An economic model with genetic algorithms

SANDOR KARAJZ, Ph.D. Associate Professzor

e-mail: karajz.sandor@uni-miskolc.hu 1. Introduction The success of a market modelling basically depends on an accurate definition of factors influencing it and of appropriate weighing. These factors can be well identified if the corporate stakeholders are analysed and the factors of a determining character in a particular issue are selected. 2. Corporate environment Corporate behaviour that is actually shaped by corporate management can be influenced by the following external factors: • competitors, • government intervention through the application of regulatory policy tools, • players and consumers of sales markets, • markets of production factors, that is suppliers. In order to model the amount of emitted pollutants, the analysis of the above-mentioned micro-environmental factors has to be conducted. It is they that commonly define the extent of corporate sensitivity to environmental issues. In addition, analysis of the corporate environmental management in which tis environmental sensitivity is reflected – namely, the corporate behaviour - is also required. This behaviour is primarily expressed in the environment-oriented strategies of a company.

Socialenvironment

Ecoligicalenvironment

Economic environment

Technologicalenvironment

Politicalenvironment

Publicity

State,Media,Civilinitiative

Purchasing market

Corporate

Sales market

Competitors

Customers, merchantconsumers

Suppliers, financiersjob applicants

Macroenvironment Microenvironment

Figure1: Micro- and macroenviroment of the corporate

3. The model of genetic algorithms

There are two levels at which an environment-oriented analysis can be conducted: corporate and sector levels. In both cases the fundamental aim is to effectively model the extent of the environmental burden, taking into account the particular conditions. When modelling is performed by the application of genetic algorithms, the genetic procedures (selection, recombination and mutation) can be applied in one or several companies. The modelling at corporate level assumes that a single-population or, at a higher level, a multi-population model is created. In the case of a single-population model the agents of genetic algorithms are environment-oriented corporate behavioural opportunities and strategies that can be implemented in a permanent, but continuously changing micro and macro environment at a given moment. The total population is made up of the total factors mentioned above. In a multi-population model there are two genetic algorithms that run parallel. In the first algorithm, on the basis of a company level algorithm, the environmental strategies applied and the environmental burdens belonging to them are defined for each company separately. These strategies make up the initial population of the algorithm running at a higher level. When a particular algorithm is applied, the extent of the pollution emitted by all companies can be defined. On the following page a model applied for defining the initial population will be introduced. 3.1. Defining the initial population

The initial population can be defined by mapping all relevant corporate ‘behaviour patterns’. Relevant corporate ‘behaviour patterns’ are environment-oriented corporate strategies. The scope of these patterns is defined by external and internal factors of corporate operations. Internal factors encompass current and potential technologies as well as available human and real capital. External factors have already been mentioned above. The figure below illustrates the system of relations.

CompetitorsRegulatoryinstruments

(state intervention)

Suppliers(input market)

Consumers(output market)

Environmentally relevant company(Environment oriented strategies)

Coding

Company’s chromosome

Objective function

Phenotype(Environmental load)

Figure2: Defining of the base population

Since the company is assumed to be able to affect the environment, the system of

double relation between external factors and the company illustrated in the figure is accepted. This basically has an effect on the potential environment-oriented strategies, that is, the circle of algorithm agents. In the current modern economy social civil initiatives, environmental organisations and social advocacy groups exert an ever-increasing pressure on environmental protection activities of companies that are heavily polluting the environment, which has a great impact a company’s chosen strategy. After the environment-oriented corporate factors have been defined, strategic elements need formalising, namely encoding, so that genetic algorithms can be run. As a result of this, the so-called corporate ‘chromosomes’ evolve, which have already adjusted the strategic elements to the mathematical methods of genetic algorithms and which provide a proper form for them. At the initial stage of modelling the initial environment-relevant strategies must be characterised by an objective function, which establishes the degree of environmental burden for the strategy or, using the terminology of genetic algorithms, the phenotype of genotype is defined. After this, algorithms built on genetic processes can actually be performed. 3.2. External factors determining environment friendly corporate behaviour

The first step in defining the initial population is to determine the environmentally relevant corporate factors very precisely. They are supposed to be affected by four external environmental factors mentioned above. Their knowledge and the determination of how and how much they affect the environment-oriented behaviour of a company is also essential in establishing an integrated environmental-economic model. 3.2.2. Competitors

