MCDM 2004, Whistler, B. C. Canada August 6-11, 2004

MULTIOBJECTIVE DECISION MAKING FOR PAPERMAKING Jari Hämäläinen Department of Applied Physics, University of Kuopio, P.O. Box 1627, FIN-70211 Kuopio, Finland (Earlier at Metso Paper Inc., Jyväskylä, Finland) mailto:[email protected]

Kaisa Miettinen Helsinki School of Economics, P.O. Box 1210, FIN-00101 Helsinki, Finland mailto:[email protected]

Elina Madetoja, Marko M. Mäkelä Department of Mathematical Information Technology, University of Jyväskylä, P.O. Box 35 (Agora), FIN-40014 University of Jyväskylä, Finland mailto:[email protected] , mailto:[email protected]

Pasi Tarvainen Numerola Oy (Inc.), Väinönkatu 11 A, FIN-40100 Jyväskylä, Finland mailto:[email protected]

Keywords: Multiple-criteria decision making, interactive multiobjective optimization, pulp and paper industry, decision support system Summary: Pulp and paper industry foresees that mathematical modeling and decision support systems are among the most potential future technologies in process automation, for example, to develop competitiveness of the industrial sector. Our answer to the technology pull is a virtual paper machine and an intelligent decision support system based on mathematical modeling and multiobjective optimization. In this paper, we describe a realization of such a virtual paper machine and associated decision support tool for papermaking. Furthermore, some very encouraging numerical results of multiobjective optimization are given based on mathematical models validated with a pilot paper machine. 1. Introduction We as typical consumers of printed paper products do not bother about paper quality parameters like basis weight, thickness and resulting density, strength properties or gloss, among others. Instead, it is important for us that complex notations or detailed figures are printed clearly in journals and books, and all the pages seem and feel the same for the reader. So, what we do care a lot, is ink absorption and missing dots, which are results of paper quality properties. Some printing properties as well as qualitative paper properties are conflicting. On the other hand, paper producers want to maximize their profitability. Better paper quality means higher price, but only to some extend; paper quality is also a market-share issue. In addition, energy consumption should be minimized, cheaper fillers and fibers should be used as much as possible instead of expensive chemical pulp, and of course, production amount should be maximized. Production amount depends clearly on the speed and the width of a papermaking machine, but also on runnability and efficiency of the papermaking process. If a paper machine is being run too fast or the paper is not strong enough, the process is disturbed and

more of web breaks will follow resulting in more downtime for the process. Thus, controlling the whole papermaking process taking into account paper quality, efficiency, production amount, costs as well as environmental aspects, is very complex and, therefore, new modeling, optimization and decision support tools enabling such an overall approach are required. Because of several conflicting objectives, we need tools of multiobjective optimization. Investment costs of a new pulp or paper mill are huge, hundreds of millions euros. Furthermore, the annual production of one paper machine can be up to several hundred thousands tons of paper. Efficiency of such papermaking production lines is obviously one of the most important goals when developing new paper machines and process automation systems. On the other hand, today's trend is to include more and more unit processes (like coating and calendering) into the same production line. However, because efficiency of each unit process is less than 100 % in practice, efficiency of a chain of such processes will decrease as the number of unit processes increases. This trend is pushing process automation technology from local unit process controls towards global automation systems to handle the whole process and the multiple objectives simultaneously. Furthermore, traditional feedback controls are giving way to modelpredictive controls. TAPPI (Technical Association of Pulp and Paper Industry, see: www.tappi.org) organized a Forest, wood and paper industry technology summit in May 2001. As a conclusion, the process automation work group (see: www.tappi.org/content/pdf/tech_summit/Process_Automation.pdf) regarded mathematical modeling and related decision making tools as one of the most potential technologies to enhance process automation in the future. The group ended up pointing out the following three focus areas: Process visibility sensors, decision making tools, and control system techniques (see also Brown, 2001). In this paper, we follow these visions by giving our contribution to the technology pull for modern decision making tools in the pulp and paper industry. Our approach is first to model the whole papermaking line, that is, the paper machine, instead of treating only individual machine parts and the corresponding unit processes and their submodels, as has been mainly done so far. Secondly, we make use of the simulation model -based optimization by integrating the line model with multiobjective optimization. In this way, we can consider the papermaking process as a whole and take the multiple conflicting criteria into account simultaneously. The model includes papermaking process (i.e., flow of water, fibers, fillers and other papermaking substances), qualitative paper properties as well as runnability and efficiency of the machine. Both deterministic and stochastic submodels for process and qualitative properties have been developed. By integrating those submodels, the whole papermaking line is modeled and the resulting simulation model is called a virtual paper machine. The virtual paper machine has approximately the same parameters to specify machine dimensions and control actions as the real paper machine has. The virtual paper machine is described in Section 3. We use as a multiobjective optimization tool the NIMBUS method that is an interactive method. (Miettinen and Mäkelä, 1995) By integrating then virtual paper machine together with NIMBUS, we obtain a preliminary version of the decision support system. The input parameters of the virtual paper machine can be used as decision variables in optimization. Furthermore, the desired paper quality properties and the economical way to run a machine can be set to objectives to be optimized by the NIMBUS method. By means of such an intelligent and interactive decision support system, a papermaking expert can search for the best compromise solution between numerous criteria describing different paper quality properties, efficiency and others. We believe that our approach, described in Section 4, is a novel way to analyze complicated decision tasks that arise in the paper production. At the end of the paper, we present encouraging numerical results of using multiobjective optimization for controlling the whole papermaking process.

