Skip to main content
SpringerLink
Log in

A Probability Collectives Approach for Multi-Agent Distributed and Cooperative Optimization with Tolerance for Agent Failure

  • Chapter
Agent-Based Optimization

Part of the book series: Studies in Computational Intelligence ((SCI,volume 456))

Abstract

Centralized systems are vulnerable to single point failures that may severely affect their performance. On the other hand, in the case of a distributed and decentralized algorithm, the system is more robust as it is controlled by its autonomous subsystems or agents. This chapter intends to demonstrate the inherent ability of a distributed and decentralized agent-based optimization technique referred to as Probability Collectives (PC) to accommodate agent failures. The approach of PC is a framework for optimization of complex systems by decomposing them into smaller subsystems to be further treated in a distributed and decentralized way. The system can be viewed as a Multi-Agent System (MAS) with rational and self-interested agents optimizing their local goals. At the core of the PC optimization methodology are the concepts of Deterministic Annealing in Statistical Physics, Game Theory and Nash Equilibrium. A specially developed Circle Packing Problem (CPP) with a known true optimum solution will be solved to demonstrate the ability of the PC approach to tolerate instances of agent failure. The strengths, weaknesses and future research directions of the PC methodology will also be discussed.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Kulkarni, A.J., Tai, K.: Probability Collectives: A Multi-Agent Approach for Solving Combinatorial Optimization Problems. Applied Soft Computing 10(3), 759–771 (2010)

    Article  Google Scholar 

  2. Wolpert, D.H.: Information Theory – The Bridge Connecting Bounded Rational Game Theory and Statistical Physics. In: Braha, D., Minai, A.A., Bar-Yam, Y. (eds.) Complex Engineered Systems, pp. 262–290. Springer (2006)

    Google Scholar 

  3. Bieniawski, S.R.: Distributed Optimization and Flight Control Using Collectives. PhD Dissertation, Stanford University, CA, USA (2005)

    Google Scholar 

  4. Kulkarni, A.J., Tai, K.: Probability Collectives for Decentralized, Distributed Optimization: A Collective Intelligence Approach. In: Proceedings of the IEEE International Conference on Systems, Man, and Cybernetics, pp. 1271–1275 (2008)

    Google Scholar 

  5. Kulkarni, A.J., Tai, K.: Probability Collectives: A Decentralized, Distributed Optimization for Multi-Agent Systems. In: Mehnen, J., Koeppen, M., Saad, A., Tiwari, A. (eds.) Applications of Soft Computing, pp. 441–450. Springer (2009)

    Google Scholar 

  6. Prothmann, H., Rochner, F., Tomforde, S., Branke, J., Müller-Schloer, C., Schmeck, H.: Organic Control of Traffic Lights. In: Rong, C., Jaatun, M.G., Sandnes, F.E., Yang, L.T., Ma, J. (eds.) ATC 2008. LNCS, vol. 5060, pp. 219–233. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  7. Akcelik, R.: Trafic Signals: Capacity and Timing Analysis, Australian Road Research Board (ARRB) Research Report, 123 (1981)

    Google Scholar 

  8. Stevanovic, A., Martin, P.T., Stevanovic, J.: VISGAOST: VISSIM-based Genetic Algorithm Optimization of Signal Timings. In: Proceedings of the 86th Transportation Reaseach Board Meeting (2007)

    Google Scholar 

  9. Branke, J., Goldate, P., Prothmann, H.: Actuated Traffic Signal Optimization using Evolutionary Algorithms. In: Proceedings of the 6th European Congress and Exhibition on Intelligent Transport Systems and Services (2007)

    Google Scholar 

  10. Prothmann, H., Branke, J., Schmeck, H., Tomforde, S., Rochner, F., Hahner, J., Muller-Schloer, C.: International Journal of Autonomous and Adaptive Communications Systems 2(3), 203–225 (2009)

    Article  Google Scholar 

  11. Bazzan, A.L.C.: A Distributed Approach for Coordination of Traffic Signal Agents. Autonomous Agents and Multi-Agent Systems 10, 131–164 (2005)

    Article  Google Scholar 

  12. Bhadra, S., Shakkotai, S., Gupta, P.: Min-cost selfish multicast with network coding. IEEE Transactions on Information Theory 52(11), 5077–5087 (2006)

    Article  Google Scholar 

  13. Xi, Y., Yeh, E.M.: Distributed algorithms for minimum cost multicast with network coding in wireless networks. In: Proceedings of 4th International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks (2006)

