Multi-objective optimal design of groundwater remediation systems: application of the niched Pareto genetic algorithm (NPGA)

Abstract A multiobjective optimization algorithm is applied to a groundwater quality management problem involving remediation by pump-and-treat (PAT). The multiobjective optimization framework uses the niched Pareto genetic algorithm (NPGA) and is applied to simultaneously minimize the (1) remedial design cost and (2) contaminant mass remaining at the end of the remediation horizon. Three test scenarios consider pumping rates for two-, five-, and 15 fixed-location wells as the decision variables. A single objective genetic algorithm (SGA) formulation and a random search (RS) are also applied to the three scenarios to compare performances with NPGA. With 15 decision variables, the NPGA is demonstrated to outperform both the SGA algorithm and the RS by generating a better tradeoff curve. For example, for a given cost of $100,000, the NPGA solution found a design with 75% less mass remaining than the corresponding RS solution. In the 15-well scenario, the NPGA generated the full span of the Pareto optimal designs, but with 30% less computational effort than that required by the SGA. The RS failed to find any Pareto optimal solutions. The optimal population size for the NPGA was found by sensitivity analysis to be approximately 100, when the total computational cost was limited to 2000 function evaluations. The NPGA was found to be robust with respect to the other algorithm parameters (tournament size and niche radius) when using an optimal population size. The inclusion of niching produced better results in terms of covering the span of the tradeoff curve. As long as some niching was included, the results were insensitive to the value of the parameter that controls niching ( σ share >0).

[1]  Jeffrey Horn,et al.  Multiobjective Optimization Using the Niched Pareto Genetic Algorithm , 1993 .

[2]  Robert A. Marryott,et al.  Optimal Groundwater Management: 1. Simulated Annealing , 1991 .

[3]  Peter J. Fleming,et al.  Multiobjective optimization and multiple constraint handling with evolutionary algorithms. I. A unified formulation , 1998, IEEE Trans. Syst. Man Cybern. Part A.

[4]  Susan D. Pelmulder,et al.  On the development of a new methodology for groundwater‐Driven health risk assessment , 1998 .

[5]  A. Mayer,et al.  Pump‐and‐treat optimization using well locations and pumping rates as decision variables , 1997 .

[6]  John J. Grefenstette,et al.  Genetic algorithms and their applications , 1987 .

[7]  R. Allan Freeze,et al.  Convergence of Stochastic Optimization and Decision Analysis in the Engineering Design of Aquifer Remediation , 1999 .

[8]  David E. Goldberg,et al.  Genetic Algorithms with Sharing for Multimodalfunction Optimization , 1987, ICGA.

[9]  Gunar E. Liepins,et al.  Some Guidelines for Genetic Algorithms with Penalty Functions , 1989, ICGA.

[10]  Jeffrey Horn,et al.  The nature of niching: genetic algorithms and the evolution of optimal, cooperative populations , 1997 .

[11]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[12]  Jonathan F. Sykes,et al.  Alternative Formulations for Optimal Ground-Water Remediation Design , 1995 .

[13]  T. Culver,et al.  Constraint Handling for Genetic Algorithms in Optimal Remediation Design , 2000 .

[14]  S. Ranjithan,et al.  Using genetic algorithms to solve a multiple objective groundwater pollution containment problem , 1994 .

[15]  Bithin Datta,et al.  Development of multiobjective management models for coastal aquifers , 1999 .

[16]  Vernon L. Snoeyink,et al.  Evaluating GAC adsorptive capacity , 1983 .

[17]  Charles S. Sawyer,et al.  Groundwater Remediation Design Using a Three‐Dimensional Simulation Model and Mixed‐Integer Programming , 1995 .

[18]  P. Gill,et al.  Aquifer Reclamation Design: The Use of Contaminant Transport Simulation Combined With Nonlinear Programing , 1984 .

[19]  Graham E. Fogg,et al.  Random-Walk Simulation of Transport in Heterogeneous Porous Media: Local Mass-Conservation Problem and Implementation Methods , 1996 .

[20]  Steven M. Gorelick,et al.  A model for managing sources of groundwater pollution , 1982 .

[21]  J. Eheart,et al.  Using Genetic Algorithms to Solve a Multiobjective Groundwater Monitoring Problem , 1995 .

[22]  B. Wagner.  Recent advances in simulation-optimization groundwater management modeling (95RG00394) , 1995 .

[23]  D. McKinney,et al.  Genetic algorithm solution of groundwater management models , 1994 .

[24]  David E. Goldberg,et al.  A niched Pareto genetic algorithm for multiobjective optimization , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[25]  J. David Schaffer,et al.  Proceedings of the third international conference on Genetic algorithms , 1989 .