Transport Optimization:
Methods & Codes

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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 simulation-optimization 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 gradient-based 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: 0-442-01348-5; 1997, John Wiley & Sons, ISBN: 0-471-28536-6

• Parameter Structure Identification Using Tabu Search and Simulated Annealing
  Zheng, C. and P.P. Wang, 1996, Advances in Water Resources, 19(4), pp.215-224

• Optimal Remediation Policy Selection under General Conditions
  Wang, M. and C. Zheng, 1997, Ground Water, 35(5), pp.757-764
• 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.519-530
• An Integrated Global and Local Optimization Approach for Remediation System Design
  Zheng, C., and P.P. Wang, 1999, Water Resources Research, 35(1), pp.137-146

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• 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. 2415-2425
     
  • 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. 2523-2532

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• ATOPT – Advective Transport Optimization
  Ann E. Mulligan, amulligan@whoi.edu, Woods Hole Oceanographic Institution, and David P. Ahlfeld, ahlfeld@ecs.umass.edu, University of Massachusetts

  ATOPT 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. 23-44.

  • A New Code for MODFLOW-Coupled Groundwater Management of Unconfined Aquifers
    Ahlfeld, D.P., R.G. Riefler, and A.E. Mulligan, 1998, Proceedings of MODFLOW'98 Conference, October 4-8, 1998, Golden, Colorado, pp. 431-438

  • Optimal 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. 2285-2294.
  • 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): 636-644.
  • 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 15-19, 1998, p. 83-89.

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• 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, non-isothermal flows in fractured-porous 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 LBNL-46746, Lawrence Berkeley National Laboratory, Berkeley, CA

  • Using Simulation-Optimization Techniques to Improve Multiphase Aquifer Remediation
    Finsterle, S., and K. Pruess, 1995, Proceedings, TOUGH Workshop '95, March 20-22, p. 181-186, Report LBL-37200, Lawrence Berkeley Laboratory, Berkeley, CA

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• 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. 19-39.

  • 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. 415-427.

  • Dynamic Optimal Control for Groundwater Remediation with Flexible Management Periods
    Culver, T.B., and C.A. Shoemaker, 1992, Water Resources Research, 28(3), pp. 629-641.

  • Optimal Control for Groundwater Remediation by Differential Dynamic Programming with Quasi-Newton Approximations
    Culver, T.B., and C.A. Shoemaker, 1993, Water Resources Research, 29(4), pp. 823-831.

  • Nonlinear Weighted Feedback Control of Groundwater Remediation under Uncertainty
    Whiffen, G.J., and C.A. Shoemaker, 1993, Water Resources Research, 29(9), pp. 3277-3289.

  • Approximate Mixed-Integer Nonlinear Programming Methods for Optimal Aquifer Remediation Design
    McKinney, D.C., and M-D. Lin, 1995, Water Resources Research, 31(3), pp. 731-740

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• 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. 2493-2508

  • Design 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.2549-2561

  • Multi-Period 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 25-29, 2000, Calgary, Alberta, Canada

  • Developing OptimalWater Resources Management Strategies
    Aly, A.H., aly@waterstoneinc.com, and Sean W. Fleming, WaterStone Environmental Hydrology and Engineering, Inc.

  • Reducing Costs of Pump-And-Treat 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., and P.P. Wang, 1996, Advances in Water Resources, 19(4), pp. 215-224.

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• 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 information-passing 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. 861-867

  • Neural-Network-Based 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. 563-574

  • Characterization 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. 483-497

  • Optimization 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. 457-481

  • Optimal 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. 2523-2532.

  • An Adaptive Long-Term 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 Conference

  • Determining 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

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• Outer Approximation

  The outer approximation is an algorithm for Mixed-Integer 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.

  • Multi-Period 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 25-29, 2000, Calgary, Alberta, Canada

  • Groundwater 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. 3371-3378

  • The Solution of Groundwater Quality Management Problems Have Non-Convex 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. 1091-1100

  • A Multi-Period 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.

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• 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 real-coded 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. 137-146.

  • Groundwater Resource Management Models: A comparison of Genetic Algorithms and Nonlinear programming
    McKinney, D.C., daene_mckinney@mail.utexas.edu, G.B. Gates, and M-D. Lin, 1994, Computational Methods in Water Resources X, Peters, A., et al., (eds.), pp. 859 - 866, Kluwer Academic Publishers, Dordrect, The Netherlands

  • Aquifer Remediation Design: Nonlinear Programming and Genetic Algorithms
    McKinney, D.C., daene_mckinney@mail.utexas.edu, G.B. Gates, and M-D. Lin, 1994, Proceeding of ASCE Specialty Conference on Water Resources Planning and Management, ASCE, pp. 254-257, 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.1897-1906

  • Genetic Algorithms for the Design of Groundwater Remediation Systems
    McKinney, D.C., daene_mckinney@mail.utexas.edu, and M-D. 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 1996

  • Enhancements to Genetic Algorithm for Optimal Ground-Water Management
    Morshed, J. and J.J. Kaluarachchi, jkalu@cc.usu.edu, 2000, Journal of Hydrologic Engineering, 5(1): pp: 67-73

  • Multi-Objective Decision-Making for Environmental Remediation
    Alex Mayer¹, Jeff Horn², Carl Enfield³ Michigan Technological University¹, Northern Michigan University², US EPA³. 2002.

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• 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):2523-2532.

  • 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. 651-657.

  • Peralta, R. C. 2001. Simulation/optimization applications and software for optimal ground-water and conjunctive water management In Proc. MODFLOW and Other Modeling Odysseys 2001. (ed. by Seo, et al.), Pub. IGWMC, Golden, CO. p. 691-694.

  • 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 784-788.

  • Peralta, R. C. 2003. SOMOS Simulation/Optimization Modeling System. In Proceedings, MODFLOW and More 2003: Understanding through Modeling. 819-823.

  • 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

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