A Minimal Developmental Model Can Increase Evolvability in
Soft Robots
Sam Kriegman

Nick Cheney

Morphology, Evolution & Cognition Lab
University of Vermont
Burlington, VT, USA
sam.kriegman@uvm.edu

Creative Machines Lab
Cornell University
Ithaca, NY, USA

arXiv:1706.07296v1 [] 22 Jun 2017

Francesco Corucci

Josh C. Bongard

The BioRobotics Institute
Scuola Superiore Sant’Anna
Pisa, Italy

Morphology, Evolution & Cognition Lab
University of Vermont
Burlington, VT, USA

ABSTRACT

1

Different subsystems of organisms adapt over many time scales,
such as rapid changes in the nervous system (learning), slower
morphological and neurological change over the lifetime of the organism (postnatal development), and change over many generations
(evolution). Much work has focused on instantiating learning or
evolution in robots, but relatively little on development. Although
many theories have been forwarded as to how development can aid
evolution, it is difficult to isolate each such proposed mechanism.
Thus, here we introduce a minimal yet embodied model of development: the body of the robot changes over its lifetime, yet growth
is not influenced by the environment. We show that even this
simple developmental model confers evolvability because it allows
evolution to sweep over a larger range of body plans than an equivalent non-developmental system, and subsequent heterochronic
mutations ‘lock in’ this body plan in more morphologically-static
descendants. Future work will involve gradually complexifying
the developmental model to determine when and how such added
complexity increases evolvability.

Many theories have been proposed as to how development can
confer evolvability. Selfish gene theory [8] suggests that prenatal
development from a single-celled egg is not a superfluous byproduct
of evolution, but is instead a critical process that ensures uniformity among genes contained within a single organism and in turn
their cooperation towards mutual reproduction. Developmental
plasticity, the ability of an organism to modify its form in response
to environmental conditions, is believed to play a crucial role in the
origin and diversification of novel traits [17]. Others have shown
that development can in effect ‘encode’, and thus avoid on a much
shorter time scale, constraints that would otherwise be encountered
and suffered by non-developmental systems [15].
Several models that specifically address development of embodied agents have been reported in the literature. For example Eggenberger [11] demonstrated how shape could emerge during growth
in response to physical forces acting on the growing entity. Bongard
[3] adopted models of genetic regulatory networks to demonstrate
how evolution could shape the developmental trajectories of embodied agents. Later, it was shown how such development could
lead to a form of self-scaffolding that smoothed the fitness landscape and thus increased evolvability [2]. Miller [16] introduced a
developmental model that enabled growing organisms to regrow
structure removed by damage or other environmental stress.
In the spirit of Beer’s minimal cognition experiments [1], we
introduce here a minimal model of morphological development in
embodied agents (figure 2). This model strips away some aspects
of other developmental models, such as those that reorganize the
genotype to phenotype mapping [3, 11, 15] or allow the agent’s
environment to influence its development [14, 16]. We use soft
robots as our model agents since they provide many more degrees
of developmental freedom compared to rigid bodies, and can in
principle reduce human designer bias. Here, development is monotonic and irreversible, predetermined by genetic code without any
sensory feedback from the environment, and is thus ballistic in
nature rather than adaptive.
While biological development occurs along a time axis, it has
been implied in some developmental models that time provides only
an avenue for regularities to form across space, and that only the
resulting fixed form — its spatial patterns, repetition and symmetry
— are necessary for increasing evolvability. Compositional pattern

CCS CONCEPTS
•Computing methodologies → Mobile agents;

KEYWORDS
Morphogenesis; Heterochrony; Development; Artificial life; Evolutionary robotics; Soft robotics.
ACM Reference format:
Sam Kriegman, Nick Cheney, Francesco Corucci, and Josh C. Bongard. 2017.
A Minimal Developmental Model Can Increase Evolvability in Soft Robots.
In Proceedings of GECCO ’17, Berlin, Germany, July 15-19, 2017, 8 pages.
DOI: http://dx.doi.org/10.1145/3071178.3071296
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GECCO ’17, Berlin, Germany
© 2017 ACM. 978-1-4503-4920-8/17/07. . . $15.00
DOI: http://dx.doi.org/10.1145/3071178.3071296

INTRODUCTION

GECCO ’17, July 15-19, 2017, Berlin, Germany

Kriegman et al.

