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Applied Soft Computing 10 (2010) 1119–1126

Contents lists available at ScienceDirect

Applied Soft Computing

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / a s o c

A multi-objective genetic algorithm applied to autonomous underwater vehiclesfor sewage outfall plume dispersion observations

Ana Moura a,b,∗, Rui Rijo a,c, Pedro Silva c, Sidónio Crespo c

a Instituto de Engenharia de Sistemas e Computadores-Coimbra (INESC-Coimbra), Coimbra, Portugalb University of Aveiro, Campus Universitário de Santiago, 3810-193 Aveiro, Portugalc Escola Superior de Tecnologia e Gestão de Leiria (ESTG), IPL, Portugal

a r t i c l e i n f o

Article history:Received 11 May 2009

Received in revised form 27 April 2010

Accepted 11 May 2010

Available online 19 May 2010

Keywords:

Multi-Objective

Genetic algorithms and autonomous

underwater vehicle

a b s t r a c t

This work presents a multi-objective genetic algorithm to solve route planning problem for multi-ple autonomous underwater vehicles (AUVs) for interdisciplinary coastal research. AUVs are mobile

unmanned platforms that carry their own energy and are able to move themselves in the water with-out intervention from an external operator. Using AUVs one can provide high-quality measurements

of physical properties of effluent plumes in a very effective manner under real oceanic conditions. TheAUV’s route planning problem is a combinatorial optimization problem, where the vehicles must travel

through a three-dimensional irregular space with all dimensions known. Therefore, minimization of thetotal travel distance while considering the maximum number of water samples is the main objective.

Besides theAUV kinematics restrictions other considerations must be taken into account to theproblem,like the ocean currents. The practical applications of this approach are the environmental monitoring

missions which typically require the sampling of a volume of water with non-trivial geometry for whichparallel line sweeping might be a costly solution. Some real-life test problems and related solutions arepresented.

© 2010 Elsevier B.V. All rights reserved.

1. Introduction

The studies to detect and map sewage plumes using differ-

ent types of techniques show very complex structures. Severaltasks for sewage outfall plume dispersion observations in oceanareperformed in order to measure the particles’ concentration. Theobserved plume patchiness can be due to one or a combination of

factors [1–3] whichinclude: variationsin currents and stratificationduring time intervals; internal tides due to the outfall; limitationsof sampling in terms of resolution of time andspaceand inadequatenumber of critical variables. A rapid sampling is then expected to

reduce time and space variability.Autonomous underwater vehicles (AUVs) are used to detect

and map sewage plumes. The AUVs specially designed for coastalwaters monitoring [4] are low cost and lightweight. The reduced

weight and dimensions make them extremely easy to handle,requiring no especial equipment for launching and recovering andthey are able to accommodate a wide range of oceanographic sen-sors, according to mission objectives. To plan this kind of missions

∗ Corresponding author at: Department of Economy, Management and Indus-

trialEngineering, University of Aveiro, Campus Universitáriode Santiago, 3810-193Aveiro, Portugal. Tel.: +351 234370200.

E-mail address: [email protected] (A. Moura).

the AUV’s routes must be planned. In this case we are dealingwith a combinatorial problem that could be dealt like the three-dimensional travelling salesman problem. In this work each AUV

navigates through the entire plume and takes the maximum num-ber of wastewater samples in a minimum time. More than one (inthis case two) AUV could be used in order to have feasible samplesof the plume wastewater. So, assuming more than one vehicle, the

problem is formulated as a vehicle routing problem (VRP), consid-ering one depot (AUV launch point) and a certain number of clients(sampling points) that must be visited by a fleet of homogeneousvehicles (AUV).

The core of this work is the AUV’s route planning problem thatis a combinatorial optimization problem, where the vehicles must

travel through a three-dimensional irregular space with all dimen-sions known. The main objectives are the minimization of the

total travel distance/time and the maximization of the number of wastewater samples. We do not specify that either the number of wastewater samples or the total travel distance takes priority. Thetwo dimensions of this problem to be optimized are considered to

be separated dimensions of a multi-objective space. So it is clearthat the AUV’s route planning problem can be tackled as an evolu-tionary multi-objective decision-making process, more specificallya multi-objective optimization problem (MOP). Using the Pareto

ranking procedure, each of these problem characteristics is keptseparated and there is no attempt to unify them. Moreover the

1568-4946/$ – see front matter © 2010 Elsevier B.V. All rights reserved.

