Abstract: A technique for obtaining a (nearly) optimal scheme using multiple management periods has been developed. The method has been developed for very large scale combinatorial optimization problems. Simulated annealing has been extended to this problem. An importance function is developed to accelerate the search for good solutions. These tools have been applied to groundwater remediation problems at Lawrence Livermore National Laboratory (LLNL). A deterministic site-specific engineering-type flow and transport model (based on the public domain code SUTRA) is combined with the heuristic optimization technique. The objective is to obtain the time-varying optimal locations of the remediation wells that will reduce concentration levels of volatile organic chemicals in groundwater below a given threshold at specified areas on the LLNL site within a certain time frame and subject to a variety of realistic complicating factors. The cost function incorporates construction costs, operation and maintenance costs for injection and extraction wells, costs associated with piping and treatment facilities, and a performance penalty for well configurations that generate flow and transport simulations that exceed maximum concentration levels at specified locations. The resulting application reported here comprises a huge optimization problem. The importance function detailed in this paper has led to rapid convergence to solutions. The performance penalty allows different goals to be imposed on different geographical regions of the site; in this example, short-term off-site plume containment and long-term on-site cleanup are imposed. The performance of the optimization scheme and the effects of various trade-offs in management objectives are explored through examples using the LLNL site.
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Bongard's work focuses on understanding the general nature of cognition, regardless of whether it is found in humans, animals or robots. This unique approach focuses on the role that morphology and evolution plays in cognition. Addressing these questions has taken him into the fields of biology, psychology, engineering and computer science.
Danforth is an applied mathematician interested in modeling a variety of physical, biological, and social phenomenon. He has applied principles of chaos theory to improve weather forecasts as a member of the Mathematics and Climate Research Network, and developed a real-time remote sensor of global happiness using messages from Twitter: the Hedonometer. Danforth co-runs the Computational Story Lab with Peter Dodds, and helps run UVM's reading group on complexity.
Laurent studies the interaction of structure and dynamics. His research involves network theory, statistical physics and nonlinear dynamics along with their applications in epidemiology, ecology, biology, and sociology. Recent projects include comparing complex networks of different nature, the coevolution of human behavior and infectious diseases, understanding the role of forest shape in determining stability of tropical forests, as well as the impact of echo chambers in political discussions.
Hines' work broadly focuses on finding ways to make electric energy more reliable, more affordable, with less environmental impact. Particular topics of interest include understanding the mechanisms by which small problems in the power grid become large blackouts, identifying and mitigating the stresses caused by large amounts of electric vehicle charging, and quantifying the impact of high penetrations of wind/solar on electricity systems.
Bagrow's interests include: Complex Networks (community detection, social modeling and human dynamics, statistical phenomena, graph similarity and isomorphism), Statistical Physics (non-equilibrium methods, phase transitions, percolation, interacting particle systems, spin glasses), and Optimization(glassy techniques such as simulated/quantum annealing, (non-gradient) minimization of noisy objective functions).