Showing papers by "Hitoshi Yanami published in 2009"

An effective implementation of a symbolic-numeric cylindrical algebraic decomposition for quantifier elimination

Abstract: Recently quantifier elimination (QE) has been of great interest in many fields of science and engineering. In this paper an effective symbolic-numeric cylindrical algebraic decomposition (SNCAD) algorithm and its variant specially designed for QE are proposed based on the authors' previous work and our implementation of those is reported. Based on analysing experimental performances, we are improving our design/synthesis of the SNCAD for its practical realization with existing efficient computational techniques and several newly introduced ones. The practicality of the SNCAD is now examined by a number of experimental results including practical engineering problems, which also reveals the quality of the implementation.

Multi-objective optimal design support device and method taking manufacturing variations into consideration

Abstract: A logical expression indicating a logical relation between arbitrary two or three objective functions, of a plurality of mathematically approximated objective functions is computed. A feasible region/sensitivity information display unit displays the feasible region in arbitrary objective space according to it. An inverse image computation unit computes a point or area in design space corresponding to arbitrary design parameters in relation to a point or area specified by a user in the feasible region of the objective space. A feasible region/sensitivity information display unit displays the distribution state of the corresponding point or area as sensitivity information in relation to the specified point or area in the feasible region.

Multi-objective optimal design improvement support device, its method and storage medium

Abstract: 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.

Multi-Objective Design Based on Symbolic Computation and Its Application to Hard Disk Slider Design

Abstract: We propose a new approach to tackling multi-objective optimization problems. Our method uses symbolic computation called quantifier elimination. From experimental data we first make an approximated polynomial model for each objective function and then solve a first-order formula related to those functions to find the feasible region, which contains information on the Pareto optimal front. Our approach has an advantage over classical numerical optimization methods that return only one optimal point at a time. Furthermore, by introducing into a formula an adjusting point and a new variable that restricts the parameter ranges we can visualize how the objective functions locally behave. This idea leads us to a new criterion for measuring the robustness against production tolerance. We also show how our methods are applied to the design problem of a hard disk slider.

Multi-objective optimal design support device, method and program storage medium

Abstract: 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.

Device and method for classifying/displaying different design shape having similar characteristics

Abstract: 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.

Optimal solution relation display apparatus and optimal solution relation display method

Abstract: 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.

Design support apparatus

Abstract: 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.

Multipurpose optimization design support device, method, and program

Abstract: PROBLEM TO BE SOLVED: To utilize a multipurpose optimization design support technology to be used for the design of the slider shape of hard disk etc. available for design support by executing visualization based on objective functions subjected to formula manipulation in a short period of time. SOLUTION: The set of a plurality of objective functions corresponding to the set of the samples of input parameters is calculated by 101. 102 calculates the objective functions by polynomial approximation based on the calculation result of 101. On the basis of a QE method or the like, 103 calculates a logical expression showing a logical relationship between optional two or three objective functions among the plurality of objective functions calculated by mathematical expression approximation, as an inter-objective function logical expressions. On the basis of the inter-objective function logical expression, 104 displays a region which can be taken by the values of the objective functions, as a possible region, and at the same time, when a user traces on the palate boundary of the possible region, the 104 displays the way of change of design parameters. Also, when the user traces on the palate boundary of the possible region related with a certain objective space, the 104 displays the way of change of the objective function values of the other objective space. COPYRIGHT: (C)2009,JPO&INPIT

Multi-purpose optimization design support device, method and program under consideration of manufacture variation

Abstract: PROBLEM TO BE SOLVED: To execute visualization (display of Pareto boundary or the like) based on objective functions in a short time, and to obtain a relation between objective functions under the consideration of manufacture variation (manufacture error) and design parameters or the other objective functions while properly displaying Pareto optimal solution based on this in a multi-purpose optimization design support technology to be used for the design of the slider shape of a hard disk. SOLUTION: A logical formula showing a logical relation among any two or three objective functions among a plurality of mathematical equation approximated objective functions is calculated (101 to 104). A possible region on any objective space is displayed based on the calculation results (105). Corresponding points or corresponding regions on a design space corresponding to any design parameters are calculated corresponding to designation points or designation regions by a user on the possible region on the object space (107). The distribution state of the corresponding points or the corresponding regions displayed as sensitivity information so as to be associated with the designation points or designation regions on the possible region (105). COPYRIGHT: (C)2009,JPO&INPIT

Design support apparatus, method, and program

Abstract: PROBLEM TO BE SOLVED: To enable a designer to determine a designable range by efficiently calculating a relation between design variables including design parameters or a design condition even when there are many design parameters and a function expression for calculating each design amount is complicated, as regards design support techniques for supporting the whole designs in manufacturing. SOLUTION: A logical expression substitution unit 103 substitutes a part of a logical expression input by a logical expression input unit 102 or an objective function approximation polynomial from an objective function modeling unit 101 with a substitution variable. A quantifier elimination unit 104 eliminates a design variable to which a quantifier is attached from the logical expression obtained by the substitution to thereby generate a relational expression including the substitution variable and the design variables without any attached quantifier. A sampling point generation unit 105 generates a plurality of sampling points corresponding to the design variables and the substitution variable included in the relational expression. A possible range computation unit 106 computes a possible range that the relational expression can take. A possible range display unit 107 displays the possible range. COPYRIGHT: (C)2010,JPO&INPIT

Support apparatus using objective function

Abstract: 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.

Multipurpose optimization design support apparatus and method considering geometric characteristics of design object shape, and program

Abstract: PROBLEM TO BE SOLVED: To efficiently calculate an objective function according to a design object shape in a cost calculation technique such as multipurpose optimization design support technique used for design of a slider shape for hard disk or the like.SOLUTION: A parameter set generation part 103 sequentially obtains parameter sets each composed of a plurality of types of parameters for design object shape, and sequentially generates parameter sets while sequentially changing each parameter in a range shown by the range data thereof. An objective function calculation part 107 calculates an objective function based on a predetermined calculation, and supports to determine an optimum design object shape and a parameter set corresponding to the design object shape based on the objective function.

Multi-objective optimization design support apparatus, method, and program

Abstract: PROBLEM TO BE SOLVED: To reduce the computational complexity of QE (Quantifier Elimination)/CAD (Cylindrical Algebraic Decomposition) related to a multi-objective optimization design supporting technique to be used for design SOLUTION: When an input logical expression generated by a logical-expression-with-qualifier generation unit 102 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 104 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 as the value of the predetermined design variable, but selects it as the cell information for an output of a logical expression without a qualifier COPYRIGHT: (C)2011,JPO&INPIT