Multi-objective optimization for free-phase LNAPL recovery using evolutionary computation algorithms

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Multi-objective optimization for free-phase LNAPLrecovery using evolutionary computation algorithmsZoi Dokou a & George P. Karatzas aa Department of Environmental Engineering, Technical University of Crete, Chania, 73100,Greece E-mail:Version of record first published: 15 Feb 2013.

To cite this article: Zoi Dokou & George P. Karatzas (2013): Multi-objective optimization for free-phase LNAPL recovery usingevolutionary computation algorithms, Hydrological Sciences Journal, DOI:10.1080/02626667.2012.754103

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1Hydrological Sciences Journal – Journal des Sciences Hydrologiques, 2013http://dx.doi.org/10.1080/02626667.2012.754103

Multi-objective optimization for free-phase LNAPL recovery usingevolutionary computation algorithms

Zoi Dokou and George P. Karatzas

Department of Environmental Engineering, Technical University of Crete, Chania 73100, [email protected]

Received 12 April 2012; accepted 13 September 2012; open for discussion until 1 August 2013

Editor Z.W. Kundzewicz; Associate editor L. See

Citation Dokou, Z. and Karatzas, G.P., 2013. Multi-objective optimization for free-phase LNAPL recovery using evolutionarycomputation algorithms. Hydrological Sciences Journal, 58 (2), 1–15.

Abstract A nonlinear, multi-objective optimization methodology is presented that seeks to maximize free productrecovery of light non-aqueous phase liquids (LNAPLs) while minimizing operation cost, by introducing the novelconcept of optimal alternating pumping and resting periods. This process allows more oil to flow towards theextraction wells, ensuring maximum free product removal at the end of the remediation period with minimumgroundwater extraction. The methodology presented here combines FEHM (Finite Element Heat and Mass transfercode), a multiphase groundwater model that simulates LNAPL transport, with three evolutionary algorithms: thegenetic algorithm (GA), the differential evolution (DE) algorithm and the particle swarm optimization (PSO)algorithm. The proposed optimal free-phase recovery strategy was tested using data from a field site, located nearAthens, Greece. The PSO and DE solutions were very similar, while that provided by the GA was inferior, althoughthe computation time was roughly the same for all algorithms. One of the most efficient algorithms (PSO) waschosen to approximate the optimal Pareto front, a method that provides multiple options to decision makers. Whenthe optimal strategy is implemented, although a significant amount of LNAPL free product is captured, a spreadingof the LNAPL plume occurs.

Key words free product LNAPL recovery; multi-objective optimization; Pareto front; genetic algorithm; differential evolution;particle swarm optimization

Optimisation multi-objectif utilisant des algorithmes d’évolution pour la récupération de LLPNAlibresRésumé Nous présentons une méthode d’optimisation non-linéaire et multi-objectif visant à maximiser larécupération de liquides légers en phase non aqueuse (LLPNA) tout en minimisant les coûts d’exploitation, enintroduisant une nouvelle stratégie de périodes optimales de pompage et de pause alternées. Ce procédé permetl’écoulement de davantage de pétrole vers les puits d’extraction, et assure une élimination maximum de produit àla fin de la période de dépollution tout en minimisant l’extraction d’eaux souterraines. La méthodologie présen-tée ici combine FEHM, un modèle d’écoulement souterrain multiphasique simulant le transport des LLPNA,avec trois algorithmes d’évolution: l’algorithme génétique (AG), l’algorithme à évolution différentielle (ED) etl’optimisation par essaims particulaires (OEP). Cette stratégie de récupération a été testée à l’aide des donnéesd’un site situé près d’Athènes, en Grèce. Les solutions de l’OEP et l’ED étaient très similaires tandis que celle del’AG était moins intéressante, alors que le temps d’exécution était à peu près le même pour tous les algorithmes.L’algorithme le plus performant (OEP) a été choisi pour se rapprocher du front de Pareto optimal, méthode quioffre plusieurs options aux décideurs. Lorsque la stratégie optimale est mise en œuvre, même si une quantitéimportante de LLPNA est récupérée, on observe cependant la propagation d’un panache de LLPNA.

Mots clefs récupération de LLPNA libres; optimisation multi-objectif; front de Pareto; algorithme génétique; algorithme àévolution différentielle; optimisation par essaims particulaires

© 2013 IAHS Press

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mailto:[email protected]

mailto:[email protected]

2 Zoi Dokou and George P. Karatzas

INTRODUCTION

Light non-aqueous phase liquids (LNAPLs) suchas petroleum hydrocarbons (oil, gasoline, dieseletc.) and organic solvents are responsible for thecontamination of groundwater reserves worldwide.Problems associated with these contaminants arisefrom disposal dumps, petroleum refineries, leakingstorage tanks and pipelines and accidental spills(Chrysikopoulos et al. 2003). There exist numeroussites worldwide (Hinchee et al. 1991, Lu et al. 1999,Bass et al. 2000, Banks et al. 2003, Khaitan et al.2006, Gidarakos and Aivalioti 2007, Qin et al. 2008)that have been contaminated by LNAPLs and thenumber is growing rapidly.

LNAPL migration is a complex process that isaffected by various parameters, the most importantof them being gravity forces, which cause verticalmigration, and capillary forces, which cause hori-zontal spreading. During the vertical migration ofLNAPL some will remain behind, trapped in thevadose zone (residual saturation). When LNAPLreaches the capillary zone it accumulates, creatingan oil table that rests directly above the water table,often causing a depression on the water table due toits weight. Finally, some of the LNAPL partitions intothe groundwater through dissolution causing long-term groundwater contamination (Qin et al. 2009).

Successful remediation of contaminated sites isessential for the protection of human health, butit can prove to be a costly and time consumingtask. To this end, researchers have directed theirefforts towards developing tools that can improve thetime-efficiency and cost-effectiveness of groundwaterremediation strategies. Such tools are algorithms thatcouple groundwater contaminant transport simula-tion models with optimization techniques (Dokou andKaratzas 2010).

Since the LNAPL remediation process involvesdifferent tasks, such as clean-up of the residualLNAPL phase, free-product recovery and removal ofthe dissolved phase, various techniques have beendeveloped to accomplish the optimization of eachtask. In recent years, most researchers have focusedon optimizing the removal of LNAPLs dissolved ingroundwater using the pump-and-treat method, whichhas been the most commonly-used remediation strat-egy (Gorelick et al. 1984, Ahlfeld et al. 1988, Changet al. 1992, Culver and Shoemaker 1992, Karatzasand Pinder 1993, 1996, Johnson and Rogers 1995,Rizzo and Dougherty 1996, Papadopoulou et al.2003, 2007, Hilton and Culver 2005, Babbar andMinisker 2006).

Several studies have also been devoted to opti-mizing bioremediation designs using a variety ofmethods, such as: analytical derivatives (Minskerand Shoemaker 1996, 1998); evolutionary algo-rithms (binary-coded genetic algorithm, real-codedgenetic algorithm and derandomized evolution strat-egy); direct search methods and derivative-based opti-mization methods (Yoon and Shoemaker 1999); mul-tiscale derivatives (Liu and Minisker 2002, 2004);a genetic algorithm integrated with constrained dif-ferential dynamic programming (Hsiao and Chang2002); and a combination of stepwise cluster analysis,nonlinear optimization and artificial neural networks(Huang et al. 2006).

