Simulation-Based Interactive Multiobjective Optimization in ...

EngOpt 2008 - International Conference on Engineering Optimization Rio de Janeiro, Brazil, 01 - 05 June 2008.

Simulation-Based Interactive Multiobjective Optimization in Wastewater Treatment Jussi Hakanen∗ , Kristian Sahlstedt† , Kaisa Miettinen∗ ∗

Dept. of Mathematical Information Technology, P.O. Box 35 (Agora), FI-40014 University of Jyv¨ askyl¨ a, Finland e-mail: [email protected], [email protected] † P¨ oyry Environment Oy, P.O. Box 50, FI-01621 Vantaa, Finland e-mail: [email protected]

1. Abstract This paper deals with developing tools for wastewater treatment plant design. The idea is to utilize interactive multiobjective optimization which enables the designer to consider the design with respect to several conflicting evaluation criteria simultaneously. This is especially important because the requirements for wastewater treatment plants are getting more and more strict. By combining a process simulator to simulate wastewater treatment and an interactive multiobjective optimization software to aid the designer during the design process, we obtain a practically useful tool for decision support. The applicability of our methodology is illustrated through a case study related to municipal wastewater treatment where three conflicting evaluation criteria are considered. 2. Keywords: Wastewater treatment, interactive methods, multicriteria optimization, IND-NIMBUS, simulation 3. Introduction Operational requirements of wastewater treatment plants (WWTPs), notably the effluent limits of nitrogen and phosphorus, are becoming more and more strict because of increased emphasis on environmental values. Consequently, more complex wastewater treatment processes are gaining ground. At the same time, the requirements for economical efficiency (for example, minimizing plant footprint and the consumption of chemicals and energy) as well as for operational reliability are also tightening. This makes the design of a WWTP a complex process involving trade-offs between a number of conflicting economical and operational criteria. Therefore, a simplified approach where all the aspects are gathered together, usually as estimated total costs, and optimized is not adequate anymore. To guarantee a final design which takes into account all the relevant criteria related to wastewater treatment, we propose an interactive design strategy that utilizes numerical simulation of wastewater treatment processes combined with an efficient interactive multiobjective optimization method. This enables the designer to simultaneously consider the process from different perspectives and optimally balance the final design between different conflicting design criteria. The WWTP design has been previously considered by optimizing only one objective function, that in one way or another describes the costs of the process to be minimized (see, for example, [4, 10, 11, 16]). So far, we have found only one paper in this field that deals with multiple objectives and there the idea is to produce an approximation of all the compromise solutions to the multiobjective optimization problem considered [3]. In this paper, we concentrate on utilizing modern optimization techniques to provide decision support for the designer which helps him/her to locate the best trade-offs between different competing design alternatives. By utilizing interactive multiobjective optimization in the design process, the designer is able to learn about the problem and about the interdependences between the conflicting design criteria. In addition, (s)he can concentrate only on those compromises that are of interest to him/her. When compared to the approach in [3], our interactive approach is more computationally efficient because we do not try to approximate all the compromise solutions of which many can be uninteresting to the designer. This kind of an interactive design tool is an entirely novel approach in WWTP design, although such tools are succesfully utilized in other fields. The possibilities of this interactive design strategy are here illustrated by reporting results from a case study which deals with the optimization of a WWTP operation in terms of energy and chemical consumption, operational safety and effluent quality. In the future, the work will be extended to include also factors influencing investment costs, notably the volumes of different process units.

