Efficiently solving: a large-scale integer linear program using a customized genetic algorithm

Abstract

Many optimal scheduling and resource allocation problems involve large number of integer variables and the resulting optimization problems become integer linear programs (ILPs) having a linear objective function and linear inequality/equality constraints. The integer restrictions of variables in these problems cause tremendous difficulty for classical optimization methods to find the optimal or a near-optimal solution. The popular branch-and-bound method is an exponential algorithm and faces difficulties in handling ILP problems having thousands or tens of thousands of variables. In this paper, we extend a previously-suggested customized GA with four variations of a multi-parent concept and significantly better results are reported. We show variations in computational time and number of function evaluations for 100 to 100,000-variable ILP problems and in all problems a near-linear complexity is observed. The exploitation of linearity in objective function and constraints through genetic crossover and mutation operators is the main reason for success in solving such large-scale applications. This study should encourage further use of customized implementations of EAs in similar other applications.