Market competition actually determines the corporate behaviour and how environmental friendly a company is. The scope of competitors also must be defined, which can be done on several levels. In a narrow sense of the word a company’s competitor is a partner company that offers similar products and services at a similar price to the same circle of customers. By giving a broader definition of the word on different levels, a company’s competitor is any company that competes for the money of the same customers. Meffert (1992) offers the following steps in providing analyses of competitors: • defining the circle of competitors, • identifying their strategies, • identifying their objectives, • determining their strong and weak points, • estimating their reaction, • selecting competitors that can be attacked or avoided Since environmental protection is a determining competition factor in different sectors, two extremely different definitions are taken into consideration when the definition of the word ‘competitor’ is offered. A company must obtain the following information when accessing the competition situation: • the danger of new competitors emerging on the market, • the threat of new products that can replace the available ones,

• the extent of involvement of competitors in purchasing, producing, distributing and recycling of products (stricter legal regulations and an increasing demand for troubleshooting in environmental protection),

• the willingness of sector competitors to cooperate with each other in solving emerging ecological problems

• the extent of corporate rivalry outside the economic sector (offering environmentally-friendly products)

The greater environmental awareness is, the higher the ecological expectations towards

products are. Consequently, eco friendly products generate a supplementary ‘profit’, namely they are products having a minimal ecological footprint. This additional factor increases the chance of an eco-friendly ‘newcomer’ to carve a share from the established market. ‘Frosh’, a producer of detergents, is a good example to illustrate how a new product can break into an established market – that of detergents -in a short period of time. 3.2.3. Government interference and liberal regulatory tools

One of the external factors having an impact on environment-oriented corporate strategy and intensively analysed is the government, whose influence is reflected in its regulatory tools of environmental policy. The current state-of-the–art tool system theoretically includes a number of elements, but practically speaking, normative regulation is dominating. This material introduces both conventional, orthodox tools that are frequently applied in every day practice, and modern ones, the so-called state-of-the–art tools. The technical literature includes numerous comparative analyses of these tools (Zittel, 1996; Stengel, 1997;), but all of them limited their comparison to three fundamental types of conventional tools (normative regulation, taxes and the pollution rights market).

Regulatory tools of environmental policy can be classified on the basis of different criteria. One of the possible grouping criteria is their impact on the government budget, which encompasses three categories. There are tools that are not of fiscal character, and thus, affect neither the expenditure nor the revenue budget. The rest of the regulatory tools have an impact either on the expenditure or on the revenue of the budget (Wicke, 1991).

There is another classification and grouping method which is based on the degree linearization unlike regulatory tools. This method is only briefly introduced in this teaching material and follows the principle of growing degree liberalisation (from normative regulations to volunteer undertakings).

Normative regulatory tools have always played a key role in environmental policy-making. They are the most widespread direct form of regulations using provisions of law. They are basically of administrative character and are based on bans and limitations and enhance the prohibition and limitation of environmental damage. There are different forms of normative tools: bans, licences and emission norms.

The regulatory form known as the Pigouvian tax is a tax (public burden) levied on polluters, which increases the costs of their activities by the amount of the damage caused by them and theoretically channels the market in a positive direction. The externality effects, namely the suffered environmental damage, are internalised by the taxes imposed. Targeting equilibrium between social and individual expenditure results in a decrease in production and emission if profit maximisation is the primarily aim. The tax revenues generated this way are generally spent on covering the environmental expenditure.

Trading with pollution rights as a special method of imposing limits on emission of pollutants was formulated by scientists at the end of 1960s. In this case the costs of environmental damage are internalised through division of pollution rights. This assumes the

estimation of marginal value for a particular geographical territory and establishes some degree of pollution as the unit of pollution rights. This is the basis on which pollution rights trading is performed. On this special market the price of per–unit pollution is calculated from pollution-remediation marginal costs. Following this principle, environmental remediation is performed where the lowest clean-up expenditures are incurred, which results in cost-effective prevention. The major problem of pollution rights trading lies in the equal primary division of emission rights and in high transaction costs.

As for liberal measures, the self-policing launched by the US Environmental Protection Agency is an innovative and controversial tool based on voluntarily disclosure regulatory violations. Companies conduct an environmental audit and make the results public. The environmental audit is a documented and an objective evaluation of the operation and management of a company designed to protect the environment. The forms that have evolved in the past few years are as follows: eco-auditing, acquisition auditing, liability auditing and compliance auditing. The information collected from the audit is a double-edged sword, since it provides data about company’s compliance with environmental legislation and requirements, but it can also be used for potential legal sanctions. Due to its dual character this tool can only be efficient if proper guarantees are developed. For instance, the innovative policy adopted by EPA in 1996 designed to encourage the voluntary disclosure of the environmental non-compliance clearly formulates the factors promoting the adoption of self-policing, on the one hand, and the obligations to be met by entrepreneurs during the audit, on the other. There is no doubt that a voluntary audit will not replace the compulsory and the required audit.

