a dynamic programming approach for solving nonlinear knapsack problems

nonlinear knapsack problems (nkp) are the alternative formulation for the multiple-choice knapsack problems. a powerful approach for solving nkp is dynamic programming which may obtain the global op-timal solution even in the case of discrete solution space for these problems. despite the power of this solu-tion approach, it computationally performs very slowly when the solution space of the problems grows rap-idly. in this paper the authors developed a procedure for improving the computational efficiency of the dy-namic programming for solving knp. they incorporate three routines; the imbedded state, surrogate con-straints, and bounding scheme, in the dynamic programming solution approach and developed an algorithmic routine for solving the knp. an experimental study for comparing the computational efficiency of the pro-posed approach with the general dynamic programming approach is also presented.