    Google Scholar 

  14. Yuan, J., Li, Z., Yu, W., Li, B.: A cross-layer optimization framework for multicast in multi-hop wireless networks. In: First International Conference on Wireless Internet, pp. 47–54 (2005)

    Google Scholar 

  15. Chatterjee, M., Sas, S.K., Turgut, D.: An on-demand weighted clustering algorithm (WCA) for ad hoc networks. In: Proceedings of 43rd IEEE Global Telecommunications Conference, pp. 1697–1701 (2000)

    Google Scholar 

  16. Amerimehr, M.H., Khalaj, B.K., Crespo, P.M.: A Distributed Cross-Layer OptimizationMethod for Multicast in Interference-Limited Multihop Wireless Networks. Journal onWireless Communications and Networking, Article ID 702036 (2008)

    Google Scholar 

  17. Mohammad, H.A., Babak, H.K.: A Distributed Probability Collectives Optimization Method for Multicast in CDMA Wireless Data Networks. In: Proceedings of 4th IEEE Internatilonal Symposium on Wireless Communication Systems, art. No. 4392414, pp. 617–621 (2007)

    Google Scholar 

  18. Ryder, G.S., Ross, K.G.: A probability collectives approach to weighted clustering algorithms for ad hoc networks. In: Proceedings of Third IASTED International Conference on Communications and Computer Networks, pp. 94–99 (2005)

    Google Scholar 

  19. Wolpert, D.H., Tumer, K.: An introduction to Collective Intelligence. Technical Report, NASA ARC-IC-99-63, NASA Ames Research Center (1999)

    Google Scholar 

  20. Wolpert, D.H., Strauss, C.E.M., Rajnarayan, D.: Advances in Distributed Optimization using Probability Collectives. Advances in Complex Systems 9(4), 383–436 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  21. Basar, T., Olsder, G.J.: Dynamic Non-Cooperative Game Theory. Academic Press, London (1995)

    Google Scholar 

  22. Vasirani, M., Ossowski, S.: Collective-Based Multiagent Coordination: A Case Study. In: Artikis, A., O’Hare, G.M.P., Stathis, K., Vouros, G.A. (eds.) ESAW 2007. LNCS (LNAI), vol. 4995, pp. 240–253. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  23. Huang, C.F., Chang, B.R.: Probability Collectives Multi-agent Systems: A Study of Robustness in Search. In: Pan, J.-S., Chen, S.-M., Nguyen, N.T. (eds.) ICCCI 2010, Part II. LNCS, vol. 6422, pp. 334–343. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  24. Huang, C.F., Bieniawski, S., Wolpert, D., Strauss, C.E.M.: A Comparative Study of Probability Collectives Based Multiagent Systems and Genetic Algorithms. In: Proceedings of the Conference on Genetic and Evolutionary Computation, pp. 751–752 (2005)

    Google Scholar 

  25. Smyrnakis, M., Leslie, D.S.: Sequentially Updated Probability Collectives. In: Proceedings of 48thIEEE Conference on Decision and Control and 28th Chinese Control Conference, pp. 5774–5779 (2009)

    Google Scholar 

  26. Sislak, D., Volf, P., Pechoucek, M., Suri, N.: Automated Conflict Resolution Utilizing Probability Collectives Optimizer. IEEE Transactions on Systems, Man and Cybernetics: Applications and Reviews 41(3), 365–375

    Google Scholar 

  27. Wolpert, D.H., Antoine, N.E., Bieniawski, S.R., Kroo, I.R.: Fleet Assignment Using Collective Intelligence. In: Proceedings of the 42nd AIAA Aerospace Science Meeting Exhibit (2004)

    Google Scholar 

  28. Bieniawski, S.R., Kroo, I.M., Wolpert, D.H.: Discrete, Continuous, and Constrained Optimization Using Collectives. In: 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, vol. 5, pp. 3079–3087 (2004)

    Google Scholar 

  29. Kulkarni, A.J., Tai, K.: Probability Collectives: A Distributed Optimization Approach for Constrained Problems. In: Proceedings of IEEE World Congress on Computational Intelligence, pp. 3844–3851 (2010)

    Google Scholar 

  30. Kulkarni, A.J., Tai, K.: Solving Constrained Optimization Problems Using Probability Collectives and a Penalty Function Approach. International Journal of Computational Intelligence and Applications 10(4), 445–470 (2011)

    Article  MATH  Google Scholar 

  31. Autry, B.: University Course Timetabling with Probability Collectives. Master’s Thesis, Naval Postgraduate School Montery, CA, USA (2008)