Phylogenetic Time (T )
T =0

T = 47

T = 24

T = 69

T = 88

Ontogenetic time (t)
t=0
T = 47

t=2

t=4

t=6

t=8

Actuation cycle
t=7
T = 47

t = 7.05

t = 7.10

t = 7.15

t = 7.20

Figure 1: The evolutionary history of an Evo-Devo robot. One of the five phylogenies is broken down into five ontogenies which
is in turn shown at five points in its actuation cycle. Voxel color indicates the remaining development. Blue for shrinkage, red
for growing, and green for no further change. This robot is featured in video at https://youtu.be/gXf2Chu4L9A.
producing networks (CPPNs, [19]) explicitly make this assumption
in their abstraction of development which collapses the time line
to a single point. While CPPNs have proven to be an invaluable
resource in evolutionary robotics [6], we argue here that discarding
time may in some cases reduce evolvability and that there exist
fundamental benefits of time itself in evolving systems.
In this paper, we examine two distinct ways by which ballistic
development can increase evolvability. First, we show how an ontogenetic time scale provides evolution with a simple mechanism
for inducing mutations with a range of magnitude of phenotypic
impact: mutations that occur early in the life time of an agent have
relatively large effects while those that occur later have smaller
effects. This is important since, according to Fisher’s geometric
model [12], the likelihood a mutation is beneficial is inversely proportional to its magnitude: Small mutations are less likely to break
an existing solution. Larger exploratory mutations, although less
likely to be beneficial on average, are more likely to provide an
occasional path out of local optima. Second, we posit that changing
ontogenies diversify targets for natural selection to act upon, and

that advantageous traits ‘discovered’ by the phenotype during this
change can become subject to heritable modification through the
‘Baldwin Effect’ [10].
Hinton and Nowlan [14] relied on this second effect when they
demonstrated how learning could guide evolution towards a solution to which no evolutionary path led. We consider a similar
hypothesis with embodied robots and ballistic development, rather
than a disembodied bitstring and random search. We demonstrate
how open-loop morphological development, without feedback from
the environment and without direct communication to the genotype, can similarly alter the search space in which evolution operates making search much easier. Hinton & Nowlan’s model of
learning was a type of environment-mediated development, in the
sense that developmental change stops when the ‘correct specification’ is found, and this information is then used to bias selection
towards individuals that find the solution more quickly. Our work
demonstrates that this explicit suppression of development is not
necessary; and that completely undirected morphological change
is enough to confer evolvability.

A Minimal Developmental Model Can Increase Evolvability in Soft Robots

METHODS

1 https://github.com/skriegman/gecco-2017 contains the source code necessary for

reproducing our results.