Other researchers have focused on optimiz-ing different remediation techniques, such asbioslurping—using a set of regression submodelsdescribing the system response to water and gaspumping and oil skimming in hydrocarbon recovery(Yen and Chang 2003), bioventing (Diele et al.2002) and soil vapour extraction (SVE)—using amixed-integer programming model to determinethe optimum number of wells, their locations andpumping rates (Sawyer and Kamakoti 1998).

There are a few studies that have attemptedto optimize free product recovery of LNAPLs.Specifically, Cooper et al. (1998) presented a method-ology for optimizing free product recovery froma single well that combines simulation, nonlinearregression and optimization, neglecting the economicaspects of the problem. They used MINOS, an opti-mization algorithm that solves linear or nonlinearproblems. In order to solve nonlinear problems it uti-lizes projected Lagrangian and augmented reduced-gradient algorithms. Qin et al. (2007) coupled numer-ical modelling, a multivariate regression method anda genetic algorithm to optimize a vacuum-enhancedfree product recovery (VFPR) process. Their methodincluded environmental and economic effects, andprovided a means to analyse the trade-offs betweenthem. A related work by Qin et al. (2008) optimizeda similar process, namely the dual-phase vacuumextraction (DPVE), using a multiphase flow simula-tor and cluster analysis in conjunction with a geneticalgorithm to solve a multi-objective optimizationproblem.

Optimizing free-phase product recovery is acomplex problem that usually involves multipleconflicting objectives, such as the requirement ofminimizing the remediation cost while taking intoaccount the environmental aspects (maximizationof free product recovery). Thus, multi-objectiveformulations are of great use when trying to solve

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Multi-objective optimization for free-phase LNAPL recovery 3

such problems. Multi-objective optimization modelshave been employed by researchers in order to solvesimilar problems. Ritzel et al. (1994) used a geneticalgorithm to solve a multi-objective groundwater pol-lution containment problem (vector-evaluated GAand Pareto GA). Erickson et al. (2002) used a nichedPareto genetic algorithm for the optimization ofa pump-and-treat system that simultaneously mini-mizes the remedial cost and the contaminant masswhich remains at the end of the remediation period.McPhee and Yeh (2006) developed an experimentaldesign-based methodology for groundwater manage-ment using multi-objective programming for param-eter estimation that was solved by combination ofa genetic algorithm and gradient-based optimizationtechniques.

Recently, there has been a growing inter-est in using evolutionary algorithms for solvinggroundwater remediation problems. These modelsare global, population-based methods that provide analternative to traditional linear or nonlinear optimiza-tion models. The disadvantage of using linear opti-mization methods is that the linearity assumption isoften unrealistic in field applications. While conven-tional nonlinear methods (classical, dynamic, mixed-integer) have a strong mathematical representation,they are not very attractive for real-world applicationsdue to the large requirements in computational effortrelated to complex nonlinear manipulations (Qin et al.2009). Specific to the problems of pump-and-treat,or free product recovery, the functions of variousgroundwater system components (e.g. system cost)may be discontinuous or highly complicated; thus, thecalculation of the related derivatives with respect tothe decision variables can be problematic (McKinneyand Lin 1994). This renders evolutionary algorithmsmore attractive for solving this type of problems. Theinterested reader is referred to Mayer et al. (2002) andQin et al. (2009) for an extensive literature review ofthe recent developments associated with optimizationtechniques applied to site remediation.

As a continuation of the work performed pre-viously, the focus of this paper is to developa simulation-optimization model that couples amultiphase flow simulation model using three evo-lutionary algorithms: the genetic algorithm (GA),the differential evolution (DE) algorithm and theparticle swarm optimization (PSO) method, takinginto account both the environmental and economicaspects of the remediation problem. More specifi-cally, the goal is to achieve maximum LNAPL freeproduct removal at least cost by optimizing boththe pumping rates on each well and the remediation

time. A concept that has not been previously mod-elled or optimized is introduced in this work. Thisconcept involves optimal alternating pumping andresting periods, to allow more oil to flow towardsthe extraction wells, ensuring maximum free prod-uct removal at the end of the remediation period withminimum groundwater extraction. The performanceof the proposed optimal free-phase recovery algo-rithms (GA, DE and PSO) is compared using datafrom a field site contaminated with LNAPLs, locatednear Athens, Greece. Then, one of the most efficientalgorithms (PSO) was chosen in order to approxi-mate the optimal Pareto front as a means of providinginsight into the trade-offs between the two objec-tives, information critical for the decision-makingprocess.

METHODOLOGY

Multiphase flow simulator

For the purpose of simulating the LNAPL transportin the subsurface, FEHM (Finite Element Heat andMass transfer code), a groundwater model developedby the Los Alamos National Laboratory, USA, wasused. This model was initially designed to assist inthe understanding of flow fields and mass transportin the saturated and unsaturated zones below the areaof the Yucca Mountain, which is both hydrologicallyand geologically complex. Its purpose is to simulatemass transfer for multiphase flow within porous andpermeable media, and noncondensible gas flow withinporous and permeable media (Zyvoloski et al. 1999).

In this work, isothermal NAPL-water transportwas assumed. This assumption is generally valid forshallow subsurface transport, where pressure is prac-tically constant and physicochemical properties arenot affected significantly by temperature fluctuations(Chen et al. 2006). The model uses a pressure formu-lation and solves two conservation equations; one forliquid (free-phase) NAPL and one for liquid water:

ε∂Sl(x, t)

∂t+ ∇ · ql(x, t) = Fl(x, t) (1)

ql(x, t) = −λl(x, t) [∇ · Pl(x, t) + ρlg] (2)

λl(x, t) = k(x)krl Sl(x, t)

μl(3)

The above equations are subject to the followinginitial conditions:

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Pl(x, 0) = Pl0(x), x ∈ �

Pl(x, t) = Plt(x, t), x ∈ ΓA

ql(x, t) · n(x) = Ql(x, t), x ∈ ΓB

(4)

where l denotes liquids (l = w for water and l = n forNAPL); Sl are the water or NAPL saturations, withSw + Sn = 1; ql(x,t) are the water or NAPL fluxes;Fl(x,t) is a source or sink term; λl(x,t) is liquid mobil-ity; Pl(x,t) is the fluid pressure; ρl is fluid density;k(x) is the intrinsic permeability of the porous media;krl is the water or NAPL relative permeability; μl isthe liquid dynamic viscosity; Pl0(x) is the initial pres-sure in the domain; Plt(x,t) is the prescribed pressureon a Dirichlet boundary segment Γ A; Ql(x,t) is theprescribed fluid flux across Neumann boundary seg-ments Γ B; g is the gravity vector; n(x) is the outwardunit vector normal to the boundary Γ B and ε is theporosity. The input to the model consists of an initialdescription of the fluid pressure as well as media prop-erties. The output consists of the final fluid pressureand the volume fraction of water-NAPL (Zyvoloskiet al. 1999).

