具有复杂的约束条件,受到发电、供水、防洪等目标的制约。作为多目标非线性优化调度问题,为了解决传统算法中存在结果受初值参数影响较大、容易陷入局部最优解、收敛速度不理想等问题,首次尝试将萤火虫算法引入梯级水库优化调度研究中。在传统萤火虫算法模仿自然界萤火虫捕食求偶行为的基础上,对其进行优化与改进,引入目标空间中解的Pareto支配关系比较萤火虫荧光亮度,比较其优化解,采用轮盘赌法确定萤火虫每次更新过程中的移动路径,利用精英保留策略建立多目标萤火虫模型。通过典型的梯级水电站进行仿真计算,研究结果表明,改进的多目标萤火虫算法在优化过程中具有较强的寻优能力,能更好地进行全局搜索和局部搜索,计算过程中具有良好的稳定性,并且计算效率较高,优于遗传算法(GA)、粒子群算法(PSO)和蚁群算法(ACO),为多阶段、多约束的梯级水电站水库群中长期优化调度问题提供了新的途径和新方法。     

Multi-objective Coverage-based ACO Model for Quality Monitoring in Large Water Networks

A numerical procedure is presented for the optimization of the position of water quality monitoring stations in a pressurized water distribution system (WDS). The procedure is based on the choice of the set of sampling stations which maximizes the monitored volume of water while keeping the number of stations at minimum. The optimization model is formulated in terms of integer programming, and the solution of the mathematical problem is efficiently approximated by means of a multi-objective multi-colony ant algorithm. A built-in routine is developed for calculation of the water fraction matrix and integrated into the general modeling structure to facilitate data entry and storage to minimize problems associated with water fraction matrix determination for varying scenarios and coverage criteria for any scenario. The proposed methodology is very robust in analyzing the effects of different scenarios and/or number of potential monitoring stations by eliminating the need of employing an off-line routine for coverage matrix identification. Robustness, ease of generalization, multi-objective nature, and computational efficiency are the main characteristics and novelty of the proposed approach. Monitoring stations are optimally located in a large-scale real-world network with 104 nodes and multiple demands using the proposed ACO models. The set of non-dominated solutions forming the Pareto front for a number of monitoring stations and the total coverage of the system are also presented.