An effective multi-objective approach to prioritisation of sewer pipe inspection

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1 An effective multi-objective aroach to rioritisation of sewer ie insection L. Berardi 1 *, O.Giustolisi 1, D.A. Savic 2 and Z. Kaelan 2 1 Technical University of Bari, Civil and Environmental Engineering Deartment, via Orabona 4, Bari, Italy 2 Centre for Water Systems, School of Engineering, Comuting and Mathematics, University of Exeter, North Park Road, Exeter, EX4 4QF, England, UK *Corresonding author, l.berardi@oliba.it ABSTRACT Condition assessment of ies is the reliminary ste in the decision making rocess for roactive sewer rehabilitation. In a risk-based decision context the set of sewers to be insected first should be identified based on the trade-off between the risk of failure and the cost of insections. In this aer the ies are selected for insection by solving a multiobjective otimization roblem where the following factors are considered simultaneously: the total cost of the insection rogramme and the risk of emergency reair due to blockages and collases. A multi-objective genetic algorithm (MOGA) is used to identify a set of Pareto-otimal insection rogrammes. Regardless of the roven effectiveness of the geneticalgorithm aroach, the scrutiny of MOGA-based insection strategies shows that they can differ significantly from each other, even when having comarable costs. Thus, a further rioritization rocess is roosed here, which is based on the ie rankings obtained using the frequency of each ie being selected among MOGA solutions. The new set of insection schemes is obtained by rogressively adding ies according to their riority. This is of direct relevance to decision makers as it allows the most effective insection lanning to be achieved based on the available funds. The roosed aroach is demonstrated on a real large sewer system in the UK. KEYWORDS Decision suort; genetic-algorithms; multi-objective otimisation; ie insection; rioritization. INTRODUCTION The sewer system is one element of urban infrastructure that is exected to oerate without interrutions. Condition assessment and rehabilitation of such buried systems are erformed continuously to maintain a desired level of service. A roactive aroach to sewer asset management is of key imortance for reventing uncontrolled deterioration and for reducing both direct and indirect costs (social, environmental and third arty damage) associated with sewer failures. Existing guidelines for condition assessment and rehabilitation of sewer assets suggest rioritization of insections should be the reliminary ste in the decision-making rocess. Information on hysical integrity and hydraulic caacity coming from direct insections hels to select the best rehabilitation intervention otions (WRc, 2001; Bennis et al., 2003). Hitherto, many literature works on develoing rehabilitation lans for sewer and drainage systems are available. They range from Markov based models (Burgess, 1990) to multi-objective Berardi et al. 1

2 otimization aroaches (Reyna et al., 1994). However, little interest has been devoted to the develoment of decision suort tools for lanning insections. The simlest aroach is the condition assessment algorithm develoed by WRc (2001), which has become the industry standard. Two other aroaches roosed in the literature are based either on the assessment of imact factors (McDonald and Zhao, 2001) or on the use of Bayesian belief networks (Hahn et al., 2002) to figure out where the roensity and the consequences of failures are high enough to justify direct insections. They are aimed at eliciting exert knowledge of the system and using available asset data to rioritize ie surveys. In a risk-based decision making rocess for selecting the set of ies to be insected it is necessary to consider the trade-off between economic, technical and management objectives. Accordingly, an insection rogramme can be seen as one of the solutions of a multiobjective otimization roblem where decision variables are sewers (ies) to investigate and objectives embody distinct rationales. During the last two decades, multi-objective genetic algorithms (MOGA) have roven to be effective search-and-otimization techniques caable of solving comlex roblems (Goldberg, 1989). In site of their good erformance in many water system design and management alications (Halhal et al., 1997), it has been observed that MOGA generate intervention strategies which do not rovide any exlicit rioritization of actions that should be undertaken (Berardi et al., 2007). For examle, in the case of water distribution systems, ie relacement strategies obtained by MOGA can differ significantly from each other even when having comarable costs. This drawback becomes