Transport Optimization:
Methods & Codes
This page lists both computational methods and codes that are used for to optimize systems with simulation of transport of contaminants. Since there are new methods and codes are emerging in this field in addition to revisions to existing programs, references and supporting research have also been included.
 ModGA
 MGO (Modular Groundwater Optimizer)
 ASAP – Adaptive Simulated Annealing Package
 ATOPT – Advective Transport Optimization
 iTOUGH2
 Gradient Methods
 Simulated Annealing
 Artificial Neural Network
 Outer Approximation
 Genetic Algorithm
 SOMOS
ModGA Developed by Chunmiao Zheng of the University of Alabama, ModGA, a simulationoptimization model, can be used for optimal design of groundwater hydraulic control and remediation systems under general field conditions. The model couples genetic algorithms (GA), a global search technique inspired by biological evolution, with MODFLOW and MT3D.
MGO
(Modular Groundwater Optimizer)
Developed by Chunmiao Zheng of the University of Alabama, the MGO code couples the
MODFLOW and MT3D simulators with three global optimization methods, i.e.,
genetic algorithm, simulated annealing, and tabu search, which are linked by a common
input/output structure and integrated with a gradientbased optimization module to
reduce the computational burden.
References (for both ModGA and MGO):
Applied Contaminant Transport Modeling: Theory and Practice
Zheng, C. and G. Bennet, 1995, Van Nostrand Reinhold,
ISBN: 0442013485; 1997, John Wiley & Sons, ISBN: 0471285366Parameter Structure Identification Using Tabu Search and Simulated Annealing
Zheng, C. and P.P. Wang, 1996, Advances in Water Resources, 19(4), pp.215224 Optimal
Remediation Policy Selection under General Conditions
Wang, M. and C. Zheng, 1997, Ground Water, 35(5), pp.757764  Ground Water
Management Optimization Using Genetic Algorithms and Simulated Annealing:
Formulation and Comparison
Wang, M. and C. Zheng, 1998, Journal of American Water Resources Association, 34(3), pp.519530  An Integrated Global and
Local Optimization Approach for Remediation System Design
Zheng, C., and P.P. Wang, 1999, Water Resources Research, 35(1), pp.137146

Adaptive Simulated Annealing
A C language package which provides the framework and mechanisms for optimization of complex systems using simulated annealing.
 Comparison
of a Genetic Algorithm and Mathematical Programming to the Design of
Groundwater Cleanup Systems
Aly, A.H. and R.C. Peralta, 1999, Water Resources Research, 35(8), pp. 24152425
 Optimal
Design of Aquifer Cleanup Systems under Uncertainty Using A Neural Network and
A Genetic Algorithm
Aly, A.H., and R.C. Peralta, 1999, Water Resources Research, 35(8), pp. 25232532
 Comparison
of a Genetic Algorithm and Mathematical Programming to the Design of
Groundwater Cleanup Systems

ATOPT – Advective Transport Optimization
Ann E. Mulligan, amulligan@whoi.edu, Woods Hole Oceanographic Institution, and David P. Ahlfeld, ahlfeld@ecs.umass.edu, University of MassachusettsATOPT is an advective control model that uses both contaminant pathline and capture zone simulation to constrain plume capture designs. The advective transport model explicitly represents advective transport while neglecting dispersion and contaminant decay reactions. ATOPT couples MODFLOW and MODPATH, and allows constraints to be placed on advective transport, time to capture, hydraulic head, and pumping rates.
Mulligan, A. E., and D. P. Ahlfeld, 2001, Optimal plume capture design in unconfined aquifers, J. Smith and S. Burns, eds., Physicochemical groundwater remediation, Kluwer Academic, p. 2344.
A New Code for MODFLOWCoupled Groundwater Management of Unconfined Aquifers
Ahlfeld, D.P., R.G. Riefler, and A.E. Mulligan, 1998, Proceedings of MODFLOW'98 Conference, October 48, 1998, Golden, Colorado, pp. 431438Optimal Management of Flow in Groundwater Systems
Ahlfeld, D.P. and A.E. Mulligan, 2000, Academic Press, San Diego Advective Control of
Groundwater Contaminant Plumes: Model Development and Comparison to Hydraulic
Control
Mulligan, A.E. and D.P. Ahlfeld, 1999, Water Resources Research, 35(8), pp. 22852294.  Mulligan, A.E., 2001, Water supply planning in contaminated aquifers, Proceedings of the World Water and Environmental Resources Congress, American Society of Civil Engineers, Orlando, FL, May 2001.
 Mulligan, A. E., and D. P. Ahlfeld, 2002, A new interior point boundary projection method for solving nonlinear groundwater pollution control problems, Operations Research, 50(4): 636644.
