Multi-agent Slime Mould Computing: Mechanisms, Applications and Advances

The giant single-celled slime mould Physarum polycephalum has inspired developments in bio-inspired computing and unconventional computing substrates since the start of this century. This is primarily due to its simple component parts and the distributed nature of the ‘computation’ which it approximates during its growth, foraging and adaptation to a changing environment. Slime mould functions as a living embodied computational material which can be influenced by external stimuli. The goal of exploiting this material behaviour for unconventional computation led to the development of a simple multi-agent approach to the approximation of slime mould behaviour. The basis of the model is a simple dynamical pattern formation mechanism which exhibits self-organised formation and subsequent adaptation of collective transport networks. The system exhibits emergent properties such as relaxation and minimisation and it can be considered as a virtual material, influenced by the external application of spatial concentration gradients. In this chapter we give an overview of this multi-agent approach to unconventional computing. We describe its computational mechanisms and different generic application domains, together with concrete example applications of material computation. We examine the potential exploitation of the approach for computational geometry, path planning, combinatorial optimisation, data smoothing and statistical approximation applications.

[1]  Pedro Larrañaga,et al.  Genetic Algorithms for the Travelling Salesman Problem: A Review of Representations and Operators , 1999, Artificial Intelligence Review.

[2]  Andrew Adamatzky,et al.  Developing Proximity Graphs by Physarum polycephalum: Does the Plasmodium Follow the Toussaint Hierarchy? , 2009, Parallel Process. Lett..

[3]  Jeff Jones A morphological adaptation approach to path planning inspired by slime mould , 2015, Int. J. Gen. Syst..

[4]  Thomas Stützle,et al.  Ant Colony Optimization , 2009, EMO.

[5]  T. Niizato,et al.  Minimal model of a cell connecting amoebic motion and adaptive transport networks. , 2008, Journal of theoretical biology.

[6]  Jeff Jones,et al.  Characteristics of Pattern Formation and Evolution in Approximations of Physarum Transport Networks , 2010, Artificial Life.

[7]  Jeff Jones,et al.  Material approximation of data smoothing and spline curves inspired by slime mould , 2014, Bioinspiration & biomimetics.

[8]  Jeff Jones,et al.  Towards Physarum Engines , 2012, ArXiv.

[9]  Toshiyuki Nakagaki,et al.  Physarum solver: A biologically inspired method of road-network navigation , 2006 .

[10]  Susan Stepney,et al.  The neglected pillar of material computation , 2008 .

[11]  Steven Fortune,et al.  A sweepline algorithm for Voronoi diagrams , 1986, SCG '86.

[12]  Andreas W. Liehr,et al.  Voronoi diagrams in barrier gas discharge , 2002 .

[13]  J. Hopfield,et al.  Computing with neural circuits: a model. , 1986, Science.

[14]  Moshe Sipper,et al.  Design, Observation, Surprise! A Test of Emergence , 1999, Artificial Life.

[15]  Andrew Adamatzky,et al.  The Formation of Voronoi Diagrams in Chemical and Physical Systems: Experimental Findings and Theoretical Models , 2004, Int. J. Bifurc. Chaos.

[16]  Jeff Jones Mechanisms Inducing Parallel Computation in a Model of Physarum polycephalum Transport Networks , 2015, Parallel Process. Lett..

[17]  Tomohiro Shirakawa,et al.  Cell Motility Viewed as Softness , 2012, Int. J. Artif. Life Res..

[18]  Godfried T. Toussaint,et al.  On the role of kinesthetic thinking in computational geometry , 2003 .

[19]  V. A. Teplov,et al.  A continuum model of contraction waves and protoplasm streaming in strands of Physarum plasmodium. , 1991, Bio Systems.

[20]  J. A. Jump STUDIES ON SCLEROTIZATION IN PHYSARUM POLYCEPHALUM , 1954 .

[21]  T. Ueda,et al.  Reversal of thermotaxis with oscillatory stimulation in the plasmodium of Physarum polycephalum , 1988 .

[22]  Jeff Jones,et al.  Approximation of Statistical Analysis and Estimation by Morphological Adaptation in a Model of Slime Mould , 2015, Int. J. Unconv. Comput..

[23]  Atsuko Takamatsu,et al.  Environment-dependent morphology in plasmodium of true slime mold Physarum polycephalum and a network growth model. , 2009, Journal of theoretical biology.

