A method for determining symbolic and all numerical solutions in design optimization based on monotonicity analysis and solving polynomial systems is presented in this paper. Groebner Bases of the algebraic system equ...A method for determining symbolic and all numerical solutions in design optimization based on monotonicity analysis and solving polynomial systems is presented in this paper. Groebner Bases of the algebraic system equivalent to the subproblem of the design optimization is taken as the symbolic (analytical) expression of the optimum solution for the symbolic optimization, i.e. the problem with symbolic coefficients. A method based on substituting and eliminating for determining Groebner Bases is also proposed, and method for finding all numerical optimum solutions is discussed. Finally an example is given, demonstrating the strategy and efficiency of the method.展开更多
Based on monotonicity analysis and computer symbolic manipulating technique,a procedure for determining constraints compatibility in design optimization hasbeen proposed in this paper. By using the proposed method rel...Based on monotonicity analysis and computer symbolic manipulating technique,a procedure for determining constraints compatibility in design optimization hasbeen proposed in this paper. By using the proposed method relationshipsbetween constrains can be determined and the optimization is greatly simplifid.The method is code with intelligent production systems.展开更多
文摘A method for determining symbolic and all numerical solutions in design optimization based on monotonicity analysis and solving polynomial systems is presented in this paper. Groebner Bases of the algebraic system equivalent to the subproblem of the design optimization is taken as the symbolic (analytical) expression of the optimum solution for the symbolic optimization, i.e. the problem with symbolic coefficients. A method based on substituting and eliminating for determining Groebner Bases is also proposed, and method for finding all numerical optimum solutions is discussed. Finally an example is given, demonstrating the strategy and efficiency of the method.
文摘Based on monotonicity analysis and computer symbolic manipulating technique,a procedure for determining constraints compatibility in design optimization hasbeen proposed in this paper. By using the proposed method relationshipsbetween constrains can be determined and the optimization is greatly simplifid.The method is code with intelligent production systems.
