The Selective Fixing Algorithm for the closest string problem

Abstract

A hybrid heuristic algorithm based on integer linear programming is proposed for the closest string problem (CSP). The algorithm takes a rough feasible solution in input and iteratively selects variables to be fixed at their initial value until the number of free variables is small enough for the remaining problem to be solved to optimality by an ILP solver. The new solution can then be used as input for another iteration of the algorithm and this approach is repeated a predefined number of times. The procedure is denoted as Selective Fixing Algorithm (SFA). SFA has first been tested on standard instances available from the literature, which is denoted as rectangular having string length larger than the number of strings. Then, this approach has also been tested on the so-called square instances (having string length equal to the number of strings) and rectangular inverse instances (having string length smaller than the number of strings). Computational experiments indicate that SFA globally outperforms the state-of-the-art heuristics.