Large neighborhood search for the most strings with few bad columns problem

Abstract

In this work we consider the following N P -hard combinatorial optimization problem from computational biology. Given a set of input strings of equal length, the goal is to identify a maximum cardinality subset of strings that dier maximally in a pre-dened number of positions. First of all we introduce an integer linear programming model for this problem. Second, two variants of a rather simple greedy strategy are proposed. Finally, a large neighborhood search algorithm is presented. A comprehensive experimental comparison among the proposed techniques shows, rst, that larger neighborhood search generally outperforms both greedy strategies. Second, while large neighborhood search shows to be competitive with the stand-alone application of CPLEX for small and medium sized problem instances, it outperforms CPLEX in the context of larger instances.Keywords: Most strings with few bad columns, integer linear programming, large neighborhood search. * A preliminary version of this work appeared at

Construct, Merge, Solve and Adapt Versus Large Neighborhood Search for Solving the Multi-dimensional Knapsack Problem: Which One Works Better When?

“…In such a case LNS will most probably have advantages over CMSA. An example of such a problem is the most strings with few bad columns problem [16].…”

On the role of metaheuristic optimization in bioinformatics

“…As expected, the authors find that using CPLEX to tackle the ILP model provides the optimal solution for small and medium instances in reasonable amounts of time, but the heuristic methods scale much better for large instances. Finally, Lizárraga et al (2017) present a large neighborhood search (LNS) approach, which relies on the ILP solver CPLEX as a subroutine to get, at each iteration, the best possible neighbor in a large neighborhood of the current solution. According to the results, the LNS tends to outperform greedy strategies.…”

“…Finally, Lizárraga et al. (2017) present a large neighborhood search (LNS) approach, which relies on the ILP solver CPLEX as a subroutine to get, at each iteration, the best possible neighbor in a large neighborhood of the current solution. According to the results, the LNS tends to outperform greedy strategies.…”