2. Decision support system for papermaking Papermaking experts, like managers, R&D-engineers and operators, need new capabilities that can enhance their ability to make optimal decisions quickly. They can benefit from decision support tools that provide useful, computer-revised information rather than a mass of data. Combining such information with process understanding helps a papermaking expert to control the papermaking line and make reasonable choices of its contradictory process and quality targets. A decision support tool for papermaking can be determined in many ways. What we mean by a virtual paper machine -based decision support tool is a software that supports a papermaking expert to control the papermaking line taking into account the contradictory process, quality, and runnability targets. The basis of the decision support tool is what we call the virtual paper machine, that is, a simulation model for the whole papermaking line which is reliable enough, accurate enough, and predictive enough for realistic simulations. This model should also be furnished with approximately the same parameters to specify machine dimensions and control actions as a real paper machine has. By using the virtual paper machine, the papermaking expert can test and analyze different machine concepts and running conditions. By means of the decision support tool governed by the virtual paper machine, the papermaking expert can move from a trial-and-error approach to a computer-aided decision process. Namely, with this system she or he does not operate with input parameters determining papermaking line and running conditions, but exactly with those papermaking line output parameters that are essential to make strategic and other decisions. The decision support tool then determines the control setups and other input parameters associated to process and quality values decided by the papermaking expert. The decision support system should be an interactive tool that together with the expert seeks optimal process and quality parameters for an existing or new papermaking line. Based on above discussion, we next list the most important requirements that are set to the virtual paper machine and related papermaking decision support tool: • •

•

•

•

•

From unit-process approach to papermaking line modeling: Relationships among multiple process variables and their local and non-local responses should be presented to an expert. Fast, accurate and predictive responses: The virtual paper machine should give fast and reliable information about the papermaking process in terms of interactions among operating parameters and cause/effect relationships. Therefore, it should contain a large assortment of process and quality models consisting of both extrapolatable physics-based as well as fast data-based empirical models. Flexibility to test and analyse different machine setups and running conditions: The virtual paper machine should contain various machine constructions and line concepts. In addition, it should allow the simulation of customised papermaking lines as well as unit-process investigations. Computer-aided decision support: The virtual paper machine itself produces state information about the chosen process, that is, process conditions and quality properties for given concepts and setups. Moreover, it should contain tools for evaluation of the process and paper quality as well as methodology to improve the process conditions and/or paper quality. In other words, the system should be able to automatize all or, at least, some steps of the design process. Modeling platform: The virtual paper machine should reflect the current stage of papermaking modeling; as new process and device models are developed, they should be available in the system. Also, it should offer analysis tools or their interfaces, at least. Usability of virtual paper machine and decision support tool: The virtual paper machine and associated decision support tool should be developed for papermaking expert, not for modeling or optimization expert, for instance.