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The rest of this paper is organized as follows. First in Section 4, we briefly introduce wastewater treatment and describe the problem we are considering. Section 5 is devoted to interactive multiobjective optimization and the optimization methods we are using, namely NIMBUS and IND-NIMBUS. In Section 6, we report the results of applying these tools to the case study described in Section 4 along with some discussion of the results obtained. Finally, we make some conluding remarks about the study and give topics for future research. 4. On modelling wastewater treatment 4.1. Background Mathematical modelling of WWTPs began gaining ground in the 1990s when experience on modelling solutions and computer power increased simultaneously. The overwhelming majority of modelling considers the activated sludge process (ASP), globally the most common method of wastewater treatment. In this process, biomass (which is called activated sludge) suspended in the wastewater to be treated is cultivated and maintained in an aerated bioreactor. The wastewater is purified, i.e. organic carbon, nitrogen and phosphorus are removed, during its retention in the bioreactor. The bioreactor is followed by a clarifier basin, in which the biomass is separated by gravitational settling and returned to the bioreactor, and the treated wastewater is directed as overflow to futher treatment or to discharge. Excess activated sludge is removed from the process and treated separately. The schematical flow sheet of the process is presented in Figure 1.

Figure 1: A flowchart of wastewater treatment process considered. The activated sludge model (ASM) family developed by the Task Group of International Water Association has been established as a standard for ASP modelling [9]. These are mechanistic models, in which the various phenomena occurring in the bioculture are described by first to third order differential equations. The reaction rates of different substances, e.g. fractions of organic carbon and nitrogen, are obtained by integrating the differential equations over time and factoring them with substance-specific stoichiometric coefficients. These coefficients are based on continuity of key parameters (total chemical oxygen demand, total nitrogen, total phosphorus, charge), which ensures model integrity. The models are nonlinear, reflecting the nonlinear nature of microbial growth and solids separation. 4.2. Description of wastewater treatment process considered The process model used in this study describes a nitrifying activated-sludge process. The biological process is a plug-flow reactor with five sections. All sections are equipped with bottom fine bubble aerators. The biochemical reactions are modelled with ASM3 [9]. Sodium carbonate is dosed as a 5% solution to compensate for alkalinity consumed by nitrification. The wastewater treated by the process corresponds to typical Finnish mechanically and chemically pre-treated municipal wastewater. The secondary clarifier is modelled as a 10-layer one-dimensional settler. Solids separation is modelled with the Takacs double-exponential model [17]; no biological reactions are assumed to take place in the clarifier. Default values are used for all kinetic and stoichiomteric model parameters of ASM3 and the Takacs model. The oxygen concentration in the biological process is PI-controlled, with a default setpoint of 2.0 g/m3 in 2

