2004 Volume 55 Issue 5 Pages 252-261
It is significant to obtain optimal solutions or high-quality approximate solutions for multidimensional nonlinear integer programming problems with many decision variables or with large dimensions. It is known that a surrogate constraint method is effective for solving multidimensional problems. The method translates the multidimensional problem into a one-dimensional problem using a surrogate multiplier. When the obtained optimal solution to the surrogate problem is not optimal to the original problem, it is said that there exists a surrogate duality gap between the translated one-dimensional problem and the original multidimensional problem. Nakagawa has recently proposed an improved surrogate constrain (ISC) method that closes the surrogate duality gap and can provide an exact solution to the original problem. The ISC method needs an optimal surrogate multiplier for the surrogate problem. In order to obtain the optimal surrogate multiplier to the problem associated with the original problems with large dimensions, some computational problems should be solved to reduce execution time and working area of memory. Nakagawa et al. have proposed an algorithm that improves Dyer's method for calculating optimal surrogate multipliers. The improved Dyer algorithm proposed reduces the execution time by removing the hyperplanes of the polyhedron that does not influence the calculation of optimal multipliers. In this paper, the effect of the parameters (ratio of Reducing Polyhedron (RP) and period of RP procedure) used in the improved Dyer algorithm is investigated on execution time and the number of executing times by computational experiments. Effective values of the parameters are found for solving the large-scale multidimensional nonlinear integer programming problems in a practical amount of time.
