Soft Computing

, Volume 21, Issue 17, pp 4925–4938 | Cite as

Formal framework for distributed swarm computing: abstract model and properties



Swarm computing is an emerging computing paradigm suitable for solving difficult optimization problems by employing a nature-inspired search for solutions. A set of entities called swarm entities populates a digital space that emulates a real physical environment. The digital space acts as a container of swarm entities by providing the basic functionalities for the entities management including processing and migration. Swarm entities are modeled as computational objects that follow a specific set of behavioral laws of natural inspiration. The entities are organized as a swarm, i.e., they coordinate, collaborate and act by exchanging information either directly or indirectly via the environment, seeking to solve a difficult computational optimization problem. Our main research result reported in this paper is the proposal of a new formal computational model of a generic distributed framework for swarm computing. Our model captures the basic computational properties of the swarm using the formal language of Finite State Process algebra. The proposed model is simple, clear and abstract, i.e., technology independent. It can serve as a starting basis for further refinement and subsequent development of new concurrent and/or distributed implementations using the available distributed computing technologies.


Swarm computing Formal model Process algebra 


Compliance with Ethical Standards

Conflict of interest

Amelia Bădică and Costin Bădică declares 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.


  1. Abolhasanzadeh B, Jalili S (2016) Towards modeling and runtime verification of self-organizing systems. Expert Syst Appl 44:230–244CrossRefGoogle Scholar
  2. Andrei O, Kirchner H (2013) Runtime verification for biochemical programs. Electr Notes Theor Comput Sci 297:27–46 ElsevierCrossRefMATHGoogle Scholar
  3. Antuña L, Araiza-Illan D, Campos S, Kerstin E (2015) Symmetry reduction enables model checking of more complex emergent behaviours of swarm navigation algorithms. In: Dixon C, Tuyls K (eds) 16th annual conference: towards autonomous robotic systems. TAROS 2015, Lecture notes in computer science, vol 9287. Springer, Berlin, pp 26–37Google Scholar
  4. Bădică C, Budimac Z, Burkhard H-D, Ivanović M (2011) Software agents: languages, tools, platforms. Comput Sci Inf Syst 8(2):255–298CrossRefGoogle Scholar
  5. Bădică A, Bădică C (2010) Specification and verification of an agent-based auction service. In: Papadopoulos GA, Wojtkowski W, Wojtkowski G, Wrycza S, Zupancic J (eds) Information systems development. Springer, New York, pp 239–248Google Scholar
  6. Bădică A, Bădică C (2011) FSP and FLTL framework for specification and verification of middle-agents. Appl Math Comput Sci 21(1):9–25MATHGoogle Scholar
  7. Bădică A, Bădică C, Brezovan M (2015) FSP modeling of a generic distributed swarm computing framework. In: Novais P, Camacho D, Analide C, El Fallah-Seghrouchni A, Bădică C (eds) Intelligent distributed computing IX. 9th international symposium on intelligent distributed computing—IDC’2015, vol 616, Springer, Berlin, pp 177–186Google Scholar
  8. Ben-Ari M (2008) Principles of the spin model checker. Springer, BerlinMATHGoogle Scholar
  9. Beni G, Wang J (1993) Swarm intelligence in cellular robotic systems. In: Dario P, Sandini G, Aebischer P (eds) Robots and biological systems: Towards a new bionics? NATO ASI series, vol 102. Springer, Berlin, pp 703–712CrossRefGoogle Scholar
  10. Cicirelli F, Forestiero A, Giordano A, Mastroianni C (2016) Transparent and efficient parallelization of swarm algorithms. ACM Trans Auton Adapt Syst 11(2), Article 14, ACMGoogle Scholar
  11. Coulouris G, Dollimore J, Kindberg T, Blair G (2011) Distributed systems. Concepts and design, 5th edn. Addison Wesley, San FranciscoMATHGoogle Scholar
  12. Dixon C, Winfield AFT, Fisher M, Zeng C (2012) Towards temporal verification of swarm robotic systems. Robot Auton Syst 60(11):1429–1441 ElsevierCrossRefGoogle Scholar
  13. Dorigo M, Stützle T (2004) Ant colony optimization. MIT Press, CambridgeMATHGoogle Scholar