Mediation is a way of resolving disputes assisted by a third and impartial person. This form of dispute resolution has already been applied successfully in the USA and Canada for several years, but in Europe few attempts have been made to use mediation. This procedure is a conflict resolution tool and a conflict regulation process in which the polluter and the pollutee – on a voluntarily basis – personally meet within the framework of negotiations initiated by authorities. In North America mediation is primarily used for reconciliation so that parties can avoid judicial proceedings regarding pollution and other issues related to environmental damage. The parties concerned are motivated to enter mediation since they can save a huge amount of time and money, if an agreeable solution is achieved. As for efficiency and effectiveness of this tool, there are doubts regarding the cooperation of parties after settlement of their disputes.

In contrast to mediation, voluntary environmental undertakings are a widely spread practice in Europe, but not in the USA. This is the most liberal method of the above-listed ones since it operates completely on a voluntary basis and companies do not enter into an agreement or a contract of cooperation. The terms and conditions are defined by companies and not by the state. The disadvantage of this is that due to the lack of sanctions, the promised undertakings might be a sham. In practice, companies enter into agreement to jointly conduct action plans on a voluntarily basis on sector or alliance levels. 3.2.4. Input markets and suppliers

Companies purchase one part of the resources necessary for production in the input market, for instance, materials, spare parts and so on. In the input market their partners and suppliers are generally other companies. Since markets are becoming more and more environmentally conscious and companies conduct more and more environmentally-friendly activities, suppliers are also compelled to enter into competition in the input market similar to that in the output market. Suppliers who fail to provide environmentally-friendly raw

materials or semi-finished products, can build only weak negotiating positions, whereas suppliers who offer the most environmentally-friendly products can considerably strengthen their negotiating positions.

The threat of substitute products on the suppliers’ side is extremely serious. For instance, when the phosphate substitute product (SASIL) was introduced in the market, producers of phosphate lost their market shares. A similar case happened to suppliers of asbestos when its substitute product was launched. It can be concluded that the situation resulting from the competition in the input market triggered a similar situation in the output market.

Environmentally-oriented market competition between suppliers has a considerable impact on companies emerging as buyers in the market, since this basically determines the environmentally-friendly character of raw materials, which affects both the characteristic features of products of consumer companies and their environmental burden.

In an imagined integrated environmental economics model the raw materials and resources provided by suppliers also have a great impact on corporate strategies relevant to the environment. 3.2.5. Output markets and consumer behaviour

Output markets and their players have a considerable impact on behaviour opportunities relevant to the environment. For them –as the topic shows – the fundamental behaviour form is the environmentally-conscious consumer behaviour, which is a complex process where not only economic aspects have to be taken into account.

It is widely known that the innovation of environmentally-friendly products highly depends on the demand. Who actually are the environmentally-conscious consumers? What characteristic features do they have or should they have to become environmentally-conscious consumers? Environmentally-conscious consumers are consumers who make purchasing decisions and have developed habits that are ecologically consistent. They are aware of the fact that the production, the distribution, the consumption and the use of environmentally-friendly products trigger surplus costs. They accept these extra costs and strive to minimize them.

In a consumer market, simply offering environmentally-friendly products is not enough. There should also be consumers who are willing to buy them. As far as social and ethical aspects of this problem are concerned, company can be forced to produce environmentally-friendly products only if sales expectations have reached a certain level. This process is similar to a vicious circle, where environmentally-friendly products are not produced in a particular economy because consumers are supposed not to show any demand for them, but consumers are not interested in such products because they cannot buy these products, since there is a shortage of them in the market.

Identifying the composition of the consumers of the modelled company from the environmental point of view is of essential importance, since without this the circle of potential corporate strategies cannot be established exactly. The following figure illustrates the process of identification.

