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.     

随机梯度法在新安江模型参数 优选中的应用

基于近似梯度法及模式搜索法,提出了复合两种方法的随机优化方法。以Nash确定性系数为目标函数,对新安江模型的参数空间随机搜索后运用梯度法进行了优化,然后采用参数空间筛选策略,以获得全局最优解集。上述方法结合导数信息和随机性质的算法,使优化方法脱离局部极小解从而达到近似全局最优解集。以杨楼单元流域为应用实例进行了研究,结果表明,随机梯度法可以成功地率定概念性水文模型参数。     

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。     

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.     

Application Research of the Improved Overall Temporal and Spatial Economic Operation Model Based on Information Entropy in Large-Scale Hydropower Station

For the high dimensional and complex inner-plant economical operation problem of large hydropower station, an improved ant colony optimization with adaptive ability, inspiring ability and local search ability was proposed. Spatial optimal load distribution model and temporal unit commitment model was combined into an overall temporal and spatial economic operation model, in which an innovative ant colony model of multiple ant colonies, multiple outsets and multiple routes was adopted. Information entropy was applied to adjust the path selection strategy and pheromone updating strategy of ant colonies along with the change of its value during the iteration. Two inspiring factors were applied in the algorithm to guide the ant colonies to search for optimal paths in a more efficient and targeted way. Local search ability was guaranteed by local translation of unit start-stop points of the optimal solution in each iteration. In the optimal load distribution model, optimal distribution table was set in advance using dynamic programming, which only took account of the stable operation regions and avoided the cavitation and vibration areas for the security and stability of units. The proposed method is applied to the Three Gorges Hydroelectric plant. Compared with other methods under different water heads, this method shows optimized result under the premise of both calculation speed and stability.     

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。     

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。     

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.     

Reference Point Based Multi-Objective Optimization of Reservoir Operation: a Comparison of Three Algorithms

Traditional multi-objective evolutionary algorithms treat each objective equally and search randomly in all solution spaces without using preference information. This might reduce the search efficiency and quality of solutions preferred by decision makers, especially when solving problems with complicated properties or many objectives. Three reference point based algorithms which adopt preference information in optimization progress, e.g., R-NSGA-II, r-NSGA-II and g-NSGA-II, have been shown to be effective in finding more preferred solutions in theoretical test problems. However, more efforts are needed to test their effectiveness in real-world problems. This study conducts a comparison of the above three algorithms with a standard algorithm NSGA-II on a reservoir operation problem to demonstrate their performance in improving the search efficiency and quality of preferred solutions. Under the same calculation times of the objective functions, Pareto optimal solutions of the four algorithms are used in the empirical comparison in terms of the approximation to the preferred solutions. Three performance indicators are then adopted for further comparison. Results show that R-NSGA-II and r-NSGA-II can improve the search efficiency and quality of preferred solutions. The convergence and diversity of their solutions in the concerned region are better than NSGA-II, and the closeness degree to the reference point can be increased by 42.8%, and moreover the number of preferred solutions can be increased by more than 3 times when part of objectives are preferred. By contrast, g-NSGA-II shows worse performance. This study exhibits the performance of three reference point based algorithms and provides insights in algorithm selection for multi-objective reservoir optimization problems.

     

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.     

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.     

Modeling river water quality parameters using modified adaptive neuro fuzzy inference system

Water quality is always one of the most important factors in human health. Artificial intelligence models are respected methods for modeling water quality. The evolutionary algorithm(EA) is a new technique for improving the performance of artificial intelligence models such as the adaptive neuro fuzzy inference system(ANFIS) and artificial neural networks(ANN). Attempts have been made to make the models more suitable and accurate with the replacement of other training methods that do not suffer from some shortcomings, including a tendency to being trapped in local optima or voluminous computations. This study investigated the applicability of ANFIS with particle swarm optimization(PSO)and ant colony optimization for continuous domains(ACO_R) in estimating water quality parameters at three stations along the Zayandehrood River, in Iran. The ANFIS-PSO and ANFIS-ACO_R methods were also compared with the classic ANFIS method, which uses least squares and gradient descent as training algorithms. The estimated water quality parameters in this study were electrical conductivity(EC), total dissolved solids(TDS), the sodium adsorption ratio(SAR), carbonate hardness(CH), and total hardness(TH). Correlation analysis was performed using SPSS software to determine the optimal inputs to the models. The analysis showed that ANFIS-PSO was the better model compared with ANFIS-ACO_R. It is noteworthy that EA models can improve ANFIS' performance at all three stations for different water quality parameters.     

