Test minimization techniques aim at identifying and eliminating redundant test cases from test suites in order to reduce the total number of test cases to execute, thereby improving the efficiency of testing. In the context of software product line, we can save efforts and cost in the selection and minimization of test cases for testing a specific product by modeling the product line. However, minimizing the test suite for a product requires addressing two potential issues: 1) the reduced test suite may not cover all test requirements compared with the original suite; 2) the reduced test suite may have less fault revealing capability than the original suite. In this paper, we apply weight-based Genetic Algorithms (GAs) to minimize the test suite for testing a product, while preserving fault detection capability and testing coverage of the original test suite. The challenge behind concerns the definition of an appropriate fitness function, which is able to preserve the coverage of complex testing criteria (e.g., Combinatorial Interaction Testing criterion). Based on the defined fitness function, we have empirically evaluated three different weight- based GAs on an industrial case study provided by Cisco Systems, Inc. Norway. We also presented our results of applying the three weight-based GAs on five existing case studies from the literature. Based on these case studies, we conclude that among the three weight-based GAs, Random-Weighted GA (RWGA) achieved significantly better performance than the other ones.