Extended finite state machines are widely used in model based testing. Since testing is such a critical step from the software development process, it is important to have many different test suites, generated on different criteria. This paper presents a test suite generation algorithm for EFSMs. The algorithm produces a set of feasible transition paths that cover all transitions using a modified NSGA-II and a NSGA-III Algorithm (based on different feasibility optimization) and a Hybrid Genetic Algorithm to generate input values that trigger all the paths.