混合智能算法及其在供水水库群优化调度中的应用

将遗传算法中的进化思想和蚁群算法中的群体智能技术有效地耦合,提出了一种基于两者的混合智能算法,应用于供水水库群系统的优化调度研究中。算法利用蚁群算法的并行性、正反馈性以及良好的全局寻优能力,避免搜索陷入局部最优,同时借鉴遗传算法的进化思想,利用杂交、变异算子来进行局部寻优,使其能快速搜索到全局最优点。在种群随机搜索过程中嵌入确定性的模式搜索,使得算法同时具有随机性和确定性。结合模拟退火思想,构造了罚因子处理约束条件,使该算法对水库优化调度问题以及其他优化问题具有一定的通用性。通过实例验证,并与大系统聚合分解经典算法进行比较,结果表明该算法是可行的和有效的。     

蚁群算法在工程项目工期—费用优化问题中的应用

论述了工期—费用优化问题的原理,分析了传统优化方法的优缺点。针对工期-费用这一连续空间优化问题,综合了基于网格划分策略的连续域蚁群算法和求解旅行商问题的基本蚁群算法的思想,构造了一种改进的蚁群算法。实例计算结果表明,该方法在求解工期费用优化问题方面是有效的。     

Honey-Bees Mating Optimization (HBMO) Algorithm: A New Heuristic Approach for Water Resources Optimization

Over the last decade, evolutionary and meta-heuristic algorithms have been extensively used as search and optimization tools in various problem domains, including science, commerce, and engineering. Their broad applicability, ease of use, and global perspective may be considered as the primary reason for their success. The honey-bees mating process may also be considered as a typical swarm-based approach to optimization, in which the search algorithm is inspired by the process of real honey-bees mating. In this paper, the honey-bees mating optimization algorithm (HBMO) is presented and tested with few benchmark examples consisting of highly non-linear constrained and/or unconstrained real-valued mathematical models. The performance of the algorithm is quite comparable with the results of the well-developed genetic algorithm. The HBMO algorithm is also applied to the operation of a single reservoir with 60 periods with the objective of minimizing the total square deviation from target demands. Results obtained are promising and compare well with the results of other well-known heuristic approaches.     

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。     

Penalty-Free Feasibility Boundary Convergent Multi-Objective Evolutionary Algorithm for the Optimization of Water Distribution Systems

This paper presents a new penalty-free multi-objective evolutionary approach (PFMOEA) for the optimization of water distribution systems (WDSs). The proposed approach utilizes pressure dependent analysis (PDA) to develop a multi-objective evolutionary search. PDA is able to simulate both normal and pressure deficient networks and provides the means to accurately and rapidly identify the feasible region of the solution space, effectively locating global or near global optimal solutions along its active constraint boundary. The significant advantage of this method over previous methods is that it eliminates the need for ad-hoc penalty functions, additional ??boundary search?? parameters, or special constraint handling procedures. Conceptually, the approach is downright straightforward and probably the simplest hitherto. The PFMOEA has been applied to several WDS benchmarks and its performance examined. It is demonstrated that the approach is highly robust and efficient in locating optimal solutions. Superior results in terms of the initial network construction cost and number of hydraulic simulations required were obtained. The improvements are demonstrated through comparisons with previously published solutions from the literature.     

基于蚂蚁算法的水电站短期优化运行研究

利用蚂蚁算法的转移搜索和邻域搜索机制,构造了水电站短期优化运行蚂蚁算法模型.实例证明,蚂蚁算法能够解决具有复杂约束的水电站短期优化运行问题,算法编程简单,易于实现.为水电站短期优化运行提出了一种新的、有效的方法.     

基于混合变异策略差分进化算法的边坡滑裂面搜索研究

针对"基于反射变异策略的自适应差分进化算法"仍易陷入局部最优的问题,通过引入一个基本的变异策略提出一种基于混合变异策略(DE/current-to-rand/1)的差分进化算法。根据各变异策略生成成功子代的比率使用轮盘赌选择为各个个体选择合适的变异策略,以改善算法的全局收敛能力。将提出的算法结合有限元应力场应用于两个经典算例的边坡临界滑动面搜索及安全系数求解,与其他极限平衡法进行了对比,并使用其中一个算例作为计算模型与其他优化算法进行了收敛性能比较。统计结果验证了改进算法的性能更稳定且收敛速度较快,也验证了该算法结合有限元应力场求解边坡问题的有效性。     

Application Research of Inner-plant Economical Operation by Multi-colony Ant Optimization

A new multi-colony ant optimization (MCAO) combined with a dynamic economic distribution (DED) technique has been proposed for the economical operation of the inner-plant of a hydropower station. MCAO and DED are applied to solve the unit commitment (UC) sub-problem and the economic load distribution (ELD) sub-problem consolidating the ramp rate constraints for the entire schedule. Moreover, a patching mechanism is developed to converge quickly on the optimal solution in two respects: minimum up/down and spinning reserve. A mechanism mitigates the premature convergence by measuring the uncertainty of pheromone with information entropy. A local research technique enriches the diversity of solution space by selecting the derived solutions from the perturbation mechanism. In comparison with the genetic algorithm, the particle swarm optimization, and the ant colony optimization, the MCAO is significantly robust and provides better solutions to the economical operation problem of hydropower stations. Numerical simulations exhibit the superiority of the DED technique regarding stably and quickly consolidating the ramp rate constraints.