Comparison of Vector Operations of Open-Source Linear Optimization Kernels

Optimization is a widely used field of science in many applications. Optimization problems are becoming more and more complex and difficult to solve as the new models tend to be very large. To keep up with the growing requirements the solvers need to operate faster and more accurately. An important field of optimization is linear optimization which is very widely used. It is also often the hidden computational engine behind algorithms of other fields of optimization. Since linear optimization solvers use a high amount of special linear algebraic vector operations their performance is greatly influenced by their linear algebraic kernels. These kernels shall exploit the general characteristics of large-scale linear optimization problem models as efficiently as possible. To construct more efficient linear algebraic kernels the critical implementational factors influencing operation performance were identified via performance analysis and are presented in this paper. With the results of this analysis a new kernel has been developed for the open-source linear optimization solver called Pannon Optimizer developed at the Operations Research Laboratory at the University of Pannonia. A novel application of indexed dense vectors is also introduced which is designed specifically for linear optimization solvers. Finally a computational study is performed comparing the performance of vector operations of different linear optimization kernels to validate the high efficiency of our kernel. It shows that in case of large scale operations the indexed dense vector outperforms the state-of-the-art open-source linear optimization kernels.