An Algorithm for Nonlinear Knapsack Problems

An algorithm which recursively generates the complete family of undominated feasible solutions to separable nonlinear multidimensional knapsack problems is developed by exploiting discontinuity preserving properties of the maximal convolution. The “curse of dimensionality,” which is usually associated with dynamic programming algorithms, is successfully mitigated by reducing an M-dimensional dynamic program to a 1-dimensional dynamic program through the use of the imbedded state space approach. Computational experience with the algorithm on problems with as many as 10 state variables is also reported and several interesting extensions are discussed.