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1120 A. Moura et al. / Applied Soft Computing 10 (2010) 1119–1126

collisions between AUVs must be prevented and, according to thisthe AUV’s three-dimensional route planning, is a decision-making

process that can be solved as a MOP.The instances of the AUV routing problem may have more than

one locally optimal solution (multimodal solutions) where somesolutions may minimize the total travel distances at the expense

of number of wastewater samples. On the other hand, other solu-tions maximize the wastewater samples number while necessarilyincreasing the AUV’s total travel distance. Looking to this problemas a MOP the objective components that are mutually exclusive,

contribute to the overall result and these objective componentsaffect one another in nonlinear ways. The challenge is to find aset of values for them and an underlying solution which yield anoptimization of the overall problem.

Therefore this work presents the route planning for the AUVsas a multi-objective optimization problem solved with a geneticalgorithm (GA). Section 2 provides the state of the art in auto-matedunderwatervehicles pathplanning.The problem description

and formulation are presented in Section 3. The multi-objectivegenetic algorithm approach applied to the AUV’s route planning isdescribed in Section 4. The experimental results using real-life testproblems are presented in Section 5. A general discussionconcludes

the paper in Section 6.

2. Background

Several works of AUV’s route planning are known to the art.Most of the research on this topic deal with an attempt to find aroute that allows AUVto transit safely from one location to anotherand through a series of waypoints. Some of those works use simple

heuristic methods while others use more sophisticated methods.Literature reveal that the AUV’s route planning is formulated asa travelling salesman problem. For example, in order to solve theproblem of the route planning, Helsgaun [5] presents an effective

implementation of the Lin–Kerninghan travelling salesman heuris-tic. Later on, Chow et al. [6] propose an approximated algorithm fortask allocation problem were thekinematicconstraints on thevehi-

cle and the presence of a constant ocean current are considered.The motion of the AUV satisfies a non-holonomic constraint whichmakes the cost of going from one point to another, non-Euclideanand asymmetric.

There arealsostudies thatuse theadvantages ofmeta-heuristics

methods to solve the path-planning of autonomous mobile robots.Sugihara and Yuh [7] propose a genetic algorithm for underwaterautonomous vehicles path-planning, which generates a collision-free path in an environment with two different kinds of obstacles

(solid and hazardous obstacles). Later, Sugihara and Smith [8]present an adaptively GA approach forpath andtrajectory planningof an autonomous mobile robot. The advantage of this approachis that it could be applied in time-varying and unknown environ-

ments and has very good performance on both online and offline

motion planning in a 2D terrain. A different kind of meta-heuristic,ant colony optimization (ACO) was also used by Liu and Day [9].Here a three-dimensional collision-free path is presented applying

an optimization search algorithm based ACO for one AUV.Apart from these methodologies, different approaches have

beenapplied to AUV’s route planning problem. Warren [10] reportsan algorithm forselecting a safe path using artificialpotential fields

around obstacles.The reported algorithm introducesa costfunctionthat evaluatesa path candidate as a whole.The path parameters areoptimized in order to minimize the cost function. This algorithmis validated for two- and three-dimensional planning problems.

More recently, Yilmaz et al. [11] propose a method based on mixedinteger linear programming to solve the path-planning problem of AUVs. The formulation covers single- and multiple-vehicle cases

and single- and multiple-day formulation.

In this work, the problem is formulated as a VRP. This isbecause more than one AUV is used simultaneously in the same

plume. As the problem is complex, a multi-objective evolutionaryapproach [12] is applied. There are several published works dis-closing heuristics applied to VRP [13–16] with quality solutions.But meta-heuristics are the core of the recent work related to

VRP. Current studies show that high-quality initial solutions allowthe meta-heuristics to find better solutions rapidly [16,17]. In therecent past a number of works have been found with good solu-tions to VRP, more specifically to vehicle routingproblem withtime

windows (VRPTW) constraints,with genetic algorithms (GA). Someof them present hybridization of GA with different constructiveheuristics [18,19] and with local search [20]. Hansha and Ombuki-Berman [21] present a special case of the vehicle routing problem,

which is the dynamic vehicle routing problem and proposes a GAapproach [4] to solve it. Ombuki et al. [22] applied a hybrid search,based on GA and Tabu Search, to soft VRPTW where the multi-objective VRPTW is dealt like a single-objective optimization. A

more recent work [23] presents a multi-objective genetic approachto VRPTW in which the two objective dimensions are the numberof vehicles and the total distance. Moreover, Moura [24] presentsa work where the vehicle routing with time windows and loading

problem is studied and solved as a multi-objective optimization

problem, implemented within a GA.