more and more evident as the size of the system (i.e. the number of ies) increases. To make the MOGA solutions more effective for decision makers a ost-rocess is needed which assigns riority to every single ie. Berardi et al. (2007) demonstrated the effectiveness of rioritizing ies according to their frequency of selection among MOGA solutions. In that case (ie relacement roblem) ost-rocessed solutions were shown to outerform (in the sense of Pareto dominance) their MOGA-based counterarts, while satisfying the contiguity of relacement strategies and, thus, serving as an effective DSS. Those revious results motivate the current work, which extends those ost-rocessing analyses to the roblem of lanning insections of sewer ies. In this aer the roblem is osed as the selection of the most critical sewer ies for CCTV insection. The choice of CCTV as the unique insection technology is justified by its alicability over all existing sewer diameters and its common use for ie conditions assessment. In this aer a brief overview of multi-objective genetic algorithm for develoing a decision suort system for ie insections is outlined. The case study is then resented and the objective functions are formulated. Secial attention is aid to the descrition of failure models used, which have been obtained using a data-mining modelling technique called Evolutionary Polynomial Regression. Following this, the solutions obtained by using an MOGA, called OPTIMOGA, are scrutinized to evaluate their effectiveness to decision makers. Finally, the roosed rioritization aroach is alied to a case study and results are discussed. PLANNING SEWER INSPECTIONS WITH MULTI-OBJECTIVE GENETIC ALGORITHMS As stressed in revious section, lanning sewer insections is essentially a multi-objective otimization roblem whose solution is relevant to decision maker. In multi-objective 2 Effective rioritization of sewer ie insections

3 otimisation, after the decision-maker has defined all the objectives, he/she has to determine the multi-objective otimal zone by using the concet of the domination criterion called the Pareto domination. Each solution of the Pareto otimal set is not dominated by any other solution, i.e. in going from one solution to another, it is not ossible to imrove on one objective without making at least one of the other objectives worse. It is clear, however, that there is a need to identify as many solutions as ossible within the Pareto-otimal range to ensure that an accetable solution will be roduced and selected by the decision-maker. Several authors (e.g., Goldberg, 1989) showed that evolutionary algorithms and, in articular, genetic algorithms (GA) are more suitable than classical oint-by-oint aroaches for handling such engineering otimization roblems. Genetic algorithms are adative search methods that emulate natural evolution on the basis of referential survival, reroduction of the fittest members and maintenance of a oulation with diverse members. Because GA require scalar fitness information, a scalarization of all objectives is necessary. The introduction of Pareto dominance (Goldberg, 1989) as a driving criterion for selecting the most romising individuals (i.e., solutions) enables GA to work without the need to aggregate the individual objective functions into a single arameterized function or the need to switch between the objectives during the selection hase. Such an aroach ermits assigning fitness by considering the whole oulation rather than the individual fitness values indeendent of other solutions. The algorithm used herein is called Otimized Multi Objective Genetic Algorithm (OPTIMOGA) (Giustolisi et al. 2004). Its efficiency has been roved on benchmark tests and a wide range of alications. Imortant features of the OPTIMOGA algorithm are (i) existence and maintenance of a dynamic archive for dominant individuals during the search hase, (ii) maintenance of a variable-size oulation of individuals and (iii) rank-based fitness assignment as roosed by Fonseca and Fleming (1993). CASE STUDY AND OBJECTIVE FUNCTIONS The analyses reorted in this aer are based on a large sewer network in the UK. The database contains significant information for every single ie, but the network toological information is not available. Pie attributes (fields in the database) can be classified into the following categories: asset features (i.e. diameter, age, construction eoch, shae, material, length, gradient, cover deth, change in the angle between ustream and downstream ies); roximity to imortant locations (i.e. straight distance from the nearest hydraulic control, building, watercourse, area of vegetation and distance from sewer exeriencing historical blockages/collases along the sewerage system); surrounding environment (i.e. traffic