Grammatical Evolution Algorithm for Evolution of Swarm Behaviors

Aadesh Neupane, Michael A. Goodrich, Eric G. Mercer

Problem

- Cumbersome to design collective behaviors

- Requires experts for modeling

Solution

- Evolutionary computation to generate collective behaviors

$$\dot{R} = -aR + vnD , R(0) = R_0$$

$$\dot{O} = aR -bO +cE, O(0) = O_0$$

$$\dot{E} = q(D)bO - cE, E(0) = E_0$$

$$\dot{A} = p(D)bO - mA + wnD, A(0) = A_0$$

$$\dot{D} = mA - nD, D(0) = D_0$$

Reference: Stability of choice in the honey bee nest-site selection process

Related Work
- Evolutionary Robotics
  - Neural Nets
  - Distributed Evolution
- Grammatical Evolution
GEESE
Results
- Santa Fe Trail
- Single Source Foraging
Conclusion

Presentation Structure

Related Work - Evolutionary Robotics

Reference: Evolution of collective behaviors for a real swarm of aquatic surface robots

Swarm behaviors like homing, dispersion, clustering and monitoring by Duarte et. al
They transferred the evolved controller from simulation to real world aquatic robots and validated the key properties of swarms like scalability, flexibility, and robustness

Neural Network based controllers

Merits

Direct mapping from sensory inputs into actuators values
Provides generalized solutions
Only a few human inputs needed

Demerits

Very hard to reverse engineer
Not easy to obtain insights on the evolved collective behavior
Very difficult to modify the behaviors

Related Work - Evolutionary Robotics

Reference: GESwarm: Grammatical Evolution for the Automatic Synthesis of Collective Behaviors in Swarm Robotics

Ferrante et. al. used grammatical evolution based approach named as "GESwarm" to evolve collective behaviors for foraging problem
Individual behaviors were composed of preconditions, low-level behavior and actions
Grammatical evolution would evolve different interaction rules between the individual behaviors

Grammatical Evolution based controllers

Advantages

Disadvantages

BNF grammar and objective function enable human to shape collective tasks
Easy to analyze and modify collective behaviors

Human expert has to define the primitive low-level rules
Low-level rules need mapping to sensors and actuators values

Related Work - Distributed Evolution

Reference: odNEAT: An algorithm for distributed online, onboard evolution of robot behaviours

odNEAT

Online distributed algorithm based on NEAT evolves neural network weights along with topology
Applicable for online learning in groups of embodied agents (robots)
odNEAT performs well in aggregation in comparison with rtNEAT (centralized)

What is the outcome if we combine best features from all of these works?

A online distributed Grammatical Evolution

Related Work - Grammatical Evolution

BNF Grammar

Population of Genome

Corresponding Phenotype

Grammatical evolution: Evolving programs for an arbitrary language

Grammatical Evolution

BNF Grammar

<condition> ::= if_food_ahead(<progs>, <progs>)
<prog2>    ::= prog2(<progs>, <progs>)
<prog3>    ::= prog3(<progs>, <progs>, <progs>)
<op>    ::= left | right | move

- Santa Fe Trail Grammar

- Represented by tuple $N, T, P, S$

N -> Set of all non-terminals
T -> Set of all terminals
P -> Set of productions that map $N$ to $T$
S -> Initial start symbol

Grammatical Evolution

Genome/ Genotype / Individual

Defines the proceedings of left-derivation
${Codon}$ is a group of symbols, usually 4 or 8.

Grammatical Evolution - BNF Grammar

Mapping

Let $c$ be codon integer
$A$ denotes the left-most non-terminal in the derivation
$r_A$ denotes the number of right-hand side rules associated with the production of $A$
RHSRule = $c\%r_A$