Skip to main content
SpringerLink
Log in

Chemical reaction optimization for solving longest common subsequence problem for multiple string

  • Methodologies and Application
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

Longest common subsequence (LCS) is a well-known NP-hard optimization problem that finds out the longest subsequence of each member of a given set of strings. In computational biology, sequence alignment is a fundamental technique to measure the similarity of biological sequences, such as DNA and genome sequences. A high sequence similarity often applied to molecular structural as well as functional similarities and can be used to determine whether (and how) sequences are related. Finding the longest common subsequence (LCS) is one way to measure the similarity of sequences. It has also applications in data compression, FPGA circuit minimization, and bioinformatics, etc. Exact algorithms are impractical since they fail to solve this problem for multiple instances of long lengths in polynomial time. There are some approximations, heuristic, and metaheuristic methods proposed to solve the problem. Chemical reaction optimization (CRO) is a new metaheuristic method that mimics the nature of chemical reaction into optimization problems. In this paper, we have proposed chemical reaction optimization technique to solve the longest common subsequence problem for multiple instances. Here, we have redesigned four elementary operators of CRO for LCS problem. Operators of CRO algorithm are used to explore the search space both locally and globally. A novel correction method has been designed to correct the solution. Correction method works after each search operator to ensure the validity of the changes made by operators. Both solution quality and execution time are considered while designing the operators and the correction method. Thus proposed system brings robustness, efficiency, and effectiveness while solving MLCS problem. Our approach is compared with hyper-heuristic, ant colony optimization, beam ant colony optimization, and memory-bound anytime algorithms. The experimental results in lengths of the returned common sequences show that our proposed algorithm gives either same or better results than all other algorithms in less execution time.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  • Aho AV, Hopcroft JE, Ullman JD (1983) Data structures and algorithms. Addison Wesley Publishing Company, INc., Boston

    MATH  Google Scholar 

  • Aine S, Chakrabarti P, Kumar R (2007) Awa-a window constrained anytime heuristic search algorithm. In: IJCAI, pp 2250-2255

  • Banerjee A, Ghosh J (2001) Clickstream clustering using weighted longest common subsequences. In: Proceedings of the web mining workshop at the 1st SIAM conference on data mining, vol. 143, p 144

  • Bepery C, Abdullah-Al-Mamun S, Rahman MS (2015) Computing a longest common subsequence for multiple sequences. In: 2015 2nd international conference on electrical information and communication technology (EICT). IEEE, pp 118-129

  • Blum C (2010) Beam-ACO for the longest common subsequence problem. In: 2010 IEEE congress on evolutionary computation (CEC). IEEE, pp. 1-8

  • Blum C, Blesa M (2007) Probabilistic beam search for the longest common subsequence problem. Engineering stochastic local search algorithms. Designing, implementing and analyzing effective heuristics, pp 150–161

  • Blum C, Blesa MJ (2017) A hybrid evolutionary algorithm based on solution merging for the longest arc-preserving common subsequence problem. arXiv preprint arXiv:1702.00318

  • Blum C, Blesa MJ (2018) Hybrid techniques based on solving reduced problem instances for a longest common subsequence problem. Appl Soft Comput 62:15–28

    Article  Google Scholar 

  • Blum C, Blesa M, Lopez M (2009) Beam search for the longest common subsequence problem. Comput Oper Res 36:3178–3186

    Article  MathSciNet  MATH  Google Scholar 

  • Blum C, Blesa MJ, Calvo B (2013) Beam-ACO for the repetition-free longest common subsequence problem. In: International conference on artificial evolution (Evolution Artificielle). Springer, pp 79–90

  • Bonizzoni P, Della Vedova G, Mauri G (2001) Experimenting an approximation algorithm for the LCS. Discrete Appl Math 110(1):13–24

    Article  MathSciNet  Google Scholar 

  • Brisk P, Kaplan A, Sarrafzadeh M (2004) Area-efficient instruction set synthesis for reconfigurable system-on-chip designs. In: Proceedings of the 41st annual design automation conference. ACM, pp 395–400

  • Chen Y, Wan A, Liu W (2006) A fast parallel algorithm for finding the longest common sequence of multiple biosequences. BMC Bioinform 7(4):S4

    Article  Google Scholar 

  • Chin F, Poon CK (1994) Performance analysis of some simple heuristics for computing longest common subsequences. Algorithmica 12(4–5):293–311

    Article  MathSciNet  MATH  Google Scholar 

  • Easton T, Singireddy A (2007) A specialized branching and fathoming technique for the longest common subsequence problem. Int J Oper Res 4(2):98–104

    MathSciNet  MATH  Google Scholar 

  • Easton T, Singireddy A (2008) A large neighborhood search heuristic for the longest common subsequence problem. J Heuristics 14(3):271–283

    Article  MATH  Google Scholar 

  • Eppstein D, Galil Z, Giancarlo R, Italiano GF (1992) Sparse dynamic programming ii: convex and concave cost functions. J ACM (JACM) 39(3):546–567