all sections. Mixed liquor suspended solids concentration (CM LSS ) is PI-controlled by regulating the excess sludge flowrate. The default setpoint for CM LSS is 3.0 kg/m3 . Excess sludge is removed from the aeration basin. In addition, the wastewater temperature, influent flowrate and the maximum volume of the reactor were fixed to 12 o C, 60 000 m3 /d and 17 000 m3 , respectively. The process considered in this paper performs nitrification, i.e. oxidation of ammonium nitrogen to nitrate nitrogen by autotrophic, slow-growing micro-organisms. The biochemical reactions involved consume a lot of oxygen and alkalinity. Oxygen is supplied by aeration compressors and alkalinity partly by influent wastewater, partly by adding chemicals, e.g. Na2 CO3 . Aeration consumes energy and chemicals cost money, so minimizing the need for aeration and alkalinity addition is important for the operational economy of the plant. Another important control parameter is biomass concentration (CM LSS ) in the bioreactor, which should be kept as low as possible so that the secondary settler would not be overloaded in case of peak flows. CM LSS is controlled by the removal rate of excess sludge, which is inversely proportional to the theoretical retention time of one biomass cell in the process, i.e. sludge retention time (SRT). The nitrifying biomass requires relatively long SRT because of its low growth rate. The higher the SRT, the higher the concentration of biomass and thus the bigger the risk of clarifier overload. 4.3. Optimization in WWTP design As new treatment requirements prompt the use of more complex processes, the number of independent (and dependent) variables in the design task increases, and selection of their optimal values becomes more difficult without appropriate support. Considering different objectives (treatment results, investment costs and operational costs) and different environmental conditions in which the plant has to operate (wastewater quality, flow and temperature fluctuations) significantly increases the complexity of the problem. The optimal design and operation of a wastewater treatment plant involves e.g. selecting appropriate volumes and functions for process units and determining optimal setpoints for dissolved oxygen (DO) concentrations, sludge circulation flows and chemical dosing rates such that they optimize the behaviour of the plant, according to some pre-defined criteria, in given conditions [2]. Mathematical models are a powerful tool for this kind of optimization problems. Optimization of WWTP design and operation by modelling and simulation has been applied since the 1990s. The studies usually involve comparisons of different process schemes or control strategies. The behaviour of the considered solutions is simulated, and the results are then compared to each other, usually in terms of investment or operational costs. The comparison can be done either by engineering judgement, as is usually the case (see e.g. [5, 12]) or using an optimization algorithm (see e.g. [4, 16]). However, using only one objective function instead of several individual criteria hides the interdependencies between different criteria and, thus, makes it difficult for the decision maker (DM), who might be e.g. a designer or a plant operator, to assess the true optimality of the solution. The DM may also have non-quantifiable priorities, such as operational stability and ease of operation, which may depend on many decision variables to be optimized. For example, minimizing the concentration of activated sludge to avoid settler overload may be more important than minimizing certain residual pollutant concentrations in the effluent. Therefore, for a truly optimal design, the procedure must present the DM with solutions based on a multiobjective optimization approach, out of which (s)he can choose the best ones to be elaborated further. So, how should this optimization problem with multiple conflicting objective functions be solved? We describe some suitable optimization tools in the next section. 5. Optimization tools Practical real-world optimization problems, like the ones in wastewater treatment, often have to be considered from many different perspectives. This gives rise to several conflicting evaluation criteria as described in Section 4. When the optimization problem in question needs to be solved with respect to several conflicting criteria simultaneously, the concept of optimality needs to be redefined. The solution in single objective optimization can be regarded optimal when the objective function achieves the smallest or largest value (for minimization or maximization problems, respectively). Instead, when dealing with multiple conflicting objective functions, the solution can be seen as optimal when no objective function value can be improved without impairing any other objective. These optimal solutions are called Pareto optimal solutions or compromise solutions. Typical to these optimal solutions is that there usually are (infinitely) many of them and they all are mathematically equivalent. Solving these

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types of problems requires using the methods of multiobjective optimization (see, for example, [13] and references therein) in order to find the most preferred solution. 5.1. Interactive multiobjective optimization Usually, the aim of solving practical multiobjective optimization problems is to find the best compromise between the conflicting objective functions that is to be implemented. Because all the compromise solutions are mathematically equivalent, we must have some additional information to help us in choosing the most preferred one. In multiobjective optimization, the person who has that information is called a decision maker (or designer when we are talking about practical applications like wastewater treatment). The DM needs to be able to compare compromise solutions with the help of one’s experience in the field of the application area considered. The task of the DM is, also, to express preferences on what kind of solutions are desirable. In this way, the DM can direct the solution process and balance between conflicting objectives. Methods of multiobjective optimization can be categorized, for example, by the role of the DM [13]. The DM can express preferences before or after the method produces compromise solution(s) or the solution process can be iterative, that is, the steps of expressing preferences and generating compromise solutions alternate until the best compromise solution has been identified. In this paper, we concentrate on the last type, that is, interactive multiobjective optimization methods [13]. Interactive methods are chosen because they are computationally efficient (generate only those compromise solutions that are of interest to the DM) and they enable the DM to learn about the interrelationships between conflicting objective functions. These are important properties when dealing with practical multiobjective optimization problems. 5.2. NIMBUS and IND-NIMBUS The interactive multiobjective optimization method used in this paper is the NIMBUS method [13, 15] and, especially, it’s implementation IND-NIMBUS [14] developed for solving industrial multiobjective optimization problems (http://ind-nimbus.it.jyu.fi). IND-NIMBUS was chosen because it has been succesfully applied in other areas, for example, in chemical process design [6, 7] and designing of ultrasonic transducers [8]. The NIMBUS method is based on the idea that the DM is asked at every iteration of the iterative solution process to classify the objective functions into five classes at the current compromise solution. The classes reflect the preferences of the DM and how (s)he would like the current compromise solution to be improved. The classes are - the functions whose values should be improved as much as possible, - the functions whose values should be improved until a given aspiration level, - the functions whose values are satisfactory at the moment, - the functions whose values are allowed to impair up to a given bound and - the functions whose values can change freely. If the DM wants to go from the current compromise solution to another one, (s)he needs to classify at least one objective function into the first two classes and at least one other objective function into the last two classes. This is due to the definition of the compromise solutions. Based on the classification information given by the DM, a new optimization problem is formed and solved. The resulting solution will be a compromise solution that tries to satisfy the preferences of the DM as well as possible. In the synchronous NIMBUS method [15], several optimization problems are formed resulting in different compromise solutions corresponding to the preference information in slightly different ways. It is then up to the DM to choose the one that more closely follows his/her preferences. There is also a possibility to generate a desired number of alternative solutions between any two compromise solutions already computed to observe intermediate behaviour. More information about the NIMBUS method can be found in [15]. To apply the NIMBUS method in practice, an implementation called IND-NIMBUS [14] was developed. As already mentioned, IND-NIMBUS is devoted especially to solving industrial multiobjective 4

