Abstract:
A method, computer, and recording medium storing a program are provided which, based on local optimal solutions, more efficiently calculate an optimal global optimal solution in a global operating area. System calculates the global optimal solution by solving, using a genetic algorithm based on the local optimal solutions and the initial values, an equation, which should be satisfied by the plurality of design variables, by obtaining the plurality of combinations of design variables composing local optimal solutions for each design variable respectively calculated for each of a plurality of combinations of a plurality of operating states, and by obtaining initial values for the plurality of combinations of design variables used for calculating the global optimal solution.

Description:
This application is based on and claims the benefit of priority from Japanese Patent Application No. 2007-161819, filed on 19 Jun. 2007, the content of which is incorporated herein by reference. 
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a method, a computer, and a program for calculating an optimal solution of engine design variables. More specifically, it relates to a method, a computer, and a program for calculating an global optimal solution of design variables (e.g., valve position of exhaust gas recirculation (EGR), fuel injection timing, ignition timing, and the like) which minimize or maximize a combination of multiple objective variables (e.g., specific fuel consumption, nitrogen oxides emission concentration) for multiple combinations (modes) of multiple operating states (e.g., engine revolutions, loads, and the like) included in an operating area of the engine. 
     2. Related Art 
     Conventionally, various methods have been proposed for calculating an optimal solution of engine design variables. 
     For example, a computer expresses a certain objective variable in quadratic polynomials of multiple design variables, and calculates using a genetic algorithm or other calculating methods for each of multiple combinations of multiple operating states. Thereby, it is possible to obtain local optimal solutions of design variables which minimize or maximize the multiple combinations of the objective variables. 
     Such local optimal solutions may not be combined as is for the purpose of calculating the global optimal solution of design variables which minimize or maximize the multiple combinations of the objective variables in the entire operating area. 
     On the other hand, according to Japanese Unexamined Patent Application Publication No. Hei 11-353298, a method of calculating a comprehensive evaluated value by calculating a local preliminary evaluated value for each segmented evaluation area, and evaluating the values comprehensively, has been proposed for evaluating an engine and the like using a genetic algorithm online. 
     However, a method of further efficiently calculating a global optimal solution of design variables which minimize or maximize multiple combinations of objective variables in an entire operating area based on local optimal solutions has not been disclosed in any way in Japanese Unexamined Patent Application Publication No. Hei 11-353298. 
     SUMMARY OF THE INVENTION 
     An object of the present invention is to provide a method, a computer, and a recording medium on which a program for further efficiently calculating a global optimal solution of design variables which minimize or maximize the multiple combinations of objective variables in an entire operating area based on local optimal solutions is recorded. 
     More specifically, the present invention provides the following. 
     According to a first aspect of the present invention, a method of calculating a global optimal solution of design variables (e.g., valve position of EGR, fuel injection timing, ignition timing, and the like) which minimize or maximize a combination of a plurality of objective variables (e.g., specific fuel consumption, nitrogen oxides emission concentration, and the like) for a plurality of combinations (e.g., modes) of a plurality of operating states (e.g., engine revolutions, loads, and the like) included in an operating area of an engine using a computer includes: 
     a step of obtaining local optimal solutions of the design variables which minimize or maximize a combination of the plurality of objective variables which are calculated for each of the plurality of combinations of the plurality of operating states; 
     a step of obtaining initial values of a combination of the plurality of design variables used for calculating the global optimal solution; and 
     a step of calculating the global optimal solution by solving an equation which should be satisfied by the plurality of design variables using a genetic algorithm based on the local optimal solutions and the initial values. 
     With such configuration of the present invention, the computer 
     obtains local optimal solutions of the design variables which minimize or maximize a combination of the plurality of objective variables which are calculated for each of a plurality of combinations of the plurality of operating states; 
     obtains initial values of a combination of the plurality of design variables used for calculating the global optimal solution; and 
     calculates the global optimal solution by solving an equation which should be satisfied by the plurality of design variables, based on the local optimal solutions and the initial values, using a genetic algorithm. 
     Accordingly, the computer may calculate the global optimal solution using the genetic algorithm based on the initial values. 