[24]  Tomohiro Shirakawa,et al.  Universal Computation with Limited Resources: Belousov-zhabotinsky and Physarum Computers , 2007, Int. J. Bifurc. Chaos.

[25]  Andrew Adamatzky,et al.  Slime mould computes planar shapes , 2011, Int. J. Bio Inspired Comput..

[26]  Massimiliano Di Ventra,et al.  Memristive model of amoeba learning. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  Laurent D. Cohen,et al.  On active contour models and balloons , 1991, CVGIP Image Underst..

[28]  Godfried T. Toussaint,et al.  The relative neighbourhood graph of a finite planar set , 1980, Pattern Recognit..

[29]  C. Reinsch Smoothing by spline functions , 1967 .

[30]  Andreas Manz,et al.  Glow discharge in microfluidic chips for visible analog computing. , 2002, Lab on a chip.

[31]  A. Tero,et al.  A coupled-oscillator model with a conservation law for the rhythmic amoeboid movements of plasmodial slime molds , 2005 .

[32]  Masahiro Shimizu,et al.  Don't try to control everything!: an emergent morphology control of a modular robot , 2004, 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (IEEE Cat. No.04CH37566).

[33]  Paul H. C. Eilers,et al.  Flexible smoothing with B-splines and penalties , 1996 .

[34]  Marco Dorigo,et al.  Ant algorithms and stigmergy , 2000, Future Gener. Comput. Syst..

[35]  Jeff Jones,et al.  Influences on the formation and evolution of Physarum polycephalum inspired emergent transport networks , 2011, Natural Computing.

[36]  Jeff Jones,et al.  Computation of the travelling salesman problem by a shrinking blob , 2013, Natural Computing.

[37]  Toshiyuki Nakagaki,et al.  A Method Inspired by Physarum for Solving the Steiner Problem , 2010, Int. J. Unconv. Comput..

[38]  Jeff Jones,et al.  From Pattern Formation to Material Computation: Multi-agent Modelling of Physarum Polycephalum , 2015 .

[39]  Jeff Jones,et al.  Slime Mould Inspired Generalised Voronoi Diagrams with Repulsive Fields , 2015, ArXiv.

[40]  Demetri Terzopoulos,et al.  Snakes: Active contour models , 2004, International Journal of Computer Vision.

[41]  G. Odell,et al.  Mechanics of cytogels I: oscillations in physarum. , 1984, Cell motility.

[42]  Melanie Mitchell,et al.  An introduction to genetic algorithms , 1996 .

[43]  Toshiyuki Nakagaki,et al.  Amoebae anticipate periodic events. , 2008, Physical review letters.

[44]  Mark de Berg,et al.  Computational geometry: algorithms and applications , 1997 .

[45]  Jeff Jones,et al.  Network coarsening dynamics in a plasmodial slime mould: Modelling and experiments , 2015 .

[46]  Jeff Jones,et al.  Emergence of self-organized amoeboid movement in a multi-agent approximation of Physarum polycephalum , 2012, Bioinspiration & biomimetics.

[47]  Tomohiro Shirakawa,et al.  Computation of Voronoi Diagram and Collision-free Path using the Plasmodium of Physarum polycephalum , 2010, Int. J. Unconv. Comput..

[48]  Tetsuya Asai,et al.  Silicon Implementation of a Chemical Reaction-diffusion Processor for Computation of Voronoi Diagram , 2005, Int. J. Bifurc. Chaos.

[49]  Jeff Jones,et al.  The Emergence and Dynamical Evolution of Complex Transport Networks from Simple Low-Level Behaviours , 2015, Int. J. Unconv. Comput..

[50]  Greg Turk,et al.  Generating textures on arbitrary surfaces using reaction-diffusion , 1991, SIGGRAPH.

[51]  A. Adamatzky If BZ medium did spanning trees these would be the same trees as Physarum built , 2009 .

[52]  Jeff Jones,et al.  Representation of shape mediated by environmental stimuli in Physarum polycephalum and a multi-agent model , 2015, Int. J. Parallel Emergent Distributed Syst..

[53]  Andrew Adamatzky,et al.  Hot ice computer , 2009, 0908.4426.

[54]  Hsieh Hou,et al.  Cubic splines for image interpolation and digital filtering , 1978 .

