ACHIEVING ROBUSTNESS IN ADAPTIVE SYSTEMS

Can Hierarchies Help?

Dragana Laketic and Gunnar Tufte

Department of Computer and Information Science, Norwegian University of Science and Technology

Sem Saelands vei 7-9, NO-7491 Trondheim, Norway

Keywords:

Robustness, Adaptive systems, Environmental ﬂuctuations, Living systems organisation, Modularity, Hierar-

chies.

Abstract:

In this paper we present the latest research directions within the investigation of adaptive autonomous systems.

Originally inspired by biological solutions for performing adaptive processes, we have engaged into investi-

gating organisation of living systems with the aim of extracting useful principles for man–made systems. The

work so far has demonstrated in simulation how principles of endocrine system can be used for the initia-

tion and support of adaptive processes until the adaptation to new environmental ﬂuctuation is achieved. Our

current research considers robustness of the system and sets the stage for the investigation into hierarchical

organisation of such a system. The main question we ask is if the robustness of the proposed system could be

improved if hierarchies in its architecture and (or) functional operation are taken into account.

1 INTRODUCTION

The motivation behind the work presented herein lies

in one of the greatest challenges today’s electronic

systems face when set to operate within the harsh

varying environments. On one hand, the system needs

to adapt to variations in the environment so that it

preserves desired functionality; on the other, harsh

environments impose additional requirements which,

when summed up, come to the necessity for robust

operation. Different techniques exist for achieving ro-

bustness in such systems (see (Laketic and Haddow,

2007) for the example of extreme temperature envi-

ronments). However, achievement of the robust adap-

tive process presents an additional challenge when

adaptive systems are considered. Moreover, opera-

tions within harsh environments as a rule exclude hu-

man intervention so that the system is to operate and

adapt in autonomous fashion.

Living systems are faced with similar demands –

they need to survive despite the varying environment.

Therefore, our investigation into autonomous adap-

tive systems has lead us to taking a closer look into

the mechanisms and principles through which adap-

tation is achieved in these systems. In particular, we

have considered the processes through which a living

system preserves its homeostasis. The focus has been

set on endocrine system and its role within homeo-

static processes for performing control and communi-

cation. Through simulations on a simple model, we

have demonstrated how adaptation to a ﬂuctuation in

some environmental parameter is achieved when ini-

tiated and sustained by hormonal ﬂows.

The aim of this paper is to present our current

activities and considerations which are focused on

the living systems’ organisation, in particular its hi-

erarchical organisation and the impact the hierarchies

may have on the system’s adaptability and robustness.

In the further text, we ﬁrst present some background,

section 2, and introduce the reader to the previous

work, section 3, through the introduction of the model

of the system under investigation and brief summary

of the results achieved so far. There, we also intro-

duce novel features of such model with the aim of es-

tablishing more formal framework for tackling the ro-

bustness issue. Also, we draw a parallel between the

organisation of a living system unit and the cell within

our modular system. This all offers ﬁrmer grounds for

the introduction of hierarchical organisation as is dis-

cussed in section 4. Finally, we conclude the paper

with the discussion on the results achieved and con-

sideration of the work that lies ahead.

422

Laketic D. and Tufte G. (2010).

ACHIEVING ROBUSTNESS IN ADAPTIVE SYSTEMS - Can Hierarchies Help?.

In Proceedings of the 2nd International Conference on Agents and Artiﬁcial Intelligence - Artiﬁcial Intelligence, pages 422-427

DOI: 10.5220/0002762004220427

 SciTePress

2 PRINCIPLES TO BORROW

FROM LIVING SYSTEMS:

SETTING THE STAGE

Living systems’ viability is the result of their adapt-

ability. This remarkable ability is the result of a

long term process of evolution. More precisely, it

is through a process of coevolution with the environ-

ment that living systems have been created. As no

environment is static so the coevolutionary process

needed to account for these environmental variations

and equip the living systems with mechanisms to aid

them in survivingdespite varying environment. These

mechanisms are activated when variation in the envi-

ronment is detected or sensed, the term better suited

for a living system.