3. Problem description

The AUVs are mobile unmanned platforms that carry their ownenergy supply and are able to move themselves in the water with-outintervention of an externaloperator. Thecoreof this technologyhas been presented by several authors like Tsukioka et al. [25].

These devices are electronic vehicles with hull and actuator designand with onboard computers to support navigation systems andcommunications with control algorithms. The challenge of the AUVtechnology [25] is to develop instruments for digital telemetry,

highly accurate positioning in the sea and efficient power source.One of the applications of AUVs is in monitoring missions to studythe dilution of sewage outfall plume, because they allow high-quality measurements of physical properties of effluent plumes in

a very effective manner under oceanic conditions.A plume is a sewage outfall area (Figs. 1 and 2). Those areas

have particles concentrations that lead towards stratification. Thisstratification is one of the constraints of the problem as the sam-

pling performed by the AUVs must follow a sequence according tothat stratification and the plume’s direction depends on the inter-

Fig. 1. Plume orientation – upper vim.



A. Moura et al. / Applied Soft Computing 10 (2010) 1119–1126 1121

Fig. 2. Plume orientation – side view.

nal tides. The plume disperses rapidly over time. Therefore, it must

be covered by the AUV as quickly as possible because the samplesmust be gathered before his dispersion. Thus, one of the objectivesof the methodology is to use the advantage of the maximum timewithin which the vehicle is submerged. Moreover, the density of

stratification of the plume must also be considered. The mission(beginning of an AUV route) is initiated in the superior part of theplume. In order to achieve a better sampling, the samples must betaken in walls.This means that theplumeis divided in vertical walls

and each AUV starts the mission in the same wall but in differentcoordinates.

Another goal of this work is to obtainan efficient sampling strat-egy enabling greater improvements in spatial and temporal range.

Thus the problem presented in this work deals with the route plan-ning for more than one AUV inside the sewage outfall plume.

The AUV route planning problem can be defined like a three-dimensional travelling salesman problem. The plume geometry

could be represented witha set ofpoints thatmustbe visitedby thevehicle. The first point is placed in the discharging pipe and the lastpoint in the end of the plume. This problem has several constraintsrelated to the AUV’s kinematics and the sewage plume’s samples.

In this regard AUV kinematics’ constraints are described below:

• Minimum curve radius: between 2 and 4 m;• Vertical movement;• Velocity: between 1 to 2 m/s;• Vehicle autonomy (on batteries): 20 h;• Minimum depth navigation from the surface: 1–2 m;• Minimum depth navigation to the bottom of the sea: 2–3 m.

A sewage outfall plume has complex and patchy three-dimensional structures. The observed plume patchiness can be dueto one or a combination of factors, like ocean current leads to varia-tions in the density stratification of the wastewater and to distinct

plume behaviours; the internal tides provoked by the outfall; somelimitations of sampling in terms of time due to dispersion of theplume; and the irregular geometry of the plume. Let us considerthe following plume constraints:

• Irregular geometry;• Ocean currents speed and direction;• Dispersion of the plume;• Density stratification of the plume.

Due to thedensity stratification of the plume, thesamples mustbe taken in a specific way. Let us consider the following covering

requirements:

• 1–2 m for vertical resolution;• 5–10 m for horizontal resolution.

In this work the vertical resolution is preferred.Considering these problem constraints inherent to plumes and

AUVs, the goal is to obtain an efficient sampling strategy enabling

greater improvements in spatial and temporal range. Considering

two AUVs navigating in the same plume, other problem considera-

tions must be taken into account. The main problem is the minimalsecurity distance navigation between the two of them. This dis-tance,according the AUV’s kinematics is assumed equal to 2 m. Oneof the AUVs is considered the Master and the other one the Slave.

During the routes the Slave must recalculate his new route, everytime that the minimal security distance navigation is violated.

The main objective is to cover the entire plume with two AUVswhile the samples are taken. For each AUV the objective is to min-

imize the total travel distance/time and maximize the number of wastewatersamples while the collisions betweenthe twoAUVs areprevented.