     As a result, the computer may calculate the global optimal solution with fewer generation numbers of the genetic algorithm based on the initial values. 
     As a result, the present invention allows reduction of load on the computer for obtaining the global optimal solution. 
     Moreover, note that the computer may obtain the local optimal solutions by receiving an input from a user. Alternatively, the computer may obtain the local optimal solutions by receiving them from another computer connected via a communication network. Alternatively, the computer may obtain the local optimal solutions through calculation. More specifically, the computer may obtain the local optimal solutions by calculating an equation which is a certain objective variable expressed in a quadratic polynomial of the plurality of design variables using a genetic algorithm or other calculating methods for each of a plurality of combinations of the plurality of operating states. 
     In addition, the computer may similarly obtain the initial values by receiving an input from a user. Alternatively, the computer may obtain the initial values by receiving them from another computer connected via a communication network. 
     According to a second aspect of the present invention, with the method described in the first aspect, 
     in the step of obtaining initial values, the initial values are obtained through summation of obtained local optimal solutions of the respective design variables and local optimal solutions of the plurality of objective variables which correspond to each other when arranged in ascending or descending order. 
     With such configuration of the present invention, the computer obtains the initial values through summation of obtained local optimal solutions of the respective design variables and local optimal solutions of the plurality of objective variables which correspond to each other when arranged in ascending or descending order. 
     Accordingly, the computer may further efficiently calculate the global optimal solution using a genetic algorithm based on relatively more appropriate initial values. 
     According to a third aspect of the present invention, with the method described in the first or the second aspect, 
     in the step of calculating, the equation is the objective variables expressed in a polynomial equation of high degree including the plurality of design variables. 
     With such configuration of the present invention, the computer calculates the global optimal solution by solving a polynomial equation of high degree including the plurality of design variables which expresses the objective variables. 
     Accordingly, the computer may calculate the global optimal solution by solving a polynomial equation of high degree including the plurality of design variables which expresses the objective variables based on local optimal solutions for a plurality of design variables. 
     According to a fourth aspect of the present invention, with the method described in the first or the second aspect, 
     in the step of calculating, the equation is the objective variables expressed in an RBF (Radial Basis Function) model equation including the plurality of design variables. 
     With such configuration of the present invention, the computer calculates the global optimal solution by solving an RBF (Radial Basis Function) model equation including the plurality of design variables which expresses the objective variables. 
     Accordingly, the computer may calculate the global optimal solution by solving an equation which expresses the objective variables in an RBF (Radial Basis Function) model equation including the plurality of design variables based on local optimal solutions for a plurality of design variables. 
     Here, an equation (approximate expression) usable with the present invention is not limited to the aforementioned polynomial equation of high degree or RBF model equation, and may be a nonlinear function which can be linearized through variable conversion. For example, an exponential function, power function, logarithmic function, logistic function, or the like may be used. In addition, spline interpolation, Lagrangian interpolation, or the like for multiple variables may be used. 
     According to a fifth aspect of the present invention, with the method described in any of the first through the fourth aspects, 
     the operating states include at least revolutions of the engine and load on the engine. 
     With such configuration of the present invention, the computer may calculate the global optimal solution for the operating states which include at least revolutions of the engine and load on the engine. 
     Accordingly, the computer may calculate the global optimal solution for the operating states including at least revolutions of the engine and load on the engine, which are representative elements configuring the operating states. 
     According to a sixth aspect of the present invention, with the method described in any of the first through the fifth aspects, 
     the objective variables include at least specific fuel consumption of the engine and nitrogen oxides emission concentration. 
     With such configuration of the present invention, the computer may calculate the global optimal solution for the design variables for objective variables including at least specific fuel consumption of the engine and nitrogen oxides emission concentration. 
     Accordingly, the computer may calculate the global optimal solution of the design variables for at least specific fuel consumption and nitrogen, which are representative objective variables. 
     According to a seventh aspect of the present invention, with the method of any of the first through the sixth aspects, a program which allows execution of processing in each of the steps is used. 