For the capillary pressure and saturation relation-ship, the Brooks-Corey model was used based on thework of Reitsma and Kueper (1994), who conductedan experiment on fractured rock in order to measurethe relationship between capillary pressure and sat-uration, and concluded that the Brooks-Corey modelbest fits the laboratory data. The Brooks-Corey modelis described by the following equations:

Pc = Pd(Se)−1λ (5)

Se = Sw − Sr

1 − Sr(6)

where Pc is the capillary pressure; Pd is the entry

pressure; Se is the normalized water saturation; Sw

is the water saturation; λ is a pore size distributionindex; and Sr is a curve-fitting parameter represent-ing the irreducible water saturation. The above modelwas chosen for this particular application becausethe main geological formation found in the area ofinterest is fractured limestone.

Optimization problem

Problem formulation The objective of the pro-posed optimization algorithm is twofold: maximiz-ing the remediation efficiency (LNAPL free productremoval) while minimizing operation cost. The

extraction well locations and number were assumedfixed; thus, the capital cost associated with theirconstruction was not included in the objective func-tion. It has been observed in the field that, in orderto ensure maximum product removal, the pumpingshould be followed by a resting period that willenable the LNAPL product to flow towards the extrac-tion wells before pumping is started again. Thus, inthe optimization formulation the remediation periodcomprised two parts: a pumping period and a rest-ing period. Consequently, the decision variables ofthe problem were the NAPL pumping rates for eachwell, and the pumping and resting times. The numberof pumping–resting alternations was assumed fixed.LNAPL pumping rates instead of total liquid (oil pluswater) rates were used in the optimization problem tomodel the operation of the oil pumps that were usedin the field. These pumps were automatically turnedoff when the entire free product volume present in thewell was pumped, and started pumping again whenmore oil flowed in the well at the end of the rest-ing period. This way, a minimal amount of water ispumped from the aquifer.

The first objective of the optimization problem isassociated with the economic aspect of the free prod-uct recovery, in this case the operation cost that isdirectly proportional to the pumping rate and dura-tion, and is described by the following equation:

min c1

n∑i=1

ti

m∑j=1

Qj (7)

where c1 is the unit cost of operation; ti is the durationof each pumping period; n is the number of pumpingsub-periods; Qj the pumping rate of each well; and mis the number of pumping wells.

The second objective involves the environmentalconsiderations of the problem that are represented inthis work by the maximization of free product removalfrom all extracting wells during the entire remediat-ion period, which is described by the followingequation:

maxn∑

i=1

m∑j=1

Vij (8)

where Vij is the LNAPL free-phase volume recoveredduring each pumping period i from each extractionwell j.

In single-objective optimization problems, themain focus is on the decision variable space, whilein a multi-objective concept the interest switchesto the objective space. Due to the contradiction of

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the objective functions, it is not possible to find asingle optimal solution for all of them simultane-ously (Miettinen et al. 1998). A simple and commonapproach to overcome this problem is to combine theobjectives into a single objective function, assigningweights to each of them according to their relativeimportance (conventional weighted aggregation):

min w1c1

n∑i=1

ti

m∑j=1

Qj − w2

n∑i=1

m∑j=1

Vij (9)

where w1 and w2 are weights that define the relativeimportance of the two terms of the objective function.

An alternative to optimizing the objective func-tion with fixed weights as presented above, is todetermine a set of “Pareto optimal” designs. When thePareto optimal set is considered, a better understand-ing of the trade-offs between the two objectives isobtained. Usually, the weights are defined accordingto the decision maker’s preferences. The main charac-teristic of the points on a Pareto optimal front is thatthese are dominant, meaning that there exist no otherpoints that have smaller values for both the objectives.

In this work, two tests were done: in the first test,three optimization algorithms were compared (GA,DE and PSO) using fixed weights. In the second test,one of the most efficient algorithms (PSO) was usedin order to approximate the Pareto optimal front, per-forming multiple runs in order to span a range ofsets of weights, under the assumption that the sum-mation of the weights should equal 1 (w1 + w2 = 1).A comparable work was performed by Schaerlaekenset al. (2006) for the remediation of DNAPL contami-nation using the shuffled complex evolution algorithm(SCE).

Solution algorithms Classical optimizationalgorithms are not convenient when dealing withmulti-objective problems. The motivation behindthe choice of the three evolutionary algorithms—thegenetic algorithm (GA), the differential evolution(DE) algorithm and the particle swarm optimization(PSO)—for this problem was based on the factthat, unlike traditional gradient-based methods,population-based algorithms are less likely to gettrapped in local minima; in addition, they are ableto deal with non-differentiable and non-convexfunctions (Abido 2002).

Evolutionary algorithms are stochastic searchmethods inspired by natural biological evolution.A fixed-size population (NP) of potential solutions

is required to initialize the process. The initial pop-ulation should cover the entire parameter space andin most cases it is created randomly. The next stepinvolves the evolution of the population using geneticoperators such as crossover and mutation in orderto find superior solutions. The newly created popu-lation is then used in the next iteration (generation)of the algorithm until a stopping criterion terminatesthe process. The stopping criterion can be either inthe form of a maximum number of generations or asatisfactory fitness level. Even if the algorithm hasterminated due to a maximum number of generations,a satisfactory solution cannot be always guaranteed(Qin et al. 2009).

Genetic algorithmDuring each iteration of a genetic algorithm, individ-uals from the previous population are selected usingsome selection scheme, and are combined (crossover)in order to form a new population. Some of thoseindividuals will undergo mutation, which is a randomchange in one or more of their chromosomes. Thenumber of individuals that will be combined and/ormutated is determined by the crossover and mutationprobabilities respectively. The rest of the individualswill enter the new population unchanged (Goldberg1989).

Traditional genetic algorithms are binary coded.Nevertheless, when applied to real-world problems,real-coded evolutionary algorithms have proved morecomputationally efficient and easier to implement(Yoon and Shoemaker 2001). For this reason, inthis work a real-coded genetic algorithm was used.In addition, special attention was paid, in adopting an“elitist” scheme by replacing the individual with thelowest fitness at each generation with the best indi-vidual found up to that generation, in order to ensurethe preservation of the best solution throughout theprocedure.

Differential evolution algorithmIn DE algorithms (created by Storn and Price 1997),new individuals are created through the process ofmutation by adding the weighted difference betweentwo individuals (xr2,G, xr3,G) and a third (xr1,G), inorder to create what is called the mutated vector(ui,G+1) according to the following equation:

ui,G+1 = xr1,G + F(xr2,G − xr3,G) (10)

where r1, r2 and r3 (i = 1, 2, 3, . . . , NP) are mutuallydifferent random indexes and F is a scaling parameterbetween 0 and 2.

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The mutated vector is combined with a randomlychosen individual of the population, called the targetvector xi,G, in order to produce a trial vector uji,G+1,through the process of crossover:

uji,G+1 ={

u′ji,G+1 if randb(j) ≤ CR or j = rnbr(i)xji,G if randb(j) > CR and j �= rnbr(i)

}

j = 1, 2, . . . , D

(11)

where randb(j) is the jth evaluation of a uniform ran-dom number generator with outcome [0,1] and rnbr(i)is a randomly chosen index that ensures that uji,G+1

gets at least one parameter from u′ji,G+1 and D is the

dimensional parameter space.Finally, the fitness of the trial vector is compared

to that of the target vector and if it is greater, the trialvector replaces the target vector in the next genera-tion (selection process). During each iteration, everyindividual has to serve once as the target vector (Stornand Price 1997).