    Google Scholar 

  32. Kulkarni, A.J., Tai, K.: A Probability Collectives Appraoch with a Feasibility-based Rule for Constrained Optimization. Applied Computational Intelligence and Soft Computing, Article ID 980216 (2011)

    Google Scholar 

  33. Kulkarni, A.J., Tai, K.: Solving Sensor Network Coverage Problems Using a Constrained Probability Collectives Approach. Submitted to Applied Soft Computing (July 2011)

    Google Scholar 

  34. Deb, K.: An Efficient Constraint Handling Method for Genetic Algorithms. Computer Methods in Applied Mechanics in Engineering 186, 311–338 (2000)

    Article  MATH  Google Scholar 

  35. He, Q., Wang, L.: A Hybrid Particle Swarm Optimization with a Feasibility-based Rule for Constrained Optimization. Applied Mathematics and Computation 186, 1407–1422 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  36. Sakthivel, V.P., Bhuvaneswari, R., Subramanian, S.: Design Optimization of Three-Phase Energy Efficient Induction Motor Using Adaptive bacterial Foraging Algorithm. Computation and Mathematics in Electrical and Electronic Engineering 29(3), 699–726 (2010)

    Article  MATH  Google Scholar 

  37. Kaveh, A., Talatahari, S.: An Amproved Ant Colony Optimization for Constrained Engineering Design Problems. Computer Aided Engineering and Software 27(1), 155–182 (2010)

    Article  Google Scholar 

  38. Bansal, S., Mani, A., Patvardhan, C.: Is Stochastic Ranking Really Better than Feasibility Rules for Constraint Handling in Evolutionary Algorithms? In: Proceedings of World Congress on Nature and Biologically Inspired Computing, pp. 1564–1567 (2009)

    Google Scholar 

  39. Gao, J., Li, H., Jiao, Y.C.: Modified Differential Evolution for the Integer Programming Problems. In: Proceedings of International Conference on Artificial Intelligence, pp. 213–219 (2009)

    Google Scholar 

  40. Ping, W., Xuemin, T.: A Hybrid DE-SQP Algorithm with Switching Procedure for Dynamic Optimization. In: Proceedings of Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference, pp. 2254–2259 (2009)

    Google Scholar 

  41. Sindhwani, V., Keerthi, S.S., Chapelle, O.: Deterministic Annealing for Semi-supervised Kernel Machines. In: Proceedings of the 23th International Conference on Machine Learning (2006)

    Google Scholar 

  42. Rao, A.V., Miller, D.J., Rose, K., Gersho, A.: A Deterministic Annealing Approach for Parsimonious Design of Piecewise Regression Models. IEEE Transactions on Patternt Analysis and Machine Intelligence 21(2) (1999)

    Google Scholar 

  43. Rao, A.V., Miller, D.J., Rose, K., Gersho, A.: Mixture of Experts Regression Modeling by Deterministic Annealing. IEEE Transactions on Signal Processing 45(11) (1997)

    Google Scholar 

  44. Czabański, R.: Deterministic Annealing Integrated with ε-Insensitive Learning in Neuro-fuzzy Systems. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Żurada, J.M. (eds.) ICAISC 2006. LNCS (LNAI), vol. 4029, pp. 220–229. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  45. http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/helmholtz.html (last accessed on: December 12, 2011)

  46. Ray, T., Tai, K., Seow, K.C.: An Evolutionary Algorithm for Constrained Optimization. In: Proceedings of the Genetic and Evolutionary Computation Conference, pp. 771–777 (2000)

    Google Scholar 

  47. Ray, T., Tai, K., Seow, K.C.: Multiobjective Design Optimization by an Evolutionary Algorithm. Engineering Optimization 33(4), 399–424 (2001)

    Article  Google Scholar 

  48. Tai, K., Prasad, J.: Target-Matching Test Problem for Multiobjective Topology Optimization Using Genetic Algorithms. Structural and Multidisciplinary Optimization 34(4), 333–345 (2007)

    Article  Google Scholar 

  49. Shoham, Y., Powers, R., Grenager, T.: Multi-agent reinforcement learning: A critical survey. Department of Computer Science, Stanford University CA, USA, Technical Report (2003), http://multiagent.stanford.edu/papers/MALearning_ACriticalSurvey_2003_0516.pdf

