# Hirokazu Anai, Kawasaki JP

## Hirokazu Anai, Kawasaki JP

Patent application number | Description | Published |
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20090182538 | MULTI-OBJECTIVE OPTIMUM DESIGN SUPPORT DEVICE USING MATHEMATICAL PROCESS TECHNIQUE, ITS METHOD AND PROGRAM | 07-16-2009 |

20090182539 | MULTI-OBJECTIVE OPTIMAL DESIGN SUPPORT DEVICE, METHOD AND PROGRAM STORAGE MEDIUM - An objective function can be mathematically approximated using a prescribed number of sample sets of design parameters and sets of a plurality of objective functions computed corresponding to them. A logical expression indicating a relation between or among arbitrary two or three objective functions of the plurality of mathematically approximated objective functions is computed as an inter-objective-function logical expression and a region that the arbitrary objective function values can take is displayed as a feasible region in an objective space corresponding to the arbitrary objective functions. Furthermore, a point or area in a design space corresponding to arbitrary design parameters corresponding to a point or area specified by a user in the displayed feasible region is displayed. | 07-16-2009 |

20090326875 | DEVICE AND METHOD FOR CLASSIFYING/DISPLAYING DIFFERENT DESIGN SHAPE HAVING SIMILAR CHARACTERISTICS - A system displays an area which a desired objection function value of a plurality of objective functions as a possible area in objective space corresponding to the objective function on the basis of each of the plurality of objective function value sets calculated for a plurality of design parameter sample sets; calculates a design parameter set in design space corresponding to the neighborhood area of a position in the objective space based on the position specification in relation to position specification by a user in the possible area of the objective space; and calculates and displays a representative design shape corresponding to the calculated design parameter set. | 12-31-2009 |

20090326881 | MULTI-OBJECTIVE OPTIMAL DESIGN IMPROVEMENT SUPPORT DEVICE, ITS METHOD AND STORAGE MEDIUM - A multi-objective optical design improvement support device calculates a logical expression indicating a logical relationship among arbitrary two or three objective functions of a plurality of mathematically approximated objective functions and displays a possibility area in arbitrary objective space according to it. When a designer is not satisfied with an optimal Pareto solution, it copies a sample point group out of the initial constraints of a design parameter set in the objective space, displays its result and presents an improvement solution to the designer. When the designer finds more optimal solution than the optimal Pareto solution among the displayed improvement solutions and gives instruction, it calculates a sample point in design parameter space, corresponding to the optimal improvement solution, overlaps it with a constraint range and displays it as improvement knowledge and information. | 12-31-2009 |

20100057410 | OPTIMAL SOLUTION RELATION DISPLAY APPARATUS AND OPTIMAL SOLUTION RELATION DISPLAY METHOD - An apparatus receives input of sample sets, each including a set of values of design parameters and a set of values of objective functions; calculates objective function approximating equations; and selects, as initial candidates for an optimal design parameter set, some sets of values of design parameters corresponding to non-dominated solutions. The apparatus calculates one or more interpolating design parameter sets interpolating between two adjacent components in the candidates; and approximates values of the objective functions for each interpolating design parameter set. The apparatus selects an optimal interpolating design parameter set corresponding to a non-dominated solution in the cost evaluation for a pair of objective functions; and integrates it into the candidates. The apparatus repeats processes on the new candidates while determining the parameter distance between components of the new candidates. Finally obtained new candidates are output as final optimal design parameter sets and information relating to it is displayed. | 03-04-2010 |

20100153074 | DESIGN SUPPORT APPARATUS - A design support apparatus for determining a plurality of objective functions for modeling an object having a plurality of elements, each of the elements providing variable geometrical parameters, the design support apparatus includes a memory for storing the variable geometrical parameters and a processor for executing a process including: determining boundary information associated with specified geometrical parameters of the elements which indicate a state of contact between the elements, dividing the variable geometrical parameters into a plurality of groups on the basis of the boundary information, and determining the plurality of objective functions for each of the groups by using the variable geometrical parameters. | 06-17-2010 |

20100205574 | SUPPORT APPARATUS AND METHOD - A design support apparatus includes: a logical expression substitution unit to substitute a part of the logical expression, which includes a function expression of the design variables and a quantifier attached to the design variable, with a substitution variable; a quantifier elimination unit to generate a relational expression including the substitution variable and design variables without the quantifier by eliminating the design variable to which the quantifier is attached from the logical expression; a sampling point generation unit to generate a plurality of sampling points corresponding to the design variables and the substitution variable included in the relational expression; a possible range computation unit to compute, for each of the sampling points, a possible range that the relational expression may take, by calculating values of remaining design variables included in the relational expression based on the relational expression; and a possible range display unit to display the possible range. | 08-12-2010 |

20100332195 | MULTI-PURPOSE OPTIMIZATION DESIGN SUPPORT APPARATUS AND METHOD, AND RECORDING MEDIUM STORING PROGRAM - A design support apparatus includes a parameter set generation unit configured to obtain a plurality of types of parameters and sequentially generates parameter sets while sequentially changing each parameter, a design object shape data generation unit configured to generate design object shape data based on the parameter set and initial shape data representing an initial shape of the design object shape, a geometric penalty function value calculation unit configured to calculate a geometric penalty function value indicating suitability of geometric characteristics of the design object shape based on the design object shape data, an objective function calculation control unit configured to determine whether or not the parameter set is used to calculate an objective function based on the geometric penalty function value and an optimal value of the objective function, and an objective function calculation unit configured to calculate the objective function based on the parameter set. | 12-30-2010 |