  14. Gjondrekaj E, Loreti M, Pugliese R, Tiezzi F, Pinciroli C, Brambilla M, Birattari M, Dorigo M (2012) Towards a formal verification methodology for collective robotic systems. In: Aoki T, Taguchi K (eds), Formal methods and software engineering. 14th international conference on formal engineering methods, ICFEM 2012, , Lecture notes in computer science, vol 7635, Springer, Berlin, pp 54–70Google Scholar
  15. Hilaire V, Cossentino M, Gechter F, Rodriguez S, Koukam A (2013) An approach for the integration of swarm intelligence in MAS: an engineering perspective. Expert Syst Appl 40(4):1323–1332 ElsevierCrossRefGoogle Scholar
  16. Ilie S (2014) Survey on distributed approaches to swarm intelligence for graph search problems. Ann Univ Craiova Math Comput Sci Ser 41(2):251–270MathSciNetMATHGoogle Scholar
  17. Ilie S, Bădică C (2013) Multi-agent approach to distributed ant colony optimization. Sci Comput Program 78(6):762–774 ElsevierCrossRefGoogle Scholar
  18. Karaboga D (2010) Artificial bee colony algorithm. Scholarpedia 5(3):6915CrossRefGoogle Scholar
  19. Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of the IEEE international conference on neural networks, ICNN’1995, vol 4, pp 1942–1948Google Scholar
  20. Khakpour N, Jalili S, Talcott C, Sirjani M, Mousavi MR (2012) Formal modeling of evolving self-adaptive systems. Sci Comput Program 78(1):3–26 ElsevierCrossRefMATHGoogle Scholar
  21. Laibinis L, Troubitsyna E, Graja Z, Migeon F, Kacem AH (2014) Formal modelling and verification of cooperative ant behaviour in event-B. In: Giannakopoulou D, Salaün G (eds) Software engineering and formal methods: 12th international conference, SEFM 2014, Lecture notes in computer science. Springer, Berlin, pp 363–377Google Scholar
  22. Magee J, Kramer J (2006) Concurrency state models and java programs. World wide series in computer science, 2nd edn. Wiley, New YorkGoogle Scholar
  23. Massink M, Brambilla M, Latella D, Dorigo M, Birattari M (2013) On the use of Bio-PEPA for modelling and analysing collective behaviours in swarm robotics. Swarm Intell 7(2):201–228CrossRefGoogle Scholar
  24. Pedemonte M, Nesmachnow S, Cancela H (2011) A survey on parallel ant colony optimization. Appl Soft Comput 11(8):5181–5197 ElsevierCrossRefGoogle Scholar
  25. Peña J, Rouff CA, Hinchey M, Ruiz-Cortés A (2011) Modeling NASA swarm-based systems: using agent-oriented software engineering and formal methods. Softw Syst Model 10(1):55–62 SpringerCrossRefGoogle Scholar
  26. Petcu D (2002) Parallel explicit state reachability analysis and state space construction. In: Proceedings of the second international symposium on parallel and distributed computing, ISPDC’2003, Ljubljana, Slovenia, pp 207–214Google Scholar
  27. Poli R, Kennedy J, Blackwell T (2007) Particle swarm optimization: an overview. Swarm Intell 1(1):33–57 SpringerCrossRefGoogle Scholar
  28. Rashedi E, Nezamabadi-pour H, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf Sci 179(13):2232–2248 ElsevierCrossRefMATHGoogle Scholar
  29. Rouff CA, Hinchey MG, Truszkowski WF, Rash JL (2006) Experiences applying formal approaches in the development of swarm-based space exploration systems. Int J Softw Tools Technol Transfer 8(6):587–603 SpringerCrossRefGoogle Scholar
  30. Schut MC (2010) On model design for simulation of collective intelligence. Inf Sci 180(1):132–155 ElsevierCrossRefGoogle Scholar
  31. Vinh PC (2016) Concurrency of self-* in autonomic systems. Fut Gen Comput Syst 56:140–152CrossRefGoogle Scholar
  32. Yang X-S (2010) New metaheuristic bat-inspired algorithm. In: Dario P, Sandini G, Aebischer P (eds) Nature inspired cooperative strategies for optimization (NICSO 2010), Studies in computational intelligence, vol 284. Springer, Berlin, pp 65–74CrossRefGoogle Scholar
  33. Zhang P, Muccini H, Li B (2010) A classification and comparison of model checking software architecture techniques. J Syst Softw 83(5):723–744 SpringerCrossRefGoogle Scholar
  34. Zhao Y, Oberthür S, Kardos M, Rammig FJ (2006) Model-based runtime verification framework for self-optimizing systems. Electr Notes Theor Comput Sci 144(4):125–145 ElsevierCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.University of CraiovaCraiovaRomania

Personalised recommendations