4. Multi-objective genetic algorithm approach

Considering the success of applying multi-objective evolution-ary algorithm (MOEA) in finding good solutions to problems and

knowing that the GAs are suitable search engines for multi-objective problems, primarily because of their population-basedapproach,a multi-objective geneticalgorithm(MOGA) is presentedin this work in order to solve the three-dimensional AUV’s routing

problem. In this section some details of fitness evaluation, Paretostrategy and other GA features used in the developed approach aredescribed.

4.1. Initial population

An approach hasbeen developedfor AUV’s route planning prob-

lemusingthe initial population forGA. ThespacewhereAUV moves(plume) must be treated and the aspects inherent to plume andAUV’s constraintsmustbe considered. Theplumeis divided in wallsof 5 m of depth (Fig. 3).

Each AUV starts in the same wall but in different geograph-ical coordinate points. For each wall two routes are computedin a sequential way. In the end of the algorithm each wall hastwo different routes, one for each AUV, defined by a sequence of

Fig. 3. Walls’ plume division.




geographical coordinates that are generated based on the plumescovering requirements.

4.1.1. Constructive algorithmTo generate a solution for a given plume all vertical walls are

computed. First the algorithm generates one route in each wall for

one of the AUV, named Master (Fig. 4).This route isgeneratedbasedin thenearest neighbouralgorithm

and considering the entire plume and AUV’s constraints. Then theroute of the second AUV, named Slave, is generated in real time

for each wall. Each new point of the Slave’s route is compared tothe actual point of the Master’s route considering the total traveldistance and velocity of each one. If the next visiting point of theSlave is inside an area inferior to 1 m radius of the Master’s current

point,it is considered a collisionpointand in this situation theSlavemust make a detour. If not, the next point of theroute is computed.

4.1.2. Standard detours

When a collision point is detectedthe Slave must make a detourin orderto avoid a collision with the other AUV (Master). Six differ-ent standard detours (Figs. 5–7) are allowed and in each possiblecollision point one of the standard detours is chosen.

Fig. 4. Route of Master AUV.

Types1,2and5(Figs. 5–7, respectively)are the basic detours. Inthis case theSlave takes oneof thedetours andthen moves towardstheend of thewall,reverting to theinitial route.In this case theAUVdoes not take samples in the detour area. Another possibility is the

Fig. 5. Standard detour type 1.






detours type 3, 4 and 6 (Figs. 5–7, respectively). In this case, whenthe Slave takes one of these detours it first comes back to take the

samples in the detour area before reverting to the initial route.Using these standard detours, different routes are generated

for the AUV that makes the detour (Slave). The main differencebetween them is the number of samples and the total travel dis-

tance ofthe AUV that makes the detour.In thefirst typethe numberof samples and the total travel distances are smaller because inthe second type of detours the AUV comes up, takes the missingsamples from the detour area and only then reverts to the initial

route.Therefore the initial population is composed by several differ-

ent solutions. Each solution has two different routes, one route forthe Master and another for the Slave, which could contain one or

several different detours.

4.2. Selection phase and Pareto ranking procedure

In theevaluation phase,the generated solutionsare represented

with a vector, describing its performance according to a set of cri-teria. The vector must be transformed into a scalar value for GApurposes. This process is achieved by ranking the solutions of thepopulation and then assigning fitness based on rank. Individual

solutions are compared in terms of Pareto dominance. The MOGAdeveloped in this work uses Pareto ranking (often used in MOGA,like in Refs. [19,20]) as a mean of comparing solutions across themultiple objectives. The Pareto-optimal set or non-dominated set

[21] consists of all the vectors for which components cannot besimultaneously improved without having a disadvantageous effecton at least one of the remaining components.

Accordingto theobjectivefunction,two dimensions ofthe prob-

lem must be considered: total travel distance/time that must beminimized and the number of samples that must be maximized.When the total travel distance/time is minimized the number of samples is also minimized and this affects the objective function.

These two mutually dependent objective components are used toevaluate the solutions. Each candidate of the initial population is

associated to a vector v = (n,d), where n is the number of samplesand d is the total distance/time. These two dimensions are used by

the Pareto ranking procedure (Fig. 8).The Pareto ranking procedure is applied to all the vectors of the

population and a list of potential non-dominated solutions is builtaccording to the following criteria Eq. (1):

MaxVS = Max− ˛× (Max −Min) (1)

Where:

• MaxVSis themaximumadmitted size ofthe solutionvector(com-

puted as the size of the vectors in Fig. 3);• Max is the maximum vector of Pareto front;•

Min is the minimum vector of Pareto front;

Fig. 8. Pareto ranking.

