Heuristic algorithms for the bipartite unconstrained 0-1 quadratic programming problem

Abstract

We study the Bipartite Unconstrained 0-1 Quadratic Programming Problem (BQP) which is a relaxation of the Unconstrained 0-1 Quadratic Programming Problem (QP). Applications of the BQP include mining discrete patterns from binary data, approximating matrices by rank-one binary matrices, computing cut-norm of a matrix, and solving optimization problems such as maximum weight biclique, bipartite maximum weight cut, maximum weight induced subgraph of a bipartite graph, etc. We propose several classes of heuristic approaches to solve the BQP and discuss a number of construction algorithms, local search algorithms and their combinations. Results of extensive computational experiments are reported to establish the practical performance of our algorithms. For this purpose, we propose several sets of test instances based on various applications of the BQP. Our algorithms are compared with state-of-the-art heuristics for QP which can also be used to solve BQP with reformulation. We also study theoretical properties of the neighborhoods and algorithms. In particular, we establish complexity of all neighborhood search algorithms and establish tight worst-case performance ratio for the greedy algorithm.

Bilinear Assignment Problem: Large Neighborhoods and Experimental Analysis of Algorithms

“…Alternating Algorithm is a strategy well-known in non-linear programming literature as coordinate-wise descent. Similar underlying ideas are used in the context of other bilinear programming problems by various authors [18,20,25].…”

The bipartite unconstrained 0–1 quadratic programming problem: Polynomially solvable cases

“…To the best of our knowledge, BQP01 has not been thoroughly investigated in literature, especially from the point of view of polynomially solvable special cases. Some recent references on the problem considers theoretical analysis of approximation algorithms [30] and experimental analysis of heuristics [14,18]. The primary focus of this work is to identify polynomially solvable special cases of BQP01.…”