load, soil tye); service (i.e. number of roerties connected to the individual sewer and the ustream sewer); hydraulics (i.e. dry weather flow, DWF, discharge estimated from daily flow er roerty ustream of a location), deth and velocity of flow associated with DWF, estimated from stage-discharge tables, discharge and velocity under full bore conditions, estimated based on ie size and gradient); serviceability (i.e. condition grade redicted by the water comany using a Markov chain model (ECG), historic blockages and collases recorded during 5 years of monitoring, from 2001 to 2006); interventions (i.e. date of any lined sewers and length of individual sewer cleansed). As in the case of many water utilities, this large amount of information was artially corruted by some missing entries or unreliable/inconsistent data. In articular DWF hydraulic quantities were discarded as for many sewers they exceeded velocity and flow in the full bore conditions; 12 ies were also filtered out of the original 17,042 ies because of missing velocity values; information on those sewers that were rehabilitated by inserting a ie liner and in articular of the date of Berardi et al. 3

4 that action was encasulated into the age value by reducing it by 10 years, which is the tyical guarantee of the suliers of these roducts; missing ECG values were in-filled with the average ECG of sewers having the same age. Objective functions The abovementioned data have been used to develo an effective insection rogramme by using MOGA first and then the rioritization strategy roosed. Without a loss of generality, only three objective functions are formulated and otimized in the resent work: 1) the cost of insection rogramme (investment), 2) the risk of emergency reairs associated with sewer blockages and 3) the risk of emergency reairs associated with sewer collases. Cost of insection rogramme (Investment) Only CCTV insections are considered as it is the most commonly used insection technology. Costs of insections are borrowed from the work of Zhao (1998) which reort an aroximate unit cost of $/m/mm diameter (between 1.75 and $/m). All costs of both insection and reairs (see objectives 2 and 3) are exressed in Canadian dollars. Original data included diameters from 30 to 1,850 mm; however, the following analysis refers to the range mm. This is because ies smaller than 100 mm are assumed to be recording errors, while failure models develoed here are not valid for ies larger than 1000 mm (see next section). Moreover, insection costs for ies smaller than 200mm are assumed equal to the lower bound of the cost interval (i.e., 1.75 $/m) reorted in Zhao (1998). Total cost of each insection rogramme is comuted as in equation (1) f1 = ( CCCTV D L ) (1) I where C CCTV is the assumed unit cost of CCTV insection, D is ie diameter and L is ie length. The summation refers to all ies of the insected set I. Such a function should be minimized during search for otimal insection scheme. Risk of sewer blockages and collases The main aim of an insection rogramme is to collect as much information as ossible on system conditions to lan future rehabilitation/relacement works. Nevertheless, an exhaustive insection of every sewer ie would be unaffordable both in terms of the required caital and time. There are several rationales which might be considered in addition to f 1 to make insections more effective. For examle, they could accomlish the minimization of multile traffic disrutions along the same street by coordinating insections with other works on different buried utilities and/or maximizing roximity between selected ies. From a risk-based management ersective the consequences of unexected system failures should be considered. Zhao and Rajani (2002) reort that average unit cost of emergency reairs are 3.6 times higher than the average unit cost of non-emergency rehabilitation. The same work reorts that the ratio of social to direct costs can range from 1:1 to 4:1 deending on the location of failure. Accordingly, a roer insection rogramme should single out critical sewers and allow for timely interventions which might result in significant savings for water comanies/municialities. Present work considers risk of emergency reairs associated with sewer blockages and collases only. The inclusion of other objectives would require the knowledge of network 4 Effective rioritization of sewer ie insections