But ﬁrstly, the distinction between different terms

need be explained which are used throughout the text

to denote environmental variations. These distinc-

tions are primarily made based on the temporal du-

ration of the variation. The long–term variations will

be referred to as changes. Their effect is imposed over

a longer period on a scale measured from one individ-

ual’s lifetime. Therefore, effects of such variations

are noticable at the population level and are tackled

by evolutionary processes. The short–term variations,

i.e. those whose effect happens at the time scale much

shorter than individual’s lifetime, will be referred to

as disturbances.

Secondly, we need to explain the view of living

systems from the framework of the general system

theory (von Bertalanffy, 1973). Within such a frame-

work, living systems are viewed as open systems

which are in stable or steady state, a consequence of

this being preservation of homeostasis (Ganti, 2003;

Walter, 1967). Therefore, disturbance is any variation

in environment which momentarily moves the system

from its steady state. Further, we recognise that some

disturbances will lead the system to such states from

which they can re–gain the steady state after hav-

ing performed some adaptive process(es) (short–term

in comparison with coevolutionary processes), while

some of the disturbances will take the system to the

states from which they will not be able to recovertheir

stability (steady state) i.e. where they will lose their

viability and die.

The ﬁrst group of disturbances we term ﬂuctu-

ations and our previous work (Laketic et al., 2009;

Laketic and Tufte, 2009a; Laketic and Tufte, 2009b)

has considered mainly this kind of environmental

variations. Our current work considers the system’s

ability to escape from the states where no return to a

steady state is possible. This ability is considered to

be robustness of the system. To sum up, we say that a

system is robust if it can return to its steady state af-

ter it has been moved from it by some environmental

disturbance. Out of many ways in which robustness

can be improved, we are, in particular, posing a ques-

tion if hierarchical organisation of an adaptive system

could enhance the degree of the system’s robustness

and, if so, how.

3 MODEL OF THE SYSTEM

UNDER INVESTIGATION

Figure 1: Schematic view of the system’s architecture.

In order to examine adaptive processes in a man–

made system, we have made a model of such a system

as a basis for simulations. It is schematically depicted

in ﬁgure 1. Detailed introduction of the model can be

found in (Laketic et al., 2009), while at this place we

only brieﬂy number its fundamental properties: the

system is modular and consists of a number of cells

(modules), the cells are placed in a grid formation, the

cells are identiﬁed by two types of identiﬁers (physi-

cal ID referring to the cell’s position witin the grid

and encoding ID referring to the cell’s functional re-

latedness with other cells). The system’s functionality

is dependent on the functionality of its cells.

3.1 The System’s Cell

Figure 2: Schematic view of the cell’s subsystems.

ACHIEVING ROBUSTNESS IN ADAPTIVE SYSTEMS - Can Hierarchies Help?

423

0

(L,Li,Ei)

4

(RP,Li,Ei)

3

(P,Li,Ei)

1

(S,Li,Ei+/-1)

9

(P,F,Ei+/-1)

2

(R,Li,Ei)

8

(L,F,Ei+/-1)

5

(SP,Li,Ei+/-1)

6

(S,A,Ei+/-1)

7

(SP,A,Ei+/-1)

4

()

0

(L,Li+/-1,Ei+/-1)

3

()

2

()

Figure 3: Finite state machine describing the cell’s be-

haviour.

In modelling the system’s cell, several theories have

been considered which present the living system or-

ganisation (Ganti et al., 2003; Maturana and Varela,

1973; Eigen and Schuster, 1979). Their, perhaps

greatest, commonality lies in underlying cyclic na-

ture of this organisation and, as nicely put in (Ganti,

2003), that living is happening rather than being.

Ganti’s chemoton theory was chosen for further work

(Ganti et al., 2003), in which a model of a minimal liv-

ing system is presented. Such choice was motivated

by the theoretical rigour with which the theory is pre-

sented as well as for its clarity.

