scholarly journals Searching for an optimized single-objective function matching multiple objectives with automatic calibration of hydrological models

2016 ◽  
Author(s):  
Fuqiang Tian ◽  
Yu Sun ◽  
Hongchang Hu ◽  
Hongyi Li
Keyword(s):  
Objective Function ◽  
Power Function ◽  
Automatic Calibration ◽  
Efficiency Coefficient ◽  
Hydrological Models ◽  
Objective Functions ◽  
Multi Objective ◽  
Hydrological Variable ◽  
Flow Part ◽  
Single Objective

Abstract. In the calibration of hydrological models, evaluation criteria are explicitly and quantitatively defined as single- or multi-objective functions when utilizing automatic calibration approaches. In most previous studies, there is a general opinion that no single-objective function can represent all of the important characteristics of even one specific kind of hydrological variable (e.g., streamflow). Thus hydrologists must turn to multi-objective calibration. In this study, we demonstrated that an optimized single-objective function can compromise multi-response modes (i.e., multi-objective functions) of the hydrograph, which is defined as summation of a power function of the absolute error between observed and simulated streamflow with the exponent of power function optimized for specific watersheds. The new objective function was applied to 196 model parameter estimation experiment (MOPEX) watersheds across the eastern United States using the semi-distributed Xinanjiang hydrological model. The optimized exponent value for each watershed was obtained by targeting four popular objective functions focusing on peak flows, low flows, water balance, and flashiness, respectively. The results showed that the optimized single-objective function can achieve a better hydrograph simulation compared to the traditional single-objective function Nash-Sutcliffe efficiency coefficient for most watersheds, and balance high flow part and low flow part of the hydrograph without substantial differences compared to multi-objective calibration. The proposed optimal single-objective function can be practically adopted in the hydrological modeling if the optimal exponent value could be determined a priori according to hydrological/climatic/landscape characteristics in a specific watershed. This is, however, left for future study.

scholarly journals Robust multi-objective calibration strategies – possibilities for improving flood forecasting

2012 ◽  
Vol 16 (10) ◽  
pp. 3579-3606 ◽  
Author(s):  
T. Krauße ◽  
J. Cullmann ◽  
P. Saile ◽  
G. H. Schmitz
Keyword(s):  
Parameter Estimation ◽  
Objective Function ◽  
Model Performance ◽  
Data Depth ◽  
Automatic Calibration ◽  
Multi Objective ◽  
Robust Model ◽  
Robust Parameter ◽  
Robust Parameter Estimation ◽  
Single Objective

Abstract. Process-oriented rainfall-runoff models are designed to approximate the complex hydrologic processes within a specific catchment and in particular to simulate the discharge at the catchment outlet. Most of these models exhibit a high degree of complexity and require the determination of various parameters by calibration. Recently, automatic calibration methods became popular in order to identify parameter vectors with high corresponding model performance. The model performance is often assessed by a purpose-oriented objective function. Practical experience suggests that in many situations one single objective function cannot adequately describe the model's ability to represent any aspect of the catchment's behaviour. This is regardless of whether the objective is aggregated of several criteria that measure different (possibly opposite) aspects of the system behaviour. One strategy to circumvent this problem is to define multiple objective functions and to apply a multi-objective optimisation algorithm to identify the set of Pareto optimal or non-dominated solutions. Nonetheless, there is a major disadvantage of automatic calibration procedures that understand the problem of model calibration just as the solution of an optimisation problem: due to the complex-shaped response surface, the estimated solution of the optimisation problem can result in different near-optimum parameter vectors that can lead to a very different performance on the validation data. Bárdossy and Singh (2008) studied this problem for single-objective calibration problems using the example of hydrological models and proposed a geometrical sampling approach called Robust Parameter Estimation (ROPE). This approach applies the concept of data depth in order to overcome the shortcomings of automatic calibration procedures and find a set of robust parameter vectors. Recent studies confirmed the effectivity of this method. However, all ROPE approaches published so far just identify robust model parameter vectors with respect to one single objective. The consideration of multiple objectives is just possible by aggregation. In this paper, we present an approach that combines the principles of multi-objective optimisation and depth-based sampling, entitled Multi-Objective Robust Parameter Estimation (MOROPE). It applies a multi-objective optimisation algorithm in order to identify non-dominated robust model parameter vectors. Subsequently, it samples parameter vectors with high data depth using a further developed sampling algorithm presented in Krauße and Cullmann (2012a). We study the effectivity of the proposed method using synthetical test functions and for the calibration of a distributed hydrologic model with focus on flood events in a small, pre-alpine, and fast responding catchment in Switzerland.

