Memetic algorithms for optimal task allocation in multi-robot systems for inspection problems with cooperative tasks | Soft Computing Skip to main content

Advertisement

Springer Nature Link
Log in

Memetic algorithms for optimal task allocation in multi-robot systems for inspection problems with cooperative tasks

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

Abstract

Multi-robot task allocation means to distribute and schedule a set of tasks to be accomplished by a group of robots to minimize cost while satisfying operational constraints. It can be challenging to solve a large number of tasks and becomes even more challenging when tightly coupled multi-robot tasks are also taken into account. For example, it is more complex to solve problems that include tasks that have to be carried out jointly by two robots due to the resulting temporal and spatial constraints. Additionally, the complexity of task allocation increases exponentially with rising task variety. This paper focuses on multi-robot task allocation in inspection problems with both single- and two-robot tasks. A novel memetic algorithm is proposed combining a genetic algorithm with two local search schemes. Using permutation representation, eight approaches based on four basic coding strategies are designed for multi-robot task allocation of inspection problems with two-robot tasks. The performance of the memetic algorithm is evaluated in case studies on inspecting a large storage tank area of a petroleum refinery.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Japan)

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
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

Abbreviations

\(A\) :

MRTA solution candidate by permutation coding

\(A_k\) :

Task assignment and task schedule of robot \(R_k\)

\(a_i^k\) :

\(i\)-th subtask of \(A_k\)

\(B\) :

Set of individuals

\(B_j\) :

Set of best individuals in \(j\)-th generation

\(C\) :

Set of time costs

\(C_k (A_k )\) :

Time for robot \(R_k \) to complete its tasks \(A_k\)

\(c_{ijk}^t\) :

Traveling time of robot \(R_k \) from inspection position of \(P_i \) to that of \(P_j\)

\(c_{jk}^s\) :

Time robot \(R_k \) needs to carry out inspection task of \(P_j \)

\(c_{jk}^w\) :

Waiting time of robot \(R_k\) to execute \(P_j\) after arriving at the inspection position of \(P_j\)

\(E\) :

Grid map

\(e_{xy}\) :

Cell of grid map

\(f^T\) :

Function maps the set \(T\) to the set \(P\)

\(G_{\mathrm{crt}}\) :

Current generation number

\(G_{\mathrm{max}}\) :

Fixed number of generations

\(G^{a}\) :

Gene-apportion

\(g_j^{\mathrm{opt}}(i)\) :

\(i\)-th element of gene-apportion of temporary optimal individual obtained in \(j\)-th generation

\(H\) :

Threshold value for grouping subtasks using combination-based coding

\(J\) :

Cost function (completion time)

\(K\) :

Number of subpopulations

\(l_k\) :

Number of subtasks of \(A_k\)

\(l_k^z\) :

Number of genes of \(Z_k\)

\(M\) :

Submatrices of \(E\)

\(N^G\) :

Number of genes of a chromosome

\(N^P\) :

Number of subtasks

\(N^Q\) :

Number of subtask groups

\(N^R\) :

Number of robots

\(N^T\) :

Number of tasks

\(N^b\) :

Number of elements in \(B_j\) for all \(j\)

\(N^{s}\) :

Maximal size of a subtask group

\(N^x\) :

Size of grid map in \(x\) direction

\(N^y\) :

Size of grid map in \(y\) direction

\(N_{\mathrm{pop}}\) :

Population size

\(N_{\mathrm{run}}\) :

Number of runs

\(P\) :

Set of subtask

\(P_i\) :

\(i\)-th subtasks

\(P_{ijk}^{\mathrm{path}}\) :

Traveling path of robot \(R_k\) from the inspection position of \(P_i \) to that of \(P_j\)

\(Q\) :

Set of subtask groups

\(Q_i\) :

\(i\)-th subtask group

\(q_j^i\) :

\(j\)-th subtask in the sequence of \(Q_i\)

\(R\) :

Set of robots

\(R_k\) :

\(k\)-th robot

\(R_{P}\) :

Average relative performance of algorithms

\(S\) :

Set of home bases

\(S_k\) :

Home base of robot \(R_k\)