Figure3: Conceptual overview of the green consumer behavior

Let us see how a company develops a environmentally-conscious consumer behaviour in the case of a particular product. Firstly, global environmental correlations are identified. The importance of environmental values should also be established with respect to your own responsibility and effectiveness of your own activities and then the values hidden in the consumption areas should be comprehended. On the basis of correlations in the consumer area, the difference between the environmental burden caused by the product and the product supply will lead to the recognition of environmentally-friendly characteristic features. This affects the evaluation of rival values and other properties of the product. 3.2.6. Environmentally relevant corporate strategies

After the external factors have been introduced, the forms of their effects on the environmentally-oriented corporate behaviour are examined. The starting point of the discussion is that the applied production technology determines the extent of the environmental burden and the pollution. The overall mapping and the application of the technological composition actually provide a firm basis for an accurate modelling. Since corporate behaviour (technology application) is reflected in corporate strategies, it is essential to determine and understand the basic strategies.

In order to provide a framework for environmentally-oriented basic strategies, different grouping features has to be determined in order to classify basic strategies. The most important features are as follows (Meffert, 1992):

• intensity of eco-oriented adaptation, • activity direction and plane for environmental strategies • time of strategic developments and of implementation of strategic measures, • types of strategic developments, • forms of strategy execution

On the basis of integrated analysis of strategic criteria a relatively wide range of basic

strategies can be determined and the following environmentally-oriented basic strategies can be identified (Meffert, 1992):

• resistant strategy, • passive strategy, • retractive strategy, • adaptive strategy, • innovation strategy

The table below shows how basic strategies can be characterised on the basis of their

grouping features and what effects they have on different objectives:

Implementation of

strategy

Goals of competition

strategy

Social legitimacy

Ecological goals

Effects of strategy

Type of strategy

development

Time of action

implementation

Adaptation intensity

+ +(-)

+ +

+ +

�

Individual

Integrated

Proactive

Innovative

Enterprise,

market, society

-(+)

+

+

�

Individual/

co-operative

Isolated

Reactive

Adaptive

Enterprise

(market)

+(- -)

+/-

(+)

�

Individual

Isolated

Generally

reactive

Adaptive

Enterprise

(market)

-(+)

-

- -

�

-

-

-

Passive

-

-(+)

- -

- -

�

Generally

Co-operative

Isolated

Generally reactive

Passive

Market/society

(external)

Action horizon

InnovativeAdaptiveReservedPassiveResistant

Basic strategiesStrategic

characteristics

Figure4: Characteristics of basic environmental strategies

Retractive strategies are generally passive strategies as far as the intensity of eco-oriented adaptation is concerned, but on the other hand, they do not comply with market environmental criteria in order to maintain equilibrium. Resistant strategies are often reactions to environmental criteria in force, for instance, reaction to civil initiatives. They can be effective against strict environmental laws when a particular environmental law is likely to be

changed and this strategy can be applied to achieve a reduction in the environmental norms in force.

This strategy is a kind of defence tactics, similar to the ‘political strategy’, which shows a protest against social environmental needs and used collectively with other companies concerned. Resistant strategies are applied to achieve ecological objectives aiming at decreasing and avoiding the environmental burden, thus they threaten the social legitimacy of companies in the long run.

Contrary to resistant strategies, passivity is actually a ‘non-behaviour’ that is associated with neglecting environmental problems. This type of strategy does not endanger the legitimacy of companies as much as an active resistant strategy does, since it does not openly protest against environmental demands. Corporate strategic alternatives do not allow this strategy to adapt to current environmental problems, thus, this type of strategy attempts to back out of ever increasing environmental demands.

Retraction is a strategy on the factory level. For instance, a company relocates functions (production, recycling, and so on) related to environmental pollution to another country in order to comply with environmental regulations, which set pollution limits. In fact, the company does not pollute the environment any less, it simply transfers the pollution of the environment to another place. The ever intensifying international campaigns of environmental groups endanger the legitimacy of the such companies.

Eco-oriented adaptative strategies take into account environmental criteria of regulations in force and the companies’ reactions. They meet all environmental requirements without promoting prospects of environmental protection in an innovative way. Due to external forces, adaptation to solving current environmental problems is performed in isolation and in a reactive way in particular corporate areas. Adaptive strategies might be a strategy of an individual company or might characterise the behaviour of a whole sector.

