How it works

A reaction network used as a brain. Sensors feed substances into the network, the network's own reactions process them, and a motor consumes the concentration of a designated actuator species - so the robot's behaviour *is* the network's dynamics. Hand-designed networks do light-seeking and obstacle avoidance; evolved ones transfer from simulation to real hardware with little more than a scaling factor. The appeal is that computation and its substrate are not separable here.

S

abstract substances s1, s2, ...; sensor substances (b, c, d, e) receive sensor-driven inflow, the actuator substance a is read and consumed by the motor · explicit

R

Bipartite directed weighted graph G = (V, E), V = R u S. Reaction nodes have the types s1 -> s1' ; s1 + s2 -> s1' ; s1 -> s1' + s2 ; s1 + s2 -> s1' + s2' (paper eqs. 4-7). Stoichiometric edges carry the default weight k_0; a special edge S -> R carries a catalytic or inhibitory weight k in [k_min, k_max]. A catalysed node becomes X -> Y [k_0] plus X + C -> Y + C [k_0 k]. The graph must fulfil material balance: positive species weights m with M(R) m = 0. · arity 1, 2

A

lattice-2d, ode · sensor substances flow in (eq. 30); the actuator substance is consumed at rate alpha above a_min (eq. 31); the 2001 lattice reactor also removes random molecules

Parameters

What to look for

• light seeking and obstacle avoidance on a Khepera robot (1998, hand-designed enzyme-substrate network)
• evolved networks transfer between simulation and a real Khepera, with only a scale factor on sensor inflow
• the evolved kernel uses only the front and left sensor substances to raise the motor substance (fig. 14)
• genome length grows during evolution (introns, bloat) while the kernel stays small
• combined genetic + metabolic + signalling networks controlling chaotic dynamical systems (Lones et al.)

Implementation decisions

• The network is one individual of the GP system: a random reaction graph. The (mu, lambda) evolution, mutation, crossover, pathway extraction and the robot simulation act on many networks and are not generated; the v1 evolution parameter is dropped.
• Reaction nodes are drawn like mutation case 4 (type uniform over reaction_types, participants uniform over all molecules, with replacement). No-op reactions and duplicate nodes are rejected. The paper's 'grow' initialisation is not described further.
• Material balance (sec. 3.1.1) is tested as the existence of weights m >= 1 with M(R) m = 0, by linear programming. The paper's steps 4-6 set the independent weights to unity and check the rest, which can wrongly reject a balanced network whose positive solution needs other values. A node that would break the balance is rejected rather than penalised. Once the weight vector is unique, a node is kept iff it is orthogonal to it.
• Extraction garbling: eqs. 4-7 lost their primes (printed 's1 -> s1'); they are read as s1 -> s1', etc., since the unprimed forms would be no-ops.
• Catalysis: the 2001 paper only says a catalyst multiplies the rate constant by a factor. The 1998 appendix writes a catalysed reaction as a parallel mass-action channel w5 = k5 kappa [A][B][B] with k5 = k1, so a catalysed node becomes the plain reaction (k_0) plus a channel with the catalyst on both sides (k_0 k). The kappa glyph is lost in the extracted text and is restored from the table 'kappa 10'.
• Inhibition has no published functional form. An inhibited node is one mass-action reaction with k_0 whose rate dict records inhibitor and k_inhibition; a simulator must choose the inhibitory factor.
• Modifier edges: at most one per node, as mutation case 1 implies ('adding an inhibitor/catalyst if none is present'). The modifier is any molecule, with k ~ U[k_min, k_max]. p_modifier and p_inhibitor are not in the paper.
• Rate defaults: the 2001 paper gives no k_default, k_min or k_max. The defaults k_0 = 1.0 and k_min = k_max = 10 are the 1998 paper's k_i and kappa.
• Sensor inflow (eq. 30) is expressed per reactor iteration as a fraction of the reactor volume (cellsize = 1), so max_inflow = 0.1 gives 0.4 in total when all four sensor pairs read 1023, as the paper states. sensor_map and actuator_map replace the v1 callables.
• Actuator outflow (eq. 31) is recorded as outflow alpha. The threshold gate [a] > a_min is not a rate law and is kept in extras.actuators. Reactor size, fill level and cycle counts (Table 2) only size the simulation and are dropped. No initial state is set: the paper fills 50% of the lattice without giving the composition.
• The functional set (kernel, eq. 16) and pathways P(v, w) are analyses of a graph, not part of it, and are not computed. extras.reaction_graph lists each reaction node with its type, modifier and the indices of the network reactions that implement it.

Sources

• Ziegler, J. & Banzhaf, W. (2001). Evolving control metabolisms for a robot. Artificial Life 7(2):171-190. Reaction graphs sec. 3 (eqs. 4-17), material balance sec. 3.1.1, mutation sec. 3.2.1, sensors and actuators sec. 5.1-5.2 (eqs. 29-31), Tables 1-2. http://www.cs.mun.ca/~banzhaf/papers/metabolism.pdf
• Ziegler, J., Dittrich, P. & Banzhaf, W. (1998). Towards a metabolic robot control system. In Holcombe & Paton (eds.), Information Processing in Cells and Tissues, pp. 305-318. Appendix, example A: mass-action form of catalysed reactions and k = 1.0, kappa = 10. https://users.fmi.uni-jena.de/~dittrich/p/ZDB97ipcat.ps

Banzhaf & Yamamoto, Artificial Chemistries (2015), §16.1.3

Preview at default parameters

8 species · 11 reactions · status complete · seed 1

e + s2 -> s3  [mass-action k=1.0 node=r1]
b -> s2  [mass-action k=1.0 node=r2]
b + c -> d + s2  [mass-action k=1.0 node=r3 inhibitor=s3 k_inhibition=10.0]
e -> 2 a  [mass-action k=1.0 node=r4]
2 s2 -> e + s2  [mass-action k=1.0 node=r5]
2 s2 + d -> e + s2 + d  [mass-action k=10.0 node=r5 catalyst=d k_catalysis=10.0]
a + d -> s3  [mass-action k=1.0 node=r6]
b + e -> a + c  [mass-action k=1.0 node=r7]
b + e + s2 -> a + c + s2  [mass-action k=10.0 node=r7 catalyst=s2 k_catalysis=10.0]
s3 -> s1  [mass-action k=1.0 node=r8]
s3 + s2 -> s1 + s2  [mass-action k=10.0 node=r8 catalyst=s2 k_catalysis=10.0]

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