 Mulligan, A.E. and D.P. Ahlfeld, 1998, Optimal plume control based on advective transport, Computational Methods in Water Resources, Volume I, Proceedings of the XII International Conference, Crete, Greece, June 1519, 1998, p. 8389.

iTOUGH2
From Earth Sciences Division of Lawrence Berkeley National Laboratory. iTOUGH2
(inverse TOUGH2) is a computer program that provides inverse modeling capabilities for
the TOUGH2 code, a simulator for multiphase, multicomponent, nonisothermal flows in
fracturedporous media, for applications in geothermal reservoir engineering, nuclear
waste disposal, and unsaturated zone hydrology.
Demonstration of Optimization Techniques for Groundwater Plume Remediation
Finsterle, S., 2000, Report LBNL46746, Lawrence Berkeley National Laboratory, Berkeley, CA Using
SimulationOptimization Techniques to Improve Multiphase Aquifer
Remediation
Finsterle, S., and K. Pruess, 1995, Proceedings, TOUGH Workshop '95, March 2022, p. 181186, Report LBL37200, Lawrence Berkeley Laboratory, Berkeley, CA
 Gradient Methods
The gradient optimization solution techniques include 1) nonlinear programming (NLP); 2) nonlinear programming (NLP); 3) mixed integer linear programming (MILP); 4) mixed integer nonlinear programming (MINLP); and 5) differential dynamic programming (DDP). These methods evaluate the derivatives (or gradients) of the objective function with respect to the variables to be optimized; this is the reason that these methods are often referred to as "gradient" methods.
Large Scale Nonlinear Deterministic and Stochastic Optimization: Formulations Involving Simulation of Subsurface Contamination
Gorelick, S.M., 1990, Mathematical Programming, 48, pp. 1939.Aquifer Reclamation Design: The Use of Contaminant Transport Simulation Combined with Nonlinear Programming
Gorelick, S.M., C.I. Voss, P.E. Gill, W. Murray, M.A. Saunders, and M.H.Wright, 1984, Water Resources Research, 20(4), pp. 415427.Dynamic Optimal Control for Groundwater Remediation with Flexible Management Periods
Culver, T.B., and C.A. Shoemaker, 1992, Water Resources Research, 28(3), pp. 629641.Optimal Control for Groundwater Remediation by Differential Dynamic Programming with QuasiNewton Approximations
Culver, T.B., and C.A. Shoemaker, 1993, Water Resources Research, 29(4), pp. 823831.Nonlinear Weighted Feedback Control of Groundwater Remediation under Uncertainty
Whiffen, G.J., and C.A. Shoemaker, 1993, Water Resources Research, 29(9), pp. 32773289.Approximate MixedInteger Nonlinear Programming Methods for Optimal Aquifer Remediation Design
McKinney, D.C., and MD. Lin, 1995, Water Resources Research, 31(3), pp. 731740
 Simulated Annealing
Simulated annealing mimics process in which a solid is initially heated up to its melting temperature and then is cooled down slowly so that all the particles arrange themselves in the state of minimum energy where crystallization occurs. In optimization, the objective function to be minimized represents the energy in the thermodynamic process, while the optimal solution corresponds to the crystal configuration. The basic concept lies in allowing the search procedure to move occasionally "uphill".
David.Dougherty@subterra.com Optimal Groundwater Management, 1. Simulated Annealing</>
Dougherty, D.E., and R.A. Marryott, 1991, Water Resources Research, 27(10), pp. 24932508Design Optimization for Multiple Management Period Groundwater Remediation
Rizzo, D.M., and D.E. Dougherty, David.Dougherty@subterra.com, 1996, Water Resources Research, 32(8), pp.25492561MultiPeriod Objectives and Groundwater Remediation Using SAMOA: Tandem Simulated Annealing and Extended Cutting Plane Method for Containment with Cleanup
Yu, M., D. M. Rizzo, D. E. Dougherty, David.Dougherty@subterra.com, XIII International Conference on Computational Methods in Water Resources, June 2529, 2000, Calgary, Alberta, CanadaDeveloping OptimalWater Resources Management Strategies
Aly, A.H., aly@waterstoneinc.com, and Sean W. Fleming, WaterStone Environmental Hydrology and Engineering, Inc.Reducing Costs of PumpAndTreat Systems: Optimal Remedial Design Techniques
Aly, A.H., aly@waterstoneinc.com, and Gregory J. Ruskauff, WaterStone Environmental Hydrology and Engineering, Inc.Parameter Structure Identification Using Tabu Search and Simulated Annealing
Zheng, C., czheng@wgs.geo.ua.edu, and P.P. Wang, 1996, Advances in Water Resources, 19(4), pp. 215224.