Fig. 9. Chromosome representation.

• ˛ is a parameter that varies between 0 and 1 in intervals of 0.1,that defines the MaxVS value.

The list of potentiallynon-dominated solutions (LS) is composedby all solutions with a size vector that is smaller or equal to MaxVS.

The potentiallynon-dominated solutions for the crossover oper-ation are randomly selected from LS. The LS size is important for

thereproduction becausethe main idea is to selectthe best individ-uals of the population in order to guarantee that the best solution(produced by the best chromosomes) never deteriorates from onegeneration to the next. The value of ˛ is crucial to accomplish this,

because if ˛ is equal to 0 all the potentially non-dominated solu-tions belong to the list. Making a random choice, a bad solutioncould be selected for reproduction. When ˛ is equal to 1 only thetwo best potentially non-dominated solutions belong to the list.

However, the best results are achieved when ˛ is equal to 0.2.

4.3. Chromosome representation

Each potentially non-dominated solution must be encoded andthus originates a set of chromosomes. The structure of each chro-mosomeis a stringwith theset of points(geographical coordinates)visited by the two AUVs, where each point corresponds to a gene.

The sequence of genes in the chromosome defines the order inwhich each point is visited by the AUV. An example of a chro-mosome that represents a potentially non-dominated solution isshown in Fig. 9.

In order to select the potentially non-dominated solution to beencoded, the chromosome is evaluated using a Pareto ranking pro-cedure. The Pareto ranking is incorporated into the GA by replacing

the chromosome fitness with Pareto ranks described in Section 4.2.

4.4. Recombination phase

Asthe AUV’s route planning problem constraints must bealwayssatisfied, the crossover operator must not result in an unfeasi-ble solution. In the recombination phase an approximation of thebest cost route crossover (BCRC) is used. Refs. [18,19] applied the

BCRC to vehicle routing problem with time windows, Ref. [17] alsoapplied the BCRC to the dynamic vehicle routing problem and Ref.[20] applied it to vehicle routing with time windows and loadingproblem. With the BCRC one could minimize the total travel dis-

tance/time and maximize the number of samples simultaneouslywhile checking feasibility constraints. In Fig. 10 the generation of two offspring using an approximation of best cost route crossoveroperator is presented.

From the list of potential non-dominated solutions two par-ents are randomly chosen. In each parent, two contiguous genes(points of the route) are randomly selected and removed from theother parent. The algorithm tries to insert in every possible posi-

tion the two removed points creating a new solution. With thesenew solutions two new offspring are generated. The feasibility of the offspring is always guaranteed.

4.5. Mutation operator

Only a few offspring are chosen for mutation with a probability

of10%. The mutation is a small change ofthe chromosome (Fig. 11).




Fig. 10. Best cost route crossover operator.

Fig. 11. Mutation operator.

If an offspring is selected to the mutation procedure the fol-lowing sequence could be performed: First, two random pairs of

sequentialgenes are selected and swapped (within eachpair). Then,those two pairs of genes are swapped. The new solution mustbe evaluated because if any restrictions are violated the solutionbecomes unfeasible and the new offspring is not considered.

5. Computational tests

This approach was tested using some problem instances devel-oped by the authors and based in real data problems. The shape of

a standard plume is shown in the next figures:These generated problems are based on the standard shape of

the plumesand several sizesare considered.Seven different plumesare tested. Tables 1 and 2 present the results obtained using theMOGA approach for seven different plumes. Each plume is divided

in walls according to its dimensions. For each wall, the number of samples and the total travel distance (Table 1) performed by thetwo AUVs are computed. In Table 2, the tests results for the sevendifferent plumes are presented.

A plumeis characterized by its dimensionsaccordingFigs.12–14andthenumberofwalls.Foreachplume( Table2), the totaldistanceand the total number of samples are presented.

The MOGA algorithm stops when, after ten consecutives runs,

no better solutions are found. In each run, in order to build the ini-

tial population, the constructive algorithm is performed 100 timesand each time with different LS. Because of the problem’s charac-teristics the LS is usually relatively small (around ten potentially

non-dominated solutions). Depending on the size of the LS, the fol-lowingprocedure is repeated (numberof repetitions is equal to half of theLS size, plus one): selection of parents, crossover (with a rateof 0.90), mutation (with a rate of 0.10) and offspring evaluation.

