Optimizing Quadratic Functions over the Set of Permutations

Abstract

Seriation problem is widely used in many fields like archeology\cite{robinson1951method} and shotgun gene sequencing\cite{garriga2011banded,meidanis1998consecutive}. It aims to reorder a linear permutation based on given similarity information and it is an optimization problem over the set of permutation. Due to the large size of feasible set and the variable type, the seriation is an NP-hard quadratic mixed integer programming(MIP) problem. In order to solve this problem efficiently, a construction proposed recently by Goemans\cite{goemans2015smallest}, sorting network is used to constrain the solutions of the problem to be permutation and reformulate the problem. And we solve the MIP problem using heuristic method and branch and bound method and compare their performance