\(T\) :

Set of tasks

\(T_l\) :

\(l\)-th task

\(t_l\) :

Subtask for a single-robot task

\(t_{l1}, t_{l2}\) :

Two subtasks of a two-robot task

\(X\) :

MRTA solution candidate using matrix coding

\(Z\) :

Genotype of an individual - gene sequence for each robot

\(Z_k\) :

Gene sequence of robot \(R_k\)

\(z_i^k\) :

\(i\)-th gene in the sequence of \(Z_k\)

\(\tau _i^a\) :

Arrival time of robot at inspection position of \(P_i\)

\(\tau _i^s\) :

Time of robot starting inspection task \(P_i\)

\(\theta \) :

Number of subtasks of \(Q_i\)

\(\mu (i)\) :

Mean parameter of normal distribution for producing the \(i\)-th integer of new gene-apportions

\(\sigma \) :

Standard deviation of normal distribution for producing new gene-apportions

References

  • Bao Y, Hu Z, Xiong T (2013) A PSO and pattern search based memetic algorithm for SVMs parameters optimization. Neurocomputing 117:98–106

    Article  Google Scholar 

  • Bonow G, Kroll A (2013) Gas leak localization in industrial environments using a TDLAS-based remote gas sensor and autonomous mobile robot with the Tri-Max method. In: IEEE international conference on robotics and automation (ICRA), pp 987–992

  • Boughaci D, Benhamou B, Drias H (2009) A memetic algorithm for the optimal winner determination problem. Soft Comput 13(8–9):905–917

    Article  Google Scholar 

  • Caponio A, Neri F, Tirronen V (2009) Super-fit control adaptation in memetic differential evolution frameworks. Soft Comput 13(8–9):811–831

    Article  Google Scholar 

  • Castro M, Sörensen K, Vansteenwegen P, Goos P (2013) A memetic algorithm for the travelling salesperson problem with hotel selection. Comput Oper Res 40(7):1716–1728

    Article  MathSciNet  Google Scholar 

  • Créput JC, Koukam A (2008) The memetic self-organizing map approach to the vehicle routing problem. Soft Comput 12(11):1125–1141

    Article  Google Scholar 

  • Cruz J, Paternina-Arboleda C, Cantillo V, Montoya-Torres J (2013) A two-pheromone trail ant colony system-tabu search approach for the heterogeneous vehicle routing problem with time windows and multiple products. J Heuristics 19(2):233–252

    Article  Google Scholar 

  • Dias MB (2004) TraderBots: a new paradigm for robust and efficient multirobot coordination in dynamic environments. PhD thesis, Carnegie Mellon University

  • Garcia P, Caamano P, Duro RJ, Bellas F (2013) Scalable task assignment for heterogeneous multi-robot teams. Int J Adv Robot Syst 10. doi:10.5772/55489

  • Gerkey BP, Matarić MJ (2004) A formal analysis and taxonomy of task allocation in multi-robot systems. Int J Robot Res 23(9):939–954

    Article  Google Scholar 

  • Guerrero J, Oliver G (2012) Multi-robot coalition formation in real-time scenarios. Robot Auton Syst 60(10):1295–1307

    Article  Google Scholar 

  • Hoogeveen J, van de Velde S, Veltman B (1994) Complexity of scheduling multiprocessor tasks with prespecified processor allocations. Discret Appl Math 55(3):259–272

    Article  MATH  Google Scholar 

  • Jakob W, Strack S, Quinte A, Bengel G, Stucky KU, Süß W (2013) Fast rescheduling of multiple workflows to constrained heterogeneous resources using multi-criteria memetic computing. Algorithms 6(2):245–277

    Article  Google Scholar 

  • Janchiv A, Batsaikhan D, Kim GH, Lee SG (2011) Complete coverage path planning for multi-robots based on. In: 11th International conference on control, automation and systems (ICCAS), pp 824–827

  • Korošec P, Bole U, Papa G (2013) A multi-objective approach to the application of real-world production scheduling. Expert Syst Appl 40(15):5839–5853

    Article  Google Scholar 

  • Kroll A (2008) A survey on mobile robots for industrial inspection. In: International conference on intelligent autonomous systems IAS10, Baden-Baden, Germany, pp 406–414

  • Lin YI, Tien KW, Chu CH (2012) Multi-agent hierarchical negotiation based on augmented price schedules decomposition for distributed design. Comput Ind 63(6):597–609

    Google Scholar 

  • Liu C, Kroll A (2012a) A centralized multi-robot task allocation for industrial plant inspection by using A* and genetic algorithms. In: Rutkowski L, Korytkowski M, Scherer R, Tadeusiewicz R, Zadeh L, Zurada J (eds) Artificial intelligence and soft computing, vol 7268., Lecture notes in computer scienceSpringer, Berlin, pp 466–474

    Chapter  Google Scholar 

  • Liu C, Kroll A (2012b) On designing genetic algorithms for solving small- and medium-scale traveling salesman problems. Swarm and evolutionary computation, vol 7269., Lecture notes in computer scienceSpringer, Berlin, pp 283–291

  • Liu L, Shell D (2012) Large-scale multi-robot task allocation via dynamic partitioning and distribution. Auton Robot 33(3):291–307

    Google Scholar 

  • Ordoñez Müller A, Kroll A (2013) Effects of beam divergence in hand-held TDLAS sensors on long distance gas concentration measurements. In: 12th International workshop on advanced infrared technology and applications AITA-12, AITA, Turin, Italy

  • Pan Q, Wang L, Sang H, Li J, Liu M (2013) A high performing memetic algorithm for the flowshop scheduling problem with blocking. IEEE Trans Autom Sci Eng 10(3):741–756

    Article  Google Scholar 

  • Papa G, Vukašinović V, Korošec P (2012) Guided restarting local search for production planning. Eng Appl Artif Intell 25(2):242–253

    Article  Google Scholar 

  • Park H, Lee JW (2012) Task assignment and migration in wireless sensor networks via task decomposition. Inf Technol Control 41(4):340–348

    Google Scholar 

  • Ramchurn SD, Polukarov M, Farinelli A, Truong C, Jennings NR (2010) Coalition formation with spatial and temporal constraints. In: AAMAS’10, pp 1181–1188

  • Soukour AA, Devendeville L, Lucet C, Moukrim A (2013) A memetic algorithm for staff scheduling problem in airport security service. Expert Syst Appl 40(18):7504–7512

    Article  Google Scholar 

  • Xhafa F, Sun J, Barolli A, Takizawa M, Uchida K (2012) Evaluation of genetic algorithms for single ground station scheduling problem. In: IEEE 26th international conference on advanced information networking and applications (AINA), pp 299–306

  • Zhang K, Collins EG Jr, Shi D (2012) Centralized and distributed task allocation in multi-robot teams via a stochastic clustering auction. ACM Trans Auton Adapt Syst 7(2):21:1–21:22

    Google Scholar 

  • Zhang Y, Parker L (2013) IQ-ASyMTRe: Forming executable coalitions for tightly coupled multirobot tasks. IEEE Trans Robot 29(2):400–416

    Article  Google Scholar 

  • Zheng T, Zhao X (2006) Research on optimized multiple robots path planning and task allocation approach. In: IEEE International conference on robotics and biomimetics, pp 1408–1413

  • Zhou KX, Roumeliotis S (2012) A sparsity-aware QR decomposition algorithm for efficient cooperative localization. In: IEEE international conference on robotics and automation (ICRA), pp 799–806

Download references

Conflict of interest

The authors declare that they have no conflict of interest.

Author information

Authors and Affiliations

  1. Department of Measurement and Control, Mechanical Engineering, University of Kassel, Mönchebergstraße 7, 34125 , Kassel, Germany

    Chun Liu & Andreas Kroll

Authors
  1. Chun Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andreas Kroll
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chun Liu.

Additional information

Communicated by A. Castiglione.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Liu, C., Kroll, A. Memetic algorithms for optimal task allocation in multi-robot systems for inspection problems with cooperative tasks. Soft Comput 19, 567–584 (2015). https://doi.org/10.1007/s00500-014-1274-0

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-014-1274-0

Keywords

Search

Navigation