Here we concentrate on the system implementation mainly on a computing level and do not discuss the usability aspects like user interfaces and so on. To develop a virtual paper machine, we need to model the whole papermaking line, up to some accuracy. Our approach has been to make use of the unit process models developed for individual machine parts and the corresponding unit processes. Secondly, in order to realize the decision support tool, we apply the

simulation model -based optimization by integrating the line model with multiobjective optimization. In the following two sections, we shortly describe the two main computational tools related to the virtual paper machine and the decision support tool. 3. Mathematical modeling of papermaking 3.1 Papermaking process A virtual paper machine is a simulator consisting of mathematical models for paper machine unit processes, paper quality properties as well as models for runnability and efficiency of a paper machine. A typical papermaking process consists of two main parts, which are the base papermaking and the paper finishing (Gavelin, 1998). The finishing process can either be a separate machine, or an on-line process as shown in Figure 1.

Headbox and Former

Pressing

Drying

Coating Calendering

Figure 1: Paper machine and on-line finishing process. A process for the base paper forming consists of four main parts (upper process in Figure 1). The stream of fiber suspension coming from the headbox is lead to the former (also known as the wire section), where the suspension forms a paper web via dewatering. After filtration, the paper web has a porous structure, with pores filled with water. Some water located in the pores is removed by squeezing the paper web between two pressing rolls. This stage is just after the wire section and is called the pressing section. The remaining water is removed in the drying section by evaporation. This is done by contacting the paper web with a series of steam-heated cylinders. After the drying section the production continues in the finishing part (lower process in Figure 1), where the base paper is coated and calendered to obtain a smoother and glossier surface. 3.2 Modeling of papermaking process A virtual paper machine can be constructed of several different types of submodels describing papermaking unit-processes, paper quality properties and others. To start with, we have a collection of systems of partial differential equations for describing physical phenomena. For example, for the fluid flows in the headbox, we employ the Navier-Stokes equations (Hämäläinen, 1993). Furthermore, we have statistical models based on real data for describing both the water removal process and quality properties. In addition, we have as alternative submodels model surrogates (i.e., meta-models) that simplify computationally demanding submodels. These reduced submodels are useful in optimization, when we want to avoid computational burden. An example of a model surrogate used in the experiments is a polynomial submodel simplifying the physical wet pressing model (Hiltunen, 1995).

One example of a virtual paper machine is illustrated in Figure 2. It is a model for base paper in SCpaper (super-calendered) production. The virtual paper machine contains submodels for the following components: a headbox, a wire section, a pressing section, and a drying section. We have modeled each component individually and, thus, their models are originally dissimilar. Each submodel has its own input parameters and, among them are parameters coming from the previous models. The idea is that in the chain of submodels, we obtain values for the qualitative properties of the produced paper after the last submodel. The qualitative properties are considered as profiles in the cross-machine direction (in the direction of the width of a machine) of the paper machine. By means of the virtual paper machine, we want to control the quality of the produced paper and, thus, we study paper properties such as tensile strength ratio, normalized β-formation, basis weight and fiber orientation angle. The tensile strength ratio describes the ratio between the forces needed to stretch the paper both in the machine direction and the cross-machine direction until it breaks. The β-formation describes the variation in the basis weight in a small scale, whereas the basis weight is the weight in grams of one square meter of the produced paper. The last property is the fiber orientation angle that describes the directions of the fibers. If we were modeling an on-line finishing process, additional models would be included in the virtual paper machine to cover finishing processes and the related paper quality properties. Also, paper quality and runnability depends strongly on the raw material, that is, the furnish made by a stock preparation process, but it is not included here in the model.

Figure 2: Modules of a virtual paper machine simulator for base paper. 3.3 Dynamic line model generation The dynamic simulation model generation is based on the existence of several alternative submodels of various types modeling the same phenomenon. These submodels have different level of complexity. Then the dynamic simulation model generation means that the system constructs a suitable simulation model consisting of a chain of different submodels for each simulation or optimization case. In other words, the simulation model does not always contain the same submodels, but each submodel is chosen according to the problem setting to be appropriate for each particular purpose. For example, in optimization, we are able to use less time-consuming submodels to save CPU-time. The idea is that the system allows the selection of any kind of (permitted) submodel chains to be simulated. In optimization, the simulation model is constructed such that it is able to produce required outputs for evaluating the objective functions.

