Showing papers by "Hitoshi Yanami published in 2012"

An effective implementation of a symbolic-numeric cylindrical algebraic decomposition for optimization problems

Abstract: With many applications in engineering and in scientific fields, quantifier elimination (QE) has been attracting more attention these days. Cylindrical algebraic decomposition (CAD) is used as a basis for a general QE algorithm. We propose an effective symbolic-numeric cylindrical algebraic decomposition (SNCAD) algorithm for solving polynomial optimization problems. The main ideas are a bounded CAD construction approach and utilization of sign information. The bounded CAD constructs CAD only in restricted admissible regions to remove redundant projection factors and avoid lifting cells where truth values are constant over the region. By utilization of sign information we can avoid symbolic computation in the lifting phase. Techniques for implementation are also presented. These techniques help reduce the computing time. We have examined our implementation by solving many example problems. Experimental results show that our implementation significantly improves efficiency compared to our previous work.

Information processing technique for optimization

Abstract: The disclosed method includes: generating a problem for a quantifier elimination (QE) method from a cost function representing a relationship between a parameter set and a cost; executing, by a module that executes a processing for the QE method by term substitution, a processing for the problem, to obtain a first processing result; when the first processing result includes a first partial problem for which the term substitution is impossible, executing, by a module that execute a numerical analysis processing, a processing to minimize the cost for the first partial problem, to obtain a second processing result; when the first processing result includes a logical expression as a solution of a second partial problem for which the term substitution has been completed, generating data to identify a minimum cost value from the logical expression; and generating a minimum cost for the problem from at least the second processing result.

Detection method, detection device and detection program

Abstract: PROBLEM TO BE SOLVED: To reduce an arithmetic quantity required for the detection of a combination of output values which is better than the clarified combination of output values.SOLUTION: A detection device performs integration processing to each parameter of an initial parameter group reaching from the minimum parameter to the maximum parameter, and performs division processing to each parameter of a plurality of parameters after integration. The detection device gives each parameter of the plurality of parameters after division to first and second objective functions, and calculates a combination of output values of the first and second objective functions as for each parameter of the plurality of parameters after division. The detection device detects, from the calculated combination of the output values and the combination of the output values of the first and second objective functions as for each parameter of the initial parameter group, the combination as a candidate of a non-dominated solution. A graph 902 shows the state of update of the combination as the candidate of the non-dominated solution.

Display processing program, display processing method and information processor

Abstract: PROBLEM TO BE SOLVED: To present a route in a design parameter space corresponding to a given route expressed by an equation in a cost space.SOLUTION: In this method, a constraint equation is generated from an approximate equation of a cost function, a route in a cost space and a search range in a design parameter space; a logic expression of the solution of the constraint equation is acquired by a qualifier removal method; and the coordinate values of a plurality of points in the search range in the design parameter space are substituted in the logic expression of the solution of the constraint equation. As a result, it is determined whether the logic expression of the solution is true or false with regard to each of the plurality of points, and the design parameter space in which display objects containing the points determined to be true are disposed at the points is displayed.