Curtin University - Meeting Room 314.347A

Abstract
This talk studies binary quadratic programs in which the objective is defined by a Euclidean distance matrix, subject to a general polyhedral constraint set. This class of nonconcave maximisation problems includes the capacitated, generalised and bi-level diversity problems as special cases. We introduce two exact cutting plane algorithms to solve this class of optimisation problems. The new algorithms remove the need for a concave reformulation, which is known to significantly slow down convergence. We establish exactness of the new algorithms by examining the concavity of the quadratic objective in a given direction, a concept we refer to as directional concavity. Numerical results show that the algorithms outperform other exact methods for benchmark diversity problems (capacitated, generalised and bi-level), and can easily solve problems of up to three thousand variables.

Bio
Sandy is a 3rd year operations research PhD student with the Centre for Transforming Maintenance through Data Science. His main research is in decomposition techniques for integer programming as well as cutting plane methods for quadratic binary programming. During his PhD he has spent time developing and deploying several scheduling optimisation tools for industry.