scholarly journals GOPS: efficient RBF surrogate global optimization algorithm with high dimensions and many parallel processors including application to multimodal water quality PDE model calibration

2020 ◽  
Author(s):  
Wei Xia ◽  
Christine Shoemaker
Keyword(s):  
Water Quality ◽  
Global Optimization ◽  
Objective Function ◽  
Black Box ◽  
High Dimensional ◽  
Function Evaluation ◽  
Test Problems ◽  
Quality Model ◽  
Lake Water Quality ◽  
Dimensional Parameter

Abstract This paper describes a new parallel global surrogate-based algorithm Global Optimization in Parallel with Surrogate (GOPS) for the minimization of continuous black-box objective functions that might have multiple local minima, are expensive to compute, and have no derivative information available. The task of picking P new evaluation points for P processors in each iteration is addressed by sampling around multiple center points at which the objective function has been previously evaluated. The GOPS algorithm improves on earlier algorithms by (a) new center points are selected based on bivariate non-dominated sorting of previously evaluated points with additional constraints to ensure the objective value is below a target percentile and (b) as iterations increase, the number of centers decreases, and the number of evaluation points per center increases. These strategies and the hyperparameters controlling them significantly improve GOPS’s parallel performance on high dimensional problems in comparison to other global optimization algorithms, especially with a larger number of processors. GOPS is tested with up to 128 processors in parallel on 14 synthetic black-box optimization benchmarking test problems (in 10, 21, and 40 dimensions) and one 21-dimensional parameter estimation problem for an expensive real-world nonlinear lake water quality model with partial differential equations that takes 22 min for each objective function evaluation. GOPS numerically significantly outperforms (especially on high dimensional problems and with larger numbers of processors) the earlier algorithms SOP and PSD-MADS-VNS (and these two algorithms have outperformed other algorithms in prior publications).

Trust Region Based Mode Pursuing Sampling Method for Global Optimization of High Dimensional Design Problems

2015 ◽  
Vol 137 (2) ◽  
Author(s):  
George H. Cheng ◽  
Adel Younis ◽  
Kambiz Haji Hajikolaei ◽  
G. Gary Wang
Keyword(s):  
Global Optimization ◽  
Optimization Problems ◽  
Trust Region ◽  
Standard Test ◽  
Black Box ◽  
High Dimensional ◽  
Efficient Global Optimization ◽  
Test Problems ◽  
Design Problems ◽  
Design Variables

Mode pursuing sampling (MPS) was developed as a global optimization algorithm for design optimization problems involving expensive black box functions. MPS has been found to be effective and efficient for design problems of low dimensionality, i.e., the number of design variables is less than 10. This work integrates the concept of trust regions into the MPS framework to create a new algorithm, trust region based mode pursuing sampling (TRMPS2), with the aim of dramatically improving performance and efficiency for high dimensional problems. TRMPS2 is benchmarked against genetic algorithm (GA), dividing rectangles (DIRECT), efficient global optimization (EGO), and MPS using a suite of standard test problems and an engineering design problem. The results show that TRMPS2 performs better on average than GA, DIRECT, EGO, and MPS for high dimensional, expensive, and black box (HEB) problems.

scholarly journals Simulating Diurnal Variations of Water Temperature and Dissolved Oxygen in Shallow Minnesota Lakes

Water ◽  
2021 ◽  
Vol 13 (14) ◽  
pp. 1980
Author(s):  
Bushra Tasnim ◽  
Jalil A. Jamily ◽  
Xing Fang ◽  
Yangen Zhou ◽  
Joel S. Hayworth
Keyword(s):  
Water Quality ◽  
Dissolved Oxygen ◽  
Water Temperature ◽  
Shallow Lakes ◽  
Quality Model ◽  
Lake Water Quality ◽  
Ecological Processes ◽  
Turbulent Diffusion Coefficient ◽  
Hourly Data ◽  
Mean Square Errors

In shallow lakes, water quality is mostly affected by weather conditions and some ecological processes which vary throughout the day. To understand and model diurnal-nocturnal variations, a deterministic, one-dimensional hourly lake water quality model MINLAKE2018 was modified from daily MINLAKE2012, and applied to five shallow lakes in Minnesota to simulate water temperature and dissolved oxygen (DO) over multiple years. A maximum diurnal water temperature variation of 11.40 °C and DO variation of 5.63 mg/L were simulated. The root-mean-square errors (RMSEs) of simulated hourly surface temperatures in five lakes range from 1.19 to 1.95 °C when compared with hourly data over 4–8 years. The RMSEs of temperature and DO simulations from MINLAKE2018 decreased by 17.3% and 18.2%, respectively, and Nash-Sutcliffe efficiency increased by 10.3% and 66.7%, respectively; indicating the hourly model performs better in comparison to daily MINLAKE2012. The hourly model uses variable hourly wind speeds to determine the turbulent diffusion coefficient in the epilimnion and produces more hours of temperature and DO stratification including stratification that lasted several hours on some of the days. The hourly model includes direct solar radiation heating to the bottom sediment that decreases magnitude of heat flux from or to the sediment.

