Linear Programming Relax-PSO Hybrid Bound Algorithm for a Class of Nonlinear Integer Programming Problems

We present a linear programming relax-PSO hybrid bound algorithm for solving a class of nonlinear integer programming problems, the objective function of which are the sum of the products of some nonnegative linear functions and the constraint functions of which are all linear and strategy variables of which are all integer ones. In the algorithm, the lower bound of the global optimal value is determined by solving a linear programming relax which is obtained through equally converting the objective function into the exponential-logarithmic composite function and linearly lower approximating each exponential function and each logarithmic function over some rectangles and the upper bound of the global optimal value and the feasible solution of it are renewed with particle swarm optimization (PSO). It is shown by the numerical results that the linear programming relax-PSO hybrid bound algorithm is better than the branch-and-bound algorithm in the computational scale and in the computational time and in the computational precision. The algorithm overcomes the convergent difficulty of PSO too