A variable-grouping based genetic algorithm for large-scale integer programming

Abstract

To effectively reduce the dimensionality of search space, this paper proposes a variable-grouping based genetic algorithm (VGGA) for large-scale integer programming problems (IPs). The VGGA first groups IP’s decision variables based on the optimal solution to the IP’s continuous relaxation problem, and then applies a standard genetic algorithm (GA) to the subproblem for each group of variables. We compare the VGGA with the standard GA and GAs based on even variable-grouping by applying them to solve randomly generated convex quadratic knapsack problems and integer knapsack problems. Numerical results suggest that the VGGA is superior to the standard GA and GAs based on even variable-grouping both on computation time and solution quality.