Nested Bilevel Genetic Algorithms For Game-Theoretic Optimization Of Product Line Design Considering Competition

Product line design considering competition (CPLD) can be formulated as a discrete bilevel optimization model based on the Stackelberg-Nash game, which is proved to be NP-hard in nature. This paper develops a nested bilevel genetic algorithm (NBGA) for solving the CPLD problem, in which the lower-level optimization problems are solved in a nested and sequential way for given upper-level decision variables. To compute the Nash equilibrium, the sequential tatonnement procedure is adopted in the lower-level optimization. A generic integer encoding scheme is introduced to represent the upper- and lower-level product line generation and selection, respectively. The design and implementation of the NBGA is discussed in detail. Finally, an application to CPLD of mobile phones is reported to illustrate the feasibility and potential of the proposed NBGA.