5 toology which is not available for this case study. Nevertheless, the inclusion of referential selection of certain ies is quite easy to imlement, as reorted in Berardi et al. (2007). The quantification of risk usually deals with the assessment of costs (i.e. damage) related to future failures. As reair costs were not available in this case study, the following assumtions are made to quantify damage: Damages subsequent to sewer blockages and collases are assumed to be the same as both tye of failures lead to waste water flooding, service interrutions and traffic disrutions for reairs. Without loss of generality, it is assumed that the only direct cost considered is that reorted by Zhao and Rajani (2002) about the cured-in-lace ies (CIPP) method for emergency intervention scenarios. The CIPP rocess can be considered as a renovation because it incororates the existing ieline fabric into the finished roduct to roduce imroved erformance of the original ieline. The assumed cost is 5 $/m/mm diameter. Social and direct costs are incororated into damage value by multilying CIPP cost by a damage and other cost multilier, similar to that used for assessing damages due to water ie failures (Dandy and Engelhardt, 2006, Berardi et al., 2007)). Such a multilier is comuted for each ie as in equation (2). Us Tr 1 d = = 1+ d + d + d Us, Tr, wd, max( Us) max( Tr) wd + 1 where Us, Tr and wd are the number of roerties connected ustream of the sewer, the traffic load (estimated number of vehicles) on the same ie and the distance from the nearest watercourse resectively; max(us) and max(tr) are the maximum values of Us and Tr in the database. In words, d Us, is a surrogate measure for service interrution in case of sewer failure, d Tr, accounts for traffic disrution and d wd, is linked to the ossible water ollution in case of sewer flooding nearby a watercourse. Note that a more refined exression of d could be adoted if land use above the network were known. According to (2), the damage exected for a hyothetic large sewer (i.e. with a large number of roerties connected ustream), buried under a high traffic road close to a watercourse is about 4 times the direct (CIPP) rehabilitation cost (Zhao and Rajani, 2002)). A crucial element in defining a risk function is the failure rediction model. For this case study, both collase and blockage models are develoed from the available data and historical incident records. The Evolutionary Polynomial Regression (EPR) modelling technique (Giustolisi and Savic, 2006b; Giustolisi et al., 2006c) and its Multi Case Strategy variant (MCS-EPR) (Berardi and Kaelan, 2007) have been used to model collases and blockages resectively. Like the EPR modelling technique, MCS-EPR combines the evolutionary search for model structure with numerical regression for coefficient estimation (i.e., model arameters). Moreover, MCS-EPR is aimed at develoing generalized model structures by simultaneously modelling the same henomenon for a number of individual systems. It is worth remarking that using data-mining embodies the statistical aroach for redicting failures (Kleiner and Rajani, 2001), which is a cost effective way of analyzing small diameter ies only. On the contrary, large sewers would justify the develoment of hysically based models that usually require exensive insections to be validated. Accordingly, both the failure rediction models and the whole methodology reorted here are referred to sewer ies from 100 to 1000 mm diameters only (i.e. 16,875 ies in total). (2) Berardi et al. 5

6 A detailed descrition of using EPR and MCS-EPR for develoing aggregate failure models and ie-level failure rediction is reorted in Giustolisi and Berardi (2007). In brief, what distinguishes the two methodologies is the ossibility of slitting data into subsets according to failure history. In articular, MCS-EPR can be used for develoing distinct models for different subsets of ies; such models have the same mathematical structure but different arameters. A remarkable difference exists between the two models to be develoed here, which is caused by the large imbalance between the number of collases (57) and blockages (688) recorded during the 5 years of monitoring. Furthermore, only one ie exerienced multile collases (two), whereas there are 102 ies that had from 2 to 5 recorded blockages in the eriod of observation. Thus, it is ossible to have enough incident data to use MCS- EPR for blockages only, while collase model is obtained from the original EPR aroach (Berardi et al., 2008). In the former case (i.e. blockages) data were first slit into two subsets (datasets): the first, called the low blockage rate subset, includes sewers with null or one blockage recorded in 5 years; the second, called the high blockage rate subset, refers to those ies with two or more blockage events. In the latter case (i.e. collases), no division is alied to the dataset. Next, data in each dataset have been classified according to key attributes. These are the diameter (D) and the construction eoch (Era) for both tye of failures; in addition the ratio of cover deth to diameter (H/D) is used for collases and ie gradient (gr) for blockages. This distinction is consistent with the different hysical mechanisms leading to collase and blockage of a sewer ie (Berardi and Kaelan, 2007). Finally, each class has been rovided with a set of equivalent values of ossible exlanatory variables. For examle, the length-weighted average age (A), the length-weighted average diameter (D), the total length (L), the total number of sulied roerties (P) and the total number of blockages (BL) or collases (CL). Blockage models obtained by alying MCS-EPR are summarized in equation (3). BL class Pclass Lclass = asubset (3) D where subscrit class emhasizes that this is an aggregate model (i.e. all quantities refer to ie classes, each of which contain a number of ies). Parameter a subset refers to the blockage dataset considered and can be either a low = (i.e. for low blockage rate subset) or a high = (i.e. for high blockage rate subset). It follows from equation (3) that the number of blockages is inversely roortional to the ie diameter and increases with the number of roerties directly connected to the ies and with the class total length. This is consistent with the common exerience that smaller ies are more rone to clog than larger ones and that a large number of direct connections lead to more frequent obstructions. Furthermore, similarly to causes of water ie bursts, the longer the ie class the more likely it is to exerience blockages. Interestingly, none of the selected variables is time-variant. This means that the blockage rate is exected to be constant over time. The collase model obtained from EPR is given in equation (4): CL class class P A = (4) 5 class class Hclass where H is the length-weighted average of cover deth values falling into the class. Also in this case, variables selected verify hysical understanding of the described failure henomenon. The resence of age (A class ) indicate that the ageing rocess leads to material deterioration and the lack of resistance. On the other hand, the higher the cover deth (H class ) 6 Effective rioritization of sewer ie insections

7 is the lower is the direct effect of load transmission from the surface. The selection of variable P indicates a surrogate measure of class extent (size), similar to the effect of length L in the blockage model. The failure rate (the number of incidents er year) is used to assess the number of failures exected in t-years lanning horizon as in (5) and (6). λ P L b class, 0 class, 0 R alow BL, 0 BL Dclass, 0 T R BL, 0 R BL, 0 = > 2 T (5) λ () t CL P ( A + t) c = 5 class, 0 class, 0 R CL 0 0.5, 0 = Hclass, 0 T R 0 CL, 0 1 In equation (5) and (6) suerscrit R refers to quantities recorded during the T years of monitoring, while subscrit 0 means that quantities refer to the end of the monitoring eriod (i.e. t=0). The differences between the second exressions of Eqs. (5) and (6) are the result of the different actions taken after incidents are detected during the T years of monitoring. As collased ies are normally relaced, their robability of failure after relacement is assumed to be λ=0 over the lanning horizon. Blocked ies are normally just cleaned and as they are more likely to suffer further blockages due to similar hydraulic conditions their individual blockage history is used to redict future events and develo lans for insections. Coefficients b and c are ie-level coefficients that deend on the variables comuted by summation and selected by EPR (Berardi et al., 2008) (i.e. P and L for blockages and only P for collases) as reorted in exressions (7). (6) b 1 L P P = + c = 2 L P P class, 0 class, 0 class, 0 (7) The number of blockages and collases exected in a 1-year lanning horizon is as follows: 1 1 BL λ 0 0 (8) CL BL = dt CL = λ () t dt As a new insection lan is needed at the end of the lanning horizon, two new incident models need to be develoed based on the udated asset and incident records. This allows accounting for asset changes (e.g. in terms of age, gradient, diameter and so on) occurred during the lanning horizon. Risk of emergency reairs due to sewer blockages (f 2 ) and collases (f 3 ) are comuted as in equations (9) and (10) resectively. f2 = d ( CCIPP D L) BL (9) NI f3 = d ( CCIPP D L) CL (10) NI where summations refer to all non-insected ies (NI). The roduct in brackets is the rehabilitation costs of ie assuming a unit cost C CIPP of 5 $/m/mm diameter; while d is the Berardi et al. 7

