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. ¿ American Geophysical Union 1996