     According to an eighth aspect of the present invention, a computer for calculating a global optimal solution of design variables (e.g., valve position of EGR, fuel injection timing, ignition timing, and the like) which minimize or maximize a combination of a plurality of objective variables (e.g., specific fuel consumption, nitrogen oxides emission concentration, and the like) for a plurality of combinations (e.g., modes) of a plurality of operating states (e.g., engine revolutions, loads, and the like) included in an operating area of an engine includes: 
     a means of obtaining local optimal solutions of the design variables which minimize or maximize a combination of the plurality of objective variables which are calculated for each of the plurality of combinations of the plurality of operating states; 
     a means of obtaining initial values of a combination of the plurality of design variables used for calculating the global optimal solution; and 
     a means of calculating the global optimal solution by solving an equation, which should be satisfied by the plurality of design variables, based on the local optimal solutions and the initial values, using a genetic algorithm. 
     By utilizing a computer described in the eighth aspect, it is possible to anticipate the same operation and effect as the contents described in the first aspect. 
     According to a ninth aspect of the present invention, a recording medium on which a program of instructing a computer to calculate a global optimal solution of design variables which minimize or maximize a combination of a plurality of objective variables for a plurality of combinations (e.g., modes) of a plurality of operating states (e.g., engine revolutions, loads, and the like) included in an operating area of an engine, includes: 
     a step of obtaining local optimal solutions for the design variables which minimize or maximize a combination of the plurality of objective variables which are calculated for each of the plurality of combinations of the plurality of operating states; 
     a step of obtaining initial values of a combination of the plurality of design variables used for calculating the global optimal solution; and 
     a step of calculating the global optimal solution by solving an equation which should be satisfied by the plurality of design variables based on the local optimal solutions and the initial values, using a genetic algorithm. 
     By installing the program described in the ninth aspect in a computer and utilizing it, it is possible to anticipate the same operation and effect as the contents described in the first aspect. 
     According to the present invention, the computer may calculate the global optimal solution with fewer generation numbers of the genetic algorithm based on the initial values. As a result, it is possible to reduce load on the computer for obtaining the global optimal solution. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  shows an entire structure of a system  1  of a preferred embodiment according to the present invention; 
         FIG. 2  shows a structure of a server  10  and terminals  20  of the preferred embodiment according to the present invention; 
         FIG. 3  is a functional block diagram of the server  10  and the terminals  20  of the preferred embodiment according to the present invention; 
         FIG. 4  is a flowchart showing global optimal solution calculation processing flow of a preferred embodiment according to the present invention; 
         FIG. 5A  is a diagram describing a concept of global optimal solution calculation processing of the preferred embodiment according to the present invention; 
         FIG. 5B  is a diagram describing a concept of global optimal solution calculation processing of the preferred embodiment according to the present invention; 
         FIG. 5C  is a diagram describing a concept of global optimal solution calculation processing of the preferred embodiment according to the present invention; 
         FIG. 5D  is a diagram describing a concept of global optimal solution calculation processing of the preferred embodiment according to the present invention; 
         FIG. 6A  is a diagram describing a concept of initial values calculation processing of a preferred embodiment according to the present invention; 
         FIG. 6B  is a diagram describing a concept of initial values calculation processing of the preferred embodiment according to the present invention; 
         FIG. 6C  is a diagram describing a concept of initial values calculation processing of the preferred embodiment according to the present invention; 
         FIG. 6D  is a diagram describing a concept of initial values calculation processing of the preferred embodiment according to the present invention; 
         FIG. 7A  is a diagram showing an exemplary output (display) result of conventional global optimal solution calculation processing; 
         FIG. 7B  is a diagram showing an exemplary output (display) result of conventional global optimal solution calculation processing; 
         FIG. 8A  is a diagram showing an exemplary output (display) result of conventional global optimal solution calculation processing; 
         FIG. 8B  is a diagram showing an exemplary output (display) result of conventional global optimal solution calculation processing; 
         FIG. 9  is a diagram showing an exemplary output (display) result of global optimal solution calculation processing of the preferred embodiment according to the present invention; 
         FIG. 10A  is a diagram showing an exemplary output (display) result of conventional global optimal solution calculation processing; 
         FIG. 10B  is a diagram showing an exemplary output (display) result of conventional global optimal solution calculation processing; 
         FIG. 11A  is a diagram showing an exemplary output (display) result of conventional global optimal solution calculation processing; 
         FIG. 11B  is a diagram showing an exemplary output (display) result of conventional global optimal solution calculation processing; and 
         FIG. 12  is a diagram showing an exemplary output (display) result of global optimal solution calculation processing of the preferred embodiment according to the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Embodiments according to the present invention are described as follows while referring to the drawings. 