The current implementation of the dynamic generation is based on the usage of the submodel outputs for identifying the simulation case: The user defines desired output(s) to be simulated or optimized and, based on that, the software fixes a chain of submodels to be the associated simulation model. After that, the system checks that the resulting simulation model (chain) is compatible and contains only those submodels necessary to produce desired outputs. The dependencies between the submodels and the outputs of the submodel can be defined in databases, which are used during the model generation. More information about the dynamic simulation model generation can be found in (Madetoja et al.). 4. Computer-aided decision support based on the NIMBUS method Developing intelligent decision support systems based on the virtual paper machine and multiobjective optimization is a potential basis for handling complex papermaking processes. In this section, we explain the main ideas of this approach. 4.1 Multiobjective optimization In general, we define a multiobjective optimization problem as follows

min ( f1 ( x ),..., f k ( x ) ) subject to x ∈ S ,

(1)

where f ( x ) = ( f1 ( x ),..., f k ( x ) ) is a vector of objective functions or an objective vector and x is a T

vector of decision variables from the feasible set S ⊂ ℜ defined by constraint functions. We denote the image of the feasible set by f ( S ) = Z and call as a feasible objective set. If some objective function n

fi is to be maximized, it is equivalent to consider minimization of − f i . In multiobjective optimization optimality is understood in the sense of Pareto optimality. A decision vector x * is Pareto optimal, if there does not exist another objective vector x such that

f i ( x ) ≤ f i ( x * ) for all i = 1,..., k and f j ( x ) < f j ( x * ) for at least one index j . These Pareto optimal solutions constitute a Pareto optimal set. From a mathematical point of view, all of them are equally good and they can be regarded as equally valid compromise solutions of the problem considered. Because vectors cannot be ordered completely, there exists no trivial mathematical tool in order to find the most satisfactory solution as the final one. Thus, an expert of the problem known as a decision maker can participate in the solution process and in one way or the other, determine which of the Pareto optimal solutions is the most desired to be the final solution. Sometimes, methods for multiobjective optimization are divided into four classes according to role of the decision maker. First, there are methods with no decision maker, where the final solution is chosen by some mathematical algorithm. The three other classes are a priori, a posteriori and interactive methods, where the decision maker participates in the solution process before or after it or iteratively. We concentrate on the last-mentioned method in this paper. It is often useful for the decision maker to know the ranges of objective functions in the Pareto optimal set. An ideal objective vector gives lower bounds for the objective functions in the Pareto optimal set and it is obtained by minimizing each objective function individually subject to the constraints. The upper bounds of objective functions in the Pareto optimal set are usually difficult to calculate, and thus their values are approximated, for example, by pay-off tables (Miettinen, 1999). Our main idea in developing the intelligent decision support system is to integrate the virtual paper machine together with an interactive multiobjective optimization method. The method we are using is NIMBUS (Miettinen, 1999; Miettinen and Mäkelä, 1995) and so far we have been able to prepare a

preliminary integration of these two systems (Madetoja, 2003; Hämäläinen et al, 2002; Hämäläinen et al, 2003; Madetoja et al, 2003). 4.2 NIMBUS method

In interactive multiobjective optimization methods, it is important that the information given to and asked from the decision maker is easily understandable. The NIMBUS method is based on the idea of classification of objective functions. From a cognitive point of view, classification can be considered as an acceptable task for human decision makers (Larichev, 1992). In NIMBUS, the decision maker participates in the solution process continuously and iteratively. Finally, he or she decides, which of the Pareto-optimal solutions, is the most desired one. During the solution process, the decision maker classifies objective functions at the current Pareto optimal point into five classes, which are the following: 1. 2. 3. 4. 5.

Functions whose values should be improved. Functions whose values should be improved until a desired aspiration level. Functions whose values are satisfactory at the moment. Functions whose values can be impaired until a given bound. Functions whose values can change freely.

By classifying the objective functions the decision maker gives preference information and, based on that, scalarized single objective optimization problems can be formed. There are four different subproblems available in NIMBUS at the moment (Miettinen and Mäkelä 2002), and thus, the decision maker can choose if he or she wants to see one to four new solutions after each classification. The scalarized subproblems can be solved with appropriate single objective optimizers. Each of the subproblems generates a solution taking the classification information into account in a slightly different way. The NIMBUS method offers also a possibility to produce alternative, intermediate solutions between any two different solutions, for example, originating from two different scalarized subproblems. The main stages of the solution process in the NIMBUS method are described in Figure 3.