Figure 2: A screenshot of IND-NIMBUS. optimization problems like, for example, WWTP design. IND-NIMBUS provides the DM with a graphical user-interface (GUI) to aid in directing the interactive solution process of the NIMBUS method. A screenshot of the GUI is shown in Figure 2. The GUI of IND-NIMBUS consists of several tabs for different actions, for example, classification, generating alternatives, visualization, numerical values for solutions obtained and adjusting method parameters. Figure 2 shows the classification tab where the current compromise solution is shown on the left side while all the compromise solutions generated so far during the solution process are shown on the right. The lower right corner of the tab is for keeping track of the best candidates the DM has found so far. In the visualization tab, there are several different types of visualizations available for the DM in evaluating and comparing the compromise solutions obtained to assist in analysing their performance according to the different criteria considered. As already mentioned, solving a multiobjective optimization problem means balancing between the conflicting criteria in order to find the most preferred compromise to be implemented in practice. In our case, it means balancing between the amount of residual ammonium nitrogen in the treated wastewater, the usage of alkalinity chemical and the power consumption of the process. In other words, we have three conflicting objective functions. To solve the problem described in Section 4, we combined IND-NIMBUS and the commercial process simulator GPS-X (http://www.hydromantis.com/software02.html). This combination provides us a tool to support in designing (new) wastewater treatment plants that can consider the plant at the same time from many different aspects implying conflicting evaluation criteria. (Note that other process simulators could also be used.) In this way, the DM obtains a more realistic overall picture of the problem and can make the decisions based on versatile information. In addition, with the help of this interactive tool, (s)he is able to learn about the behaviour of the problem and, if necessary, can change his/her opinions as new information is gained. The learning aspect is a novel possibility when compared to previously used methods where usually only total costs were minimized. Converting all evaluation criteria to money can lead to unnecessary simplifications because it is not easy to estimate all costs and this may result in loss of information about the problem. 6. Case study To illustrate the applicability of the interactive solution strategy presented in Section 5, we report the results of solving a case study described in Section 4.

