A GPU-Enabled Compact Genetic Algorithm for Very Large-Scale Optimization Problems

Andrea Ferigo,Giovanni Iacca

doi:10.3390/math8050758

Abstract

The ever-increasing complexity of industrial and engineering problems poses nowadays a number of optimization problems characterized by thousands, if not millions, of variables. For instance, very large-scale problems can be found in chemical and material engineering, networked systems, logistics and scheduling. Recently, Deb and Myburgh proposed an evolutionary algorithm capable of handling a scheduling optimization problem with a staggering number of variables: one billion. However, one important limitation of this algorithm is its memory consumption, which is in the order of 120 GB. Here, we follow up on this research by applying to the same problem a GPU-enabled “compact” Genetic Algorithm, i.e., an Estimation of Distribution Algorithm that instead of using an actual population of candidate solutions only requires and adapts a probabilistic model of their distribution in the search space. We also introduce a smart initialization technique and custom operators to guide the search towards feasible solutions. Leveraging the compact optimization concept, we show how such an algorithm can optimize efficiently very large-scale problems with millions of variables, with limited memory and processing power. To complete our analysis, we report the results of the algorithm on very large-scale instances of the OneMax problem.

Highlights

In recent years, several application domains have shown a constantly growing need for efficient optimization algorithms capable of handling problems with a very large number of decision variables, i.e., problems in the order of thousands, or even millions, of variables
We performed the experiments on the OneMax problem using the Google R Colab service, which provides a machine powered by an Intel R XeonTM 4 CPU @ 2.20 GHz, 25 GB RAM, with an NVIDIA R P100 GPU
There is a constant demand for ever more efficient optimization techniques. This is especially true for large-scale optimization problems, for which one usually needs large computational resources—in terms of processing power and memory—to obtain a reasonable solution in feasible time

Summary

Introduction

Several application domains have shown a constantly growing need for efficient optimization algorithms capable of handling problems with a very large number of decision variables, i.e., problems in the order of thousands, or even millions, of variables. Programming (MILP), and as such can be solved by popular commercial or open-source solvers such as CPLEX [1], Gurobi [2], or glpk [3]. While these solvers are guaranteed to find the optimal solutions, when it comes to solve problems with a very large number of variables, they hit a roadblock. As reported in [4], even on some Linear Programming problems, these solvers are not able to find a feasible solution in feasible time: the so-called “curse of dimensionality”.

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Results

Conclusion