WO2000073861A1

WO2000073861A1 - Method and device for designing or optimizing a technical system

Info

Publication number: WO2000073861A1
Application number: PCT/DE2000/001565
Authority: WO
Inventors: Regina Hellwig
Original assignee: Siemens Aktiengesellschaft
Priority date: 1999-05-26
Filing date: 2000-05-17
Publication date: 2000-12-07
Also published as: JP2003501714A; EP1183574A1

Abstract

The invention relates to a method for designing or optimizing a technical system, according to which the technical system presents at least two defined target functions. Each target function is influenced by a defined number of continuous parameters whose values are taken from a defined continuous range of values, and a defined number of discrete parameters whose values are taken from a discrete range of values. The values assigned to the continuous and discrete parameters are combined in a discrete-continuous parameter vector (xC, xD), where xC designates the values of the continuous parameters and xD the values of the discrete parameters.

Description

description

Method and device for designing or optimizing a technical system

The invention relates to a method and a device for designing or optimizing a technical system.

For the design of a complex technical system or the optimization of the system during the operating phase, a multitude of different parameters are often of interest, which can also have different effects on certain properties or requirements of the system. The representation of the characteristics of system properties can be adopted by target functions, which each parameter with a scalar size, i.e. the objective function value.

In practice, this poses the problem of finding value assignments for the parameters in which the objective function values represent the best possible compromise of the different desired properties and requirements. For this purpose, the target functions are usually formulated so that the smaller the scalar value of the target function, the more positive the desired properties.

Since the target functions will practically never have the property that they all assume minimal values for the same parameter assignment, it is necessary to find one or more parameter assignments that are as good as possible with regard to all target functions. These parameter assignments or points are called efficient or pareto-optimal with regard to the target functions.

A point under consideration is defined as pareto-optimal if there is no further point with the property that the further point is equally good in all goals (the target function one has a value less than or equal to) and is better in at least one target (the objective function has a lower value) than the point under consideration.

Known methods for solving such multi-goal problems (multi-goal minimization problems) deal with either the solution of continuous or discrete multi-goal problems.

In practice, when designing or optimizing technical systems, it is often necessary to consider both continuous and discrete parameters. A continuous parameter is understood to be a parameter that can assume values from a range of values that is continuous at least in sections, while a discrete parameter is understood to mean a parameter that can only assume values from a discrete range of values.

For example, the technical system can be the preheating section for the feed water of a steam power plant. The preheating section is supplied with hot steam, which is taken from the turbine or turbines in areas of low, medium or high pressure. The preheating section comprises several heat exchangers of different types, which serve to supply the thermal energy contained in the steam supplied to the cold feed water and to preheat it.

The discrete design or optimization parameters to be taken into account are, for example, the existence of a heat exchanger at a certain point, the type of heat exchanger (desuperheater, condensation preheater, condensate cooler or the combination of the heat exchanger comprising a desuperheater, condensation preheater, condensate cooler), the position of the heat exchanger (relative to several possible steam extraction positions on the turbines) etc.

For example, the pressure and temperature of the one matched steam supplied and the temperature and pressure of the steam leaving the heat exchanger or the temperature of the condensate leaving the heat exchanger are taken into account.

The problem now is that the multi-target minimization explained above must take into account both continuous and discrete parameters.

Some of the previously known design processes for technical systems only use solution processes for continuous multi-target optimization. This means that discrete parameters must be assigned a certain value assignment from the outset. In this way, the specialist entrusted with the problem has to make a certain selection for the discrete parameters from the outset, thus introducing certain preferences into the solution. This harbors the risk that advantageous solutions that require a value assignment for the discrete parameters that does not appear to be advantageous at first glance will not be found.

Another part of known design processes for technical systems discretizes the continuous parameters, i.e. the continuous value ranges are discretized. Discrete multi-target optimization methods are used to solve the then discrete multi-target problem. This procedure has the disadvantage that valuable information is lost when the continuous parameters are discretized, for example information which is contained in the slope or curvature or, more generally, in the n-differentiated functions.

