Improved LP‐based algorithms for the closest string problem

In a recent paper by Liu et al. [Exact algorithm and heuristic for the closest string problem, Computers & Operations Research 2011;38:1513–20], a polynomial time heuristic procedure is proposed for the closest string problem (CSP). Such heuristic called $\mathrm{LDDA}\_\mathrm{LSS}$ is a combination of a previously published approximation algorithm and local search strategies. This paper points out that an instant algorithm deriving a feasible solution directly from the continuous relaxation solution of a standard ILP formulation of CSP already strongly outperforms $\mathrm{LDDA}\_\mathrm{LSS}$ both in terms of solution quality and computing time. Two core based procedures are then proposed that further improve the results of the instant algorithm. Based on these results, we conclude that such LP‐based approaches for their efficiency and simplicity should be used as a benchmark for future heuristics on CSP.