 Artificial Neural Network
An artificial neural network (ANN) is a biological inspired computational system that (1) comprises individual processing or computational elements with associated memory, (2) is interconnected in some informationpassing topology, (3) operates largely in parallel, and (4) has some ability to adapt its functioning to its inputs and outputs. The belief that "intelligent" system might be developed from the collective behavior of many of these interconnected processing elements has led to the development of neural net models. Most neural network applications use the neural network to approximate the simulation model in the optimization model. Another optimization method is still needed to solve the optimization problem.
A Feedback Neural Network Approach to Optimization: An Application in Groundwater Remediation Design
Ranjithan, S., J.H.Garrett Jr., garrett@cmu.edu, and R. Ganeshan, 1991, Intelligent Enginnering through Artificial Neural Networks, Proceedings of ANNIE’91: Conference on Artificial Neural Networks in Engineering, 31(3), pp. 861867NeuralNetworkBased Screening for Groundwater Reclamation under Uncertainty
Ranjithan, S., J.W. Eheart, and J.H.Garrett Jr., garrett@cmu.edu, 1993, Water Resources Research, 29(3), pp. 563574Characterization of Aquifer Properties Using Artificial Neural Networks: Neural Kriging
Rizzo, D.M., Donna.Rizzo@subterra.com, D.E. Dougherty, David.Dougherty@subterra.com, 1994, Water Resources Research, 30(2), pp. 483497Optimization of Groundwater Remediation Using Artificial Neural Networks with Parallel Solute Transport Modeling
Rogers, L.L., and F.U. Dowla, 1994, Water Resources Research, 30(2), pp. 457481Optimal Design of Aquifer Cleanup Systems under Uncertainty Using A Neural Network and A Genetic Algorithm
Aly, A.H. aly@waterstoneinc.com, and R.C. Peralta, peralta@cc.usu.edu, 1999, Water Resources Research, 35(8), pp. 25232532.An Adaptive LongTerm Monitoring and Operations System (aLTMOs™) for Optimization in Environmental Management
Rizzo, D.M., Donna.Rizzo@subterra.com, D.E. Dougherty, David.Dougherty@subterra.com, and M. Yu, Subterranean Research, Inc. in ASCE Joint Water 2000 ConferenceDetermining Optimal Pumping Policies for a Public Supply Wellfield Using A Computational Neural Network With Linear Programming
Coppola, E.A., emery@hwr.arizona.edu, F. Szidarovszky, and M. Poulton, AGU Spring Meeting 2000
 Outer Approximation
The outer approximation is an algorithm for MixedInteger Nonlinear Programming (MINLP) that relies on accumulation of linearizations to bound the objective function and feasible region. This method solves a sequence of approximations to a mathematical program where the approximating problem contains the original feasible region. Examples are cutting plane algorithms and relaxation. This method has the potential to solve groundwater management problems related to hydraulic gradient control and/or mass transport optimization problems.
MultiPeriod Objectives and Groundwater Remediation Using SAMOA: Tandem Simulated Annealing and Extended Cutting Plane Method for Containment with Cleanup
Yu, M., D. M. Rizzo, Donna.Rizzo@subterra.com, D. E. Dougherty, David.Dougherty@subterra.com, XIII International Conference on Computational Methods in Water Resources, June 2529, 2000, Calgary, Alberta, CanadaGroundwater Management Using Numerical Simulation and the Outer Approximation Method for Global Optimization
Karatzas, G.P., karatzas@emba.uvm.edu, and G.F. Pinder, 1993, Water Resources Research, 29(10), pp. 33713378The Solution of Groundwater Quality Management Problems Have NonConvex Feasible Region Using A Cutting Plane Optimization Technique
Karatzas, G.P., karatzas@emba.uvm.edu, and G.F. Pinder, 1996, Water Resources Research, 32(4), pp. 10911100A MultiPeriod Approach for the Solution of Groundwater Management Problems Using the Outer Approximation Method
Karatzas, G.P., karatzas@emba.uvm.edu, A.A. Spiliotopoulos, and G.F. Pinder, 1996, Proceedings of the North American Water and Environment Congress '96, American Society of Civil Engineers.
 Genetic Algorithm
Genetic algorithm mimics the biological evolution based on Darwinist theory (survival of the fittest), where the strongest (or any selected) offspring in a generation are more likely to survive and reproduce. The method starts with a number of possible solutions, referred to as the first generation of the population. Each of the possible solutions is referred to as an individual, then encoded as either binary or realcoded string (called chromosome). For each individual, the objective function is evaluated. During the course of the search, new generations of individuals are reproduced from the old generations through random selection, crossover, and mutation based on certain probabilistic rules. The selection is in favor of those interim solutions with lower objective function values (in a minimization problem). Gradually, the population will evolve toward the optimal solution.