Particle swarm optimization algorithmThe PSO algorithm mimics the behaviour of swarmsof animals. In this method, each individual is con-sidered as a particle in multidimensional space witha specific position and velocity that keeps track ofthe best position it has achieved so far (Eberhart andKennedy 1995). The collection of particles is calleda swarm, a term analogous to the population term inGAs and DEs. At each iteration, a particle moves toa new position in space by adding a velocity to itscurrent position. The velocity term is a random com-bination of three components: one causing the particleto continue moving in the direction it was moving inthe previous iteration (inertia component), one caus-ing the particle to move towards the best position ithas ever been in (cognitive component) and a thirdsteering the particle towards the best position of anyparticle of the entire swarm or in its neighbourhood(social component).

This can be summarized by:

vi(t) = vi(t − 1) + φ1rand1(pi − xi(t − 1)

)

+ φ2rand2(pg − xi(t − 1)

) (12)

xi = xi(t − 1) + vi(t) (13)

where vi is the velocity of the particle; φ1 and φ2

are positive numbers (weights); rand1 and rand2 are

uniformly-distributed random numbers in the range[0,1]; and pi and pg are the best previously recordedpositions of the ith particle and of the entire swarm,respectively. During the implementation of the PSO,

there are certain parameters that need to be takeninto account in order to avoid the “explosion” of theswarm, and to speed convergence. These include theselection of the maximum velocity, the accelerationconstant and the constriction factor or inertia constant(del Valle et al. 2008). In the literature, different meth-ods are given to define these parameters. In this work,the maximum velocity is limited using a multiplierthat is usually between 0 and 1 as follows:

vmax = kxmax (14)

where k is the multiplier and xmax is the upper boundof the variable.

The acceleration constant controls the movementof the particle driven by its own experience (φ1) andthe experiences of the other particles of the swarm(φ2). It has been found empirically that, even whenthe maximum velocity and the acceleration constantare defined correctly, the particles may still diverge.There are widely-used methods that can overcomethis problem: the constriction factor method (Clercand Kennedy 2002) and the inertia weight method(Shi and Eberhart 1998). The method selected hereinis the constriction factor method which updates equa-tion (12) as follows:

vi(t) = χ {vι(t − 1) + φ1rand1 (pi − xi(t − 1))

+ φ2rand2(pg − xi(t − 1)

)} (15)

χ = 2∣∣∣2 − φ − √φ2 − 4φ

∣∣∣ , φ = φ1 + φ2 > 4 (16)

Although PSO is considered an evolutionary algo-rithm there exist some differences between PSOand genetic and DE algorithms, which are consid-ered more traditional evolutionary algorithms, butthe procedure is analogous. In general, PSO uti-lizes information exchange only among the particle’s

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own previous experience and the experience of thebest particle in the swarm (or swarm neighbour-hood), instead of being carried from “parents” tooffspring as in evolutionary algorithms. In evolution-ary techniques, there are three main operators: selec-tion, crossover and mutation. In PSO, the crossoveroperator does not exist, but the concept of acceler-ating a particle towards its previous best position,as well as towards the best overall position or thebest position of the particles in the neighbourhood isanalogous to the crossover. The PSO approach uti-lizes a directional position updating operation witha kind of built-in memory that resembles mutation.PSO does not utilize selection, nor the survival ofthe fittest concept, given that all particles are mem-bers of the swarm for the entire run (Eberhart and Shi1998).

While the genetic and DE algorithms have beensuccessfully applied in the field of groundwaterhydrology and contaminant transport by manyresearchers (Rogers et al. 1995, Yoon and Shoemaker1999, Erickson et al. 2001, Zhang et al. 2005, Babbarand Minisker 2006, Karterakis et al. 2007, Mayerand Endres 2007, Trichakis et al. 2009, Cardiff et al.2010, Papadopoulou et al. 2010), there are fewer andmore recent applications of the PSO algorithm inthese fields (Matott et al. 2006, Gaur et al. 2011, Tianet al. 2011).

FIELD APPLICATION AND RESULTS

LNAPL model

The applicability of the proposed strategy and therelative effectiveness of the three evolutionary algo-rithms were demonstrated through field application.The study area is located near Athens, Greece.The environmental assessment performed at the siterevealed significant hydrocarbon contamination in allthree phases (free-phase product, soil vapour andgroundwater solutes). Soil, soil-gas, groundwater andoil product samples were collected, and piezometriclevel measurements were performed in the spring of2001. Shallow boreholes of a large diameter weredrilled in the area in order to collect groundwaterand free product samples. The initial investigationdetected a free-phase product plume with an areaof 150 000 m2, an estimated mean product thick-ness of 0.2 m and a maximum apparent thickness of1.11 m. According to the measurements, the generalgroundwater flow is towards the sea. The groundwaterflow and transport model constructed for the sitefocuses on LNAPL free-phase transport and removal.

The geological background of the study area wasdetermined by borehole data, which indicated that themain geological formation encountered in the area isa grey to greyish-white limestone consisting of a frac-tured upper part that extends 1–6 m below the groundsurface. This part constitutes an unconfined aquiferwhich was vertically discretized in two numerical lay-ers. The horizontal discretization of the study areawas implemented using a quadrilateral finite-elementmesh consisting of 902 nodes and 832 elements.

The study aquifer is shallow; thus, the physico-chemical properties are not affected significantly bytemperature fluctuations. This makes the isothermalNAPL-water transport assumption valid for this work.In addition, since only the free product recovery isoptimized, it can be assumed that the model resultswill not be significantly affected by this assumption.

A single porosity model was used that replacesthe hydraulic conductivity and porosity values ofthe fractured system with their locally-averaged,smoothed values. Practically, the fractured formationis represented as an equivalent porous medium byreplacing the primary and secondary porosity andhydraulic conductivity distribution with a continuousporous medium with equivalent hydraulic properties(Dokou and Pinder 2011). This method has beenwidely used in similar applications because of itssimplicity compared to the dual porosity (Zyvolovskiet al. 2008) or discrete fracture (Dokou and Karatzas2012) methods, which require a large amount of dataand more complex modelling. The influence of frac-tures on the LNAPL movement can be significant;however, since no such data were available for thisparticular site, the modelling approach had to be sim-plified. This field study serves as a demonstration ofthe applicability of the optimization methodology andthe comparison of the three evolutionary algorithmsin general; if the proposed optimization methodologyis chosen to be applied in the field, a more detailedinvestigation of the nature of the fracture networkat the site will be needed in order to achieve moreaccurate modelling of the fractured aquifer.

The initial hydraulic head distribution for eachlayer was obtained by interpolation of field mea-surements, corrected for the effect of the floatingoil product. The correction was performed using thefollowing equation:

hc = hm + ρ0

ρwH0 (17)

where hc is the corrected hydraulic head value, hm themeasured hydraulic head, H0 the LNAPL thickness

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Fig. 1 Field site domain, flow boundary conditions and calibrated hydraulic head field.

measured at the well, ρ0 the LNAPL density and ρw

the water density.The calibration process of the flow field, per-

formed by fine tuning of the flow boundary conditionsand using data from nine locations (H1–H9 in Fig. 1),achieved a good fit between modelled hydraulic headvalues and measured head data (R2 = 0.85, Fig. 2).The calibration was performed using measurements

taken in May 2001 as initial data and measurementscollected in May 2008 as target data.