Vk (t)
Volume

2

All experiments1 were performed in the open-source soft-body
physics simulator Voxelyze, which is described in detail in Hiller
and Lipson [13].
We consider a locomotion task for soft robots composed of a
4 × 4 × 3 grid of voxels (see figure 1 for example). Each voxel within
and across robots is identical with one exception: its volume. At
any given time, a robot is completely specified by an array of resting
volumes, one for each of its 48 constituent voxels. If the resting volumes are static across time then a robot’s genotype is this array of
48 voxel volumes; however, because we enforce bilateral symmetry,
a genome of half that size is sufficient. On top of the deformation
imposed by the genome, each voxel is volumetrically actuated according to a global signal that varies sinusoidally in volume over
time (figure 2). The actuation is a linear contraction/expansion from
their baseline resting volume.
Under this type of rhythmic actuation, many asymmetrical mass
distributions will elicit locomotion to some extent. For instance, a
simple design, with larger voxels in its front half relative to those in
its back half, may be mobile when its voxels are actuated uniformly.
Although this design would be rather inefficient since it most likely
drags much of its body across the floor as it moves. More productive
designs are not so intuitive, even with this fixed controller.
An individual is evaluated for 8 seconds, or 32 actuation cycles.
The fitness was taken to be the distance, in the positive y direction,
the robot’s center of mass moved in 8 seconds, normalized by the
robot’s total volume. Thus, a robot with volume 48 that moves a
distance of 48 will have the same fitness — a fitness of one — as a
similarly shaped but smaller robot with volume 12 that moves a
distance of 12. Distance here is measured in units that correspond
to the length of a voxel with volume one. If, however, a robot rolls
over onto its top layer of voxels it is assigned a fitness of zero and
evaluation is terminated. This constraint prevents a rolling ball
morphology from dominating more interesting gaits.
We have now built up all of necessary machinery of our first type
of robot which we shall call the Evo robot. Populations of these
robots can evolve: body plans change from generation to generation
(phylogeny); but they can not develop: body plans maintain a fixed
form, apart from actuation, while they behave within their lifetime
(ontogeny).
We consider a second type of robot, the Evo-Devo robot, which
inherits all of the properties of the Evo robot but has a special
ability: Evo-Devo robots can develop as well as evolve. These robots
are endowed with a minimally complex model of development in
which resting volumes change linearly in ontogeny. We call this
ballistic development to distinguish it from environment-mediated
development. Ballistic development is monotonic with a fixed rate
predetermined by a genetic program; its onset and termination
are constrained at birth and death, respectively; it is strictly linear,
without mid-course correction. The volume of the k th voxel in
an Evo-Devo robot changes linearly from a starting volume, vk 0 ,
to a final volume, vk1 , within the lifetime of a robot (figure 2).
Accordingly, the genotype of a robot that can develop is twice as
large as that of robots that cannot develop, since there are two

GECCO ’17, July 15-19, 2017, Berlin, Germany
Evo

Vk (t)

Evo-Devo

"
vk1
#
"
vk0
#
Lifetime

t

"
vk0
#

t

Figure 2: The voxel picture. The k th voxel in an Evo robot
maintains a fixed resting volume, vk 0 , throughout the robot’s lifetime. Sinusoidal actuation is applied on top of the
resting volume. In contrast, the k th voxel in an Evo-Devo robot changes linearly from a starting volume, vk 0 , to a final
volume, vk 1 , over the robot’s entire lifetime. Growth, the
case when vk 1 > vk0 , is pictured here, but shrinkage is also
possible and occurs when vk 1 < vk 0 . When vk 1 = vk 0 , EvoDevo voxels are behaviorally equivalent to Evo voxels. Voxels actuate at 4 Hz in our experiments (for 8 sec or 32 cycles)
however actuation is drawn here at a lower frequency to better convey the sinusoidal volumetric structure in time.

parameters (vk 0 and vk 1 ) that determine the volume of the k th
voxel at any particular time. Although it is important to note that
the space of possible morphologies (collection of resting volumes)
is equivalent both with and without development.

2.1

From gene to volume.

Like most animals, our robots are bilaterally symmetrical. We build
this constraint into our robots by constraining the 24 voxels on the
positive x side of the robot to be equal to their counterparts on the
other side of the y axis. Instead of 48 Evo genes, therefore, we end
up with 24.
A single Evo gene stores the resting length, sk , of the k th voxel,
which is cubed to obtain the resting volume, r k (t), at any time, t,
during the robot’s lifetime.
r k (t) = sk3

k = 1, 2, . . . , 24

(1)

