Sustainable Development

Formal Definition and

Modeling

Alexander Makarenko

Institute for applied systems analysis

NTUU „KPI”, Prospect Pobedy 37, 03056,

Kiev-56, Ukraine

makalex@i.com.ua

ABSTRACT

The general questions of sustainable development - the conception, examples and limitations of implementation are considered.

General principles for formalization of notion of sustainable development are discussed.

Different models are considered for study of sustainable development.

Relation stability\transformation had been investigated.

The implementation of transformation process in large socio –economic systems as the application of operational researches.

The consideration of mental aspects of SD.

I. COMMON DEFINITIONS OF

SUSTAINABLE DEVELOPMENT The concept of sustainable development has a long history of its essential

components. First of all it needs to remark many natural science investigations and ecology. Another part is demography (may be since the works of Maltus). First explicit implementation and first working tool for considering SD is system dynamics since the work of Forester, Meadows and others (Iscvt, 2002; MIT, 2002). Important role also has played the concepts and the models of the World by I. Wallerstain, B. Fuller, A.Frank. One of the past focal point of SD was world leaders conference at Rio- de Janeiro (1992), and last Summit at Johannesbourg (2002), where some definitions and prospects had been formulated.

But the experience since 1992 had followed to necessity of further improvement in concepts (see many conferences: (Euroscience, 2002) and others). There are many reasons for this. Of course main is permanent changes in recent world closely connected to global processes. But it exists some intrinsic problems in SD which force to further development of approach. First of all the main definition of sustainable development is verbal and conventional. A little number of quantitative approach exist (system dynamics and some types models for modeling large- scales processes -(Spangenberg et al., 2001) and multi- agent approach (Beckenbach, (2001); Iscvt, (2002)), indexes (Zgurovski&Gvishiani, 2008). The leak of full operational models follows the shortage of sustainable development indexes (Spangenberg et al., 2001; Iscvt, (2002)) which needs for practical planning.

Basic description of SD

“"Sustainable development is development that meets the needs of the present without compromising the ability of future generations to meet their own needs.

It contains within it two key concepts:

• the concept of 'needs', in particular the essential needs of the world's poor, to which overriding priority should be given; and

• the idea of limitations imposed by the state of technology and social organization on the environment's ability to meet present and future needs."

- following G.H.Bruntland Commission (1987)

That is there exists discrepancy between the natural resources and between determined by economics and history way of their exploitation.

Some factors in SD process

Usual representations of

parameters in SD processes

Trajectories of system in case of

fatal restrictions of resources

Possibilities of sustainable

trajectories

Case of possible change of leading

resources

II. FORMALIZAQTION OF

SUSTAINABILITY AND SD

Necessary components for SD:

Resources

Restrictions on resources

-- Evolutionary aspects

Goal of the system

Existing of many generations

Indexes of sustainability

-- Decision – making

Mental properties of peoples and cultural aspects

Environment

Technology …

Parameters and structures in SD(1)

Therefore in a next section we will make an effort give some primary considering to formalization of the SD notion.

At first we will indicate structures and notions which it follows to take into account in a task about local SD.

1. We will designate the parameters of the system and their description (external, internal, managers and etc.) Set of parameters {Par}. We in this subsection will not consider in the details of property of these (and elements of description the following), and only we will make an effort select, what structures it follows to consider. So, for example, we without the special necessity will not consider possible metrical and topology structures, ordering relations, symmetries and dr. on the great number {Par}.

2. Equations which describe the systems and processes {Equat}.

3. Set of trajectories of the systems {Traj}.

4. Limitations on trajectories and parameters of the system – set {Ώ} and

set of boundaries of limitations {∂Ώ}.

5. Set of criteria of sustainability {SCrit} or the SD criteria {SDCrit}.

Parameters and structures in SD(2)

6. Set external handling parameters {Contr}.

7. Set presenting the age structure of population on an interval of time [0, T] {Age[0, T]}. If an interval is not indicated obviously, we will write {Age}.

8. Set of initial conditions {Init}

9. Structure of the system {StSys}, structure of processes {StProc} and structure of individuals {StInd}. These great numbers can be entered, if indeed it is known as such objects are arranged. But it is possible confidently to assume that such structures indeed exist (even if obviously about them nothing is known).

10. Additional requirements to the components (desirable) – additional to obligatory limitations {Ώ} and {∂Ώ}. We will designate them {Aux}.

11. Descriptions of process of acceptance of decisions. We will designate those {Decis}. In the case of necessity it is possible to dash them on separate components.

12. Set of nondefinetness (uncertainties) in the system {NonDef}. In the case of necessity this set also can be broken-down on components.

Description of task

We will describe now, what does it mean SD.

Definition. The SD task. To find such objects from

{Init}, {St = {StSys} ® {StProc} ® {StInd}}, {Contr}, {Decis},

such, that as a result such trajectory at evolution of the system turns out

tr € {Traj}, that is executed <tr, Cr>t € {SDCrit} ® {Aux}

where<tr, Cr>t means the calculation of value of the SD criterion in a moment

t on a trajectory tr, thus the results of calculation must at every instant to lie in {SDCrit} and in {Aux}.

Parameters and structures in SD(3)

We will show sense of determination for the best idea on simple illustrations as geometrical pictures.

We will do a few remarks here.

The remark 1. To 12 indicated higher structures it is possible to add another one – set of models {Models}, if we use the modeling.

The remark 2. At consideration of different systems it is possible in such raising to take category approach and try to select the category of the systems with the steady development CatSD.

The remark 3. Taking into account the possible multivaluedness of trajectories of the system (which can arise up from different reasons, including because SNET – includes a social component). Therefore in place of one trajectory tr it is possible to enter formulations with the bunch of trajectories Ptr.

The remark 4. It is possible also existence of fluctuations and other uncertainties (by the way, this is essential at estimation of risks). Then it is possible to take into account vagueness in objects, considering some sets from 1-13 to

{SDCrit}(NonDef), {Aux}(Nondef), {St}(NonDef).

Parameters and structures in SD(4)

Meaning the structure of Definition 1 for the SD task it is possible already to move farther and extend and at the same time go into detail determination.

Consideration of presence of many different generations (for simplicity below we speak about two generations), for example, maybe, that at two generations different criteria SD, then

{SDCrit} = {SDCrit}(Generation 1) ® {SDCritGeneration 2}

There can be different for different generation’s limitations on the managements

{RCtrl} = {RCtrl}(Generation 1) ® {RCtrl}(Generation 2)

It can be in principle, that

{SDCrit} = {SDCrit} (Generation 1) ® {MSDCrit} (Generation 2)

where {MSDCrit}(Generation 2) is the set of possible criteria of SD for second generation.

We cannot know exactly {MSDCrit}(Generation 2) by virtue of that it relies on future technologies, and actually from future knowledge {Knowl}(Generation 2)

about which we can only build guess-work (we consider that great number of current knowledge of the given generation {Knowl}(Generation 1) in the first approaching it is known – or, for example, this great number of realized in technologies knowledge).

Examples (0)

We will indicate some examples for illustration.

The example 1. We can in the first approaching set the establish set {SDCrit} as the set, where some model indexes are satisfied to the accepted pictures of SD. That is, if indexes ind, which belong set {Ind} of indexes answering the pictures of experts of SD – to the set {IndSD}.

Then a process will be with SD, if ind € {Ind}, thus ind € {IndSD} V t.

Thus, of course, many thin details of processes and conducts of the systems are not taken into account. We will mark in passing some interesting works devoted to the search of the SD indexes.

By the way, in works D.Forrestera knowledge does not enter in the complement of basic variables obviously.

The example 2. (The Chichilniska works). In them, as far as it is possible to judge, is formed on the economic considering only.

The example 3. (The Rand work). {St} changes in them in course of time, and {SDCrit} it is possible to formulate mathematically strictly.

The example 4. The cases are not eliminated, when {SDCrit} can be formed by the Lyapunov’s function.

The example 5. Evolutional economy. It is possible, in principle, to make table of comparison of the SD researches in such formalization

Examples (2)

The offered chart of consideration befits, looks like, to any variant of the SD processes (both descriptive (verbal), and concrete practical tasks or for tasks already having formalization as mathematical tasks.

Review and comparison of the mathematical raising was very useful, and in the future we hope also to present their results as table. Here we will make illustrative examples.

The Example 1. (Local SD). More simple case, if a situation does not change substantially, simple models (as a rule, this proper one of «pillars») of the system and without consideration of change of generations

It is clear, that it is possible to write down the SD criteria different (for example, speed on the trajectories, stocked energies for the management) and others.

In such kind it reminds the tasks of traffic control on the mathematical raising (traffic control with limitation).

By the way, the guided Markov’s chains from the given point of view, and then the Markov’s chains with anticipation or with a vagueness – semi-Marko’s.

It is possible the same for Lorent’s (for chaotic trajectories) – the SD loud speakers of chaos.

It is possible similarly to the same stochastic differential equalizations in partial derivative – here at the level of communication with synergetic and dissipative structures.

Simple examples (1)

Simple examples (2)

III. SD MODELING AND

INTERPRETATIONS

1D ‘presentation’ for two attractors

case

Attracting with restrictions

accounting

Transitions between attractors with

restrictions

IV. MENTALITY AND EDUCATION

All such issues are useful for considering sustainable development. The problem of sustainable development in our approach looks like the problems of the evolution of the system in the terms of attractors, and the transitions from one attractor to other (Makarenko, 2003).

For understanding and management of sustainable development the use of the concept of 'landscape' presented in the Section 2 (see for example Figure 1) may be helpful. In such case, the state of the system evolves on the ‘landscape’ to the nearest local minimum of the functional which corresponds to the ‘landscape’.

Sustainable and non-sustainable ways correspond to different minimum if the bonds between elements are constant and internal patterns of elements are fixed.

But the change of norms, beliefs, ethical norms and concepts follows to the deformation of ‘landscape’. So in this case the change of norms may push the system from one minimum to other without increasing the ‘external energy’ (functional of the system). Also, the changes in mentality can create the new minimums in the system (create the sustainable way).

Sustainable development of

knowledge and of education

The investigations on sustainable development have been related mainly with the problems on natural resources and energy.

But only now it have been recognized that very important (or just most important) became other aspect of society life – namely KNOWLEDGE.

The list of posing new problems and challenges are: the development of knowledge; the knowledge use; transfer of knowledge between generations; spreading of knowledge; reproduction of knowledge bearer (that is researchers, teachers, students) etc.

CONCLUSIONS

In this talk we describe an approach to modelling social systems and decision–making process in them which can be useful for studying the sustainable development in OR investigations.

Also some frames for formalizing SD processes is proposed

The approach is based on the models, which have the properties of associative memory and which allow to incorporate the mental peculiarity of involved individuals.

One such property – anticipation leads to the existence of multi-valued solutions (which correspond to the scenarios of system evolution). Even qualitative consideration of such property allows understanding of some aspects of decision–making processes.

REFERENCES

Dubois Daniel, 1998. Introduction to computing Anticipatory Systems. nternational Journal of Computing Anticipatory Systems, (Liege), Vol. 2, pp.3-14.

Haykin S., 1994. Neural Networks: Comprehensive Foundations. MacMillan: N.Y.,

Makarenko A., 1998. New Neuronet Models of Global Socio-Economical Processes. In 'Gaming /Simulation for Policy Development and Organisational Change' (J.Geurts, C.Joldersma, E.Roelofs eds) , Tillburg University Press. 133- 138,

Makarenko A., 2003. Sustainable Development and Risk Evaluation: Challenges and Possible new Methodologies, In. Risk Science and Sustainability: Science for Reduction of Risk and Sustainable Development of Society, eds. T.Beer, A.Izmail- Zade, Kluwer AP, Dordrecht, p. 87- 100.

Zgurovsky M., Gvishiani A., 2008. Sustainable Development Global: Simulation. Quality of Life and Security of the World Population (2005 – 2007/ 2008). Kyiv: NTUU ‘KPI’, POLITECHNIKA. 336 p.