  50. Busoniu, L., Babuska, L., Schutter, B.: A Comprehensive Survey of Multiagent Reinforcement Learning. IEEE Transactions on Systems, Man, and Cybernetics—Part C: Applications and Reviews 38(2), 156–172 (2008)

    Article  Google Scholar 

  51. Bowling, M., Veloso, M.: Multiagent learning using a variable learning rate. Artificial Intelligence 136(2), 215–250 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  52. Bowling, M., Veloso, M.: Rational and convergent learning in stochastic games. In: Proceedings of 17th International Conference on Artificial Intelligence, pp. 1021–1026 (2001)

    Google Scholar 

  53. Zhang, D., Deng, A.: An effective hybrid algorithm for the problem of packing circles into a larger containing circle. Computers & Operations Research 32, 1941–1951 (2005)

    Article  MATH  Google Scholar 

  54. Theodoracatos, V.E., Grimsley, J.L.: The optimal packing of arbitrarily-shaped polygons using simulated annealing and polynomial-time cooling schedules. Computer Methods in Applied Mechanics and Engineering 125, 53–70 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  55. Liu, J., Xue, S., Liu, Z., Xu, D.: An improved energy landscape paving algorithm for the problem of packing circles into a larger containing circle. Computers & Industrial Engineering 57(3), 1144–1149 (2009)

    Article  Google Scholar 

  56. Castillo, I., Kampas, F.J., Pinter, J.D.: Solving Circle Packing Problems by Global Optimization: Numerical Results and Industrial Applications. European Journal of Operational Research 191(3), 786–802 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  57. Garey, M.R., Johnson, D.S.: Computers and intractability: A Guide to the Theory of NP-completeness. W. H. Freeman & Co. (1979)

    Google Scholar 

  58. Hochbaum, D.S., Maass, W.: Approximation schemes for covering and packing problems in image processing and VLSI. Journal of the Association for Computing Machinery 1(32), 130–136 (1985)

    Article  MathSciNet  Google Scholar 

  59. Wang, H., Huang, W., Zhang, Q., Xu, D.: An improved algorithm for the packing of unequal circles within a larger containing circle. European Journal of Operational Research 141, 440–453 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  60. Szabo, P.G., Markot, M.C., Csendes, T.: Global optimization in geometry - circle packing into the square. In: Audet, P., Hansen, P., Savard, G. (eds.) Essays and Surveys in Global Optimization, pp. 233–265. Kluwer (2005)

    Google Scholar 

  61. Nurmela, K.J., Ostergard, P.R.J.: Packing up to 50 equal circles in a square. Discrete & Computational Geometry 18, 111–120 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  62. Nurmela, K.J., Ostergard, P.R.J.: More Optimal Packing of Equal Circles in a Square. Discrete and Computational Geometry 22, 439–457 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  63. Graham, R.L., Lubachevsky, B.D.: Repeated Patterns of Dense Packings of Equal Disks in a Square. The Electronic Journal of Combinatorics 3, R16 (1996)

    Google Scholar 

  64. Szabo, P.G., Csendes, T., Casado, L.G., Garcia, I.: Equal circles packing in a square I - Problem Setting and Bounds for Optimal Solutions. In: Giannessi, F., Pardalos, P., Rapcsak, T. (eds.) Optimization Theory: Recent Developments from Matrahaza, pp. 191–206. Kluwer (2001)

    Google Scholar 

  65. de Groot, C., Peikert, R., Wurtz, D.: The Optimal Packing of Ten Equal Circles in a Square, IPS Research Report 90-12, ETH, Zurich (1990)

    Google Scholar 

  66. Goldberg, M.: The packing of equal circles in a square. Mathematics Magazine 43, 24–30 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  67. Mollard, M., Payan, C.: Some Progress in the Packing of Equal Circles in a Square. Discrete Mathematics 84, 303–307 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  68. Schaer, J.: On the Packing of Ten Equal Circles in a Square. Mathematics Magazine 44, 139–140 (1971)

    MathSciNet  MATH  Google Scholar 

  69. Schluter, K.: Kreispackung in Quadraten. Elemente der Mathematics 34, 12–14 (1979)

    MathSciNet  Google Scholar 

  70. Valette, G.: A Better Packing of Ten Circles in a Square. Discrete Mathematics 76, 57–59 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  71. Boll, D.W., Donovan, J., Graham, R.L., Lubachevsky, B.D.: Improving Dense Packings of Equal Disks in a Square. The Electronic Journal of Combinatorics 7, R46 (2000)