The resting lengths may be any real value in the range (0.25, 1.75),
inclusive. Note that the resting volume of an Evo robot does not
depend on t, and is thus constant in ontogenetic time.
Volumetric actuation, a(t) with amplitude u, and period w, takes
the following general form in time.
a(t) = u ∗ sin(2πt/w)

(2)

Actuation is limited to ±20% and cycles four times per second
(u = 0.20, w = 0.25 sec).
However, for smaller resting volumes, the actuation amplitude
is limited and approaches zero (no actuation) as the resting volume
goes to its lower bound, 0.253 . This restriction is enforced to prevent
opposite sides of a voxel from penetrating each other, effectively
incurring negative volumes, which can lead to simulation instability.
This damping is applied only where sk < 1 (shrinking voxels) and

GECCO ’17, July 15-19, 2017, Berlin, Germany
accomplished through the following function.
(
1
sk ≥ 1
d(sk ) =
(4sk − 1)/3 sk < 1

Kriegman et al.

(3)

Thus d(sk ) is zero when sk = 0.25, and is linearly increasing in
sk ≤ 1. The true actuation, ã(t, sk ), is calculated by multiplying the
unrestricted actuation, a(t), by the limiting factor, d(sk ).
ã(t, sk ) = a(t) ∗ d(sk )

(4)

Actuation is then added to the resting volume to realize the
current volume, Vk (t), of the k th voxel of an Evo robot at time t.
Vk (t) = [sk + ã(t, sk )]3

(5)

For Evo-Devo robots, a gene is a pair of voxel lengths (sk 0 , sk 1 )
corresponding to the k th voxel’s starting and final resting lengths,
respectively. Thus, for a voxel in an Evo-Devo robot, the resting
volume at time t ∈ (0, τ ) is calculated as follows.
h
i3
t
(6)
r k (t) = sk 0 + (sk 1 − sk 0 )
τ
Where the difference in starting and final scale (sk 1 −sk 0 ) determines
the slope of linear development which may be positive (growth)
or negative (shrinkage). The current volume of the k th voxel of an
Evo-Devo robot is then determined by the following.
h

i 3
1/3
1/3
Vk (t) = r k (t) + ã t, r k (t)
(7)
Hence the starting resting volume, vk 0 , and final resting volume,
vk 1 , are the current volumes at t = 0 and t = τ , respectively.
vk 0 = Vk (0) = sk3 0

vk 1 = Vk (τ ) = sk3 1

(8)

Note that an Evo gene is a special case of an Evo-Devo gene where
sk 0 = sk 1 , or, equivalently, where vk0 = vk 1 .
For convenience, let’s define the current total volume of the
robot across all 48 voxels as Q(t).
Q(t) = 2

24
Õ

Vk (t)

(9)

k =1

We track the y position of the center of mass, y(t), as well as the
current total volume, Q(t), at n discrete intervals within the lifetime
of a robot. Fitness, F , is the sum of the distance traveled in time
interval, divided by the average volume in the interval.
n
Õ
y(t) − y(t − 1)
F =2
(10)
Q(t) + Q(t − 1)
t =1
We track y(t) and Q(t) 100 times per second. Since robots are
evaluated for eight seconds, n = 800.

2.2

A direct encoding.

This paper differs from previous evolutionary robotics work that
used Voxelyze [4–7] in that we evolve the volumes of a fixed collection of voxels, rather than the presence/absence of voxels in
a bounding region. Another difference is that we do not employ
the CPPN-NEAT evolutionary algorithm [19], but instead use a
direct encoding with bilateral symmetry about the y axis. A comparison of encodings in our scenario is beyond the scope of this
paper. However we noticed that the range of evolved morphologies

here, under our particular settings, was much smaller than that of
previous work which used voxels as building blocks, and that it is
easier to reach extreme volumes for individual voxels using a direct
encoding.
Apart from the difference in encoding, this work is by in large
consistent with this previous work. We use the same physical environment as Cheney et al. [6]: a wide-open flat plain. The material
properties of our voxels are also consistent with the ‘muscle’ voxel
type from the palette in this work; although these voxels had a
fixed resting volume of one (sk = 1 for all k). Our developmental
mechanism is strongly based on Corucci et al. [7], which used
volumetric deformation in a closed-loop pointing task.

2.3

Evolutionary search.

We employ a standard evolutionary algorithm, Age-Fitness-Pareto
Optimization (AFPO, [18]), which uses the concept of Pareto dominance and an objective of age (in addition to fitness) intended to
promote diversity among candidate designs. For 30 runs, a population of 30 robots is evolved for 2000 generations. Every generation,
the population is first doubled by creating modified copies of each
individual in the population. Next, an additional random individual is injected into the population. Finally, selection reduces the
population down to its original size according to the two objectives
of fitness (maximized) and age (minimized).
The same number of parent voxels are mutated, on average,
in both Evo and Evo-Devo children. Mutations follow a normal
distribution (σ = 0.75) and are applied by first choosing what
parameter types to mutate, and then choosing which voxels to
mutate. For Evo robots, we simply visit each voxel (on the positive
x side) of the parent and, with probability 0.5, mutate its single
parameter value. For Evo-Devo parents, we flip a coin for each
parameter to be mutated (if neither will be mutated, flip a final coin
to choose one or the other). This results in a 25% chance of mutating
both, and a 37.5% chance of mutating each of the two individual
parameters alone. Then we apply the same mutation process as
before in Evo robots: loop through each voxel of the parent and,
with probability 0.5, mutate the selected parameter(s).

2.4

An artificially rugged landscape.

We did not fine-tune the mutation hyperparameters (scale and
probability), but intentionally chose a relatively high probability of
mutation in order to elicit a large mutational impact in an attempt
to render evolutionary search more difficult. This removes easy to
follow gradients in the search space — ‘compressing’ gentle slopes
into abrupt cliffs — which make ‘good designs’ more difficult to find.
Any one of these good solutions then, to a certain extent, become
like Hinton & Nowlan’s ‘needle in a haystack’ [14].
Note that there are other ways to enforce rugged fitness landscapes, and such landscapes are naturally occurring in many systems, though our particular task/environment is not one of them.
Future work should investigate these tasks and environments with
a fine-tuned mutation rate.

A Minimal Developmental Model Can Increase Evolvability in Soft Robots

3.2

Random designs
Density

Evo
Evo-Devo

−10

−5

0

5

10

Vol-normed distance
Figure 3: One thousand randomly generated robots for each
group. The horizontal axes measure fitness: volume normalized distance in the positive y direction. The best overall designs are the best Evo robots since they maintain their good
form as they behave. However, most designs are immobile
(mode at zero) and Evo-Devo robots are more likely to move
(less mass around zero) since they explore a continuum of
body plans rather than a single static guess.

RESULTS

In this section we present the results of our experiments2 and
indicate statistical significance under the Mann-Whitney U test
where applicable.

3.1

Random search.

To get a sense of the evolutionary search space, prior to optimization, we randomly generated one thousand robots from each group
(figure 3). The horizontal axes of figure 3 measure the fitness (equation 10) of our randomly generated designs. The top portion of this
figure plots the histogram of relative frequencies, using equal bin
sizes between groups. The mode is zero for both groups, meaning
that the majority of designs are immobile.
The best possibility here is to randomly guess a good Evo robot
since this good morphology is utilized for the full 32 actuation cycles.
This is why the best random designs are Evo robots. However, the
Evo-Devo distribution contains much less mass around zero than
the Evo distribution. It follows that it is more likely that an EvoDevo robot moves at all, if only temporarily, since this only requires
some interval of the many morphologies it sweeps over to be mobile.
Also note that while the total displacement may be lower in the
Evo-Devo case, since these robots ‘travel’ through a number of
different morphologies, they may pass through those which run
at a higher instantaneous speed (but spend less of their lifetime in
this morphology).
2 https://youtu.be/gXf2Chu4L9A

directs to a video overview of our experiments.

