A hybrid approach to resolving a differentiable integer program

A general nonlinear integer program has been shown to be difficult to solve. Therefore, formal studies were focused on special types of nonlinear integer programs with different assumptions. Since a genetic algorithm searches among candidate designs of a system so that good solutions can be identified, and the generalized reduced gradient method can find an approximate solution of a differentiable integer program, therefore, in this study, a hybrid approach was proposed with an algorithm for a differentiable integer program problem. Though the proposed method guarantees a local optimum, global optima were obtained for all test problems with considerably efficient computations. This paper proposes an algorithm to solve differentiable integer programming problems. After linear approximation of the objective function and the constraints, a genetic algorithm is designed to provide an initial solution and to search for a feasible direction at the integer points so that a better integral point can be found. Theoretical analysis and experimental investigation are presented. The result shows that the proposed method guarantees a local optimum and for 12 test problems, the global optima are all obtained.