8 multilier as in equation (2). In decision suort context, both tyes of failure models and objective functions should be udated yearly by using new data records. The imlicit working hyothesis here is that condition assessment is adequate to take the right measures and avoid unexected incidents in 1 year time horizon. Also f 2 and f 3 are minimized during search and otimization. FROM MOGA SOLUTIONS TO PRIORITISED INSPECTIONS As mentioned above, the selection of set of sewers to be insected is erformed by using a multi-objective genetic algorithm (OPTIMOGA). Here each insection scheme is reresented by a chromosome whose length equals the number of sewer ies considered (i.e. 16,875 corresonding to about 780 km of ieline) and the only decision variable is to insect (i.e. value 1) or not to insect (i.e. value 0). Such an exhaustive coding identifies a huge global search sace of 2 16,875 solutions. In order to allow for an adequate balance between exloration and exloitation of the Pareto front, each OPTIMOGA run erformed for 500 generations. Furthermore, the otimization was reeated 5 times to take into account the effects of different starting oulations. Figure 1. Analysis of OPTIMOGA solutions. Number of solutions in each 1% cost interval (left). Percentage of ies simultaneously selected for insection among all solutions within the same cost intervals (right). Scrutiny of returned relacement schemes revealed the following issues. Both the number of returned solutions (different insection schemes) and ies selected vary considerably over the 5 runs. Pareto solutions in the close roximity of each other in the objective sace differ considerably in the decision sace (i.e., the set of ies selected for insection are different from solution to solution). In articular, all renewal schemes falling into overlaing intervals of 1% of the total-insection cost (i.e. investment for the whole network CCTV survey) were investigated. Figure 1 deicts the number of solutions falling into each cost interval (left) and the ercentage of common ies (i.e. simultaneously selected) over all ies in the same cost interval (right). For the sake of clarity, figures refer to one of the 5 runs only. Horizontal axis reorts the investment required for the cheaest solution in each interval. It is evident that the most oulated cost intervals are those between about 30% and 65% of the insection that would involve all ies. However, this cost interval shows also a very low ercentage of ies common to neighbouring solutions. This means that, given a monetary budget for insections, the decision manager has to choose among a number of ossible otimal alternatives, which are substantially different from each other. Figure 1 (left) shows also that the cheaest cost intervals are as oulated as the most exensive ones (on average) but the ercentage of common ies is very different. 8 Effective rioritization of sewer ie insections

9 In articular, solutions u to 30% of the total-insection cost (associated with the commonly available budgets) contain about 3% of common ies on average. Also in this case the selection among these solutions is quite a hard task. As shown in Figures 1-right, MOGA solutions range from about 20% to 80/% of the total-insection cost, without any solutions u to 20% and between 80% and 100%. None of the ies has been selected by all of the solutions returned in a single run. These facts suggest that once a given insection scheme is considered by the decision maker, it is imossible to move to the next insection rogramme without changing most of the selected ies. Of course, such an observation neither undermines the effectiveness of multiobjective genetic algorithms nor it deals with the correctness of the solutions obtained, which are near Pareto-otimal with resect to all objectives considered. Rather, such behaviour can be exlained by the slow finishing roblem of genetic algorithms (Kaelan, 2002). The roblem manifests itself as the difficulty in converging toward the real Pareto front due to the lack of selection ressure toward the end of a GA run. In order to overcome such a drawback and develo a ractical decision suort aroach, the solutions obtained by OPTIMOGA have been ost-rocessed. All solutions returned over the 5 runs are considered in order to imrove the statistical significance of the final ranking scheme. Pies have been ranked according to the number of times they were selected by the multi-objective genetic algorithm. In this way the evolutionary search-and-otimization rocedure is used to create an archive of otimal insection olicies. Once ies have been sorted, a new set of intervention schemes is created. For a given budget, the most advisable work lan can be obtained by adding the insection costs of all ies sorted in decreasing order of riority until the monetary constraint is reached. Furthermore, the nearest less exensive course of actions differs by just one ie from the more exensive neighbour. The less exensive solution assumes that condition assessment of the removed ie is less urgent from the statistical oint of view. Figure 