Improved Trust Region Based MPS Method for High-Dimensional Expensive Black-Box Problems

2013 ◽  
Author(s):  
George H. Cheng ◽  
Adel Younis ◽  
Kambiz Haji Hajikolaei ◽  
G. Gary Wang
Keyword(s):  
Optimization Problems ◽  
Trust Region ◽  
Black Box ◽  
High Dimensional ◽  
Test Problems ◽  
Design Variables ◽  
Low Dimensionality ◽  
Improve Algorithm ◽  
Improved Performance ◽  
Better Than

Mode Pursuing Sampling (MPS) was developed as a global optimization algorithm for optimization problems involving expensive black box functions. MPS has been found to be effective and efficient for problems of low dimensionality, i.e., the number of design variables is less than ten. A previous conference publication integrated the concept of trust regions into the MPS framework to create a new algorithm, TRMPS, which dramatically improved performance and efficiency for high dimensional problems. However, although TRMPS performed better than MPS, it was unproven against other established algorithms such as GA. This paper introduces an improved algorithm, TRMPS2, which incorporates guided sampling and low function value criterion to further improve algorithm performance for high dimensional problems. TRMPS2 is benchmarked against MPS and GA using a suite of test problems. The results show that TRMPS2 performs better than MPS and GA on average for high dimensional, expensive, and black box (HEB) problems.

Surrogate Optimization of Computationally Expensive Black-Box Problems with Hidden Constraints

2019 ◽  
Vol 31 (4) ◽  
pp. 689-702 ◽  
Author(s):  
Juliane Müller ◽  
Marcus Day
Keyword(s):  
Objective Function ◽  
Optimization Problems ◽  
Black Box ◽  
Direct Search ◽  
Test Problems ◽  
Large Set ◽  
Mesh Adaptive Direct Search ◽  
Surrogate Optimization ◽  
Computationally Expensive ◽  
Hidden Constraints

We introduce the algorithm SHEBO (surrogate optimization of problems with hidden constraints and expensive black-box objectives), an efficient optimization algorithm that employs surrogate models to solve computationally expensive black-box simulation optimization problems that have hidden constraints. Hidden constraints are encountered when the objective function evaluation does not return a value for a parameter vector. These constraints are often encountered in optimization problems in which the objective function is computed by a black-box simulation code. SHEBO uses a combination of local and global search strategies together with an evaluability prediction function and a dynamically adjusted evaluability threshold to iteratively select new sample points. We compare the performance of our algorithm with that of the mesh-based algorithms mesh adaptive direct search (MADS, NOMAD [nonlinear optimization by mesh adaptive direct search] implementation) and implicit filtering and SNOBFIT (stable noisy optimization by branch and fit), which assigns artificial function values to points that violate the hidden constraints. Our numerical experiments for a large set of test problems with 2–30 dimensions and a 31-dimensional real-world application problem arising in combustion simulation show that SHEBO is an efficient solver that outperforms the other methods for many test problems.

Simulations of water quality and oxythermal cisco habitat in Minnesota lakes under past and future climate scenarios

2012 ◽  
Vol 47 (3-4) ◽  
pp. 375-388 ◽  
Author(s):  
Xing Fang ◽  
Shoeb R. Alam ◽  
Heinz G. Stefan ◽  
Liping Jiang ◽  
Peter C. Jacobson ◽  
...  
Keyword(s):  
Water Quality ◽  
Lake Water ◽  
Fish Habitat ◽  
Future Climate ◽  
Climate Scenarios ◽  
Quality Model ◽  
Lake Water Quality ◽  
Oligotrophic Lakes ◽  
Minnesota Lakes ◽  
Average Standard Error