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6.1. Case description As said, in our example, the DM operates on three objectives to be minimized, namely the residual ammonium nitrogen concentration [gN/m3 ], the dose of alkalinity chemical [m3 /d] and the consumption of energy by aeration [kW ]. In what follows, we will denote them by N , A and E, respectively. The primary objective N should be kept at a sufficiently low level while the other two objectives should be minimized. The decision variables in our optimization problem are CM LSS [kg/m3 ], alkalinity chemical dosign rate [m3 /d] and the O2 -concentration in the last section of the reactor [g/m3 ]. The upper bounds used for the decision variables are 6.0, 500 and 2.5, respectively, while the lower bound for each is zero. Note that all the decision variables are continuous. The decision variables are coded into the process simulator and are automatically adjusted during the multiple simulation runs; the DM only adjusts the desired values of the objectives. As constraints of the optimization problem, we set restrictions for alkalinity of treated wastewater, that is, we require that the alkalinity remains between 1.5 and 2.0 moles/m3 . To implement the wastewater treatment model described in Section 4, we used the commercial GPS-X process simulator (http://www.hydromantis.com/software02.html) as already mentioned. The optimization problem was solved with IND-NIMBUS. The optimization problems produced by the NIMBUS method were solved by using the Controlled Random Search algorithm [1]. The DM involved in the solution process is an expert in the problem field in question. Next, we decribe the solution process. 6.2. Interactive solution process At the beginning of the interactive solution process with NIMBUS, approximations of the bounds for the values of the objective functions in the set of compromise solutions are computed. These bounds help the DM in classification because (s)he gets some idea of what kind of values are possible to achieve. In addition, the bounds are used by the NIMBUS method for scaling purposes. The approximations of the lower (best) and upper (worst) bounds for the objective functions in our case were (0.03, 0.45, 308) and (31.5, 354, 599), respectively. The solution process starts from the so-called neutral compromise solution (NCS) that is approximately in the middle of the set of compromise solutions [18]. In other words, NCS is the first compromise solution that is shown to the DM. In our case, NCS had the objective function values (8.05, 218, 460). The value of N was not tolerable and indicated that, with these settings, the process would not work. Therefore, the DM made the first classification to improve the value of N until 1, and allowed the value of A to increase up to 330. The value of E was satisfactory at the moment. In addition, the DM wanted to see three new compromise solutions. The resulting compromise solutions were (3.52, 286, 490), (1.69, 326, 506) and (4.90, 298, 477). As can be seen, it was not possible to fully satisfy the classification specified. Of the new solutions found, the second one seemed to be the most promising. However, the value of N was still a bit too high. Therefore, the DM made the next classification to minimize N further until 0.5. In addition, he was willing to let the value of E increase up to 510 and allowed A to change freely. This time, he wanted to see two new compromise solutions. The following solutions were obtained: (1.11, 336, 515) and (0.55, 347, 528). The latter solution obtained had the value of N below 1 and that was chosen as the basis for the next classification. The value 0.55 was so low that the DM was willing to let it increase up to 1. Then, the DM wanted to study if the value of E could be minimized while letting the value of A change freely. He wanted to see three new solutions and the following ones were obtained: (9.36, 246, 448), (30.2, 7.23, 308) and (0.90, 333, 519). As can be seen from the solutions obtained, the first two were not acceptable but the third one seemed to be pretty good. At this stage, the DM was almost satisfied. Finally, he wanted to generate alternative solutions between the solutions (1.11, 336, 515) and (0.55, 347, 528) obtained after the second classification. By doing this, he wanted to see how the solutions would change when the value of N goes from 1.11 to 0.55. The number of alternative solutions was set to two resulting in compromise solutions (0.92, 336, 519) and (0.72, 332, 524). Now the DM was happy with the solution process and did not want to continue. The objective function values in the compromise solutions computed (numbered from NCS to 11) are shown in Table 1. To select the best compromise solution he needed to further analyze the solutions obtained which is done next.

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Table 1: Objective function values for the compromise solutions computed during the interactive solution process.

lower upper NCS 2 3 4 5 6 7 8 9 10 11

residual ammonium nitrogen concentration [gN/m3 ] 0.03 31.5 8.05 3.52 1.69 4.90 1.11 0.55 9.36 30.2 0.90 0.92 0.72

alkalinity chemical dosing rate [m3 /d] 0.45 354 218 286 326 298 336 347 246 7.23 333 336 332

aeration energy consumption [kW ] 308 599 460 490 506 477 515 528 448 308 519 519 524

6.3. Discussion As the desired level of the main criterion, concentration of ammonium nitrogen in the effluent, is fulfilled completely or almost by solutions 5, 6, 9, 10 and 11, only these are discussed further. The values of the decision variables in the compromise solutions are shown in Table 2. Table 2: Decision variable values for the compromise solutions computed during the interactive solution process.