    Google Scholar 

  72. Lubachevsky, D., Graham, R.L.: Curved hexagonal packing of equal circles in a circle. Discrete & Computational Geometry 18, 179–194 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  73. Szabo, P.G., Specht, E.: Packing up to 200 Equal Circles in a Square. In: Torn, A., Zilinskas, J. (eds.) Models and Algorithms for Global Optimization, pp. 141–156 (2007)

    Google Scholar 

  74. Mladenovic, N., Plastria, F., Urosevi, D.: Formulation Space Search for Circle Packing Problems. LNCS, pp. 212–216 (2007)

    Google Scholar 

  75. Mldenovic, N., Plastria, F., Urosevi, D.: Reformulation Descent Applied to Circle Packing Problems. Computers and Operations Research 32, 2419–2434 (2005)

    Article  Google Scholar 

  76. Huang, W., Chen, M.: Note on: An Improved Algorithm for the Packing of Unequal Circles within a Larger Containing Circle. Computers and Industrial Engineering 50(2), 338–344 (2006)

    Article  Google Scholar 

  77. Liu, J., Xu, D., Yao, Y., Zheng, Y.: Energy Landscape Paving Algorithm for Solving Circles Packing Problem. In: International Conference on Computational Intelligence and Natural Computing, pp. 107–110 (2009)

    Google Scholar 

  78. Liu, J., Yao, Y., Zheng, Y., Geng, H., Zhou, G.: An Effective Hybrid Algorithm for the Circles and Spheres Packing Problems. In: Du, D.-Z., Hu, X., Pardalos, P.M. (eds.) COCOA 2009. LNCS, vol. 5573, pp. 135–144. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  79. Stoyan, Y.G., Yaskov, G.N.: Mathematical Model and Solution Method of Optimization Problem of Placement of Rectangles and Circles Taking into Account Special Constraints. International Transactions in Operational Research 5, 45–57 (1998)

    MATH  Google Scholar 

  80. Stoyan, Y.G., Yaskov, G.N.: A Mathematical Model and a Solution Method for the Problem of Placing Various-Sized Circles into a Strip. European Journal of Operational Research 156, 590–600 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  81. George, J.A.: Multiple Container Packing: A Case Study of Pipe Packing. Journal of the Operational Research Society 47, 1098–1109 (1996)

    MATH  Google Scholar 

  82. George, J.A., George, J.M., Lamar, B.W.: Packing Different-sized Circles into a Rectangular Container. European Journal of Operational Research 84, 693–712 (1995)

    Article  MATH  Google Scholar 

  83. Hifi, M., M’Hallah, R.: Approximate Algorithms for Constrained Circular Cutting Problems. Computers and Operations Research 31, 675–694 (2004)

    Article  MATH  Google Scholar 

  84. Wolpert, D.H., Macready, W.G.: No Free Lunch Theorems for Optimization. IEEE Transactions on Evolutionary Computation 1(1), 67–82 (1997)

    Article  Google Scholar 

  85. Ng, E.Y.K., Tai, K., Ng, W.K., Acharya, R.U.: Optimization of the Pharmacokinetic Simulation Models for the Nanoparticles-in-Nanoshapes Hybrid Drug Delivery System Using Heat Diffusion Analogy. In: Rajendra Acharya, U., Tamura, T., Ng, E.Y.K., Lim, C.M., Suri, J.S. (eds.) Distributed Diagnosis and Home Healthcare, pp. 211–230. American Scientific Publishers (2010)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore, 639798, Singapore

    Anand J. Kulkarni & Kang Tai

Authors
  1. Anand J. Kulkarni
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kang Tai
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Anand J. Kulkarni .

Editor information

Editors and Affiliations

  1. Gdynia Maritime University, Str. Morska 81-87, Gdynia, 81-225, Poland

    Ireneusz Czarnowski

  2. Gdynia Maritime University, Str. Morska 81-87, Gdynia, 81-225, Poland

    Piotr Jędrzejowicz

  3. , Polish Academy of Science, Systems Research Institute, Str. Newelska 6, Warszawa, 01-447, Poland

    Janusz Kacprzyk

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Kulkarni, A.J., Tai, K. (2013). A Probability Collectives Approach for Multi-Agent Distributed and Cooperative Optimization with Tolerance for Agent Failure. In: Czarnowski, I., Jędrzejowicz, P., Kacprzyk, J. (eds) Agent-Based Optimization. Studies in Computational Intelligence, vol 456. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34097-0_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-34097-0_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-34096-3

  • Online ISBN: 978-3-642-34097-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation