This paper presents a new methodology for improving the efficiency and generality of Genetic Algorithms (GA). The methodology provides the novel function of adaptive parameter adjustment during each evolution generation of GA. The important characteristics of the methodology are mainly from the following two aspects: (1) superior performance members in GA are preserved and inferior performance members are deteriorated to enhance search efficiency towards optimal solutions; (2) adaptive crossover and mutation management is applied in GA based on the transformation functions to explore wider spaces so as to improve search effectiveness and algorithm robustness. The research was successfully applied for a luggage design chain to generate optimal solutions (minimized lifecycle cost). Experiments were conducted to compare the work with the prior art to demonstrate the characteristics and advantages of the research.