Evolution.

The results of the evolutionary algorithm are displayed in figure
4a. In the earliest generations, evolution is consistent with random
search and the best Evo robots start off slightly better than the
best Evo-Devo robots. However, the best Evo-Devo robots quickly
overtake the best Evo robots. At the end of optimization there is a
significant difference between Evo and Evo-Devo run champions
(U = 122, p < 0.001).
We also chose to reevaluate Evo-Devo robots with their development frozen at their median ontogenetic morphologies (figure 4b).
For each robot, we measure the robot’s fitness (equation 10) at this
midlife morphology with development frozen, for two seconds. Selection is completely blind to this frozen evaluation. It exists solely
for the purpose of post-evolution analysis, and serves primarily
as a sanity check to make sure Evo-Devo robots are not explicitly
utilizing their ability to grow/shrink to move faster.
Development appears to inhibit locomotion to some degree as
the best morphologies run slightly faster with development turned
off, particularly in earlier generations. A significant difference,
at the 0.001 level, between Evo robots and Evo-Devo robots with
development frozen at midlife, occurs after only 108 generations
compared to 255 generations with development enabled. Note
that the midlife morphology is not necessarily the top speed of
an Evo-Devo robot. In fact it is almost certainly not the optimal
ontogenetic form since the best body plan may occur at any point
in its continuous ontogeny, including the start and endpoints.

3.3
3

GECCO ’17, July 15-19, 2017, Berlin, Germany

Closing the window.

Once an Evo-Devo robot identifies a good body plan in its ontogenetic sweep, its descendants can gain fitness by ‘suppressing’ development around the good plan through heterochronic mutations.
This can be accomplished by incrementally closing the developmental window, the interval (sk 0 , sk 1 ), for each voxel, around the good
morphology. In the limit, under a fixed environment, this process
ends with a decedent born with the good design from the start and
devoid of any developmental at all (sk 0 = sk 1 for all voxels). This
phenomenon, best known as the Baldwin Effect, is instrumental in
evolution because natural selection is a hill-climbing process and
therefore blind to needles in a haystack, good designs (local optima)
to which no gradient of increased fitness leads. The developmental
sweep, however, alters the search space in which evolution operates,
surrounding the good design by a slope which natural selection
can climb [14].
To investigate the relationship between development and fitness,
we add up all of the voxel-level development windows to form a
individual-level summary statistic, W . We define the total development window, W , as the sum of the absolute difference of starting
and final resting lengths across the robot’s 48 voxels.
W =

48
Õ
k =1

abs(sk1 − sk 0 )

(11)

Overall there is a strong negative correlation between fitness,
F , and the total development window, W , in Evo-Devo robots
(figure 5). To achieve the highest fitness values a robot needs to
have narrow developmental windows at the voxel level. However,
this statistic doesn’t discriminate between open/closed windows

GECCO ’17, July 15-19, 2017, Berlin, Germany

Fitness

25

a.

Evo
Evo-Devo

60

20

15
25

10

Frozen midlife

b.

20
15
10

5

5

Development window

Vol-normed distance

Kriegman et al.

50
40
30
20
10

0

0
0

500

1000

1500

2000

Generation
Figure 4: For thirty runs, a population of thirty robots is
evolved for two thousand generations. (a) Best of generation
fitness for Evo and Evo-Devo robots. (b) The same robots are
reevaluated with development frozen at their midlife morphology. Means are plotted with 95% bootstrapped confidence intervals.

early/late in evolution. To show what sorts of development window/evolutionary time relationships eventually lead to highly fit
individuals, we grab the lineages of only the most fit individuals
at the end of evolutionary time (figure 6). In the most fit individuals, development windows tend to first increase slightly in
phylogeny before decreasing to their minimum, or close nearby.
The age objective in AFPO lowers the selection pressure on younger
individuals which allows them to explore, through larger developmental windows, a larger portion of design space until someone in
the population discovers a locally optimal solution which creates a
new selection pressure for descendants with older genetic material
to ‘lock in’ or canalize this form with smaller developmental windows. These results further suggests that development itself is not
optimal, it is only helpful in that it can lead to better optima down
the road once the window is closed.