Calculate a strating point

User: Classify the objective functions and specify aspiration levels and bounds, if necessary. Formulate the subproblems and solve them. Present the old and the new solutions to the user.

Yes User: Specify User: Do you want to see different their number. alternatives?

Calculate and present the alternatives to the user.

No User: Select the most preferred alternative.

Yes

User: Do you want to continue?

No

Stop.

Figure 3: The NIMBUS method.

WWW-NIMBUS (Miettinen and Mäkelä 2000), a software implementing the NIMBUS method, can be used for academic purposes via the Internet at http://nimbus.mit.jyu.fi. WWW-NIMBUS offers several underlying single objective solvers to be used, for example, methods based on real-coded genetic algorithms (Miettinen et al., 2003) and sub-gradient bundle based methods (Mäkelä and Neittaanmäki, 1992). It also contains different visualization tools to illustrate solutions to the decision maker, and a symbolic (sub)differentiation tool. In the intelligent decision support system to be designed, the decision maker should be able to work interactively with the decision support tool to find the best compromise between the selected criteria related to different qualitative paper properties, efficiency of production process and others. Therefore, the system should be flexible for different types of usage and different users. What is a very important, phase of solution processes should be computationally efficient so that the interactivity will not be lost. 4.3 Sensitivity analysis using model-based differentiation

In order to realize an interactive decision support tool based on simulation models, we can make use of model-based differentiation. Namely, it allows us to use gradient-based single objective optimizers, which are usually more efficient than optimizers not utilizing gradient information. A similar idea was introduced by the name of generalized sensitivity equations in (Sobieszczanski-Sobieski, 1990). Typically, in real world problems, the problem formulation requires that the simulation model is solved before objective functions can be evaluated. In the model-based differentiation, we utilize the same idea in gradient calculations. Then the simulation model produces both the output (the state of the system) and the derivatives of the output with respect to the chosen decision variables. We employ also automatic differentiation techniques with the model-based differentiation to be able to avoid calculation errors and to hide calculation from the user. In our computer realization, the model-based differentiation is linked together with the dynamic line model generation (see Section 3.3) in the sense that only the derivatives that are determined using the dynamic line model generation are calculated for the optimization method. The overall sensitivity analysis implementation has been described in (Madetoja et al.) 5. Numerical experiments

0.31

0.31

0.30

0.30 Normalized B-formation

Normalized B-formation

In this section, we describe the use of a decision support tool based on the virtual paper machine. We start with a simple example illustrating the conflicting nature of the qualitative base paper properties in the wet-end of a paper machine (consisting of headbox, forming and pressing sections). In addition to some process control objectives, we have three qualitative properties to be minimized: β-formation, tensile strength ratio and air permeance (porosity) that are shown in Figure 4 as pair-wise graphs. As can be seen, better (i.e. smaller) tensile strength ratios lead to a poor β-formation (i.e. high values) and vise versa. In addition, a good β-formation can only be obtained by allowing high air permeance values.

0.29 0.28 0.27 0.26 0.25

0.28 0.27 0.26 0.25 0.24

0.24 0.23 2.80

0.29

0.23

2.82

2.84

2.86

2.88

2.90

Tensile strength ratio

2.92

2.94

2.96

450

475

500

525

550

575

600

Air permeance

Figure 4: Normalized β-formation as a function of tensile strength ratio (MD/CD) and air permeance.

625

The solutions in Figure 4 are all Pareto optimal. In other words, none of their components can be improved without impairing at least one of the others. The graphs in Figure 4 show some interdependencies of the optimized criteria lying on the Pareto optimal front. The example in Figure 4 is too simple to show the real complexity of controlling papermaking, but it gives an idea of the multiobjective nature of papermaking. In a real case, it becomes even more crucial to have a good multiobjective decision support tool in order to learn about the conflicting nature of the several objectives and to find the best solution, the best decision how to make good paper. 5.1 Problem setting

