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Both Genetic Algorithm (GA) and Linear Programming (LP) are effective optimization algorithms. LP is very efficient for optimizing linear problems. GA can attain very good solutions for integer non-linear problems, but it takes more time. To solve the very complex nested optimization problems, we propose a hybrid algorithm to combine the merits from both LP and GA algorithms in this paper. We use GA to optimize the parent problem, and LP/GA hybrid algorithm to solve the sub problem. The Stock Reduction Problem (SRP) is a typical example of complex nested optimization problems. Our experiments have shown that our new hybrid algorithm can solve the SRP very fast with excellent results.