Longest common substring in Longest Common Subsequence's solution service: A novel hyper-heuristic

The Longest Common Subsequence (LCS) is the problem of finding a subsequence among a set of strings that has two properties of being common to all and the longest. The LCS has applications in computational biology and text editing, among many others. Due to the NP-hardness of the general longest common subsequence, numerous heuristic algorithms and solvers have been proposed to give the best possible solution for different sets of strings. None of them has the best performance for all types of sets. In addition, there is no method to specify the type of a given set of strings. Besides that, the available hyper-heuristic is not efficient and fast enough to solve this problem in real-world applications. This paper proposes a novel hyper-heuristic to solve the longest common subsequence problem using a new criterion to classify a set of strings based on their similarity. To do this, we offer a general stochastic framework to identify the type of a given set of strings. Following that, we introduce the set similarity dichotomizer (S²D) algorithm based on the framework that divides the type of sets into two. This algorithm is introduced for the first time in this paper and opens a new way to go beyond the current LCS solvers. Then, we present our proposed hyper-heuristic that exploits the S²D and one of the internal properties of the given strings to choose the best matching heuristic among a set of heuristics. We compare the results on benchmark datasets with the best heuristics and hyper-heuristics. The results show that our proposed dichotomizer (i.e., S²D) can classify datasets with 98% of accuracy. Also, our proposed hyper-heuristic obtains competitive performance in comparison with the best methods and outperforms best hyper-heuristics for uncorrelated datasets in terms of both quality of solutions and run time factors. All supplementary files, including the source codes and datasets, are publicly available on GitHub.¹.