An initial hydrocarbon free-phase distributionwas created by interpolating existing LNAPL thick-ness field measurements from May 2008 (Fig. 3(a)).The estimated volume of free product in the aquiferis 472.3 m3. The location of the 20 pumpingwells that are already installed on site (P1–P10 and

00

H9 H7 H8

H5 H4

H2

H1

R2 = 0.85

0.4

0.9

1.4

1.9

2.4

2.9

3.4

3.9

4.4

4.9

0.9 1.9 2.9Measured head (m)

Mod

el h

ead

(m)

3.9 4.9

Fig. 2 Comparison between measured and calibrated hydraulic head values.

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Fig. 3 (a) Initial LNAPL distribution and location of extraction wells; (b) Final LNAPL thickness distribution after the PSOoptimal pumping strategy has been implemented.

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M1–M10) and are used for the recovery of theLNAPL free product is also shown in Fig. 3(a)and (b).

The hydraulic conductivity field of the modelarea is considered heterogeneous. The main modelarea has a hydraulic conductivity of 2 × 10-3 m s-1

and, additionally, there are three lenses (of the samedepth as the rest of the domain) with hydraulic con-ductivities of 3.1 × 10-4, 1.9 × 10-4 and 4.3 × 10-4

m s-1 around wells M9, M10 and P9, respectively, andone with a value of 1.1 × 10-4 m s-1 north of wellM10. These values were determined by pumping testsperformed on site.

Due to the lack of actual capillary pressure–saturation measurements at the study site, labora-tory measurements in fractured limestone taken byReitsma and Kueper (1994) were used herein. TheBrooks-Corey type model was found to fit their datamore closely as compared to the van Genuchtenmodel. The actual fitting parameters (Pd is repre-sented as equivalent height of water in cm) are pre-sented in Table 1 along with other model parameters,such as the porosity, hydrocarbon density and viscos-ity that were obtained either from site measurementsor the literature.

Optimization problem

Evolutionary algorithms evaluation and com-parison In the first part of the field application, threeoptimization algorithms were compared (GA, DE andPSO) using fixed objective function weights (w1 =0.1, w2 = 0.9). The calibrated FEHM model was usedin conjunction with the optimization algorithms inorder to select an optimal remediation strategy forthe LNAPL contamination in each case. For all algo-rithms, a population of 25 individuals (or particles forthe PSO) was used in each generation, and a max-imum number of 500 iterations was defined as the

Table 1 Groundwater flow and LNAPL transport modelparameters.

Parameter Value

Equivalent porosity 0.03Hydrocarbon density 878.7 kg m-1

Hydrocarbon viscosity 6.04 × 10-4 Pa sNumber of pumping/resting periods 10Brooks-Corey modelλ 2.4Pd 2.9 cmSr 0.05

stopping criterion in all three cases, corresponding to12 500 calls to the simulation model. The initial pop-ulation was created randomly in all cases. Previousresearch (Arifovic 1998, Abido 2002) has shown thatthe choice of initial values for evolutionary algorithmscan affect their performance in the sense that theyinfluence their convergence speed, but not the finaloptimal solution obtained by the algorithm. The num-ber of iterations in this work was chosen to be largeenough to minimize this effect.

In order to select the parameter values that wouldproduce the best results for the three algorithms, dif-ferent sets of parameters were tested. For each algo-rithm two parameters were adjusted: the crossover(Pc) and mutation probabilities (Pm) for the GA, thecrossover (Cr) and scaling parameter (F) for the DEand the multiplier for the maximum velocity (k) andacceleration constants (φ1 = φ2) for the PSO. Theparameters selected for this test were based on ini-tial values taken from the literature (Goldberg 1989,Price et al. 2005, del Valle et al. 2008) and werekept within each parameter bounds. The number ofindividuals (or particles) was kept at 25, but feweriterations (100) were performed to reduce the compu-tational effort. The results of this test are summarizedin Table 2 with the first column containing the optimalparameter values determined by this procedure: Pc =0.8 and Pm = 0.1 for the GA, Cr = 0.8 and F = 0.5 forthe DE, and k = 0.3 and φ1 = φ2 = 2.05 (correspond-ing to a constriction factor of χ = 0.729) for the PSO.The result for the acceleration constants is consistentwith findings of other researchers (del Valle et al.

Table 2 Test for the selection of the optimal algorithmparameter values.

PSO

k 0.3 0.2 0.4 0.6Objective value −154.172 −150.503 −153.901 −152.175φ1 = φ2 2.05 2.5 3 3.5Objective value −154.172 −144.504 −144.646 −143.359

GA

Pc 0.8 0.6 0.7 0.9Objective value −142.872 −142.498 −141.838 −141.752Pm 0.1 0.05 0.2 0.3Objective value −142.872 −142.103 −141.976 −141.513

DE

Cr 0.8 0.6 0.7 0.9Objective value −152.796 −152.549 −152.114 −146.989F 0.5 0.1 0.8 1.2Objective value −152.796 −146.783 −146.566 −143.626

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Table 3 Optimization parameters.

Parameter Value

Population number 25Maximum number of iterations 500Pumping rate bounds: Qmin, Qmax 0 kg s-1, 0.2 kg s-1

Time period bounds 0.2–10 dCost coefficient: c1 1 C m-3

Weights: w1, w2 0.1–0.9

2008). It should be noted here that, although thereis no absolute guarantee that the same parameterswill be the optimal when 500 iterations are per-formed, this test is able to provide good estimates ina reasonable timeframe. All other optimization modelparameters are summarized in Table 3. Note that thecost coefficient was selected in order to make thetwo objectives comparable and does not correspondto the real cost of remediation; it is used only as a“relative” cost.

The optimal solutions obtained from the threeoptimization approaches are presented in Table 4.Although the three algorithms started from a sim-ilar initial objective value, the GA’s performancewas inferior to that of the other two algorithms,converging with a slow rate towards a significantlylarger objective value than the other two algorithms.

Specifically, the genetic algorithm converged to anobjective value of –144.43, while the other two algo-rithms achieved very similar objective values, that ofthe DE being slightly smaller (–181.55) than that ofthe PSO (–180.59). This finding is consistent withthe results of other researchers (Abido 2002) whohave noted that the GA’s inability to control thebalance between local and global exploration of thesearch space (unlike PSO) can lead to prematureconvergence.

The optimal objective function values for the DEand PSO algorithms are very similar. The optimalvalue for the DE is slightly better than that of thePSO for the 500 iterations that were chosen as theconvergence criterion. However, the PSO convergesmuch faster to a nearly optimal solution and remainsalways better than the DE for the iterations 180–485,as can be observed in Fig. 4. This means that, if asmaller convergence criterion was used, PSO wouldhave found a significantly better solution than the DE.The free product removal achieved by the GA, DE andPSO algorithms was 171.6, 205.6 and 204.2 m3, cor-responding to removal of 36.3%, 43.5% and 42.3%,respectively. The total remediation time according tothe optimal strategies chosen by each algorithm was101.3 d for the GA, 78.95 d for the DE and 71.22 dfor the PSO.

