On a linearization technique for solving quadratic set covering problem and variations

TL;DR

This paper critiques a previous linearization method for the quadratic set covering problem, revealing inaccuracies and evaluating its heuristic performance through experiments, showing mixed effectiveness across problem classes.

Contribution

It identifies inaccuracies in prior linearization techniques and provides an experimental evaluation of their heuristic effectiveness compared to CPLEX.

Findings

Algorithm is effective for some problem classes

Algorithm performs poorly for other classes

Highlights need for careful validation of linearization methods

Abstract

In this paper we identify some inaccuracies in the paper by R.R. Saxena and S.R. Arora, A Linearization technique for solving the Quadratic Set Covering Problem, Optimization, 39 (1997) 33-42. In particular, we observe that their algorithm need not guarantee optimality, contrary to what is claimed. Experimental analysis with the algorithm has been carried out to evaluate its merit as a heuristic and compared with CPLEX. The results disclose that for some class of problems the algorithm is reasonably effective while for some other class, it's performance is very poor. we also discussion similar inaccuracies in another related paper.