The running time for the MOGA algorithm is less than 1 min.Results were obtained usinga Centrino Core2Duo [email protected] GHz.This means that the AUV’s routes could be computed in real time,so could be applied on field.

Comparing those results with real data obtained from moni-toring missions previously performed, the developed approach ispromising because for all plumes the total travel time of the AUVs

is reduced.

As one can conclude (Table 2) a mission time in a plume withbig volume(Plume6) could take around 18 h considering the AUV’s

velocity 2 m/s. Those results are applicable in practice because thevehicle’s autonomy is 20 h.

With the introduction of the second AUV, with the guarantee of collisionavoidance and the real time route planning possibility, the

number of samples per mission is increased.

Fig. 12. Top side of a plume.

Fig. 13. Lateral side of a plume.




Table 1

Detailed results of a plume.

Plume 1 (Ai = 10; Li= 30; Lf= 75; Cf = 70) wall number (depth×width)

Wall 1 (10×30) Wall 2 (10×30) Wall 3 (9×35) Wall 4 (9×35) Wall 5 (8×40)

Distance Samples Distance Samples Distance Samples Distance Samples Distance Samples

AUV l 340 76 340 76 359 79 359 79 368 80

AUV 2 211 42 256 51 255 48 22 3 45 256 48

Wall 6 (8×40) Wall 7 (7×45) Wall 8 (7×55) Wall 9 (6×55) Wall 10 (5×55)Distance Samples Distance Samples Distance Samples Distance Samples Distance Samples

AUV l 368 80 367 79 447 95 391 83 335 71

AUV 2 339 65 400 77 233 44 180 36 265 49

Wall 11 (4×60) Wall 12 (3×60) Wall 13 (2×65) Wall 14 (1×75) Wall 15 (1×75)

Distance Samples Distance Samples Distance Samples Distance Samples Distance Samples

AUV l 304 64 243 51 197 41 151 31 75 15

AUV 2 255 51 596 116 170 34 235 47 157 31

Table 2

Results of seven plumes.

Dimensions (Ai–Li–Lf–Cf) Number of walls Total distance/time Total number of samples

AUV1 AUV2 AUV1 AUV2

Plume 1 10–30–75–70 15 4644 4031 1000 784

Plume 2 17–80–160–200 35 44,947 32,523 9357 6345

Plume 3 20–60–120–150 25 29,950 22,132 6280 4376

Plume 4 10–50–100–120 19 9862 5778 2080 1130

Plume 5 28–40–180–75 10 17,367 14,729 3651 2930

Plume 6 25–98–220–290 53 12/602 98,162 26,210 19,420Plume 7 30–80–200–250 46 11,5136 92,765 23,752 18,418

Fig. 14. Front side of a plume.

6. Conclusions

With this work one proposes to solve a route planning problemapplied to autonomous underwater vehicles. The main objectivesare the minimization of the total travel distance and the maximiza-tion of the number of samples, while the collisions between AUVs

are prevented.There areseveral works in literature that deal with thisproblem

using heuristics and meta-heuristics methods, but till now noneof them uses a multi-objective approach. The problem is a multi-

objective decision-making process, where the two dimensions of the problem are considered to be separated in a multi-objective

space. In order to solve it, a multi-objective genetic algorithmapproach is developed and presented. The MOGA developed in this

work uses Pareto ranking as a means of comparing solutions acrossthe multiple objectives. Anothernovel issue presented in this workis the way that the approach deals with AUV collisions avoidance.The main idea is to provide several detours possibilities, where

some of them improve the first component of the objective func-tion and others improve the second [11] component of objectivefunction. Several feasible detours are computed and the best one,in terms of objective function improvement, is chosen. It will be

interesting, as future work, to study the effects in terms of globalsolution, if in each collision point the detour could be chosen by adecision-maker according the mission needs.

The results obtained with the MOGA algorithm confirm that

this approach can be applied in real time as it requires compar-

atively short amount of time in achieving a good quality solution.Therefore, it is possible to apply the solution approach on the field

because the data of the plume can be updated and the routes gen-erated according the field conditions in real time. Analyzing theresults obtained using two AUVs one can conclude that the num-bers of wastewater samples in a plume are increased and this leads

to what is expected, that is, a faster sampling reducing time andspace variability.

Acknowledgement

AníbalMatosfrom Departmentof Electrical andComputer Engi-

neering of FEUP (Faculdade de Engenharia da Universidade doPorto).

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