An Integrated Global and Local Optimization Approach for Remediation System Design
Zheng, C. czheng@wgs.geo.ua.edu, and P.P. Wang, 1999, Water Resources Research, 35(1), pp. 137146.Groundwater Resource Management Models: A comparison of Genetic Algorithms and Nonlinear programming
McKinney, D.C., daene_mckinney@mail.utexas.edu, G.B. Gates, and MD. Lin, 1994, Computational Methods in Water Resources X, Peters, A., et al., (eds.), pp. 859  866, Kluwer Academic Publishers, Dordrect, The NetherlandsAquifer Remediation Design: Nonlinear Programming and Genetic Algorithms
McKinney, D.C., daene_mckinney@mail.utexas.edu, G.B. Gates, and MD. Lin, 1994, Proceeding of ASCE Specialty Conference on Water Resources Planning and Management, ASCE, pp. 254257, New York, N.Y.Genetic Algorithm Solution of Groundwater Management Models
McKinney, D.C., daene_mckinney@mail.utexas.edu, and M.D. Lin, 1994, Water Resources Research, 30(6), pp.18971906Genetic Algorithms for the Design of Groundwater Remediation Systems
McKinney, D.C., daene_mckinney@mail.utexas.edu, and MD. Lin, 1996, Proceedings of North American Water and Environment Congress, ASCE, New York, N.Y.Applicability of Genetic Algorithm in Ground Water Simulation and Optimization
Morshed, J. and J.J. Kaluarachchi, jkalu@cc.usu.edu, Proceedings of ModelCARE 96, International Conference on Calibration and Reliability in Ground Water Modeling, Golden, CO, September 1996Enhancements to Genetic Algorithm for Optimal GroundWater Management
Morshed, J. and J.J. Kaluarachchi, jkalu@cc.usu.edu, 2000, Journal of Hydrologic Engineering, 5(1): pp: 6773MultiObjective DecisionMaking for Environmental Remediation
Alex Mayer^{1}, Jeff Horn^{2}, Carl Enfield^{3} Michigan Technological University^{1}, Northern Michigan University^{2}, US EPA^{3}. 2002.
 SOMOS
SOMOS has been developed by Dr. Richard Peralta, the Systems Simulation and Optimization Laboratory (SS/OL) of Utah State University, and HydroGeoSystems Group. SOMOS is a powerful, broadly applicable, and adaptable family of Simulation/Optimization (S/O) modules for hydraulic and transport optimization. SOMOS can be used to optimize cleanup and containment of any plume that can be modeled by MODFLOW and MT3DMS. SOMOS employs wide ranges of constraints and objective functions (maximize mass removal, minimize mass remaining, minimize maximum concentration remaining, minimize cost and many others). SOMOS includes genetic algorithm linked with tabu search, simulated annealing linked with tabu search, artificial neural network (ANN), and response function options. SOMOS has been used on many sites, all successfully. All pump and treat systems constructed based on SOMOS designs have operated successfully and per design. At: http://www.usurf.org/units/wdl you will be able to find directions to the most recent SOMOSWEB updates and additional references.
Aly, A.H. and R.C. Peralta. 1999. Optimal design of aquifer clean up systems under uncertainty using a neural network and a genetic algorithm. Water Resources Research, 15(8):25232532.
Peralta, R. C. 2001. Remediation sim./opt. demonstrations. In Proceedings of MODFLOW and Other Modeling Odysseys. 2001. Eds, Seo, Poeter, Zheng and Poeter, Pub. IGWMC. p. 651657.
Peralta, R. C. 2001. Simulation/optimization applications and software for optimal groundwater and conjunctive water management In Proc. MODFLOW and Other Modeling Odysseys 2001. (ed. by Seo, et al.), Pub. IGWMC, Golden, CO. p. 691694.
Peralta, R. C., Kalwij, I. M. and S. Wu. 2003. Practical simulation/optimization modeling for groundwater quality and quantity man. In MODFLOW & More 2003: Understanding through Modeling. (ed. by Poeter, et al.) IGWMC, Golden, CO. p 784788.
Peralta, R. C. 2003. SOMOS Simulation/Optimization Modeling System. In Proceedings, MODFLOW and More 2003: Understanding through Modeling. 819823.
Peralta, R. C., Kalwij, I. M. and B. Timani. 2004. Optimizing complex plume pump and treat systems for Blaine Naval Ammunition Depot, Nebraska. In Proceedings of EWRI 2004 World Congress. Am. Soc. Civil Eng. 7 p.
Systems Simulation/Optimization Laboratory and HydroGeoSystems Group. 2001. Simulation/Optimization MOdeling System (SOMOS)users manual. SS/OL, Dept. of Biological and Irrigation Engineering, Utah State University, Logan, Utah. 457 p.
For additional references go to: http://www.usurf.org/units/wdl