Table 4 Optimal pumping strategies for the GA, DE and PSO regarding pumping rates and pumpingand resting times.

Pumpingwell

Q (kg s-1) Time t (d)

GA DE PSO GA DE PSO

P1 0.06 0.38 0.37 Pump1 5.63 3.71 1.34P2 0.02 0.16 0.20 Rest1 9.72 6.02 4.38P3 0.03 0.24 0.29 Pump2 0.61 1.32 0.20P4 0.01 0.43 0.01 Rest2 9.95 9.80 5.98P5 0.14 0.11 0.33 Pump3 0.79 0.12 0.25P6 0.03 0.08 0.38 Rest3 9.78 4.38 2.86P7 0.10 0.23 0.50 Pump4 1.91 0.10 0.20P8 0.04 0.49 0.07 Rest4 9.19 8.75 10.00P9 0.04 0.14 0.07 Pump5 0.57 0.11 1.27P10 0.01 0.15 0.19 Rest5 9.88 9.20 8.11M1 0.03 0.01 0.17 Pump6 0.64 0.66 3.24M2 0.06 0.15 0.35 Rest6 9.89 6.74 5.29M3 0.08 0.19 0.14 Pump7 0.09 0.53 0.90M4 0.01 0.37 0.01 Rest7 9.66 8.59 7.37M5 0.08 0.03 0.17 Pump8 0.90 1.72 0.25M6 0.01 0.23 0.01 Rest8 8.51 9.07 7.88M7 0.02 0.04 0.38 Pump9 0.67 0.41 0.20M8 0.02 0.16 0.01 Rest9 8.68 3.68 9.96M9 0.01 0.09 0.22 Pump10 1.32 0.33 0.20M10 0.03 0.16 0.03 Rest10 2.64 3.71 1.34

Objective function value−144.43 −181.55 −180.59 Total 101.3 78.95 71.22

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Fig. 4 Convergence rate of GA, DE and PSO algorithms.

In Fig. 3(b), the final LNAPL thickness dis-tribution after implementing the optimal pumpingstrategy of the PSO is presented. Similar figures wereproduced for the other algorithms, but are not pre-sented for brevity. While the LNAPL thickness isreduced to zero in all 20 pumping wells, as expected,the maximum LNAPL head observed in the con-taminated area reaches 0.32 m. The relatively highLNAPL head is observed in the area down gradientfrom wells M3 and P5. This suggests that when usingthe existing pumping wells in the area, the contam-ination cannot be fully contained and some productmight escape, moving towards the sea. This is alsoevident when comparing the initial and final LNAPLdistributions (Fig. 3(a) and (b)); while the maximumLNAPL thickness has been reduced from 0.71 to 0.32,a relatively small spreading of the LNAPL plume hasoccurred, thus the plume’s extent has been slightlyincreased.

Pareto front approximation In the second test,the PSO algorithm, which was found to be the mostefficient, together with the DE, for the fixed-weightmulti-objective optimization problem studied above,was used in order to approximate the Pareto optimalfront of the same optimization problem by means ofperforming multiple runs. The goal of this test wasto analyse the trade-offs between cost and LNAPLremoval. Optimization was performed for the follow-ing sets of weights: 0–1, 0.1–0.9, 0.3–0.7, 0.5–0.5,0.7–0.3, 0.9–0.1 and 1–0. The seven Pareto pointsobtained from this procedure are shown in Fig. 5.Although the original optimization problem involvedthe maximization of the recovered LNAPL as a sec-ond objective, in Fig. 5 the LNAPL that remains inthe system after the end of the remediation periodis plotted in order for the results to be comparablewith previous works (Shaerlaekens et al. 2006). Thefirst and last Pareto points are calculated by single

Fig. 5 Calculated Pareto points.

objective optimization since one of the weights is zeroin each case. The first point does not take into accountthe cost and achieves the maximum LNAPL removal,while the last point minimizes cost without takinginto account the LNAPL removal; thus the objec-tive values in this case are both zero, correspondingto the “no-action” scenario. The values of the twoobjectives (cost and remaining LNAPL) ranged sig-nificantly from 0 to 95.5 for the cost and from 257.0 to472.3 m3 for the LNAPL volume remaining in thesubsurface. From the graph in Fig. 5, it is evident thata large increase in cost is required in order to removethe last fraction of LNAPL free product. The bestalternatives for the decision maker would be to chooseone of the next two points on the Pareto front (eitherthe 0.1–0.9 or the 0.3–0.7) that achieve an acceptablelevel of remediation with a significantly smaller cost,although from a mathematical point of view all Paretopoints are equally good and the selection of a strategyshould be performed taking into account other crite-ria, such as the project budget and the environmentalregulations.

CONCLUSIONS

A methodology for modelling and optimizing LNAPLrecovery was presented that included the calibrationof a multiphase model using data from a field sitenear Athens, Greece, the construction of a multi-objective optimization problem that optimized boththe pumping rates and pumping and resting times ofthe LNAPL free product taking into account the costof remediation and environmental considerations, thecomparison of three optimization algorithms in termsof efficiency and the calculation of the Pareto optimalfront using one of the two algorithms that were foundto be the most efficient.

The solutions obtained using the PSO and DEoptimization algorithms were very similar concerning

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the pumping rates and times and the optimal objec-tive function values. The GA did not perform as well,although the computation time needed to performthe same number of algorithm iterations for all algo-rithms was roughly the same. Specifically, the geneticalgorithm converged to a larger objective value (–144.43) than the other two algorithms, which achievedvery similar objective values, with that of the DEbeing slightly smaller (–181.55) than that of the PSO(–180.59). However, the PSO converges to a nearlyoptimal solution much faster and remains always bet-ter than the DE for a large fraction of the algorithmiterations (iterations 180–485). Thus, it can be saidthat, if a convergence stopping criterion was used, or ifa smaller number of iterations was chosen as a conver-gence criterion, then the computation time needed bythe PSO in order to find a satisfactory solution wouldbe much smaller than by the DE.

The Pareto optimal front, which is a method ofanalysing the trade-offs between the two objectives,was also calculated using the PSO algorithm. Allpoints on the Pareto front are considered mathemat-ically optimal, but the choice lies in the hands ofthe decision makers and depends on different param-eters that are not taken into account directly by theoptimization problem, such as the project budgetand the local environmental regulations regarding themaximum allowed contamination levels.

Although a significant amount of LNAPL freeproduct is captured by the optimal strategies (about43% of the product found in the system for thetwo most efficient algorithms), the graphical plotof the remaining LNAPL thickness in the studyarea indicates that, using the existing network ofextraction wells, the maximum LNAPL thicknesshas been reduced from 0.71 to 0.32. However, asmall spreading of the LNAPL plume has occurred;thus, the plume’s extent has been slightly increased.Consequently, future work should focus on identi-fying optimal locations for drilling new wells thatcan satisfactory contain and remove the LNAPL freeproduct in the area.

Acknowledgements The Los Alamos NationalLaboratory is gratefully acknowledged, for allowingthe use of the FEHM simulator, and especially thecode development team leader, George Zyvoloski,for his valuable help with the program.