Contrary to adaptative strategies innovation-based strategies mean that not depending on social and market environmental demands, companies define ecological problems and apply strategies encompassing all corporate areas. 3.2.7. Encoding

The following step in the model is to integrate strategic and technological factors of different types and units of measurements, that is to encode them. The basic feature of genetic algorithms is that they store features - agents’ chromosomes - of a population in a binary way, that is, in a binary vector. Apart from binary codes, integeres, floating point numbers and multi-dimensional chromosomes can be used. When applying the conventional approach, a vector or a chromosome can be as follows: x = <x1, x2,…, xn>. Genomes are individual elements of chromosomes, but it can happen that a chromosome section of a particular length is needed to encode a particular feature. For instance, x =<1,0,1,1,0,0,1> is a chromosome where the second, the fifth and the sixth allel (value) of the gene is 0 and the rest of the alleles are 1, while another chromosome y = <<0,1,1>,0> consists of two genes. Here, the allele of the first gene is <0,1,1>, and the allele of the other gene is 0.

There are two types of encoding: conventional encoding and the Gray encoding. While performing encoding different units of measurements have to be synchronised. If their analysis or/and fitness functions require the existence or non-existence of only one particular factor needed as input , a simple yes/no, that is 1/0 is needed in the case of binary coding. If a quantitative value is encoded, the conventional or the Gray coding is applied.

It is obvious that a binary encoding has advantages and shortcomings. Its advantage is that current data processing devices generally support it and in the case of a large population the agents’ characters can be processed into a compact and single form. Its disadvantage is

that the weight of the encoded factors depends on their position in the chromosome (the weight of the factors standing at the beginning of the code is higher than that of those in later positions). The above-mentioned Gray code is a special encoding system used for eliminating the shortcomings of the conventional binary encoding. The table below shows the binary code and the Gray code of different decimal numbers.

Figure5: Comparison of the binary- and Gray-code

The Hamming-deviation (D) was used to compare methods of coding. It shows the number to be inverted in order to obtain one binary code from another. It is clearly seen from the table that for the Gray code this value is even, but in the conventional binary code this value is changing. Let us examine a simple problem. We take a decimal number = 105, and after coding is performed there is a mutation on the 4th place: The conventional binary code is as follows: 1101001⇒1100001 (after decoding = 97, deviation 8)

The Gray code is as follows: 1011101⇒1010101 (after decoding = 102, deviation 3) It is clearly seen that the deviation in the mutation in the Gray code is smaller. A note must be made that in the majority of cases this is true. However, there is a decimal number where the deviation is greater for the Gray code.

The economic importance of the difference between the two types of coding has basically become essential due to mutation. In the case of the Gray code a mutation is less important than in the case of a conventional code. This means that in the random mutation (inaccurate imitation of the strategy of another corporation or inadequacies of information flow) the torsion is lower, whereas in the case of directed mutation (conscious technological change) may not bring the expected outcome. The application of the Gray coding system may have advantages and disadvantages in modelling. Encoding works very accurately if the method is chosen to each factor. Consequently, in general, a profound knowledge of gene boundaries and their mapping is of utmost importance. The exact position of a particular gene has to be accurately spotted (a bit group responsible for a factor), otherwise false results will be obtained when placed in the objective function.

After all possible strategy variations have been encoded, the coded forms (chromosomes) of all possible corporate strategies are obtained, and can then be selected, recombined and mutated.

3.2.8. Objective function

The next step in defining the initial population is to evaluate the possible strategic variations, namely the amount of pollution caused by different strategic opportunities. This can be defined by an objective function. In our model on the basis of complex environmentally relevant elements of corporate strategy objective functions establish pollution levels, that is, the phenotype of genotype as used in the terminology of genetic algorithms.

In our model it is necessary to separate the objective function from the fitness function, because in the case of genetic algorithms a distinction should be drawn between the chances of agents’ replication and its successful outcome The objective functions of genetic algorithms measure the success of a particular agent with regards to the objectives to be optimized, whereas fitness functions evaluate the chances of replication of an agent. The objective of our model– which has to be represented by objective functions- is to define the environmental burden and to decrease this. However, the triggering factor of the company is the complex corporate objective systems represented by the objective function. In simple models of genetic algorithms there are two factors that are considered to be similar and it is assumed that there is a direct proportion between the success of a chromosome and its chances of replication. However, optimization problems highly determine whether the agents best meeting the optimum have the best chances for replication. The form of the objective function and the fitness function of genetic algorithms depends greatly on the problem to be solved, thus there are no general rules which would predetermine this.