    Article  MathSciNet  MATH  Google Scholar 

  • Guénoche A (2004) Supersequences of masks for oligo-chips. J Bioinform Comput Biol 2(03):459–469

    Article  Google Scholar 

  • Guenoche A, Vitte P (1995) Longest common subsequence to multiple strings. Exact and approximate algorithms. TSI-Technique et Science Informatiques-RAIRO 14(7):897–916

    Google Scholar 

  • Hakata K, Imai H (1992) The longest common subsequence problem for small alphabet size between many strings. Algorithms Comput 650:469–478

    Article  MathSciNet  Google Scholar 

  • Hirschberg DS (1975) A linear space algorithm for computing maximal common subsequences. Commun ACM 18(6):341–343

    Article  MathSciNet  MATH  Google Scholar 

  • Ho Wc (2017) A fast algorithm for the constrained longest common subsequence problem with small alphabet. Proceedings of the 34th workshop on combinatorial mathematics and computation theory, Taichung, Taiwan, May 19–20, 2017

  • Hsu W, Du M (1984) Computing a longest common subsequence for a set of strings. BIT Numer Math 24(1):45–59

    Article  MathSciNet  MATH  Google Scholar 

  • Huang K, Yang CB, Tseng KT, et al (2004) Fast algorithms for finding the common subsequence of multiple sequences. In: Proceedings of the international computer symposium. IEEE Press, pp 1006–1011

  • Irving RW, Fraser CB (1992) Two algorithms for the longest common subsequence of three (or more) strings. In: Annual symposium on combinatorial pattern matching. Springer, pp 214–229

  • Islam MR, Asha ZT, Ahmed R (2015) Longest common subsequence using chemical reaction optimization. In: 2015 2nd international conference on electrical information and communication technology (EICT). IEEE, pp 29–33

  • James J, Lam AY, Li VO (2011) Evolutionary artificial neural network based on chemical reaction optimization. In: 2011 IEEE congress on evolutionary computation (CEC). IEEE, pp 2083–2090

  • Jansen T, Weyland D (2007) Analysis of evolutionary algorithms for the longest common subsequence problem. In: Proceedings of the 9th annual conference on genetic and evolutionary computation. ACM, pp 939–946

  • Jiang T, Li M (1995) On the approximation of shortest common supersequences and longest common subsequences. SIAM J Comput 24(5):1122–1139

    Article  MathSciNet  MATH  Google Scholar 

  • Johtela T, Smed J, Hakonen H, Raita T (1996) An efficient heuristic for the LCS problem. In: Third South American workshop on string processing, WSP 96:126–140

  • Korkin D, Wang Q, Shang Y (2008) An efficient parallel algorithm for the multiple longest common subsequence (MLCS) problem. In: 37th international conference on parallel processing, 2008, ICPP’08. IEEE, pp 354–363

  • Lam AY, Li VO (2012) Chemical reaction optimization: a tutorial. Memet Comput 4(1):3–17

    Article  Google Scholar 

  • Likhachev M, Gordon GJ, Thrun S (2004) Ara*: Anytime a* with provable bounds on sub-optimality. In: Advances in neural information processing systems, pp 767–774

  • Likhachev M, Ferguson D, Gordon G, Stentz A, Thrun S (2008) Anytime search in dynamic graphs. Artif Intell 172(14):1613–1643

    Article  MathSciNet  MATH  Google Scholar 

  • Li Y, Li H, Duan T, Wang S, Wang Z, Cheng Y (2016) A real linear and parallel multiple longest common subsequences (MLCS) algorithm. In: Proceedings of the 22nd ACM SIGKDD international conference on knowledge discovery and data mining. ACM, pp 1725–1734

  • López-Ibánez M, Dubois-Lacoste J, Stützle T, Birattari M (2011) The irace package: iterated racing for automatic algorithm configuration. IRIDIA, Universite Libre de Bruxelles, Brussels, Belgium, Technical Report TR/IRIDIA/2011-004

  • Maier D (1978) The complexity of some problems on subsequences and supersequences. J ACM (JACM) 25(2):322–336

    Article  MathSciNet  MATH  Google Scholar 

  • Mousavi SR, Tabataba FS (2012) An improved algorithm for the longest common subsequence problem. Comput Oper Res 39:512–520

    Article  MathSciNet  MATH  Google Scholar 

  • Ning K (2010) Deposition and extension approach to find longest common subsequence for thousands of long sequences. Comput Biol Chem 34(3):149–157

    Article  MathSciNet  MATH  Google Scholar 

  • Peng Z, Wang Y (2017) A novel efficient graph model for the multiple longest common subsequences (MLCS) problem. Front Genet 8:104

    Article  Google Scholar 

  • Saifullah CK, Islam MR (2016a) Chemical reaction optimization for solving shortest common supersequence problem. Comput Biol Chem 64:82–93

    Article  Google Scholar 

  • Saifullah CK, Islam MR (2016b) Solving shortest common supersequence problem using chemical reaction optimization. In: 2016 5th International conference on informatics, electronics and vision (ICIEV). IEEE, pp 50–55

