Joshua B. Kollat

A framework for Visually Interactive Decision-making and Design using Evolutionary Multi-objective Optimization (VIDEO)

This study presents a framework for Visually Interactive Decision-making and Design using Evolutionary Multi-objective Optimization (VIDEO). The VIDEO framework allows users to visually navigate large multi-objective solution sets while aiding decision makers in identifying one or more optimal designs. Specifically, the interactive visualization framework is intended to provide an innovative exploration tool for high-order Pareto-optimal solution sets (i.e., solution sets for three or more objectives). The framework is demonstrated for a long-term groundwater monitoring (LTM) application in which users can explore and visualize tradeoffs for up to four design objectives, simultaneously. Interactive functionality within the framework allows the user to select solutions within the objective space and visualize the corresponding monitoring plans performance in the design space. This functionality provides the user with a holistic picture of the information provided by a particular solution, ultimately allowing them to make a more informed decision. In addition, the ease with which the framework allows users to navigate and compare solutions as well as design tradeoffs leads to a time efficient analysis, even when there are thousands of potential solutions.

Numerical and visual evaluation of hydrological and environmental models using the Monte Carlo analysis toolbox

The detailed evaluation of mathematical models and the consideration of uncertainty in the modeling of hydrological and environmental systems are of increasing importance, and are sometimes even demanded by decision makers. At the same time, the growing complexity of models to represent real-world systems makes it more and more difficult to understand model behavior, sensitivities and uncertainties. The Monte Carlo Analysis Toolbox (MCAT) is a Matlab library of visual and numerical analysis tools for the evaluation of hydrological and environmental models. Input to the MCAT is the result of a Monte Carlo or population evolution based sampling of the parameter space of the model structure under investigation. The MCAT can be used off-line, i.e. it does not have to be connected to the evaluated model, and can thus be used for any model for which an appropriate sampling can be performed. The MCAT contains tools for the evaluation of performance, identifiability, sensitivity, predictive uncertainty and also allows for the testing of hypotheses with respect to the model structure used. In addition to research applications, the MCAT can be used as a teaching tool in courses that include the use of mathematical models.

The value of online adaptive search: a performance comparison of NSGAII, ε-NSGAII and εMOEA

This paper demonstrates how adaptive population-sizing and epsilon-dominance archiving can be combined with the Nondominated Sorted Genetic Algorithm-II (NSGAII) to enhance the algorithms efficiency, reliability, and ease-of-use. Four versions of the enhanced Epsilon Dominance NSGA-II (e-NSGAII) are tested on a standard suite of evolutionary multiobjective optimization test problems. Comparative results for the four variants of the (e-NSGAII demonstrate that adapting population size based on online changes in the epsilon dominance archive size can enhance performance. The best performing version of the (e-NSGAII is also compared to the original NSGAII and the (eMOEA on the same suite of test problems. The performance of each algorithm is measured using three running performance metrics, two of which have been previously published, and one new metric proposed by the authors. Results of the study indicate that the new version of the NSGAII proposed in this paper demonstrates improved performance on the majority of two-objective test problems studied.

Parallel Evolutionary Multi-Objective Optimization on Large, Heterogeneous Clusters: An Applications Perspective

Real-world operational use of parallel multi-objective evolutionary algorithms requires successful searches in constrained wall-clock periods, limited trial-and-error algorithmic analysis, and scalable use of heterogeneous computing hardware. This study provides a cross-disciplinary collaborative effort to assess and adapt parallel multi-objective evolutionary algorithms for operational use in satellite constellation design using large dedicated clusters with heterogeneous processor speeds/architectures. A statistical, metric-based evaluation framework is used to demonstrate how time-continuation, asynchronous evolution, dynamic population sizing, and epsilon dominance archiving can be used to enhance both simple master–slave parallelization strategies and more complex multiple-population schemes. Results for a benchmark constellation design coverage problem show that simple master– slave schemes that exploit time-continuation are often sufficient and potentially superior to complex multiple-population schemes.

Comparison of Multi-Objective Evolutionary Algorithms for Long-Term Monitoring Design

This study compares the performances of four state-of-the-art evolutionary multiobjective optimization (EMO) algorithms: the Non-Dominated Sorted Genetic Algorithm II (NSGAII), the Epsilon-Dominance Non-Dominated Sorted Genetic Algorithm II (ε-NSGAII), the Epsilon-Dominance Multi-Objective Evolutionary Algorithm (εMOEA), and the Strength Pareto Evolutionary Algorithm 2 (SPEA2), on a four-objective long-term groundwater monitoring (LTM) design test case. The LTM test case objectives include: (i) minimize sampling cost, (ii) minimize contaminant concentration estimation error, (iii) minimize contaminant concentration estimation uncertainty, and (iv) minimize contaminant mass estimation error. The 25-well LTM design problem was enumerated to provide the true Pareto-optimal solution set to facilitate rigorous testing of the EMO algorithms. The performances of the four algorithms are assessed and compared using three runtime performance metrics (convergence, diversity, and εperformance), two unary metrics (the hypervolume indicator and unary ε-indicator) and the firstorder empirical attainment function. Results of the analyses indicate that the ε-NSGAII greatly exceeds the performance of the NSGAII and the εMOEA. The ε-NSGAII also achieves superior performance relative to the SPEA2 in terms of search effectiveness and efficiency. In addition, the ε-NSGAII’s simplified parameterization and its ability to adaptively size its population and automatically terminate results in an algorithm which is efficient, reliable, and easy-to-use for water resources applications.