In the models offered by Arifovic (1994) no difference was made between the objective and the fitness functions. We might not be right when assuming that the basic and the only objective of the company to be modelled is the reduction of its burden on the environment. This could be considered to be the only objective if other elements of the company were not put into a disadvantageous position. Formulating this idea more precisely, it means if compatibility, the target of maximum profit in the long run, productivity and other factors were not neglected, that is, while they were permanent, perhaps pollution could be reduced. However, this cannot be achieved without bringing about changes in the external conditions. It is obvious that this condition would considerably limit the circle of strategies to be applied. The pollution itself is affected by several strategic factors. Consequently, the function formulating the only objective has to consider several factors (current elements of the strategy) to be an input.

It can be concluded that in the relevant model a distinction should be made between objective and fitness functions, because in real life a company does not make decisions focusing only on one dominant objective, but on a system of complex objectives. Furthermore, partners entering into business relations with the company (in the market and outside it) do not always automatically reward the reduction of the burden on the environment, as a result of which the issue of environmental protection does play a central role in the objective system of the company. That is the reason why the success and the biotic potential of the company strategy – determined on the basis of the objective function – are separated. 3.2.9. Selection of the basic model

Before the genetic processes are run – basically due to election and selection – a decision should be made as to which model of genetic algorithms is to be adopted. It should be decided

whether to replace all parents by an offspring by making just one selection step (canonical genetic algorithms) or to replace only a few (steady-state genetic algorithms). This decision can be made only after the current optimisation problem is known. Both methods have advantages and shortcomings:

• If all parents are replaced, its potential consequence is that the best agent of the population may be lost. On the other hand, this type of genetic algorithms will never get into a situation when only some perfect agents are concentrated in a population (the population diversity decreases) and the space to be examined from the optimisation point of view decreases, that is the system remains in a local optimum and will not able to shift from it.

• If the whole pool of parents is not replaced, the outcome will be quite the opposite. The population will strongly converge to the optimum, since there are some agents who are much stronger than the others, and the population will never reach a better state. However, the best agent will not be lost and the average quality of the population will not decrease.

When steady-state genetic algorithms are applied, the generation replacement is very simple, since only a few agents – generally the ones with low fitness values – are replaced. The advantage of this is that the successful agents (good solutions) tend to remain in the population for a longer period of time. This replacement process is very similar to the process in the case of canonical genetic algorithms: two parents randomly chosen from the population will reproduce offsprings. After this a copy is made of them that recombines. This is followed by a mutation. The newly evolved agents are evaluated with the help of objective functions. If two agents with similar values evolve, one of them is deleted from the population. This special selection is performed until the number of offspring accounts for q. After this, q number of agents from the pre-existing pool– the ones with low fitness function – are replaced by offsprings (Álmos, 2002).

When steady-state genetic algorithms are applied, the rate of mutation and recombination may increase, since successful agents are protected in the population by the above-mentioned generation change strategy. As a result, the algorithms obtain a more powerful optimization character. On the other hand, steady-state genetic algorithms are not applicable for optimisation problems where the agents are evaluated stochastically, because a danger may arise that when evaluated at random the worst agents –due to the stochastic influence - may obtain a relatively high fitness function. These actually ‘bad’ agents may remain in the population for a longer period of time owing to the selection strategy,.

In our model canonical genetic algorithms are worth applying only when the pollution present in a huge amount is not hazardous and our objective is to achieve a slow and a long-term decrease in pollution. Otherwise, when the modelled company produces hazardous waste and wants to decrease this waste very quickly and in a large amount, steady-state genetic algorithms should be applied. Another important decision in our model is how many parental chromosomes to delete (in the worst case n amount) if steady-state genetic algorithms are applied. The above-mentioned objectives will define the number of chromosomes to be deleted. The more hazardous the waste is and the larger amount of it is generated, the fewer chromosomes are to be deleted.

The application of genetic algorithms and our model will be successful if the agents of the population retain their diversity for a long time, which considerably increases the effectiveness of recombination and adaptability to changes in the environment. This heterogeneity and diversity is supported by genetic algorithm techniques that apply different procedures and maintain genetic deviations resulting from cohabitation that are found in natural ecological systems.