  • Saifullah CK, Islam MR, Mahmud MR (2018) Chemical reaction optimization algorithm for word detection using pictorial structure. In: International conference on emerging technology in data mining and information security (IEMIS) (Accepted. To appear)

  • Sankoff D, Kruskal JB, (1983) Time warps, string edits, and macromolecules: the theory and practice of sequence comparison. In: Sankoff D, Kruskal JB (eds) Reading: Addison-Wesley Publication (1983)

  • Sellis TK (1988) Multiple-query optimization. ACM Trans Database Syst (TODS) 13(1):23–52

    Article  Google Scholar 

  • Shyu SJ, Tsai CY (2009) Finding the longest common subsequence for multiple biological sequences by ant colony optimization. Comput Oper Res 36(1):73–91

    Article  MathSciNet  MATH  Google Scholar 

  • Singireddy A (2003) Solving the longest common subsequence problem in bioinformatics. Master, Kansas State University 1(1):1–10

  • Sivanandam S, Deepa S (2007) Introduction to genetic algorithms. Springer, Berlin

    MATH  Google Scholar 

  • Storer J (1988) Data compression. Elsevier, Amsterdam

    Google Scholar 

  • Tabataba FS, Mousavi SR (2012) A hyper-heuristic for the longest common subsequence problem. Comput Biol Chem 36:42–54

    Article  MathSciNet  MATH  Google Scholar 

  • Truong TK, Li K, Xu Y (2013) Chemical reaction optimization with greedy strategy for the 0–1 knapsack problem. Appl Soft Comput 13(4):1774–1780

    Article  Google Scholar 

  • Tsai Y, Hsu J (2002) An approximation algorithm for multiple longest common subsequence problems. In: Proceeding of the 6th world multiconference on systemics, cybernetics and informatics, SCI, pp 456–460

  • Tseng KT, Chan DS, Yang CB, Lo SF (2018) Efficient merged longest common subsequence algorithms for similar sequences. Theor Comput Sci 708:75–90

    Article  MathSciNet  MATH  Google Scholar 

  • Vadlamudi SG, Aine S, Chakrabarti PP (2011) A memory-bounded anytime heuristic-search algorithm. IEEE Trans Syst Man Cybern Part B (Cybern) 41(3):725–735

    Article  Google Scholar 

  • Van Den Berg J, Shah R, Huang A, Goldberg K (2011) Ana: anytime nonparametric a. In: Proceedings of twenty-fifth AAAI conference on artificial intelligence (AAAI-11)

  • Wang Q, Korkin D, Shang Y (2009) Efficient dominant point algorithms for the multiple longest common subsequence (mlcs) problem. In: IJCAI, pp 1494–1500

  • Wang Q, Pan M, Shang Y, Korkin D (2010) A fast heuristic search algorithm for finding the longest common subsequence of multiple strings. In: AAAI

  • Wang Q, Korkin D, Shang Y (2011) A fast multiple longest common subsequence (MLCS) algorithm. IEEE Trans Knowl Data Eng 23(3):321–334

    Article  Google Scholar 

  • Wang X, Wu Y, Zhu D (2016) A polynomial time algorithm for a generalized longest common subsequence problem. In: Green, pervasive, and cloud computing. Springer, pp 18–29

  • Xu J, Lam AY, Li VO (2010) Parallel chemical reaction optimization for the quadratic assignment problem. In: World congress in computer science, computer engineering, and applied computing, Worldcomp 2010

  • Xu J, Lam AY, Li VO (2011) Chemical reaction optimization for task scheduling in grid computing. IEEE Trans Parallel Distrib Syst 22(10):1624–1631

    Article  Google Scholar 

  • Yang J, Xu Y, Shang Y, Chen G (2014) A space-bounded anytime algorithm for the multiple longest common subsequence problem. IEEE Tans Knowl Data Eng 26(11):2599–2609

    Article  Google Scholar 

  • Yao X (1991) Optimization by genetic annealing. In: Proceedings of the second australian conference on neural networks, pp 94–97

  • Zhu D, Wang X (2016) A fast algorithm for solving a generalized longest common subsequence problem. ICSIC 2016 Committees Executive Committee , p 1

Download references

Author information

Authors and Affiliations

  1. Khulna University, Khulna, 9208, Bangladesh

    Md. Rafiqul Islam, C. M. Khaled Saifullah, Zarrin Tasnim Asha & Rezoana Ahamed

Authors
  1. Md. Rafiqul Islam
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. M. Khaled Saifullah
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zarrin Tasnim Asha
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Rezoana Ahamed
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Md. Rafiqul Islam.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

Additional information

Communicated by V. Loia.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Islam, M.R., Saifullah, C.M.K., Asha, Z.T. et al. Chemical reaction optimization for solving longest common subsequence problem for multiple string. Soft Comput 23, 5485–5509 (2019). https://doi.org/10.1007/s00500-018-3200-3

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-018-3200-3

Keywords

Search

Navigation