     [Entire System Structure] 
       FIG. 1  shows an entire structure of a system  1  of a preferred embodiment according to the present invention. 
     A server  10  is connectable to terminals  20  via a communication network  30 . A computer of a preferred embodiment according to the present invention may be provided as the system  1  which is configured with the server  10  and the terminals  20 . Alternatively, it may be provided as a stand-alone computer (e.g., only the terminal  20 ). 
     In addition, the communication network  30  which connects the terminals  20  and the server  10  may be provided, not just as one which provides wired communication, but as one of various types of communication networks which correspond to the technical idea of the present invention, such as one which provides wireless communication via a base station such as a cellular phone and the like, or one which provides communication with wireless LAN via an access point and the like. 
     [Hardware Structure of Server  10 ] 
     As illustrated in  FIG. 2 , the server  10  is configured with a control unit  110 , an input unit  120 , a display unit  130 , a storage unit  140 , and a communication interface unit  150  which are connected via a bus  160 . 
     The control unit  110  may be configured with a CPU (Central Processing Unit), controls the entire server  10 , and achieves various means described later in cooperation with such hardware by reading and executing programs stored in the storage unit  140 , for example. 
     The storage unit  140  is an example of a storage medium storing the program, and may be a hard disk, semiconductor memory, or the like. The program may be stored on a portable storage medium (such as a CD or the like) to store the program in the storage unit  140 . The input unit  120  may be achieved with a keyboard, a mouse, or the like. The display unit  130  may be achieved with a liquid crystal display, a cathode-ray tube CRT, or the like. The communication interface unit  150  may be achieved with a LAN adapter, a modem adapter, or the like. 
     The aforementioned example mainly describes the server  10 ; however, the aforementioned function may be provided by installing a program into a computer and running the computer as a server apparatus. Accordingly, the function provided by the server described as an embodiment of the present invention may be provided by performing the aforementioned method using the computer, or by installing the aforementioned program in the computer and executing it. 
     [Hardware Structure of Terminal  20 ] 
     Here, the terminals  20  may have the same structure as the aforementioned server  10 . Note that the terminals  20  may be communication terminals other than so-called general purpose computers (PCs), such as cellular phones, PDAs (personal data assistants), or the like. 
     The terminal  20  is configured with a control unit  210 , an input unit  220 , a display unit  230 , a storage unit  240 , and a communication interface unit  250  which are connected via a bus  260 . 
     [System Functional Structure] 
       FIG. 3  is a functional block diagram of the server  10  and the terminal  20  of the preferred embodiment of the present invention. 
     The input unit  120  of the server  10  configures an input block  1201 . Similarly, the input unit  220  of the terminal  20  configures an input block  2201 . Moreover, the communication interface unit  150  of the server  10  configures a communication interface block  1501  and a communication interface block  1502 . Similarly, the communication interface unit  250  of the terminal  20  configures a communication interface block  2501  and a communication interface block  2502 . Furthermore, the control unit  110  of the server  10  configures a local optimal solution calculating block  1101 , a global optimal solution calculating block  1102 , and an initial values calculating block  1103 . Similarly, the control unit  210  of the terminal  20  configures a local optimal solution calculating block  2101 , a global optimal solution calculating block  2102 , and an initial values calculating block  2103 . In addition, the storage unit  140  of the server  10  is stored with local optimal solutions  1401  and initial values  1402 . Similarly, the storage unit  240  of the terminal  20  is stored with local optimal solutions  2401  and initial values  2402 . Moreover, the display unit  130  of the server  10  configures an output block  1301 . Similarly, the display unit  230  of the terminal  20  configures an output block  2301 . 
