We propose a hybrid algorithm (called ALPINE) between Genetic Algorithm and Dantzig's Simplex method to approximate optimal solutions for the Flexible Job-Shop Problem. Locally, Simplex is extended for the JSP linear program to reduce the number of infeasible solutions while solution quality is improved with an operation order search. Globally, a niche-based evolutionary strategy is employed to gain parallelization while solution diversity is maintained in two ways; composite dispatching rulebased population initialization and memory-based machine assignment. Performance results on benchmark problems show that ALPINE outperforms existing hybrid techniques with a new global optima found for the 10x7 Flexible Job Shop Problem.