2 shows the insection schemes returned by OPTIMOGA and those obtained after rioritization. The figure deicts the rojections of the objective sace on the lanes f 1 - f 2 (Investment - Risk of blockages) and f 1 - f 3 (Investment - Risk of collases). Figure 2. Comarison between OPTIMOGA solutions and rioritised insection rogramme. Plot of Risk of blockages vs. Required Investment (left). Plot of Risk of collases vs. Required Investment (right). The axes of investment and risk functions are scaled between 0 and 1. Figure 2 reorts investment needed for insection rogrammes on the horizontal axis as it is of direct relevance to decision makers. It is evident that rioritized schemes are Pareto-dominant with Berardi et al. 9

10 resect to all OPTIMOGA solutions. Furthermore, the rioritized front shows a quick reduction in both risk functions just after 162 ie are selected for insection. The inflection oint in Figure 2 (left and right) reresents an insection rogramme with the cost of about 1% of the total network survey cost and allows risk due to blockages and collases (i.e., reduction in emergency reairs) to be reduced aroximately 33 and 47%, resectively. Ranking solutions on a MOGA-based Pareto front was used by Kaelan (2002) and Kaelan et al. (2005) to comare some MOGA solutions with other ranking aroaches on the roblem of samling design found in the literature. Similarly to that work, Figures 2 show also the comarison with two ie rankings obtained by using greedy algorithms. Each of them starts with an emty set of otimal solutions and adds one ie at a time; such ie is the one with the current highest ratio between risk reduction and investment. In the first case (i.e. Rbl/C) risk reduction refers to blockages, in the second case (i.e. Rcl/C) it refers to collases. It is evident that each of these ranking schemes dominates the others when evaluated into the roer two-objective sub-sace (e.g. Rbl/C in f 1 - f 2 lane), while it is dominated in the oosite case (e.g. Rbl/C in f 1 - f 3 lane). Figure 2 shows that the roosed ranking scheme reresents a balance between the two rationales in the low investment region, which is the more interesting from a decision maker ersective. The obtained solutions are fairly referable u to 19% of total-insection investment. Furthermore, all solutions before the inflection oint aroximate very well both rankings, i.e., Rbl/C and Rcl/C. This is because ies with highest risk of both blockage and collase events are selected first. These observations are likely to be of general validity, i.e. even when other ranking algorithms based on one objective at a time are alied. A further analysis has been erformed to verify whether rioritized strategies are Pareto efficient with resect to each other. The result shows that 178 solutions out of 16,785 are Pareto-dominated by others. However, the first dominated solution occurs after the selection of 185 sewers, hence beyond the inflection oint in Figure 2. Furthermore, just 18 out of 5,859 rioritized solutions are sub-otimal within the range 0-30% of the total insection investment. Remaining sub-otimal solutions are sread through the front of rioritized solutions with an increasing density towards more exensive ones. This aarent drawback can be exlained by the insufficient ressure of selection in such a large search sace and could be easily overcome by including additional objective(s) during the otimization rocess. In articular such objective(s) could reresent manager-secific references on ie selection as in Berardi et al DISCUSSION AND CONCLUSIONS This work resents and discusses the alication of a multi-objective genetic algorithm (OPTIMOGA) to selection of otimal sewer ie insection schemes in a real, large sewer network. Analysis of solutions from multile OPTIMOGA runs unveils a lack of contiguity between the otimal set of insections obtained. This makes insection strategies less effective to decision makers that have to select among a large set of feasible ie combinations. The rioritization scheme alied here consists of ranking ies on the basis of the frequency with which they aear among all otimal solutions returned by one or more runs of the evolutionary search-and-otimization engine. This methodology is aimed at exosing the most critical ies to satisfy a given set of objective functions simultaneously. The case study considered objective functions describing the total investment required and the risk of emergency reairs subsequent to sewer blockages and/or collases. Both collase and blockage models are develoed by using the Evolutionary Polynomial Regression technique. The cost of CCTV insections and CIPP reairs are borrowed from literature on the subject. Damages due to unexected sewer failures take into account both direct (reair) and 10 Effective rioritization of sewer ie insections