Furthermore, known design methods, whether discrete or continuous, try to incorporate the decision-maker preferences into the search for suitable parameter assignments. This can mislead a process and make the decision maker aware of interesting parameter evidence. robbing. Renounce known design methods that reproducing the at ^¬ preferences are usually capable only under very restrictive conditions to the problem of finding all Pareto optima.

On the basis of this prior art, the invention is based on the object of creating a method and a device for designing or optimizing a technical system, all possible parameter assignments being found which are optimal with respect to the target functions.

The invention solves this problem with the combinations of features of claims 1 and 14, respectively.

According to the invention, the discrete-continuous multi-target optimization problem is broken down into a plurality of continuous multi-target optimization problems, each with a fixed parameter assignment for the discrete parameters. The number of continuous optimization problems is determined by the number of possible different parameter assignments for the discrete parameters. The continuous-pareto-optimal value assignments for the continuous parameters found in this way (with a specific value assignment for the discrete parameters in each case) are then searched with a discrete search strategy for points which are pareto-opto al with respect to the target functions (value assignments for all parameters) .

Splitting the discrete-continuous optimization problem ensures that no information contained in the continuous part of the problem is lost, as would be the case if this part were discretized.

According to the preferred embodiment of the invention, the discrete search strategy comprises a series connection of several discrete sub-searches, each with a required number of steps, each step of the sub-search method A pairwise comparison of a reference point (one current reference point per sub-search) taken from the continuously continuous pareto-optimal points is carried out with another continuous-pareto-optimal point. The sub-search procedure operates stochastically on pairs of points, consisting of the reference point of the sub-search (first partner) and the comparison point currently under consideration (second partner), a stochastically selected continuously-pareto-optimal point.

The use of a stochastic method e sub-search ensures a reduction of the theoretically infinite, in practice still extremely high numerical effort. In addition, such methods provide results that are more or less independent of the number of start point pairs or the selection of the start point pair. In addition, there is the advantage that the expert entrusted with the design of the technical system does not have to bring any preferences into the solution process from the outset and can theoretically determine all possible pareto-optimal points with a positive probability.

According to an embodiment of the method according to the invention, in each sub-search step, starting from the current pair of standpoints, each of the neighboring pairs of points for the pairwise comparison of the comparison point of this pair of neighboring points with the reference point with a predetermined probability from the available, the Stand pair of neighboring points selected.

The reference point serving as the starting point for the search strategy can be selected at random, with the continuously pareto-optimal points being assigned a uniform probability distribution. Since the search strategy is aimed at finding a Pareto optimum for each start reference point that dominates it, it can be guaranteed that all Pareto-Optima have the best possible chance of being found.

According to a preferred embodiment of the method according to the invention, the stochastic method, which processes a sub-search problem, is such that, starting from the pair of standpoints, a stochastically generated pair of neighboring points is jumped to when the comparison ratio of the pair of neighboring points is at least as high "Good" is like that of the standpoint pair, in other words:

• If the reference point of the sub-search dominates the comparison point in the pair of standing points, it does not matter how the reference point and the comparison point are in relation to each other in the pair of neighboring points;

• If there are no dominances in the pair of standing points between the reference point and the comparison point, this must also apply to the pair of neighboring points or the comparison point must dominate the reference point;

• If the comparison point dominates the reference point in the pair of standing points, this must also be the case in the pair of neighboring points.

If the comparison ratio in the neighboring point pair is “worse” than in the standing point pair, the neighboring point pair is accepted with a predetermined probability less than 1 and greater than 0 as a new standing point pair. As a consequence, a proposed neighboring point pair is surely always started if the comparison point dominates the reference point.

According to the preferred embodiment of the invention, the current reference point of a sub-search is recognized as the Pareto optimum if the stochastic method is based on a agreed number of examined pairs of points, which can be determined by a given termination criterion, does not provide a pair of points at which the comparison point dominates the current reference point. If this is not the case, the comparison point of the pair of result points becomes the current reference point of a further sub-search. In an analogous manner, sub-searches are appended to one another until a sub-search ends with the information that their reference point is pareto-optimal.

To find several or, if possible, all Pareto-Optima, several sequences of sub-searches can be started simultaneously or successively from different, mutually non-dominating reference points.