3.4

The effect of mutations.

In addition to the parameter-sweeping nature of its search, developmental time provides evolution with a simple mechanism for
inducing mutations with a range of magnitude of phenotypic impact. The overall mutation impact in our experiments is conveyed
in figure 7 through 2D histograms of child and parent fitness. Recall that a child is created through mutation by each individual
(parent) in the current population. These plots include the entire
evolutionary history of all robots in every run. There are relatively
so few robots with negative fitness that the histograms need not

−5

0

5

10

15

20

25

Fitness
Figure 5: The relationship between the amount of development at the individual level (W ) and fitness (F ). The fastest
individuals have small developmental windows surrounding a fast body plan.

extend into this region since they contain practically zero density
and would appear completely white.
The diagonal represents equal parent and child fitness, a behaviorally neutral mutation. Hexagons below the diagonal represent
detrimental mutations: lower child fitness relative to that of its parent. Hexagons above the diagonal represent beneficial mutations:
higher child fitness relative to that of its parent. Mutations are generally detrimental for both groups, particularly in later generations
once evolution has found a working solution. For Evo robots (figure 7a), most if not all of the mass in the marginal density of child
speed is concentrated around zero. This means that mutations to an
Evo robot are almost certain to break the existing parent solution,
rendering a previously mobile design immobile.
The majority of Evo-Devo children, however, are generally concentrated on, or just below the diagonal in figure 7b. This general
pattern holds even in later generations when evolution has found
working solutions with high fitness. It follows that mutations to
an Evo-Devo robot may be phenotypically smaller than mutations
to an Evo robot, even though they use the same mutation operator.
Furthermore, figure 7b displays a high frequency of mutations with
a wide range of magnitude of phenotypic impact including smaller,
low-risk mutations which are useful for refining mobile designs; as
well as a range of larger, higher-risk mutations which occasionally
provide the high-reward of jumping into the neighborhood of a
more fit local optima at a range of distances in the fitness landscape.
Now let’s define the impact of developmental mutations, M, as
the relative difference in child (FC ) and parent fitnesses (F P ), for

A Minimal Developmental Model Can Increase Evolvability in Soft Robots

prefer Evo robots (with a low mutation rate) since they reside in
a smaller search space. But how low should the mutation rate
be? It may in fact be difficult to know a priori which mutation
rate is optimal. It is also important to recognize that while we use
mutation rate here to artificially tune the ruggedness of the fitness
landscape, in a naturally rugged landscape we presumably would
not have direct access to such an easily tunable parameter to ‘undo’,
or smooth-out the ruggedness.
Moreover, we know that there exist contexts in which developmental flexibility can permit the local speeding up of the basic,
slow process of natural selection, thanks to the Baldwin Effect [9].
Our new data suggests that even open-loop morphological change
increases the probability of randomly finding (and subsequently
‘locking in’) a mobile design (figure 3), and that this probability is
increasing in the amount of change (figure 6) even though ballistic
development and fitness are inversely correlated (figure 5). The
staticity of Evo robots prevents this local speed-up which can place
them at a significant disadvantage in rugged fitness landscapes.