Pareto Artificial Life Algorithm for Multi-Objective Optimization

2011 ◽  
Vol 4 (2) ◽  
pp. 43-60
Author(s):  
Jin-Dae Song ◽  
Bo-Suk Yang
Keyword(s):  
Objective Function ◽  
Artificial Life ◽  
Pareto Set ◽  
Function Optimization ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Single Function ◽  
Artificial Life Algorithm ◽  
Single Objective

Most engineering optimization uses multiple objective functions rather than single objective function. To realize an artificial life algorithm based multi-objective optimization, this paper proposes a Pareto artificial life algorithm that is capable of searching Pareto set for multi-objective function solutions. The Pareto set of optimum solutions is found by applying two objective functions for the optimum design of the defined journal bearing. By comparing with the optimum solutions of a single objective function, it is confirmed that the single function optimization result is one of the specific cases of Pareto set of optimum solutions.

Pareto Artificial Life Algorithm for Multi-Objective Optimization

2013 ◽  
pp. 100-115
Author(s):  
Jin-Dae Song ◽  
Bo-Suk Yang
Keyword(s):  
Objective Function ◽  
Artificial Life ◽  
Pareto Set ◽  
Function Optimization ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Single Function ◽  
Artificial Life Algorithm ◽  
Single Objective

Most engineering optimization uses multiple objective functions rather than single objective function. To realize an artificial life algorithm based multi-objective optimization, this paper proposes a Pareto artificial life algorithm that is capable of searching Pareto set for multi-objective function solutions. The Pareto set of optimum solutions is found by applying two objective functions for the optimum design of the defined journal bearing. By comparing with the optimum solutions of a single objective function, it is confirmed that the single function optimization result is one of the specific cases of Pareto set of optimum solutions.

Development of a Stepped Calibration Approach for XAJ Hydrological Model

2013 ◽  
Vol 405-408 ◽  
pp. 2222-2225
Author(s):  
Qian Li ◽  
Wei Min Bao ◽  
Jing Lin Qian
Keyword(s):  
Root Mean Square Error ◽  
Objective Function ◽  
Traditional Method ◽  
Hydrological Model ◽  
Model Performance ◽  
Layer By Layer ◽  
Mean Square ◽  
Objective Functions ◽  
Single Objective ◽  
Calibration Approach

This paper discusses the conceptual stepped calibration approach (SCA) which has been developed for the Xinanjiang (XAJ) model. Multi-layer and multi-objective functions which can make optimization work simpler and more effective are introduced in this procedure. In all eight parameters were considered, they were divided into four layers according to the structure of XAJ model, and then calibrated layer by layer. The SCA procedure tends to improve the performance of the traditional method of calibration (thus, using a single objective function, such as root mean square error RMSE). The compared results demonstrate that the SCA yield better model performance than RMSE.

Solving realistic reactive power market clearing problem of wind-thermal power system with system security

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Sravanthi Pagidipala ◽  
Sandeep Vuddanti
Keyword(s):  
Power System ◽  
Reactive Power ◽  
Power Market ◽  
Operating Conditions ◽  
Objective Functions ◽  
Market Clearing ◽  
Load Model ◽  
Multi Objective ◽  
Reactive Power Market ◽  
Single Objective

Abstract This paper proposes a security-constrained single and multi-objective optimization (MOO) based realistic security constrained-reactive power market clearing (SC-RPMC) mechanism in a hybrid power system by integrating the wind energy generators (WEGs) along with traditional thermal generating stations. Pre-contingency and post-contingency reactive power price clearing plans are developed. Different objective functions considered are the reactive power cost (RPC) minimization, voltage stability enhancement index (VSEI) minimization, system loss minimization (SLM), and the amount of load served maximization (LSM). These objectives of the SC-RPMC problem are solved in a single objective as well as multi-objective manner. The choice of objective functions for the MOO model depends on the load model and the operating condition of the system. For example, the SLM is an important objective function for the constant power load model, whereas the LSM is for the voltage-dependent/variable load model. The VSEI objective should be used only in near-critical loading conditions. The SLM/LSM objective is for all other operating conditions. The reason for using multiple objectives instead of a single objective and the rationale for the choice of the appropriate objectives for a given situation is explained. In this work, the teaching learning-based optimization (TLBO) algorithm is used for solving the proposed single objective-based SC-RPMC problem, and a non-dominated sorting-based TLBO technique is used for solving the multi-objective-based SC-RPMC problem. The fuzzy decision-making approach is applied for extracting the best-compromised solution. The validity and efficiency of the proposed market-clearing approach have been tested on IEEE 30 bus network.

scholarly journals Multi-Objective Calibration of a Distributed Hydrological Model in a Highly Glacierized Watershed in Central Asia