According to another embodiment of the method according to the invention, the sequence of sub-searches after the detection of a reference point as Pareto-Optimum with the comparison point of the pair of results as the reference point of the first subsequent sub-search can be used to find several or if possible all Pareto-Optima continue, which is more likely than not to be dominated by the Pareto optimum (by definition this point cannot of course dominate the Pareto optimum), ie with a point that is more likely to be "as good" as the pareto optimum as worse. This point will usually not itself represent a pareto optimum (but can!), so that the search strategy proceeds from this point to another pareto -Optimum can get.

According to the preferred embodiment of the method according to the invention, the Metropolis algorithm is used as the stochastic method for the sub-searches.

According to one embodiment of the invention, when solving the current discrete sub-problem, the information that continuously-pareto-optimal points each have a fixed value assignment of the discrete parameters is mutually exclusive not dominate, can be used to reduce the search space for the discrete sub-search.

For example, in a sub-search, all of the continuous-pareto-optimal points belonging to the solution set of the continuous multi-target optimization problem for a first parameter assignment for the discrete parameters can be excluded from the search space if it was found that a solution to the solution set of the continuous multi-target Optimization problem for a second parameter assignment for the continuous-pareto-optimal point belonging to the discrete parameters dominates at least one of the points belonging to the solution set mentioned and is the reference point of the sub-search.

Further embodiments of the invention result from the subclaims.

The invention is explained in more detail below with reference to an embodiment shown in the drawing.

The single figure shows a block diagram of a device for carrying out the method according to the invention.

The technical system 1 shown schematically in the single figure is described by m _c continuous parameters and m _D discrete parameters. The pareto-optimal parameter assignments are output by the device 3 for design via an output unit 5. The parameter assignment can be output by an output unit 3 designed for this purpose as a screen. This will generally be required by the expert entrusted with the design of the technical system. Furthermore, as shown in the figure, it is also conceivable that a specific one of the possibly several found pareto-optimal parameter assignments are output directly to the technical system 1 in the form of signals. As a result, the technical system 1 can also be optimized during its operation. The device 3 further comprises a processor unit 7 and a plurality of memories or memory areas assigned to it, namely the program memory or memory area 9, the memory or memory area 11 for the target functions and the memory or memory area 13 for the value ranges of the individual continuous or discrete parameters.

In addition to the structure of the target functions, data about variable constants of the target functions can be entered into the memory area 11 for the target functions via a receiving unit 15. These can be parameters which, according to the procedure for the design or optimization of the technical system, are not freely selectable within certain value ranges; In particular, parameters y _{s of} the system 1 that cannot be directly influenced by the device 3 or variables y _υ describing environmental influences on the technical system can be taken into account in this way.

In this way, a system 1 which is in operation can be adapted to changed environmental conditions or changed system-inherent conditions and can be optimized or tracked accordingly. The system parameters y _s , which are not freely selectable or are not available for the design or optimization, can be detected, for example, by means of measuring devices (for example, the technical system integrated), which are not shown in detail, and can be supplied to the device 3 of the device 3. In the same way, the environmental sizes γ _υ or sizes of other (for example upstream or downstream or higher-level technical or other systems) can be input via the emitting unit 15.

The emitting unit 15 also serves at the same time for the manual input of the value ranges required for the system description for the target functions into the memory 13. understandably, the input can also be made by data transmission from another computer or the like.

The program memory 9 contains a program which is used to determine the one or more pareto-optimal parameter assignments for the m _c continuous parameters and m _D discrete parameters. To solve the continuously discrete optimization problem, the parameters are combined to form a continuously discrete parameter vector (X _C , X _D ). With the n target functions fι (x _c , XD) to f _n (x _c , XD) the multi-target optimization problem can be written as:

Parameter assignments for the parameter vector (X _C , XD) are therefore sought which are as good as possible with regard to the target functions, ie in which the target functions simultaneously assume the lowest possible value.

This discrete-continuous multi-target optimization problem I is broken down into a plurality of purely continuous optimization problems

for a permissible value assignment x _D for the number m _{D of} the discrete parameters. The number of purely continuous optimization problems II results from the number of permitted different value assignments for the discrete parameters.