Estimating the Impacts of Climate Change and Population Growth on Flood Discharges in the United States

AbstractThis study reflects a portion of the riverine analysis for a Federal Emergency Management Agency initiative to estimate the economic risks associated with climate and land use change to the U.S. National Flood Insurance Program. Specifically, this paper investigates how the 1% annual chance flood discharge, Q1% (equivalent to a 100-year return period flood), may change based on climate change and population projections through the year 2100. Watershed characteristics and observations of climate indicators at 2,357 U.S. Geological Survey gauging stations were used to develop regression relationships to estimate Q1%. Projections of the climate indicators that measure extremes in temperature and precipitation from a suite of global climate models were then used within a Monte Carlo sampling framework to estimate future changes to Q1% throughout the United States, while also translating the uncertainty resulting from multiple climate model projections into uncertainty in estimating the future Q1%. Pop...

Trade Space Exploration: Assessing the Benefits of Putting Designers “Back-in-the-Loop” during Engineering Optimization

Trade space exploration is a promising decision-making paradigm that provides a visual and more intuitive means for formulating, adjusting, and ultimately solving engineering design optimization problems. This is achieved by combining multi-dimensional data visualization techniques with visual steering commands to allow designers to “steer” the optimization process while searching for the best, or Pareto optimal, designs. After introducing the trade space exploration paradigm and visual steering capabilities that we developed, we compare the performance of different combinations of visual steering commands implemented by two users to a multi-objective genetic algorithm executed “blindly” on the same problem with no human intervention. The results indicate that the visual steering commands—regardless of the order and combination in which they are invoked—provide a 4–7× increase in the number of Pareto solutions obtained for a given number of function evaluations when the human is “in-the-loop” during the optimization process. As such, this study provides empirical evidence of the benefits of interactive visualization-based strategies to support engineering design optimization and decision-making. Future work is also discussed.

Computational Scaling Analysis of Multiobjective Evolutionary Algorithms in Long-Term Groundwater Monitoring Applications

This study contributes a detailed assessment of how increasing problem sizes (measured in terms of the number of decision variables being considered) impacts the computational complexity of using multiple objective evolutionary algorithms (MOEAs) to solve long-term groundwater monitoring (LTM) applications. The Epsilon-Dominance Non-Dominated Sorted Genetic Algorithm II (ε-NSGAII), which has been shown to be an efficient and reliable MOEA, was chosen for the computational scaling study. Four design objectives were chosen for the analysis: (i) sampling cost, (ii) contaminant concentration estimation error, (iii) local uncertainty, and (iv) contaminant mass estimation error. The true Pareto-optimal solution set was generated for 18 through 25 well LTM test cases in order to provide for rigorous algorithm performance assessment for problems of increasing size. Results of the study indicate that the ε-NSGAII exhibits quadratic computational scaling with increasing LTM problem size. However, if the user is willing to accept an approximation to the Pareto-optimal solution set, ε-dominance can be used to reduce the computational scaling of MOEAs to be linear with increasing problem sizes. This study provides a basis for advancing the size and scope of water resources problems that can be effectively solved using MOEAs.

SALIENT ISSUES IN COMPARING PERFORMANCE OF MULTI-OBJECTIVE EVOLUTIONARY ALGORITHMS

Numerous performance metrics have recently been developed to assist in evaluating the relative eectiveness of evolutionary multi-objective optimization (EMO) algorithms. Comparison of EMO algorithms is extremely challenging because performance metrics must account for both convergence (distance from true objective tradeos) and diversity (representation of full extent of objective tradeos). This paper demonstrates how to eectively compare the performance of dierent EMO implementations using two state-of-the-art performance metrics (-performance and the binary -indicator metric) and identifies some of the diculties that arise in assuring that the chosen metric is as informative as possible. Two EMO performance comparison case studies are presented: (i) a performance comparison on a suite of two-objective test functions and (ii) a performance comparison of a hydrologic model calibration problem. Results of the first case study indicate that the -performance metric can provide a great deal more runtime information concerning algorithm performance than the binary -indicator metric which only provides comparative information regarding final performance. Case study two demonstrates a dierent problem type whereby the computational constraints of the problem limit the ability of the -performance metric in providing sucient performance information. In this case, the binary -indicator metric is more robust at providing the most information concerning algorithm performance.