REFERENCES

Abido, M.A., 2002. Optimal power flow using particle swarm opti-mization. Journal of Electrical Power, 24 (7), 563–571.

Ahlfeld, D.P., Mulvey, J.M., and Pinder, G.F., 1988. Contaminatedgroundwater remediation design using simulation, optimiza-tion, and sensitivity theory: 2. Analysis of a field site. WaterResources Research, 24 (3), 443–452.

Arifovic, J., 1998. Stability of equilibria under genetic-algorithmadaptation: an analysis. Macroeconomic Dynamics, 2, 1–21.

Babbar, M. and Minsker, B.S., 2006. Groundwater remediationdesign using multiscale genetic algorithms. Journal of WaterResources Planning and Management, ASCE, 132 (5),341–350.

Banks, M.K., et al., 2003. Degradation of crude oil in the rhizosphereof Sorghum bicolor. International Journal of Phytoremediation,5 (3), 225–234.

Bass, D.H., Hastings, N.A., and Brown, R.A., 2000. Performanceof air sparging systems: a review of case studies. Journal ofHazardous Materials, 72 (2–3), 101–119.

Cardiff, M., et al., 2010. Cost optimization of DNAPL source andplume remediation under uncertainty using a semi-analyticmodel. Journal of Contaminant Hydrology, 113 (1–4), 25–43.

Chang, L.C., Shoemaker, C.A., and Liu, P.L.F., 1992. Optimaltime-varying pumping rates for groundwater remediation—application of a constrained optimal-control algorithm. WaterResources Research, 28 (12), 3157–3173.

Chen, M.J., et al., 2006. A stochastic analysis of transient two-phase flow in heterogeneous porous media. Water ResourcesResearch, 42, W03425, doi:10.1029/2005WR004257.

Chrysikopoulos, C.V., et al., 2003. Mass transfer coefficient and con-centration boundary layer thickness for a dissolving NAPL poolin porous media. Journal of Hazardous Materials, 97 (1–3),245–255.

Clerc, M. and Kennedy, J., 2002. The particle swarm—explosion, sta-bility, and convergence in a multidimensional complex space.IEEE Transactions in Evolutionary Computation, 6 (1), 58–73.

Cooper, G.S., Peralta, R.C., and Kaluarachchi, J.J., 1998. Optimizingseparate phase light hydrocarbon recovery from contaminatedunconfined aquifers. Advances in Water Resources, 21 (5),339–350.

Culver, T.B. and Shoemaker, C.A., 1992. Dynamic optimal-controlfor groundwater remediation with flexible management periods.Water Resources Research, 28 (3), 629–641.

del Valle, Y., et al., 2008. Particle swarm optimization: basic concepts,variants and applications in power systems. IEEE Tranactionson Evolutionary Computation, 12(2), 171–195.

Diele, F., Notarnicola, F., and Sgura, I., 2002. Uniform air veloc-ity field for a bioventing system design: some numericalresults. International Journal of Engineering Science, 40 (11),1199–1210.

Dokou, Z. and Karatzas, G.P., 2010. Employing evolutionaryalgorithms for optimizing free phase LNAPL recovery. In:J. Carrera, ed. Proceedings of the XVIII international confer-ence on computational methods in water resources, 21–24 June,Barcelona, Spain: Technical University of Cataluña.

Dokou, Z. and Karatzas, G.P., 2012. Saltwater intrusion estima-tion in a karstified coastal system using density-dependentmodelling and comparison with the sharp-interface approach.Hydrological Sciences Journal, 57 (5), 985–999.

Dokou, Z. and Pinder, G.F., 2011. Extension and field applicationof an integrated DNAPL source identification algorithm thatutilizes stochastic modelling and a Kalman filter. Journal ofHydrology, 398 (3–4), 277–291.

Eberhart, R. and Kennedy, J., 1995. A new optimizer using particleswarm theory. In: Proceedings of the 6th international sym-posium on micro machine and human science, 4–6 October,Nagoya, Japan. Piscataway, NJ: IEEE Service Center, 39–43.

Eberhart, R. and Shi, Y., 1998. Comparison between genetic algo-rithms and particle swarm optimization. In: Proceedings ofthe 7th international conference on evolutionary programming,25–27 March, San Diego, CA. Berlin: Springer, 611–616.

Dow

nloa

ded

by [

Tec

hnic

al U

nive

rsity

of

Cre

te]

at 0

2:54

15

Febr

uary

201

3


Erickson, M., Mayer, A., and Horn, J., 2001. The niched Paretogenetic algorithm 2 applied to the design of groundwaterremediation systems. In: Evolutionary multi-criterion optimiza-tion, Lecture Notes in Computer Science, 1993/2001, 681–695.

Erickson, M., Mayer, A., and Horn, J., 2002. Multi-objective optimaldesign of groundwater remediation systems: application of theniched Pareto genetic algorithm (NPGA). Advances in WaterResources, 25 (1), 51–65.

Gaur, S., Chahar, B.R., and Graillot, D., 2011. Analytic elementsmethod and particle swarm optimization based simulation-optimization model for groundwater management. Journal ofHydrology, 402 (3–4), 217–227.

Gidarakos, E. and Aivalioti, M., 2007. Large scale and long termapplication of bioslurping: the case of a Greek petroleum refin-ery site. Journal of Hazardous Materials, 149 (3), 574–581.

Goldberg, D.E., 1989. Genetic algorithms in search, optimization andmachine learning. Boston, MA: Addison-Wesley Longman.

Gorelick, S.M., et al., 1984. Aquifer reclamation design—the useof contaminant transport simulation combined with nonlinear-programming. Water Resources Research, 20 (4), 415–427.

Hilton, A.B.C. and Culver, T.B., 2005. Groundwater remediationdesign under uncertainty using genetic algorithms. Journal ofWater Resources Planning and Management, ASCE, 131 (1),25–34.

Hinchee, R.E., et al., 1991. Enhancing biodegradation of petroleum-hydrocarbons through soil venting. Journal of HazardousMaterials, 27 (3), 315–325.

Hsiao, C.T. and Chang, L.C., 2002. Dynamic optimal groundwatermanagement with inclusion of fixed costs. Journal ofWater Resources Planning and Management, ASCE, 128 (1),57–65.

Huang, Y.F., et al., 2006. An integrated numerical and physical mod-elling system for an enhanced in situ bioremediation process.Environmental Pollution, 144 (3), 872–885.

Johnson, V.M. and Rogers, L.L., 1995. Location analysis ingroundwater remediation using neural networks. Ground Water,33 (5), 749–758.

Karatzas, G.P. and Pinder, G.F., 1993. Groundwater-managementusing numerical-simulation and the outer approximationmethod for global optimization. Water Resources Research, 29(10), 3371–3378.

Karatzas, G.P. and Pinder, G.F., 1996. The solution of groundwaterquality management problems with a nonconvex feasible regionusing a cutting plane optimization technique. Water ResourcesResearch, 32 (4), 1091–1100.

Karterakis, S.M., et al., 2007. Application of linear programmingand differential evolutionary optimization methodologies forthe solution of coastal subsurface water management problemssubject to environmental criteria. Journal of Hydrology, 342(3–4), 270–282.