[55]  J. Sherratt,et al.  Stress-induced alignment of actin filaments and the mechanics of cytogel. , 1993, Bulletin of mathematical biology.

[56]  L. Chittka,et al.  Travel Optimization by Foraging Bumblebees through Readjustments of Traplines after Discovery of New Feeding Locations , 2010, The American Naturalist.

[57]  Gheorghe Paun,et al.  Simulation Algorithms for Computational Systems Biology , 2017, Texts in Theoretical Computer Science. An EATCS Series.

[58]  Antony Galton,et al.  What Is the Region Occupied by a Set of Points? , 2006, GIScience.

[59]  Y. Nishiura,et al.  Obtaining multiple separate food sources: behavioural intelligence in the Physarum plasmodium , 2004, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[60]  David G. Kirkpatrick,et al.  On the shape of a set of points in the plane , 1983, IEEE Trans. Inf. Theory.

[61]  Kazuyuki Aihara,et al.  Amoeba-based Chaotic Neurocomputing: Combinatorial Optimization by Coupled Biological Oscillators , 2009, New Generation Computing.

[62]  Godfried T. Toussaint,et al.  Relative neighborhood graphs and their relatives , 1992, Proc. IEEE.

[63]  M Hasegawa,et al.  Verification and rectification of the physical analogy of simulated annealing for the solution of the traveling salesman problem. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[64]  Markus Bär,et al.  A model for oscillations and pattern formation in protoplasmic droplets of Physarum polycephalum , 2010 .

[65]  A. Tero,et al.  Rules for Biologically Inspired Adaptive Network Design , 2010, Science.

[66]  D. Steve Hickey,et al.  Relationship between structure and information processing in Physarum polycephalum , 2008, Int. J. Model. Identif. Control..

[67]  T. Ueda,et al.  Emergence and transitions of dynamic patterns of thickness oscillation of the plasmodium of the true slime mold Physarum polycephalum , 2008 .

[68]  Hans-Peter Meinzer,et al.  Statistical shape models for 3D medical image segmentation: A review , 2009, Medical Image Anal..

[69]  J. Murray,et al.  On pattern formation mechanisms for lepidopteran wing patterns and mammalian coat markings. , 1981, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[70]  Andrew Adamatzky,et al.  Physarum machines: encapsulating reaction–diffusion to compute spanning tree , 2007, Naturwissenschaften.

[71]  Antony Galton,et al.  Efficient generation of simple polygons for characterizing the shape of a set of points in the plane , 2008, Pattern Recognit..

[72]  Richard Durbin,et al.  An analogue approach to the travelling salesman problem using an elastic net method , 1987, Nature.

[73]  Jeff Jones,et al.  The emergence of synchronization behavior in Physarum polycephalum and its particle approximation , 2011, Biosyst..

[74]  Ray A. Jarvis,et al.  On the Identification of the Convex Hull of a Finite Set of Points in the Plane , 1973, Inf. Process. Lett..

[75]  Atsuko Takamatsu,et al.  Frequency Coupling Model for Dynamics of Responses to Stimuli in Plasmodium of Physarum Polycephalum , 1997 .

[76]  Carl de Boor,et al.  A Practical Guide to Splines , 1978, Applied Mathematical Sciences.

[77]  A. Adamatzky,et al.  Chemical processor for computation of voronoi diagram , 1996 .

[78]  Mary A. Arugula,et al.  Network analysis of biochemical logic for noise reduction and stability: a system of three coupled enzymatic and gates. , 2008, The journal of physical chemistry. B.

[79]  Jeff Jones,et al.  Towards Programmable Smart Materials: Dynamical Reconfiguration of Emergent Transport Networks , 2011, Int. J. Unconv. Comput..

[80]  Toshiyuki Nakagaki,et al.  Flow-network adaptation in Physarum amoebae , 2008, Theory in Biosciences.

[81]  T. Niizato,et al.  An adaptive and robust biological network based on the vacant-particle transportation model. , 2011, Journal of theoretical biology.

[82]  Tomohiro Shirakawa,et al.  On Simultaneous Construction of Voronoi Diagram and Delaunay Triangulation by Physarum polycephalum , 2009, Int. J. Bifurc. Chaos.

[83]  Jeff Jones,et al.  Programmable reconfiguration of Physarum machines , 2009, Natural Computing.