In short, according to this theory, living system

consists of three subsystems: one corresponds to

metabolic network, the second carries information for

template polymerisation and the third one is a mem-

brane which divides the living system from its sur-

roundings. Conceptually, we also recognise three

subsystems within the cell of our modular system

model. The functional part of the cell i.e. the sub-

system within the cell which is performing some

functionality, corresponds to the information carry-

ing subsystem. The tuning parameters which deter-

mine operation of the functional part correspond to

the metabolic network. These parameters’ values are

being adjusted during the adaptation process so that

the functionality they inﬂuence is preserved.

It can be argued if the analogy is righteous be-

cause in living systems these subsystems can be al-

tered through evolutionary variations while in our sys-

tem it corresponds to the case when it is altered by

some adaptive processes which occur at a smaller

time scale, as distinguished in section 2. However, at

this stage we leave it as simple as that and recognise

that such choice leaves the room for further work to

include evolutionary processes as well into the subset

of processes which can alter the cell’s tuning parame-

ters.

Further, as explained in chemoton theory, these

subsystems within the living system are stoichiomet-

rically coupled. In our model this coupling is realised

through the functionality being dependent on the tun-

ing parameters value. In a real electronic system,

for example, this coupling would be realised through

functional interdependency of various electrical val-

ues involved.

Let us take a brief look into the cell’s behaviour.

The cell’s state is represented as a 3-tuple (H,A,E),

the ﬁrst value, H, referring to the hormonal ﬂows, the

second, A, to the cell’s functionality and the third, E,

to the value of some environmental parameter con-

sidered for the description of ﬂuctuation in the cell’s

environment. Their possible values are, respectively:

• H, presence or absence of hormones: L - no hor-

mone present, S - sending S hormone (the hor-

mone secreted in response to the sensed environ-

mental ﬂuctuation), R - sending R hormone (the

hormone secreted by the cell when it recognises

that the incoming S hormone comes from its func-

tionally related cell), P - passing hormone not

functionally related to the cell, SP - both S and

P, PR - both P and R;

• A, functionality the cell performs: L0, L1, L2, L3

or L4 - functionality adapted to E0, E1, E2, E3

and E4 respectively, A - adapting or F - failed to

adapt;

• E, the cell’s local environment: E0, E1, E2, E3

and E4 - ﬁve different values of the environmental

parameter under consideration.

Now, let us take a closer look into the cell’s be-

haviour with respect to hormonal secretion. Seen

through the formalism of cellular automata, our sys-

tem represents a uniform cellular automata which

means that all the cells are behaving according to

the same ﬁnite state machine, as given in ﬁgure 3.

Control variables for state transitions are following:

the change in the environmental parameter (EE), the

cell’s S hormone present (SM), the cell’s R hor-

mone present (RM), hormones from functionally un-

related cells present (HO), the incoming S hormone

recognised (RR), the incoming R hormone recognised

(FB). They have been omitted from the ﬁgure for the

sake of clarity. The states referring to cases when the

cell’s functionality is corresponding to the value of its

environmental parameter are considered stable states.

In ﬁgure 3, these are the states 0 and 3. When the

cell is in one of these two states, it is in a stable state.

When the adaptation is achieved, the cell movesto an-

other stable state which corresponds to the new value

of the environmental parameter (in ﬁgure 3 it is the

states 0 and 3 in the region to the right from the dot-

ted line, see (Laketic et al., 2009) for detailed descrip-

ICAART 2010 - 2nd International Conference on Agents and Artificial Intelligence

424

tion). Thus, our system preserves its homeostasis by

achieving (ultra)stability, which is in accordance with

the seminal work of W.R. Ashby (Ashby, 1960).

Figure 4: Cell’s functional states during adaptation process.

The information sent by the cell to its neighbours,

as dependent on the states, is as following, see ﬁg-

ure 4: ’0’ when in adapted states and not sending S

hormone (states 0,2,3 and 4), ’1’ when secreting S

hormone (1,5,6 and 7), -1 when failed to adapt (8,9).

Such functionality is included into the model for

the sake of simplicity and clarity when analysing

adaptive processes.

3.2 System’s Behaviour

Figure 5: Finite state machine describing the system’s be-

haviour.

The state of the system is dependent on the states of

its cells. We distinguish the following three states in

which the system can be:

• Stable, when all the cells are in one of the adapted,

stable states

• Adapting, when at least one of the cells is per-

forming adaptation process

• Failed to adapt, when at least one of the cells has

failed to adapt to environmental ﬂuctuation

We can relate these system states to the levels of

life as distinguished by Ganti in (Ganti, 2003; Ganti

et al., 2003). The stable state (state 0) would cor-

respond to the living system in the state living; the

state adapting to the state capable of living; ﬁnally,

the state failed to the state dead. It can be noticed

that while living systems are possible to move from

the state living to the state dead, in our state diagram

such transition is not made possible, see ﬁgure 5. This

has been made so on purpose with the aim of keeping

the attention only on adaptive processes and the abil-

ity of the system to adapt. In our case, such transi-

tion would, namely, correspond to the case when the

system’s functionality deteriorates due to some other

cause, not the environmental ﬂuctuation.

3.3 A Glimpse to Previous Findings

Figure 6: Encoding IDs and hormonal loops between func-

tionally related cells.

As mentioned, our investigation so far has considered

autonomous adaptation to environmental ﬂuctuations,

as introduced in section 2. We have examined the

possibility for the achievement of adaptation by the

assumed system and several aspects of such adapta-

tion processes. In particular, in (Laketic et al., 2009)

it has been shown how adaptation process inspired

by human hormonal control and communication can

initiate and sustain adaptation process until adapta-

tion is achieved. There, we have also considered op-

timal amounts of hormones needed for the achieve-

ment of adaptation under stochastic adaptation pro-

cess. This has been subject of particular interest be-

cause these amounts are related to the use of the sys-

tem’s resources, a requirement for the efﬁcient use of

resources being one of the ever–lasting challenges in

man–made systems. Further, in (Laketic and Tufte,

2009a) it has been pointed that adaptation may be

viewed as a result of a particular pattern formation

within the system’s tissue, see ﬁgures 6 and 7. These

patterns which arise upon the environmental ﬂuctua-

tion are due to the formation of hormonal loops and

are dependent on the functional interdependency be-

tween the system’s cells. Also, further research di-

rections have been addressed in (Laketic and Tufte,

2009b) for which the considerations presented at this

place represent a continuation of reasoning.

ACHIEVING ROBUSTNESS IN ADAPTIVE SYSTEMS - Can Hierarchies Help?

425

Figure 7: Hormonal loops during simulation runs.

Figure 8: Schematic view of hierarchical architecture based

on the underlying structure.

4 INTRODUCING HIERARCHIES

Complex adaptive systems coming from nature are

characterized by hierarchical organization. Such or-

ganization gives rise to novel properties and processes

to occur at a higher hierarchical level. In biology, hi-

erarchical structure is believed to be essential for the

correct and efﬁcient functioning of natural systems.

Hierarchical structure has been adopted in man–made

systems as well. Therefore, we would like to further

develop our model so as to incorporate different hier-

archical levels. However, this does not appear to be

a trivial task. Several possible hierarchical architec-

tures have been considered based on the criteria for

deﬁning a hierarchy.

One possibility is shown in ﬁgure 8 where higher

structural level is deﬁned based on the position of

the cells within the architecture. Cells close to each

other form organ which is assumed to perform some

functionality based on the functionality of the cells

pertaining to it. Although such introduction of hi-

erarchies may seem somewhat trivial, it bears with

it possibilities for further improvement of adaptation

process: the role of sensing the environmental ﬂuc-

tuation may be assigned to the organ instead of be-

ing performed by the cell; local control of adaptation

process may be performed by the organ; the number

of the cells pertaining to the organ may vary as the

adaptation process proceeds i.e. organ can grow and

shrink.

Further considerations with respect to this sys-

tem’s robustness may be addressed. Inclusion of the

information on the current state of adaptation process

into the dynamic formation of organs may increase

the system’s ability to avoid the dead state (state 2

in ﬁgure 5) i.e. increase its robustness according to

our deﬁnition. Moreover, the local control within the

organ may ensure that adaptation is achieved at the re-

gion which is critically affected by the environmental

ﬂuctuation before this ﬂuctuation takes effect on the

functionality of the system as a whole thereby pre-

venting it from loosing its functionality.

Figure 9: Schematic view of hierarchical architecture based

on the hormonal loops which arise upon the detection of

environmental ﬂuctuation.

However, our results have also opened new way

of thinking with respect to the introduction of hierar-

chies see (Laketic and Tufte, 2009a). Let us assume

that higher hierarchical levels become ’visible’ only

after the ﬂuctuation is detected. In ﬁgure 9, this idea

is schematically represented for the hormonal loops

which arise between functionally related cells. If

they, or similar formations, are considered higher hi-

erarchical level, then further question would be what

novel information they would contain. How would

this novel information affect system robustness?

5 DISCUSSION AND FURTHER

WORK

Autonomousadaptive systems which achieve stability

through processes analogous to the homeostatic pro-

cesses within the human body, show certain degree

of robustness to environmental ﬂuctuations. In this

paper, we have presented some initial ﬁndings into

the adaptive processes within such systems. Through

simulations, we have shown how the achievement of

ICAART 2010 - 2nd International Conference on Agents and Artificial Intelligence

426

the system’s stability (or ultrastability to put it into the

words of W.R. Ashby (Ashby, 1960)) can lead to the

preservation of the system’s homeostasis. It can be

said that the achievement of stability corresponds to

the achievement of adaptation. In this way, the system

exhibits robustness to the environmental ﬂuctuations

by preserving the stable state despite the variation in

environmental parameter(s).

However, many additional aspects of the adapta-

tion process may be considered so that the process

efﬁciency and system robustness are enhanced. One

thing would be inclusion of some long–term adaptive

process(es) in analogy to evolutionary processes, as

mentioned in section 3.1. Our work so far has as-

sumed that the architecture of the system is endowed

with adaptive mechanisms which are the result of the

coevolution with the environment. Then, we have set

to investigating these mechanisms. However, it might

be worth considering how some processes of evolu-

tionary nature could improve robustness. In this re-

spect, we think of addressing information within in-

dividual cells and the system as a whole and choosing

information content to be evolutionary unit. Further,

we have addressed possibilities for the hierarchical

organisation of the system under investigation. Such

considerations are justiﬁed by the living systems’ or-

ganisation. However, at this stage of our investiga-

tion, there is a number of issues that need be tackled.

The major ones consider the ’building’ of hierarchies

which, in this case, is not a trivial task. we argue that

in buildingup hierarchical organisationinto the model

more signiﬁcance should be given to a choice of what

information should be exchanged between the hierar-

chical levels. Useful ideas for setting the framework

might be obtained from the work related to dynamical

hierarchies (Rasmussen et al., 2001).

Moreover, if not the structure but the patterns

formed are considered a higher hierarchical level, as

is the case with the hormonal loops formation shown

in previous work (Laketic and Tufte, 2009a), then new

aspects into the very nature of the phenomena arising

at the higher level may be questioned. Is it to be pre-

dicted from the operation of individual cells? Does

it contain some fundamental novelty? Our specula-

tion is that the answers may indicate emergent na-

ture of the phenomena arising upon the occurrence

of environmental ﬂuctuation. Once the decisions on

the system’s hierarchical organisation are made, fur-

ther investigation into robustness of such systems will

be continued. Moreover, our intuition and common

sense tell us that absolute robustness does not exist.

We hope to show it and prove it within the framework

set for further simulations. With the great enthusiasm

we are looking forward to doing it.

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