Khaitan, S., et al., 2006. Remediation of sites contaminated by oilrefinery operations. Environmental Progress, 25 (1), 20–31.

Liu, Y. and Minsker, B.S., 2002. Efficient multiscale methods for opti-mal in situ bioremediation design. Journal of Water ResourcesPlanning and Management, ASCE, 128 (3), 227–236.

Liu, Y. and Minsker, B.S., 2004. Full multiscale approach for optimalcontrol of in situ bioremediation. Journal of Water ResourcesPlanning and Management, ASCE, 130 (1), 26–32.

Lu, G.P., et al., 1999. Natural attenuation of BTEX compounds:model development and field-scale application. Ground Water,37 (5), 707–717.

Matott, L.S., Rabideau, A.J., and Craig, J.R., 2006. Pump-and-treat optimization using analytic element method flow models.Advances in Water Resources, 29 (5), 760–775.

Mayer, A. and Endres, K.L., 2007. Simultaneous optimization ofdense non-aqueous phase liquid (DNAPL) source and contami-nant plume remediation. Journal of Contaminant Hydrology, 91(3–4), 288–311.

Mayer, A.S., Kelley, C.T., and Miller, C.T., 2002. Optimal design forproblems involving flow and transport phenomena in saturatedsubsurface systems. Advances in Water Resources, 25 (8–12),1233–1256.

McKinney, D.C. and Lin, M.D., 1994. Genetic algorithm solution ofgroundwater-management models. Water Resources Research,30 (6), 1897–1906.

McPhee, J. and Yeh, W.W.G., 2006. Experimental design forgroundwater modelling and management. Water ResourcesResearch, 42, W02408, doi:10.1029/2005WR003997.

Miettinen, K., Makela, M.M., and Mannikko, T., 1998. Optimal con-trol of continuous casting by nondifferentiable multiobjectiveoptimization. Computational Optimization and Applications,11 (2), 177–194.

Minsker, B.S. and Shoemaker, C.A., 1996. Differentiating a finiteelement biodegradation simulation model for optimal control.Water Resources Research, 32 (1), 187–192.

Minsker, B.S. and Shoemaker, C.A., 1998. Dynamic optimal con-trol of in-situ bioremediation of Ground Water. Journal ofWater Resources Planning and Management, ASCE, 124 (3),149–161.

Papadopoulou, M.P., Nikolos, I.K., and Karatzas, G.P., 2010.Computational benefits using artificial intelligent methodolo-gies for the solution of an environmental design problem:saltwater intrusion. Water Science and Technology, 62 (7),1479–1490.

Papadopoulou, M.P., Pinder, G.F., and Karatzas, G.P., 2003.Enhancement of the outer approximation method for the solu-tion of concentration-constrained optimal-design groundwater-remediation problems. Water Resources Research, 39 (7), 1185.

Papadopoulou, M.P., Pinder, G.F., and Karatzas, G.P., 2007. Flexibletime-varying optimization methodology for the solution ofgroundwater management problems. European Journal ofOperational Research, 180 (2), 770–785.

Price, V.K., Storn, R.M., and Lampinen, J.A., 2005. Differential evo-lution: a practical approach to global optimization. Berlin:Springer.

Qin, X.S., Huang, G.H., and Chakma, A., 2007. A stepwise-inference-based optimization system for supportingremediation of petroleum-contaminated sites. Water Airand Soil Pollution, 185 (1–4), 349–368.

Qin, X.S., Huang, G.H., and He, L., 2009. Simulation andoptimization technologies for petroleum waste managementand remediation process control. Journal of EnvironmentalManagement, 90 (1), 54–76.

Qin, X.S., et al., 2008. Simulation-based optimization of dual-phase vacuum extraction to remove nonaqueous phase liq-uids in subsurface. Water Resources Research, 44, W04422,doi:10.1029/2006WR005496.

Reitsma, S. and Kueper, B.H., 1994. Laboratory measurement ofcapillary-pressure saturation relationships in a rock fracture.Water Resources Research, 30 (4), 865–878.

Ritzel, B.J., Eheart, J.W., and Ranjithan, S., 1994. Using geneticalgorithms to solve a multiple-objective groundwater pollu-tion containment-problem. Water Resources Research, 30 (5),1589–1603.

Rizzo, D.M. and Dougherty, D.E., 1996. Design optimization formultiple management period groundwater remediation. WaterResources Research, 32 (8), 2549–2561.

Rogers, L.L., Dowla, F.U., and Johnson, V.M., 1995. Optimal field-scale groundwater remediation using neural networks and thegenetic algorithm. Environmental Science and Technology, 29(5), 1145–1155.

Sawyer, C.S. and Kamakoti, M., 1998. Optimal flow rates andwell locations for soil vapor extraction design. Journal ofContaminant Hydrology, 32 (1–2), 63–76.

Schaerlaekens, J., et al., 2006. A multi-objective optimizationframework for surfactant-enhanced remediation of DNAPL

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contaminations. Journal of Contaminant Hydrology, 86 (3–4),176–194.

Shi, Y. and Eberhart, R., 1998. A modified particle swarm opti-mizer. In: IEEE World congress on computational intelligence,4–9 May, Anchorage, AK, ISBN: 0-7803-4869-9, 69–73.

Storn, R. and Price, K., 1997. Differential evolution—a simpleand efficient heuristic for global optimization over continuousspaces. Journal of Global Optimization, 11 (4), 341–359.

Tian, N., et al., 2011. An improved quantum-behaved particle swarmoptimization with perturbation operator and its application inestimating groundwater contaminant source. Inverse Problemsin Science and Engineering, 19 (2), 181–202.

Trichakis, I.C., Nikolos, I.K., and Karatzas, G.P., 2009. Optimal selec-tion of artificial neural network parameters for the prediction ofa karstic aquifer’s response. Hydrological Processes, 23 (20),2956–2969.

Yen, H.K. and Chang, N.B., 2003. Bioslurping model for assessinglight hydrocarbon recovery in contaminated unconfined aquifer.

II: optimization analysis. Practice Periodical of Hazardous,Toxic, and Radioactive Waste Management, 7 (2), 131–138.

Yoon, J.H. and Shoemaker, C.A., 1999. Comparison of optimiza-tion methods for ground-water bioremediation. Journal ofWater Resources Planning and Management, ASCE, 125 (1),54–63.

Yoon, J.H. and Shoemaker, C.A., 2001. Improved real-coded GAfor groundwater bioremediation. Journal of Computing in CivilEngineering, 15 (3), 224–231.

Zhang, Y.Q., Pinder, G.F., and Herrera, G.S., 2005. Least cost designof groundwater quality monitoring networks. Water ResourcesResearch, 41 (8), W08412, doi:10.1029/2005WR003936.

Zyvoloski, G.A., et al., 1999. User’s manual for the FEHM applica-tion. Los Alamos, NM: Los Alamos National Laboratory.

Zyvoloski, G.A., Robinson, B.A., and Viswanathan, H.S., 2008.Generalized dual porosity: a numerical method for representingspatially variable sub-grid scale processes. Advances in WaterResources, 31 (3), 535–544.

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Documents

Multi-objective optimization for free-phase LNAPL recovery using evolutionary computation algorithms