Application of Heuristic Optimization Techniques and Algorithm Tuning to Multilayered Sorptive Barrier Design L. SHAWN MATOTT, † SHANNON L. BARTELT-HUNT, ‡ ALAN J. RABIDEAU,* ,† AND K. R. FOWLER § Department of Civil, Structural, and Environmental Engineering, University at Buffalo, 207 Jarvis Hall, Buffalo, New York 14260, Department of Civil Engineering, University of NebraskasLincoln, 203B Peter Kiewit Institute, Omaha, Nebraska 68182-0178, and Department of Mathematics and Computer Science, Clarkson University, P.O. Box 5815, Potsdam, New York 13699-5815 Although heuristic optimization techniques are increasingly applied in environmental engineering applications, algorithm selection and configuration are often approached in an ad hoc fashion. In this study, the design of a multilayer sorptive barrier system served as a benchmark problem for evaluating several algorithm-tuning procedures, as applied to three global optimization techniques (genetic algorithms, simulated annealing, and particle swarm optimization). Each design problem was configured as a combinatorial optimization in which sorptive materials were selected for inclusion in a landfill liner to minimize the transport of three common organic contaminants. Relative to multilayer sorptive barrier design, study results indicate (i) the binary-coded genetic algorithm is highly efficient and requires minimal tuning, (ii) constraint violations must be carefully integrated to avoid poor algorithm convergence, and (iii) search algorithm performance is strongly influenced by the physical-chemical properties of the organic contaminants of concern. More generally, the results suggest that formal algorithm tuning, which has not been widely applied to environmental engineering optimization, can significantly improve algorithm performance and provide insight into the physical processes that control environmental systems. Introduction Heuristic optimization algorithms have been applied to an increasing number of environmental engineering applica- tions because they are capable of overcoming common challenges of environmental problems, such as extreme nonlinearity, mixed parameter types, and the presence of local minima and/or discontinuities. With a few notable exceptions (e.g., refs 1-4), comparisons of alternative search algorithms are uncommon and often characterized by ad- hoc algorithm selection and configuration. Rardin and Uzsoy (5) argue that meaningful comparisons should be anchored by a procedure (known as algorithm tuning) in which each optimization algorithm is adapted to the specific problem under consideration to maximize algorithm performance. While algorithm tuning is uncommon in environmental studies, several systematic approaches have been proposed in the optimization literature, including the use of experi- mental techniques and/or sensitivity analysis (6), the de- velopment of self-adaptive algorithms (7), and the use of meta-optimization algorithms (8). The present work focuses on algorithm tuning via experimental techniques and, in particular, adopts the Taguchi design of experiments (DOE) approach (9), a popular method within process engineering for tuning various manufacturing processes. While Beielstein et al. (10) applied Taguchi analysis to several benchmark optimization problems, the present approach differs from ref 10 by (i) considering nonlinear behavior and interactions among tuning parameters, (ii) performing confirmation of tuning effectiveness, (iii) comparing multiple search algo- rithms, and (iv) examining a real-world environmental application. The optimization studies considered in this paper involve the design of multilayer sorptive landfill liners, an application that is representative of a broad class of remediation problems involving multiple sequential barriers or treatment units. While subsurface barrier design frequently emphasizes the minimization of advection through low permeability materi- als, several studies have demonstrated the significance of diffusion (11, 12), and this has motivated an interest in low permeability sorbing barriers capable of simultaneously controlling both advective and diffusive contaminant trans- port (13, 14). Numerous studies have modeled contaminant transport through barrier systems (15), and a few have investigated optimal barrier design using a simulation-optimization approach (16). The benchmark application for this study was a multilayer sorptive liner design problem developed in ref 16, in which sorptive materials are added to a multilayer liner to inhibit organic solute transport. A detailed problem description is provided in the Supporting Information (SI). Transport of three organic solutes [benzene, trichloroethylene (TCE), and 1,2-dichlorobenzene (1,2-DCB)] with different nonlinear sorption behavior was considered, resulting in three distinct optimization problems. This study makes a dual contribution by investigating a formal algorithm tuning methodology in the context of an important class of environmental engineering problems. Specific research objectives were to (i) assess the performance of several heuristic algorithms by comparing alternative formulations, using a DOE approach to enhance the efficiency and robustness of the process, (ii) explore techniques for integrating design constraints into the liner cost function, (iii) examine relationships between algorithm performance and liner problem formulation, and (iv) assess the merits of the Taguchi DOE approach as a formal algorithm tuning procedure. For each liner problem and for a variety of con- straint integration methods, three popular heuristic search procedures [particle swarm optimization (PSO) (17), genetic algorithms (GA) (18), and simulated annealing (SA) (19)] were applied, tuned, and compared. Algorithm analysis focused on measures of efficiency (amount of computation time required, in terms of objective function evaluations) and effectiveness (ability of an algorithm to identify the globally optimal design) and was aided by the identification of the true global optimum for each liner problem, determined via an exhaustive search involving millions of simulations on a massively parallel computing system. * Corresponding author phone: (716)645-2114 ext. 2327; fax: (716)645-3667; e-mail: rabideau@eng.buffalo.edu. † University at Buffalo. ‡ University of NebraskasLincoln. § Clarkson University. Environ. Sci. Technol. 2006, 40, 6354-6360 6354 9 ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 40, NO. 20, 2006 10.1021/es052560+ CCC: $33.50  2006 American Chemical Society Published on Web 09/21/2006