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

  • Authors:

  • Yuelin Gao;Chengxian Xu;Jimin Li

  • Affiliations:

  • Department of Information and Computation Science, Northwest Second National College, Yin Chuan 750021, China and School of Finance and Economics, Xi'an Jiaotong University, Xi'an Jiaotong Univers ...;School of Finance and Economics, Xi'an Jiaotong University, Xi'an Jiaotong University, Xi'an 710049, China;Department of Information and Computation Science, Northwest Second National College, Yin Chuan 750021, China

  • Venue:
  • Computational Intelligence and Security
  • Year:
  • 2007

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Abstract

The paper researches a class of nonlinear integer programming problems the objective function of which is the sum of the products of some nonnegative linear functions in the given rectangle and the constraint functions of which are all linear as well as strategy variables of which are all integer ones. We give a linear programming relax-PSO hybrid bound algorithm for solving the problem. The lower bound of the optimal value of the problem 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 the rectangles. The upper bound of the optimal value and the feasible solution of it are found and 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 the computational time and the computational precision and overcomes the convergent difficulty of PSO.