45
35
25
15
45

Development window

GECCO ’17, July 15-19, 2017, Berlin, Germany

35
25
15
45
35
25
15
45
35
25
15
45
35
25
15
45
35
25

4

15
85 65 45 25

85 65 45 25

85 65 45 25

85 65 45 25

Ancestor

85 65 45 25

Figure 6: Closing the window. Total development window
trajectories (in phylogeny) of the lineages of the most fit
individuals in each run. Phylogenetic time goes from left
to right: from the oldest ancestor (randomly created) to its
most recent decedent, the current run champion.
positive fitnesses only.
M=

FC
− 1;
FP

FC , F P > 0

(12)

Then the average mutational impact for early-in-the-life mutations
(any mutations that, at least in part, modify initial volumes) is
M 0 = −0.29. While the average mutational impact for late-in-thelife mutations (that modify final volumes) is M 1 = −0.10. Although
both types of mutations are detrimental on average, later-in-life
mutations are more beneficial (less detrimental) on average (p <
0.001). This makes sense in a task with dependent time steps since
a child created through a late-in-life mutation will at least start
out with the same behavior as its parent and then slowly diverge
over its life. Whereas an early-in-life mutation creates a behavioral
change at t = 0.

3.5

CONCLUSION

In this paper we introduced a minimal yet embodied model of
development in order to isolate the intrinsic effect of morphological change in ontogenetic time, without the confounding effects of environmental mediation. Even our simple developmental
model naturally provides a continuum in terms of the magnitude
of mutational phenotypic impact, from the very large (caused by
early-in-life developmental mutations) to the very small (caused
by late-in-life mutations). We predict that, because of this, such a
developmental system will be more evolvable than an equivalent
non-developmental system because the latter lacks this inherent
spectrum in the magnitude of mutational impacts.
We showed that even without any sensory feedback, open-loop
development can confer evolvability because it allows evolution to
sweep over a much larger range of body plans. Our results suggest
that widening the span of the developmental sweep increases the
likelihood of stumbling across locally optimal designs otherwise
invisible to natural selection, which automatically creates a new
selection pressure to canalize development around this good form.
This implies that species with completely blind developmental plasticity tend to evolve faster and more ‘clearsightedly’ than those
without it.
Future work will involve closing the developmental feedback
loop with as little additional machinery as possible to determine
when and how such added complexity increases evolvability.

The necessity of development.

In attempting to induce a needle-in-the-haystack fitness landscape,
as a proof of concept, we intentionally set the mutation rate and
scale fairly high. A low-resolution hyperparameter sweep (figure
8) indicates that the efficacy of ballistic development is indeed
dependent on the mutation rate: there is no significant difference
between Evo and Evo-Devo at either very low or very high rates.
Higher fitness values are obtained through smaller mutation rates,
which raises the question: Is development useful only in its ability
to decrease the phenotypic impact of mutations? If so we might

5

ACKNOWLEDGEMENTS

We would like to acknowledge financial support from NSF awards
PECASE-0953837 and INSPIRE-1344227 as well as the Army Research Office contract W911NF-16-1-0304. N. Cheney is supported
by NASA Space Technology Research Fellowship #NNX13AL37H.
F. Corucci is supported by grant agreement #604102 (Human Brain
Project) funded by the European Union Seventh Framework Programme (FP7/2007-2013). We also acknowledge computation provided by the Vermont Advanced Computing Core.

GECCO ’17, July 15-19, 2017, Berlin, Germany

25

Kriegman et al.

a.

Evo

25
20

Child fitness

Child fitness

20

b.

Evo-Devo

15
10
5

15
10
5

0

0
0

5

10

15

20

25

Parent fitness

0

5

10

15

20

25

Parent fitness

Figure 7: Mutation impact: child fitness by parent fitness (vol-normed distance). The diagonal represents a neutral mutation,
equivalent child and parent fitness. Hexagon bins below the diagonal represent detrimental mutations (child less fit than its
parent); bins above the diagonal represent beneficial mutations (child more fit than its parent).

Mutation rate sweep

Fitness

26
22
18
14
10

Evo
Evo-Devo
1

24

48

Avg Num Voxels Mutated
Figure 8: A hyperparameter sweep of mutation rate: a probability dictating the average number of voxels mutated in an
individual robot.

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