Water ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 554
Author(s):  
Huiping Ji ◽  
Gonghuan Fang ◽  
Jing Yang ◽  
Yaning Chen
Keyword(s):  
Sensitivity Analysis ◽  
Central Asia ◽  
Swat Model ◽  
Hydrological Processes ◽  
Efficiency Coefficient ◽  
Objective Functions ◽  
Data Scarcity ◽  
Multi Objective ◽  
Glacier Melt ◽  
Macro Scale

Understanding glacio-hydrological processes is crucial to water resources management, especially under increasing global warming. However, data scarcity makes it challenging to quantify the contribution of glacial melt to streamflow in highly glacierized catchments such as those in the Tienshan Mountains. This study aims to investigate the glacio-hydrological processes in the SaryDjaz-Kumaric River (SDKR) basin in Central Asia by integrating a degree-day glacier melt algorithm into the macro-scale hydrological Soil and Water Assessment Tool (SWAT) model. To deal with data scarcity in the alpine area, a multi-objective sensitivity analysis and a multi-objective calibration procedure were used to take advantage of all aspects of streamflow. Three objective functions, i.e., the Nash–Sutcliffe efficiency coefficient of logarithms (LogNS), the water balance index (WBI), and the mean absolute relative difference (MARD), were considered. Results show that glacier and snow melt-related parameters are generally sensitive to all three objective functions. Compared to the original SWAT model, simulations with a glacier module match fairly well to the observed streamflow, with the Nash–Sutcliffe efficiency coefficient (NS) and R2 approaching 0.82 and an absolute percentage bias less than 1%. Glacier melt contribution to runoff is 30–48% during the simulation period. The approach of combining multi-objective sensitivity analysis and optimization is an efficient way to identify important hydrological processes and recharge characteristics in highly glacierized catchments.

Towards Uniformly Distributed Compliance in Compliant Mechanisms: A Multi-Objective Approach

2006 ◽  
Author(s):  
Stephen L. Canfield ◽  
Daniel L. Chlarson ◽  
Alexander Shibakov ◽  
Patrick V. Hull
Keyword(s):  
Finite Element ◽  
Objective Function ◽  
Compliant Mechanisms ◽  
Optimality Criteria ◽  
Optimal Designs ◽  
Limiting Factors ◽  
Objective Functions ◽  
Multi Objective ◽  
Simple Addition ◽  
Current Formulation

Researchers in the field of optimal synthesis of compliant mechanisms have been working to develop tools that yield distributed compliant devices to perform specific tasks. However, it has been demonstrated in the literature that much of this work has resulted in mechanisms that localize compliance rather than distribute it as desired. In fact, Yin and Ananthasuresh (2003) [1] demonstrate that based on the current formulation of optimality criteria and analysis via the finite element (FE) technique, a lumped compliant device will always exist as the minimizing solution to the objective function. The addition of constraints on allowable strain simply moves the solution back from this objective. Therefore, modification to the standard optimality criteria needs to take place. Yin and Ananthasuresh [1] proposed and compared several approaches that include distributivity-based measures within the optimality criteria, and demonstrated the effectiveness of this approach. In this paper, the authors propose to build on this problem. In a similar manner, a general approach to the topology synthesis problem will be suggested to yield mechanisms in which the compliance is distributed throughout the device. This work will be based on the idea of including compliance distribution directly within the objective functions, while addressing some of the potential limiting factors in past approaches. The technique will be generalized to allow simple addition of criteria in the future, and to deliver optimal designs through to manufacture. This work will first revisit and propose several quantitative definitions for distributed compliant devices. Then, a multi-objective formulation based on a non-dominating sort and Pareto set method will be incorporated that will provide information on the nature of the problem and compatibility of employed objective functions.

The Research of Multi-Resource Equilibrium Optimization in Schedule Management

2012 ◽  
Vol 209-211 ◽  
pp. 1406-1410
Author(s):  
Yun Ning Zhang ◽  
Wei Wei Chen
Keyword(s):  
Objective Function ◽  
Basic Principle ◽  
Comprehensive Evaluation ◽  
Fuzzy Comprehensive Evaluation ◽  
Equilibrium Theory ◽  
Typical Problem ◽  
Multi Objective ◽  
Schedule Management ◽  
Theoretical Significance ◽  
Single Objective

Resource equilibrium optimization is a typical problem in Schedule Management. Based on studying multi-resource equilibrium theory thoroughly, this paper firstly gives different weights to various resources by using fuzzy comprehensive evaluation to transform multi-objective problem to single objective problem. Then, it establishes a model for multi-resource equilibrium optimization by choosing the variance of various resources’ demands as objective function. Finally, this paper describes its basic principle and steps, which has important theoretical significance.

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