These purely continuous optimization problems can be solved with known continuous multi-target optimization methods, which therefore do not require any further explanation at this point.

The continuous methods applied to the majority of problems II provide one or more points that are pareto-optimal for each problem II, which are also referred to below as continuous-pareto-optimal points. These form a search space to which a discrete search strategy is applied, which is based on a pairwise comparison of the continuously pareto-optimal points and is subdivided into several discrete sub-searches.

For the first sub-search, a point is randomly selected from the search space as a reference point. For subsequent sub-searches, the reference points each result from the comparison point of the result point pair of the previous sub-search. The reference point is then compared with other points using a stochastic method.

The comparison is based on a "better", "worse" or "equally good" statement according to the following pattern:

A point is rated "better" if it dominates another point, a point being considered dominant if it is at least equally good in all objective functions (ie has an at least equally low value) and better than that in at least one objective function Reference point.

A point is rated "worse" if it is dominated by the comparison point and "equally good" if neither point dominates the other, or vice versa. So it will set a scalar objective function that evaluates the pair of points to be compared. For example, the statement "partner 2 better than partner 1" (= pair of points "better") with "0", the statement "partner 1 better than partner 2" (= pair of points "worse") with "1" and the statement " Partner equally good "(= pair of points" equally good ") with" 0.5 ".

The Metropolis algorithm, for example, is suitable for solving the individual discrete sub-problems. A neighborhood structure is determined, which is determined by the probabilities with which each pair of points is generated from each pair of standing points.

The stochastic method applied to the individual discrete sub-optimization problem in each step either delivers a new reference point after a certain number of comparisons starting from the starting point or current reference point, or it is terminated with the statement “es” after a defined termination criterion has been reached is no better point than the current reference point ". In this case the current reference point is considered pareto-optimal.

The stochastic method which is preferably to be used should also be designed in such a way that not only better or equally good point pairs are jumped to in any case (ie with the probability “1”), but also worse point pairs with a certain probability. The latter is necessary in order to use the method not to get caught in "local minima".

If the comparison point of the result point pair of the previous sub-search dominates their reference point, this comparison point is defined as the reference point of the new sub-search and the stochastic, discrete search method is started again. If a current reference point is identified as pareto-optimal according to the aforementioned criteria, the process can be terminated after the method has been trained. However, starting from a starting reference point, only one Pareto optimum is reached. In order to record all or several Pareto-Optima, it is therefore necessary to start the search strategy described above from several different start reference points. This can be done either one after the other or simultaneously.

The starting reference points should be chosen so that they do not dominate each other. This can be done using a suitable stochastic selection.

Another possibility is not to abort the search strategy described above after recognizing a Pareto optimum, but to continue with an "equally good" point.

Claims

claims

1. method for designing or optimizing a technical system,

a) in which the technical system comprises at least two ^pre-¬ passed objective functions;

b) in which each objective function is influenced by a predetermined number of continuous parameters, the parameter values of which are taken from a predetermined continuous value range, and a predetermined number of discrete parameters, the parameter values of which are taken from a discrete value range;

c) in which a value assignment of the continuous and the discrete parameters m is combined into a discrete-continuous parameter vector (X _C , X _D ), with x _c the value assignment of the continuous parameters and x _D the value assignment of the discrete

Parameter is designated;

d) in the case of the value assignments of the parameter vector which are pareto-optimal with respect to the target functions and in each case belong to the points

(Xc, XD)

I) first, using a method for solving continuous multi-goal problems for all admissible or sensible value assignments x _{D of} the discrete parameters which, with respect to the target functions, with the discrete parameters being consistently fixed and with pareto-optimal points and associated value assignments for the continuous ones Parameters are determined; and ii) then, from the majority of the continuously pareto-optimal points using a discrete search strategy, the pareto-optimal points with respect to the continuously-discrete target functions and the associated value assignments of the discrete-continuous parameter vector (XC / D) are determined.

2. The method as claimed in claim 1, in which the discrete search strategy comprises a plurality of discrete sub-searches, each with a required number of steps, with each sub-search using a stochastic method in pairs to make comparisons of one of the continuously-pareto determined optimal points taken from the reference point can be carried out with further continuously-pareto-optimal points.