Next we present one multiobjective optimization problem and its solution process. The problem is an example of real world optimization problems, where values of the objective functions are produced by a virtual paper machine that mimics a phenomenon considered. In this example, the virtual paper machine imitated SC-paper (Super-Calendered paper) production and the model was constructed by the dynamic model generation technique and it included 23 different submodels. The optimization problem was solved with NIMBUS and an underlying subgradient based single objective optimizer (Mäkelä, Neittaanmäki; 1992). Gradient information was produced with model-based differentiation and automatic differentiation. We used all four scalarized subproblems after each NIMBUS classification. All the computations were carried out on the computer containing dual-processor system AMD Athlon(tm) XP processor 1900+ (1600 MHz) processor and 2 GB memory. The optimization problem contained altogether nine objective functions to be optimized, three to be maximized and six to be minimized. The objective functions described paper process and qualitative properties. There were functions to describe dry solids content of paper both before and after finishing in the super-calender. The objective functions described also such properties like basis weight, β-formation, and tensile strength ratio. There were four objective functions to describe gloss of the paper and PPS 10 property both on top and bottom side of paper. All the objective function values presented are normalized. The optimization problem contained 23 decision variables, which are the typical controls of paper machines. An expert was participating in solution process as a decision maker. 5.2 Interactive solution process

All the solutions are presented in Table 1such that each objective function has own column for its values and each row denotes NIMBUS classification or generation of alternative solutions. Table 2 contains all the classifications given the decision maker during the solution process. At first, NIMBUS calculated an initial solution that is presented in Table 1. Throughout the solution process the decision maker had the following aims. The dry solids content of the base paper should get as large value as possible. The basis weight value should be close to 1.0 and values of the β-formation and tensile strength ratio less or equal to 1.0 for both. The decision maker wanted the values of the PPS 10 (roughness) to be 1.0 for both top and bottom sides of paper and for the gloss of the paper on the top and bottom sides should be at least 1.0. He found it also important that the values between top and bottom sides were close to each others both for the PPS 10 and the gloss. The goal value of the dry solids content was 1.0. The solution process with the NIMBUS method contained altogether eight classifications and two generations of intermediate solutions. At the beginning, the decision maker wanted to control functions related to base paper quality and as the most important goal he wanted to optimize the basis weight value. By the first classification (see Cl. 1 in Table 2), he obtained a very good value for the basis weight and, also, the β-formation was improved. Thereafter, the decision maker wished to improve also the tensile strength ratio by keeping the values of the basis weight and β-formation stable, but this was not possible (Cl. 2 in Table 1). Thus, he tried to improve the tensile strength ratio by giving more freedom to change to the other function (see Cl. 3 in Table 2). Only very small improvements were obtained as can be seen in Table 1. He learned that there was a conflict between the β-formation and the tensile strength ratio.

Now, properties related to the base paper quality were a satisfactory level except for the tensile strength ratio, and the decision maker moved ahead to optimize also properties related to the finishing of the paper. At first, he wanted to improve PPS 10 bottom such that it would get better value that would be closer to the value of the PPS 10 top. In addition, the decision maker wanted to improve the dry solids content (Cl. 4 an Cl. 5 in Table 2). He was able to obtain a part of the desired improvements, but at the same time the basis weight value was impaired (Cl. 5 in Table 1). Next, the decision maker wanted to restore the basis weight at an acceptable level and also, still improve the dry solids content. However, he was not able to obtain both of the improvements and he chose the solution where the basis weight had an excellent value, but the dry solids content needed improvement. Then, the decision maker continued by improving the dry solids content and keeping the current value of the basis weight. Thereby, he found a solution (Cl. 6 in Table 1), where the basis weight and dry solids content had good values and in addition, the β-formation was also improved and gloss was at an acceptable level. However, the tensile strength ratio was dramatically impaired. Now, there were two very different solutions and hence, the decision maker decided to generate alternative intermediate solutions between them. The alternative solutions gave him knowledge about what kind of compromise solutions there would be between the conflicting objectives. He generated intermediate solutions twice and then he obtained a solution (see Table 1: Ge. 1 and Ge. 2) that he chose to be improved by classifications. The idea was to get small improvements without impairing obtained good values. By two classifications (Cl. 7 and Cl. 8 in Table 2) he was able to improve the basis weight, the βformation and the tensile strength ration until they reached acceptable levels (see Cl. 8 in Table 1). The compromise required that the value of base paper dry solids content was not improved much and the PPS 10 properties did not exactly obtain ideal values. Similarly, the dry solids content did not reach the ideal value, but the decision maker found it quite satisfactory. On the other hand, the values of gloss top and bottom were even better than the decision maker wanted. The decision maker was also pleased that in both the PPS 10 and gloss, the differences between the top and bottom sides were small.