A deterministic, process-oriented, dynamic and one-dimensional year-round lake water quality model, MINLAKE2010, was developed for water temperature (T) and dissolved oxygen (DO) simulations to study impacts of climate warming on lake water quality and cisco fish habitat. The DO model is able to simulate metalimnetic oxygen maxima in vertical DO profiles of oligotrophic lakes. The model was calibrated with profile data from the 28 study lakes in Minnesota; two-thirds of them are deep mesotrophic/oligotrophic lakes that support cisco, a coldwater fish species. The average standard error of estimate against measured data was 1.47 °C for T and 1.50 mg/L for DO. Oxythermal habitat parameter TDO3 (T at DO = 3 mg/L) was determined from simulated daily T and DO profiles under past and future climate scenarios in the 28 study lakes. Average annual maximum TDO3 (TDO3AM) for the 28 study lakes is projected to increase on the average of 3.2 °C under the MIROC 3.2 future scenario, while the occurrence day of TDO3AM is not much different under past and future climate scenarios. Both physical processes (mixing characteristics related to lake geometry ratio) and trophic status control temperature and DO characteristics and then affect cisco habitat in a lake.

Bayesian modelling of algal mass occurrences—using adaptive MCMC methods with a lake water quality model

2007 ◽  
Vol 22 (7) ◽  
pp. 966-977 ◽  
Author(s):  
Olli Malve ◽  
Marko Laine ◽  
Heikki Haario ◽  
Teija Kirkkala ◽  
Jouko Sarvala
Keyword(s):  
Water Quality ◽  
Lake Water ◽  
Water Quality Model ◽  
Mcmc Methods ◽  
Bayesian Modelling ◽  
Quality Model ◽  
Lake Water Quality ◽  
Adaptive Mcmc

scholarly journals Primary production and phosphorus modelling in LakeVegoritis, Greece

2014 ◽  
Vol 5 (1) ◽  
pp. 18
Author(s):  
Soultana K. Gianniou ◽  
Vassilis Z. Antonopoulos
Keyword(s):  
Water Quality ◽  
Primary Production ◽  
Model Simulation ◽  
Soluble Reactive Phosphorus ◽  
Quality Model ◽  
Lake Water Quality ◽  
Phytoplankton Primary Production ◽  
Reactive Phosphorus ◽  
Phosphorus Modelling

Primary production and phosphorus are two of the most important determinants of the water quality of lakes. Phytoplankton primary production and phosphorus cycling were modelled within a one-dimensional lake water quality model. The model was calibrated and applied to Lake Vegoritis in Greece for two different years (1981 and 1993) using daily meteorological variables and inflow rates as input data. Monthly profiles of temperature, chlorophyll-a, and oxygen concentration for these two years were used to calibrate the model. Simulation results indicate that the thermal regime of the lake strongly affects phosphorus profiles and that phytoplankton concentrations throughout the year are tightly correlated with soluble reactive phosphorus concentrations. The significant decrease in the depth and the volume of the lake from 1981 to 1993 resulted in important changes in phytoplankton and phosphorus concentrations. A sensitivity analysis was conducted to estimate the errors resulting from the uncertainty in the biochemical variables of the model and the limited data on phosphorus and phytoplankton.

scholarly journals Global optimization via neural network approximation of inverse coordinate mappings with evolutionary parameter control

2019 ◽  
Vol 10 (2) ◽  
pp. 3-31
Author(s):  
Kirill Vladimirovich Pushkaryov
Keyword(s):  
Neural Network ◽  
Global Optimization ◽  
Particle Swarm Optimization ◽  
Objective Function ◽  
Particle Swarm ◽  
Test Problems ◽  
Short Term ◽  
Swarm Optimization ◽  
Multiple Variables ◽  
Objective Function Values

A hybrid method of global optimization NNAICM-PSO is presented. It uses neural network approximation of inverse mappings of objective function values to coordinates combined with particle swarm optimization to find the global minimum of a continuous objective function of multiple variables with bound constraints. The objective function is viewed as a black box. The method employs groups of moving probe points attracted by goals like in particle swarm optimization. One of the possible goals is determined via mapping of decreased objective function values to coordinates by modified Dual Generalized Regression Neural Networks constructed from probe points. The parameters of the search are controlled by an evolutionary algorithm. The algorithm forms a population of evolving rules each containing a tuple of parameter values. There are two measures of fitness: short-term (charm) and long-term (merit). Charm is used to select rules for reproduction and application. Merit determines survival of an individual. This two-fold system preserves potentially useful individuals from extinction due to short-term situation changes. Test problems of 100 variables were solved. The results indicate that evolutionary control is better than random variation of parameters for NNAICM-PSO. With some problems, when rule bases are reused, error progressively decreases in subsequent runs, which means that the method adapts to the problem.

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