     As mentioned above, the server  10  and the terminals  20  of the preferred embodiment of the present invention may have the same structure as each other, or alternatively, they may achieve the present invention in cooperation with each other by configuring a so-called client/server by connecting to each other via the communication network  30 . 
     [Main Flow] 
       FIG. 4  is a flowchart showing a global optimal solution calculation processing flow of a preferred embodiment of the present invention. 
     Note that the server  10  and the terminals  20  of the preferred embodiment of the present invention may achieve the present invention in cooperation with each other as mentioned above. Here, a case of configuring a so-called client/server is mainly described; however, the technical scope of the present invention is not limited thereto. 
     To begin with, in step S 101 , the local optimal solutions  1401  (or the local optimal solutions  2401 ) are obtained. More specifically, the input block  1201  (or the input block  2201 ) of the server  10  (or the terminal  20 ) may receive an input from a user. Alternatively, the input block  2201  of the terminal  20  may receive an input from a user, and the communication interface block  1501  of the server  10  may receive it via the communication network  30 . Alternatively, the local optimal solution calculating block  1101  of the server  10  may calculate the local optimal solutions  1401  (or the local optimal solutions  2401 ). 
     Next, in step S 102 , the initial values  1402  (or the initial values  2402 ) are obtained. Specifically, the input block  1201  (or the input block  2201 ) of the server  10  (or terminal  20 ) may receive an input from a user. Alternatively, the input block  2201  of the terminal  20  may receive an input from a user, and the communication interface block  1501  of the server  10  may receive it via the communication network  30 . Furthermore, as described in detail below while referring to  FIG. 6 , the initial values calculating block  1103  or the initial values calculating block  2103  may calculate the initial values  1402  (or the initial values  2402 ). 
     Next, in step S 103 , a global optimal solution is calculated. More specifically, the global optimal solution calculating block  1102  of the server  10  may calculate the global optimal solution based on the local optimal solutions  1401  (or the local optimal solutions  2401 ) and the initial values  1402  (or the initial values  2402 ). 
     Next, in step S 104 , the global optimal solution is output. More specifically, the output block  1301  of the server  10  may output (display) the global optimal solution. Alternatively, the global optimal solution transmitted from the server  10  to the terminal  20  via the communication network  30  may be output (displayed) by the output block  2301  of the terminal  20 . 
       FIGS. 5A ,  5 B,  5 C, and  5 D are diagrams describing a concept of global optimal solution calculation processing of the preferred embodiment of the present invention, respectively. 
     Here, an example of a case of calculating a global optimal solution of design variables which minimize or maximize a combination of two objective variables (specific fuel consumption and nitrogen oxides emission concentration) for three combinations (modes) of multiple operating states (e.g., engine revolutions, loads, and the like) included in an engine operating area is given. 
     As illustrated in  FIGS. 5A ,  5 B, and  5 C, local optimal solutions of the design variables for three modes (mode  1  through mode  3 ) are calculated and input, respectively. In this embodiment, the global optimal solution (global Pareto solution) is calculated based on these three local optimal solutions. In this case, in the preferred embodiment according to the present invention, the global optimal solution (global Pareto solution) may be efficiently calculated with fewer generation numbers by inputting the initial values appropriately using a genetic algorithm. 
       FIGS. 6A through 6D  are diagrams describing a concept of initial values calculation processing of a preferred embodiment according to the present invention. As illustrated in  FIGS. 6A through 6C , when there are n modes for the two objective variables of specific fuel consumption and NOx (nitrogen oxides) emission concentration, for example, suffixes indicating NOx emission concentrations are appended in ascending order to local optimal solutions of the n design variables in each mode. Specifically, for example, for mode  1 , the first local optimal solution is D 11 , the second local optimal solution is D 12 , . . . , and the nth local optimal solution is D 1n . In addition, for mode  2 , the first local optimal solution is D 21 , the second local optimal solution is D 22 , . . . , and the nth local optimal solution is D 2n . In this manner, suffixes are appended to the local optimal solutions, and furthermore, of the local optimal solutions for each mode, the local optimal solutions which correspond to each other when arranged in ascending order of NOx emission concentrations are then summated. Specifically, for example, the local optimal solutions for the number of modes such as D 11 , D 21 , . . . , are summated. In addition, the resulting value is then adopted as one of the initial values for calculating the global optimal solution ( FIG. 6D ). 