3. The method as claimed in claim 2, in which, in each sub-search, starting from a pair of standpoints consisting of the current reference point of the sub-search and a continuously pareto-optimal point, with a predetermined probability from the available ones , the neighboring point pairs, neighboring point pairs, which each consist of the current reference point and a further continuously pareto-optimal point, are selected.

4. The method according to claim 2 or 3, in which the reference point serving as the starting point for the search strategy is selected randomly, with a uniform probability distribution being assigned to the continuously pareto-optimal points.

5. The method according to any one of claims 3 or 4, wherein the stochastic method for the sub-searches is such that for each sub-search a neighboring point pair generated randomly from the standpoint pair as a new one Stand-point pair is accepted if the ratio of the Vergleichsver ^¬ neighboring pair of points so falls at least "good" ^¬ as that of the stand-point pair, the comparison ratio is defined as at least as "good" when

a) in the pair of standpoints, the reference point of the sub-search dominates the comparison point and the comparison ratio of the neighboring pair of points is arbitrary;

b) in the pair of standing points neither the reference point dominates the comparison point nor vice versa and in the neighboring point pair neither the reference point dominates the comparison point nor vice versa or the comparison point dominates the reference point;

c) the reference point dominates the reference point in the pair of standing points and the reference point dominates the reference point in the pair of neighboring points; and

in which the neighboring point pair is accepted with a predetermined probability of less than 1 and greater than 0 as a new pair of standing points if the comparison ratio in the neighboring pair of points is “worse” than in the pair of standing points.

6. The method according to any one of claims 2 to 5, wherein the current reference point is recognized as the Pareto optimum if the stochastic method does not deliver a pair of points at which the. After a predetermined number of examined pairs of points, which can be determined by a predetermined termination criterion Comparison point dominates the current reference point.

7. The method according to any one of claims 2 to 6, in which for the finding of several Pareto optima the pairwise comparisons simultaneously or successively of different Chen, mutually non-dominant reference points is started.

8. The method according to any one of claims 2 to 7, in which for the finding of several Pareto-Optima the pairwise comparisons are continued after recognizing a reference point as Pareto-Optimum with a reference point which is more likely than not to be dominated by the Pareto-Optimum than is dominated.

9. Method according to one of claims 2 to 5, in which the metropolis algorithm is used as the stochastic method for the sub-searches.

10. The method according to any one of claims 2 to 9, in which a discrete scalar target function is defined for the application of the stochastic method, which evaluates the ratio of two points of a pairwise comparison.

11. The method according to claim 10, in which the discrete scalar objective function evaluates the comparison of the two points to be compared with a discrete value MIN, preferably MIN = 0, if the comparison point dominates the current reference point, preferably with a discrete value MAX MAX = 1 if the current reference point dominates the comparison point, and with a discrete value MID, preferably MID = 0.5, if neither of the two points dominates the other.

12. The method according to any one of the preceding claims, in which, in solving the current discrete sub-problem, the information that continuous-pareto-optimal points for a fixed value assignment of the discrete parameters do not dominate each other to reduce the search space for the discrete sub-search is used.

13. The method according to claim 12, in which all of the solution quantity of the continuous multi-target optimization problem for a first parameter assignment for the discrete parameters continuous-pareto-optimal points belonging to the search space of a sub-search are excluded if it was found that a the continuous-pareto-optimal point belonging to the solution set of the continuous multi-target optimization problem for a second parameter assignment for the discrete parameters is dominated by at least one of the points belonging to the solution set mentioned and is the reference point of the sub-search.

14. facility for designing or optimizing a technical system,

with a processor unit and a program stored in a working memory, which carries out the method steps according to one of the preceding claims,

with an emitting unit, by means of which the value ranges for the discrete and the continuous parameters can be entered and can be stored in a memory area, and

with an output unit, via which the pareto-optimal points can be output as data for the design of the technical system and / or as signals for optimized control of the technical system.

15. Computer program product, wherein the program m the working memory (9, 11, 13) of a data processing device or a processor unit (7) of a device according to claim 14 can be loaded and which has a code for performing the method steps according to one of claims 1 to 13 includes.