Start Cl. 1 Cl. 2 Cl. 3 Cl. 4 Cl. 5 Cl. 6 Ge. 1 Ge. 2 Cl. 7 Cl. 8

Dry solids cont.(bas e paper) f1 Max 1.0091 1.0096 1.0096 1.0096 1.0081 1.0094 1.0095 1.0094 1.0095 1.0095 1.0096

Basis weight

βformation

Tensile str. ratio

PPS 10 top

PPS 10 bottom

Gloss top

Gloss bottom

Dry solids cont.

f2 Min 1.0521 1.0003 1.0003 1.0000 1.0000 1.0589 1.0003 1.0139 1.0028 1.0026 1.0010

f3 Min 1.0556 1.0010 1.0010 1.0008 0.8716 0.9590 0.5243 0.5628 0.5319 0.8919 0.9788

f4 Min 1.0313 1.0975 1.0975 1.0976 1.1108 1.1199 1.3429 1.3102 1.3362 1.0470 0.9979

f5 Min 1.0275 0.9987 0.9987 0.9986 1.0513 1.0289 1.0836 1.0848 1.0838 1.0836 1.0826

f6 Min 1.1623 1.0600 1.0600 1.0600 1.0485 1.0495 1.1671 1.1634 1.1663 1.1156 1.1175

f7 Max 0.8666 1.1098 1.1098 1.1098 1.0902 1.0902 1.0897 1.0750 1.0868 1.0868 1.0868

f8 Max 0.9586 1.1543 1.1543 1.1543 1.0771 1.0771 1.0763 1.0690 1.0749 1.0749 1.0752

f9 Min 0.9979 1.0332 1.0332 1.0331 1.0074 1.0122 0.9996 0.9989 0.9995 1.0035 1.0034

Table 1: Results of the optimization process.

Improved

Cl. 1

Cl. 2

Cl. 3

Cl. 4

Cl. 5

f1 f2 f3 f4 f5 f6 f7 f8 f9 f1 f2 f3 f4 f5 f6 f7 f8 f9 f1 f2 f3 f4 f5 f6 f7 f8 f9 f1 f2 f3 f4 f5 f6 f7 f8 f9 f1 f2 f3 f4 f5 f6 f7 f8 f9

Improved until desired level

Satisfactory

Impaired until given bound

Change freely

Desired level/ given bound

x x 1.0 1.0 1.0 1.0

X X X x x x

1.0

x x x x

1.0

x x

1.0 1.0 1.0

x x x x x x x

1.0

x x

1.0 0.9 0.9

x x x x x x x x x

1.0

x x x

1.0

x x x x x x x x x x

1.0

Cl. 6

Cl. 7

Cl. 8

f1 f2 f3 f4 f5 f6 f7 f8 f9 f1 f2 f3 f4 f5 f6 f7 f8 f9 f1 f2 f3 f4 f5 f6 f7 f8 f9

x 1.002

x x x x x x x

1.0

x x

1.002 1.0 1.0 1.09 1.09 1.07 1.07

x x x x x x x x x x

1.002 1.0 1.0

x

1.005

x x x x x x Table 2: NIMBUS-classifications.

7. Conclusions

A decision support system for papermaking was introduced in this paper. We described functionality of such a system on a general level as well as listed desired properties of the decision support tool. A computer realization based on a combination of modeling papermaking line and interactive, multiobjective optimization was also given. Finally, a realistic decision support problem related to papermaking line was solved by means of the software. Model-based decision support systems for papermaking have potential to become commercial software products or a basis for new customer services. According to our experience multiobjective optimization gives new insight to complex and contradictory phenomena and it helps a decision maker to find the best solution. And, even a small improvement in papermaking results in a huge economical value. For example, one percent increase in the production of a paper machine means in the order of 1 million euros value of saleable production. Finally there is only one objective to be optimized, that is, maximize profitability and to make more money. From a modeling point of view, it is not obvious how to link all inputs and outputs of the virtual paper machine to an economical objective. That is why the best solution is searched via multiple objectives and by using a model-based decision support system. References

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