     Similar calculation is performed for all local optimal solutions. Specifically, for the nth local optimal solution in the aforementioned example, local optimal solutions for the number of modes such as D 1n , D 2n , . . . , are summated. The global optimal solution is calculated based on the initial values calculated as described above. In this manner, the global optimal solution is calculated more efficiently using a genetic algorithm based on the relatively more appropriate initial values. 
     Note that, as illustrated in  FIGS. 6A through 6D , products of a predetermined weight multiplied by each mode (specifically, weights for respective local optimal solutions, for example, W 1  for the first local optimal solution D 11 , W 2  for the second local optimal solution D 12 , . . . , and W n  for the nth local optimal solution D 1n ) may be summated when summating the local optimal solutions. In this case, the weights are reflected in the obtained global optimal solution. 
       FIG. 7A  and  FIG. 7B , and  FIG. 8A  and  FIG. 8B  show comparative results between calculation results of 250 generation numbers, 1000 generation numbers, 2500 generation numbers, and 5000 generation numbers using a genetic algorithm without inputting initial values for two objective variables (specific fuel consumption (q) and nitrogen oxides emission concentration (NOx)) by a conventional method, and results of a simple summation of respective local optimal solutions (objective solutions) in the case of mode  13 . 
     In  FIG. 7A , the calculation results using a genetic algorithm cannot sufficiently express the objective solutions for both ends of the global optimal solution, that is, a portion where q is low and NOx is high, and a portion where q is high and NOx is low. 
     It is apparent from  FIG. 7B  and subsequent drawings that the aforementioned problem may be gradually alleviated by increasing the generation numbers, and the fact that calculation results almost the same as the objective solutions may be obtained as a result of calculating 5000 generation numbers is apparent from  FIG. 8B . 
       FIG. 9  shows a result of calculating 250 generation numbers by inputting initial values when using a genetic algorithm as an example of the preferred embodiment of the present invention. As is apparent from the drawing, it is possible to obtain calculation results almost the same as the objective solutions even if generation numbers are few. Calculation efficiency is improved by (5000−250)/5000=95% for generation numbers compared to the conventional method. 
     Similarly,  FIG. 10A  and  FIG. 10B , and  FIG. 11A  and  FIG. 11B  show, in the case of mode  51 , by the conventional method, comparative results for calculation results of 250 generation numbers, 1000 generation numbers, 2500 generation numbers, and 5000 generation numbers using a genetic algorithm without inputting initial values for two objective variables (specific fuel consumption (q) and nitrogen oxides emission concentration (NOx)), and results of simple summation of respective local optimal solutions (objective solutions). 
     In  FIG. 10A , calculation results using a genetic algorithm cannot sufficiently express the objective solutions for both ends of the global optimal solution, that is, a portion where q is low and NOx is high, and a portion where q is high and NOx is low. An insufficient area becomes larger even compared to the case of mode  13  in  FIG. 7A . 
     It is apparent from  FIG. 10B  and subsequent drawings that the aforementioned problem may be gradually alleviated by increasing the generation numbers, and the fact that calculation results almost the same as the objective solutions may be obtained as a result of calculating 5000 generation numbers is apparent from  FIG. 11B . Nevertheless, a larger insufficient area than the case of mode  13  in  FIG. 8B  still remains. 
       FIG. 12  shows a result of calculating 250 generation numbers by inputting initial values when using a genetic algorithm as an example of the preferred embodiment according to the present invention. As is apparent from the drawing, it is possible to obtain calculation results almost the same as the objective solutions even if generation numbers are few. Calculation efficiency may be improved by (5000−250)/5000=95% for generation numbers compared to the conventional method. In addition, there is almost no insufficient area, meaning that objective solutions are being further preferably calculated than the calculation results of 5000 generation numbers using the conventional method.