Evolutionary Optimization Method for Approximating the Solution Set Hull of Parametric Linear Systems

Systems of parametric interval equations are encountered in many practical applications. Several methods for solving such systems have been developed during last years. Most of them produce both outer and inner interval solutions, but the amount of overestimation, resp. underestimation is not exactly known. If a solution of a parametric system is monotonic and continuous on each interval parameter, then the method of combination of endpoints of parameter intervals computes its interval hull. Recently, a few polynomial methods computing the interval hull were developed. They can be applied if some monotonicity and continouity conditions are fulfilled. To get the most accurate inner approximation of the solution set hull for problems with any bounded solution set, an evolutionary optimization method is applied.

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