A Population-Based Algorithm for Billion-Variable Constrained Integer Linear Programming

Among various complexities affecting the performance of an optimization algorithm, the search space dimension is a major factor. Another key complexity is the discreteness of the search space. When these two complexities are present in a single problem, optimization algorithms have been demonstrated to be inefficient, even in linear programming (LP) problems. In this paper, we consider a specific structure of an integer linear programming (ILP) problem which, although comes from a specific industry, is similar to many other practical resource allocation and assignment problems. Based on a population based optimization approach, we develop a computationally fast method to arrive at a near-optimal solution. Compared to two popular softwares (glpk and CPLEX), which are not able to handle around 300 and 2,000 integer variables while continuing to run for hours, respectively, our proposed method is able to find a near-optimal solution in less than second on the same computer. Moreover, the main highlight of this study is that our method scales in almost a linear computational complexity in handling 50,000 to one billion (10) variables. We believe that this is the first time such a large-sized real-world constrained problem is ever handled using any optimization algorithm. We perform sensitivity studies of our method for different problem parameters and these studies clearly demonstrate the reasons for such a fast and scale-up application of the proposed method.

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