20110022365 | MULTI-OBJECTIVE OPTIMIZATION DESIGN SUPPORT APPARATUS AND METHOD - An embodiment relates to a multi-objective optimization design supporting technique to reduces the computational complexity of QE/CAD. When the input logical expression generated by a logical-expression-with-qualifier generation unit is satisfied in regard to the sample point included in a certain piece of cell information for each value of the same design parameter, a first cell processing unit does not evaluate the input logical expression on the cell information including other sample points having a value equal to or smaller than the value of a predetermined design variable (for example, a design variable indicating a yield) corresponding to the sample point above, but selects it as the cell information for an output of a logical expression without a qualifier. | 01-27-2011 |

20110148867 | SHAPE OPTIMIZATION TECHNIQUE - A shape optimization method includes: obtaining parameter data including data concerning a first relational expression that causes coordinate values of plural vertexes in at least a portion of an object to be changed together and includes a parameter capable of setting values from outside; determining, according to a predetermined algorithm, a value of the parameter in the parameter data; calculating coordinates values of the plural vertexes from a second relational expression determined by the first relational expression and the determined value of the parameter; generating shape data including coordinate values of first vertexes to define the shape of the object from initial coordinate values and the calculated coordinate values; causing to execute cost calculation of the shape defined by the shape data; and outputting shape data in case of a best result of the cost calculation after repeating the aforementioned processing based on a result of the cost calculation. | 06-23-2011 |

20110295573 | MODEL EXPRESSION GENERATION METHOD AND APPARATUS - When model expressions of objective functions are generated at vertexes of a quadrilateral on a plane concerning P and N channels of transistors in SRAM, the initial number of times of simulation is allocated to each objective function at each designated vertex according to weight values set based on relationships presumed among the objective functions at each designated vertex. For each objective function at each designated vertex, first simulation is executed the allocated number of times. Furthermore, a model expression is generated from the first simulation result, and an evaluation indicator of an approximation accuracy of the model expression is calculated. Then, for each model expression, it is determined whether the corresponding model expression has influence on the yield, and based on the evaluation indicator of the corresponding model expression and presence or absence of the influence, it is determined whether additional simulation is required for the corresponding objective function. | 12-01-2011 |

20120046915 | DISPLAY PROCESSING TECHNIQUE OF DESIGN PARAMETER SPACE - This method includes: generating a constraint equation from data of an approximate expression of a cost function representing a relationship between a plurality of design parameters and a cost, data of a route in a cost space and data of a search range in a design parameter space; obtaining a logical expression of a solution for the constraint equation from a quantifier elimination processing unit that carries out a processing according to a quantifier elimination method; substituting coordinates of each of a plurality of points within the search range in the design parameter space into the logical expression of the solution to determine, for each of the plurality of points, true or false of the logical expression of the solution; and displaying the design parameter space in which a display object including a first point for which true is determined is disposed at the first point. | 02-23-2012 |

20120072385 | TECHNIQUE FOR SOLVING OPTIMIZATION PROBLEM - A method for solving an optimization problem includes: causing a cylindrical algebraic decomposition (CAD) processing unit to carry out a projection processing for a first expression that appears in a quantifier elimination problem equivalent to the optimization problem including objective functions and to generate second expressions that are projection factors of the first expression; calculating plural sets of values of the objective functions by generating plural value sets of variables in the objective functions and substituting the generated plural value sets of the variables into the objective functions; extracting points including non-dominated solutions in a space mapped by the objective functions, from plural points corresponding to the plural sets of values; calculating, for each second expression, an evaluation value concerning a distance between a corresponding second expression and each of the extracted points; and identifying a second expression whose evaluation value is minimum. | 03-22-2012 |

20120221301 | MATRIX GENERATION TECHNIQUE AND PLANT CONTROL TECHNIQUE - In this disclosure, equations to be solved in the model predictive control are transformed by using an off-line algebraic simplification method into a matrix operational expression representing a product of a coefficient matrix and a vector regarding solution inputs within a control horizon is equal to a function vector regarding target values of output states and the output states. The size of the coefficient matrix is reduced compared with the conventional matrix. Then, the matrix operational expression is solved in an online plant control apparatus with present output states and present target values of the output stats of a plant to be controlled, by the direct method, to output the solution to the plant. | 08-30-2012 |

20120239357 | VISUALIZATION TECHNIQUE OF FEASIBLE REGIONS - The disclosed method includes: generating, from model expressions, each representing a relationship between input parameters and output evaluation indicators and a range of residuals for each model expression, at least one of a first problem to calculate a region that can be feasible with the model expressions, value ranges of the input parameters and the range of the residuals for each model expression and a second problem to calculate a region that is always feasible with the model expressions, the value ranges of the input parameters and the influence of the aforementioned range; calculating a feasible region(s) for a generated problem(s) to obtain data of the feasible region(s); and generating visualization data of the feasible region(s) to output the visualization data. | 09-20-2012 |

20150025865 | MATRIX GENERATION TECHNIQUE AND PLANT CONTROL TECHNIQUE - In this disclosure, equations to be solved in the model predictive control are transformed by using an off-line algebraic simplification method into a matrix operational expression representing a product of a coefficient matrix and a vector regarding solution inputs within a control horizon is equal to a function vector regarding target values of output states and the output states. The size of the coefficient matrix is reduced compared with the conventional matrix. Then, the matrix operational expression is solved in an online plant control apparatus with present output states and present target values of the output stats of a plant to be controlled, by the direct method, to output the solution to the plant. | 01-22-2015 |