Patent ID: 7295956

Claim:
A method for using interval techniques within a computer system to solve a multi-objective optimization problem, comprising: receiving a representation of multiple objective functions (ƒ 1 , . . . ,ƒ n ) at the computer system, wherein (ƒ 1 , . . . , ƒ n ) are scalar functions of a vector x=(x 1 , . . . , x n ); receiving a representation of a domain of interest for the multiple objective functions; storing the representations in a memory within the computer system; and performing an interval optimization process to compute guaranteed bounds on a Pareto front for the objective functions (ƒ 1 , . . . , ƒ n ), wherein for each point on the Pareto front, an improvement in one objective function cannot be made without adversely affecting at least one other objective function; wherein performing the interval optimization process involves applying a direct-comparison technique between subdomains of the domain of interest to eliminate subdomains that are certainly dominated by other subdomains, wherein performing the interval optimization process involves applying a gradient technique to eliminate subdomains that do not contain a local Pareto optimum, wherein a subdomain [x] i is eliminated by the gradient technique if an intersection of certainly negative gradient regions C j for each objective function ƒ j is non-empty, ⋂ j = 1 n ⁢ C j ⁡ ( [ x ] j ) ≠ ∅ , and wherein the certainly negative gradient region C j for objective function ƒ j is the intersection of N j ([x] i ) (the negative gradient region associated with the minimum angle θ j of the gradient of ƒ j over the subdomain [x] i ) and N j ([x] i ) (the negative gradient region associated with the maximum angle θ j of the gradient of ƒ j over the subdomain [x] i ).