A Three-Stage Algorithm for the Closest String Problem on Artificial and Real Gene Sequences

The Closest String Problem is an NP-hard problem that aims to find a string that has the minimum distance from all sequences that belong to the given set of strings. Its applications can be found in coding theory, computational biology, and designing degenerated primers, among others. There are efficient exact algorithms that have reached high-quality solutions for binary sequences. However, there is still room for improvement concerning the quality of solutions over DNA and protein sequences. In this paper, we introduce a three-stage algorithm that comprises the following process: first, we apply a novel alphabet pruning method to reduce the search space for effectively finding promising search regions. Second, a variant of beam search to find a heuristic solution is employed. This method utilizes a newly developed guiding function based on an expected distance heuristic score of partial solutions. Last, we introduce a local search to improve the quality of the solution obtained from the beam search. Furthermore, due to the lack of real-world benchmarks, two real-world datasets are introduced to verify the robustness of the method. The extensive experimental results show that the proposed method outperforms the previous approaches from the literature.

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 is 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 novel 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 ($S^2D$) 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 a novel hyper-heuristic that exploits the $S^2D$ and one of the internal properties of the set 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 a higher performance of our proposed hyper-heuristic in both quality of solutions and run time factors.