NCS 2 3 4 5 6 7 8 9 10 11

CM LSS [kg/m3 ] 3.68 3.30 3.56 3.16 3.68 3.96 3.02 3.09 3.84 3.69 3.85

alkalinity chemical dosing rate [m3 /d] 218 286 326 298 336 347 246 7.23 333 336 332

O2 -concentration in last section of the reactor [g/m3 ] 0.19 1.13 0.66 1.17 0.71 0.72 1.59 0.68 0.56 0.99 0.84

Solution 6 has the lowest ammonium concentration, which is reflected as the highest aerator wire power and alkalinity consumption (see Table 1). Moreover, also the CM LSS was the highest of all options. It can be deemed that in solution 6 there is an unnecessary high consumption of aeration and chemicals and an unnecessary high sludge concentration without substantial increase of nitrification capacity or effluent quality. The remaining solutions are practically equal in terms of energy and chemical consumption and any one of them could be selected as the final solution. Because we need to have only one final solution (to be implemented), we make the decision based on the values of CM LSS (smaller values are better for implementation). For solutions 5 and 10, CM LSS is about 3.7 while for solutions 9 and 11 it is between 7

3.8 and 3.9. The final choice is thus made between solutions 5 and 10. Here, 10 is chosen because: - it gives a lower ammonium concentration with practically same CM LSS and only slightly more energy consumption than solution 5 and - lower ammonium concentration means more nitrifying biomass, which is important for operational safety in case of sudden drop of temperature and/or increase of flow. Let us add that the visualizations of IND-NIMBUS can support the final analysis carried out here between the best candidates. 7. Conclusions This study was developed to demonstrate the applicability of the combination of a simulator tool and an interactive multiobjective optimization system in solving multiobjective optimization problems. By combining the interactive multiobjective optimization tool IND-NIMBUS and the GPS-X simulator, we obtained an interactive design tool for WWTPs and could verify their operability together. With this tool, the designer is able to inspect the problematics related to WWTP design more realistically than before when (s)he can take into account various different evaluation criteria without a need to convert all the criteria into expressions about costs. Therefore, we avoid losing any information through unnecessarily simplifying the model considered. Typically, such a simplification is made just to make the optimization possible but we have here demonstrated that a more advanced and realistic approach is possible and has a lot of potential. The results obtained from the case study of WWTP design turned out to be promising and provide a good basis for further research. The logical route to proceed now is as follows: - a more complex process including multiple sludge circulations, aerated and unaerated reactor zones etc. shall be addressed (e.g. nitrogen removal by predenitrification or biological nitrogen and phosphorus removal by UCT-process), - reactor volumes and areas shall be used as decision variables, to include factors affecting investment costs and - more operational variables shall be included in the optimization, such as sludge circulation rates, DO concentrations in all aerated reactors, other chemical doses and sizes of functional reactor zones. In all, the field of WWTP design can benefit a lot when utilizing tools of interactive multiobjective optimization. 8. Acknowledgements This research was a part of the project PROSIM, Optimization of Wastewater Treatment with Process Modelling and Simulation supported by the Tekes, Finnish Funding Agency for Technology and Innovation. The authors wish to thank M.Sc. Suvi Luoma for useful comments about the manuscript. 9. References [1] M. M. Ali and C. Storey. Modified Controlled Random Search Algorithms. International Journal of Computer Mathematics, 1994, 54, 229–235. [2] E. Ayesa, B. Goya, A. Larrea, L. Larrea, and A. Rivas. Selection of Operational Strategies in Activated Sludge Processes Based on Optimization Algorithms. Water Science and Tecnology, 1998, 37, 327–334. [3] P. Bose, P. Biswas, and V. Tare. Optimal Choice of Wastewater Treatment Train by Multi-Objective Optimization. Proc. of the Joint International Conference on Computing and Decision Making in Civil and Building Engineering, 2006, Montreal, 676–685.

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