11 indirect (i.e. environmental, traffic disrution and service interrution) costs. All solutions obtained after ost-rocessing dominate all those returned by 5 runs of a multi-objective genetic algorithm. Prioritized insection schemes where also comared with two different ranking strategies, each following a benefit/cost ratio based on one objective (i.e. tye of failure) at a time. The roosed aroach is demonstrated to rovide referable solutions, at least in the low-investment interval. Finally, the analysis of Pareto dominance among the rioritized solutions reveals that some are sub-otimal. This observation is exlained by the insufficient ressure of the referential selection emloyed. The inclusion of other objectives is suggested as the straightforward remedy to both overcome this roblem and make the tool more ractical. REFERENCES Bennis S. ; Bengassem J. and Lamarre P. (2003) Hydraulic Performance Index of a Sewer Network. Journal of Hydraulic Engineering, 129(7), Berardi, L., Primativo, F. and Giustolisi, O. (2007) Exloiting multi-objective strategies for otimal rehabilitation lanning. Proceedings of Comuter and Control in Water Industry (CCWI), Ulaniki et al. (eds), Taylor & Francis Grou, London, Berardi, L., and Kaelan, Z. (2007). Multi-Case EPR strategy for the develoment of sewer failure erformance indicators. Proceedings of the World Environmental & Water Resources Congress, Tama, Florida, USA. (CD-rom version). Berardi, L., Kaelan, Z., Giustolisi, O., Savic, D., (2008) Develoment of Pie Deterioration Models for Water Distribution Systems using EPR, Journal of Hydroinformatics. 10(2), Burgess, E. H. (1990). Planning model for sewer system rehabilitation.water resources infrastructure: Needs, economics and financing, J. F. Scott and R. Khanbilvardi, eds., New York, Dandy, G.C., and Engelhardt, M.O. (2006). Multi-Objective Trade-Offs between Cost and Reli-ability in the Relacement of Water Mains. J. of Water Resources Planning and Management, ASCE 132(2), Fonseca, C.M., and Fleming, P.J. (1993). Genetic algorithms for multiobjective otimization: Formulation, discussion and generalization. Proceedings of the Fifth International Confer-ence on Genetic Algorithms, Morgan Kaufmann, San Mateo, California, , S. Forrest editor. Giustolisi O., Doglioni A., Savic D.A., and Laucelli D. (2004). A roosal for an effective multi-objective nondominated genetic algorithm: the OPTimised Multi-Objective Genetic Algorithm: OPTIMOGA. Reort 2004/07 School of Engineering, Comuter Science and Mathematics, Centre for Water Systems, University of Exeter, UK. (URL: Giustolisi, O., Savic, D.A. and Kaelan, Z. (2006b) Multi-objective evolutionary olynomial regression. Proceedings of the 7th international Conference on Hydroinformatics, HIC 2006, Nice, France, Vol.1, Giustolisi, O. and Savic, D.A. (2006c) A Symbolic Data-driven Technique Based on Evolutionary Polynomial Regression. Journal of Hydroinformatics. IWA-IAHR Publishing, UK, 8(3), Goldberg, D.E. (1989). Genetic Algorithms in Search, Otimization and Machine Learning. Addison-Wesley, Reading, Massachusetts. Halhal, D., Walters, G. A., Ouzar, D., and Savic, D. A. (1997). Water network rehabilitation with a structured messy genetic algorithm. J. of Water Resources Planning and Management, 123(3), Hahn M. A., Palmer R.N., Merril M. S. and Lukas A. B. (2002) Exert System for Prioritizing the Insection of Sewers: Knowledge Base Formulation and Evaluation. Journal of Water Resources Planning and Management, 128(2), Kaelan, Z. (2002). Calibration of water distribution system hydraulic models. PhD Thesis. Deartment of Engineering, University of Exeter. Kleiner, Y., and Rajani, B.B. (2001). Comrehensive review of structural deterioration of water mains: Statistical models. Urban Water. Elsevier, 3(3), McDonald S.E. and Zhao J.Q. (2001) Condition assessment and rehabilitation of large sewers. International Conference on Underground Infrastructure Research, University of Waterloo, Waterloo, Ontario, June 10-13, Reyna S., Delleur, J., and Vanegas, J. (1994) Multi-attribute rehabilitation of storm or combined sewer systems. Urban drainage rehabilitation rograms and techniques, W. A. Macaitis, ed., Zhao J. Q. and Rajani B. (2002) Construction and rehabilitation costs for buried ie with a focus on trenchless technologies. Research Reort No Institute for Research in Construction, National Research Council Canada, Ottawa, ON, Canada. Berardi et al. 11

12 Zhao, J.Q. (1998). Trunk Sewers in Canada APWA International Public Works Congress Seminar Series, American Public Works Association. Las Vegas, Set WRc, Sewerage Rehabilitation Manual (4th edition), WRc, Swindon, UK, Effective rioritization of sewer ie insections