The basic idea of the so-called crowding operator is that an agent is replaced by another best-fit agent. This technique prevents the population from being too homogeneous. The algorithm process is as follow: all agents are placed in a predetermined space for replication where two parents are selected at random. This is followed by the conventional recombination and mutation and the fitness values of offspring are defined. Every parent forms a pair with a best-fit offspring. The member of the pair with the highest fitness value enters the next population. The most essential element of this method is the measurement of the degree of similarity. This degree of similarity can be determined on the basis of genotypes and phenotypes. The degree of similarity between genotypes can be established by a Hamming-type deviation. In the case of phenotypes the Euclidean distance is used for this purpose. 3.2.10. Fitness function

As has already been discussed earlier – due to the subordinate role of environmental protection in the corporate objective system - objective functions and fitness functions to be separated and separately defined. Since the aim of our model is to establish the pollution level, the objective function assigns the quantity of the emitted pollutants to the feasible strategies. The success of the feasible corporate strategies does not depend only on their environmentally friendly character, and what is more, this is usually not the dominant aspect in the order of preferences. The selection of a strategy, i.e. one of the elements of corporate decisions, is determined by a multi-factor corporate target-system. Thus, in order to create the fitness function(s) representing the survival chances of the strategies in our model the considerations above have to be taken into account.

The fitness function represents the viability of the corporate strategies and production technologies appearing in the model on the basis of factors of the corporate objective system. There are several opportunities for creating a fitness function, or possibly functions. Since optimal solutions to multi-purpose decision-making problems can be provided, sometimes a determined set of efficient solutions is to be computed or established. In this case an efficient solution is the Pareto optimum. There are four groups of multi-purpose optimisation procedures.

For aggregation procedures the values of solutions of different objective functions related to agents are aggregated in one common objective function value – perhaps weighed on the basis of importance of objectives. After this the optimisation problem can be considered to be a single function problem to which generally only one solution is obtained, and not a set of Pareto-optimal solutions suitable for different objective functions.

On the principle of changeable objectives, in the case of several fitness criteria, selection is divided into as many steps as the number of criteria. In each step a group consisting of the same number of agents, who possess good results on the basis of a particular fitness criteria, is selected from the population to the pool designated for replication. Thus, agents who are suitable for several objectives have better chances for reproduction. After this selection, recombination and mutation can be performed on the elected pool of agents.

For techniques based on similarities two agents are selected at random from the population and are compared with a subset of the population also chosen at random. If one of the agents (with a higher fitness value) is dominating over the subset, he can be reproduced. If both or neither of them dominates, a so-called sharing operator selects one of the agents: the agent, in whose ‘family’ (in the circle of agents similar to him) there are fewer agents will be selected for reproduction.

Pareto-based optimization is built on rank-based selection. The least dominant agents obtain the highest rank number and do not participate in steps. The same procedure is

performed in the rest of the subset until all agents are assigned a rank number. Agents with the same rank number have the same chances for selection. Multi-purpose genetic algorithms provide several Pareto optima as a solution from which selecting the best one is difficult because of the numerous influencing factors.

For defining the fitness function in our model there is a following possibility: an aggregated fitness function can be established by weighing the elements of the complex corporate objective system according to the order of their importance. This importance ranking can be defined from the results of previous empirical research or on a theoretical basis. Values can be defined by percentage or rank weighed, however, the percentage figures seem to be more accurate since they are based on probability. In the aggregated fitness function the environment factor weighs less, thus environmentally-oriented sub-conditions are to be defined. The fitness value, namely the chances of further application of a strategic variation, does not directly depend on the strength of the environmental character of a strategy, but rather on the objectives preferred by the company. When the fitness function is defined, revenue, expenditure and profit functions applied in conventional economics can be used, but they are to be expanded so that the explanation force of the model can be increased.

It has already been mentioned that in order to define the fitness function very accurately, the importance of the environmental protection to the company is to be established, which is necessary to spot the position of the environment in the system of corporate objectives. Let us look through the process of its examination. 3.2.11. Importance of environmental protection in the corporate objective system

When the corporate eco-orientation is analysed, it is essential to determine how the environment, as a corporate objective, can fit in with the corporate complex objective system, and how the results of the corporate conventional analysis change when the analysis is extended by environmentally-oriented aspects. The analyses of corporate objective systems determine the most important objectives in almost the same way. According to the research conducted in practice the most important objectives are as follows (Meffert, 1992): • ensuring competitiveness, • maximizing profit in the long run, • productivity, • cost effectiveness, • motivating employees, • improving image, • expanding into new markets, • protecting environment, • retaining work places.

It is clearly seen that, according to the practical experience, environmental protection does not belong among the most important corporate objectives. As long as the environmental conflict is related to one of the corporate economic objectives, companies minimally meet the stipulated criteria. Only if environmental innovation is linked with objectives targeting cost effectiveness, may environment protection become the most important objective. Realisation that an environmental orientation results in corporate advantage over market competitors (if the environmentally-oriented market segment is present) is the subject of further analysis. Since reconciling ecological objectives with economic objectives is difficult for companies,

establishing how the implementation of ecological aspects affect particular elements of a corporate objective system is of essential importance.

On the basis of the results obtained from an empirical study (Meffert, 1992) it can be stated that the introduction of ecological aspects has the most unfavourable impact on short-term profit maximization and cost effectiveness. Ecological aspects do not have a considerable effect on increase in production or respecting employees. Their effect on other corporate objectives is varies, but favourable. Thus, when introducing ecological objectives special attention should be laid on optimization of benefits and disadvantages that can be obtained during introduction. This can be reached by attaining harmony between market advantages, competitive advantages and profit generation while realising that environmental protection is a competition factor is of utmost importance for a factory. 4. Genetic operations in the model

Base period(t:=0)

Defining of the base population P(0)

Selection

Evaluating of the base population

t:=t+1

Recombination

Mutation

The evaluating of the new population

The end of the process

The desired pollution level reached?Yes

No

Figure 6: Enviroment-oriented market modeling with the help of genetic algorithms

Steps for defining the initial population have already been discussed earlier. The objective of the algorithm - under particular conditions - is to minimize the pollution caused by a company. The extent of pollution from generation to generation (in the case of new strategic prospects) is to be defined by an objective function. (In the flow chart this step is shown as the evaluation of the initial population). If the expected level of pollution is not reached, genetic operations can be applied.

Agents of a new generation evolve during the process of genetic algorithms. The first step is selection, when strategies are selected on the basis of their fitness. The chances of 'survival' of strategies (agents) are determined by the degree of their fitness that can be defined by a fitness function. When the fitness function is defined, all the elements of the complex corporate objective system are to be considered. The selected strategies lay the basis for new variations. New strategies evolve during recombination. After this, by random mutation or conscious mutation (as mentioned above both types of mutation may occur in the operation of a company) final strategy variations evolve. For realistic modelling the obtained

variations are to be analysed in order to establish whether they are realistic and workable in particular conditions. It happens that during recombination and mutation unrealistic strategies evolve and have to be deleted from further processes. Then the new strategies are again evaluated by an objective function. When the desired pollution level is reached, the process is over. Otherwise, this process continues until the system complies with interruption conditions.

The fundamental condition for creating an efficient model is to know the processes and types of selection, recombination and mutation. The algorithms that are most applicable and comply with the specific features of the model are to be selected from the pool of possible algorithms.

Nissen (1997) and Schöneburg (1994) describe the processes, different functions and factors. Apart from simple algorithms we will study further possible variations of algorithms, analyse ways of supplementing the model by different subsets and interpret it by the application of multivariable fitness functions. 4.1. Selection

In our model selection is a selection process that forms environment-oriented corporate strategies – on the basis of conditions defined by external and internal corporate factors – and selects the strategies best fit for further application. It is the goodness function defined by conditions, that is, the fitness function that provides a given strategy as an opportunity is to be selected for further application. The evaluation of strategies is conducted on the basis of relative fitness values.

Selection processes can be divided into selection and election algorithms. Selection algorithms assign a replication probability value to each agent on the basis of which a total value can be defined: E(I)=n*pS(I), where n is the population agent number and pS(I) is the selection probability of the agent concerned. E(I) expresses the planned copy number of agents in the pool assigned for replication. The word ‘planned’ indicates that the actual copy number is defined when selection algorithms are running. 4.2. Selection algorithms

Fitness proportionate selection is a generally used selection algorithm where pS(I) is directly proportional to the fitness value of the actual chromosome:

∑=

Φ

Φ=

n

1jj

js

)I(

)I(p , where Φ is the fitness value, I j is the j-th agent

Rank-based and competition-based selections are alternative methods of fitness

proportionate selection. These alternative methods evolved because fitness proportionate selection possesses a relatively low selection pressure. Selection pressure is a process during which the selection affecting the phenotype, when inheritance is assumed, has an indirect impact on genotypes and finally, changes the distribution curve of one feature. The higher the selection pressure is, the more the population converges towards the optimum, and the faster it reaches a local optimum. The selection pressure is characterised by the number of generations necessary for generating a population with the application of selection algorithms which contains x-1 number of copies of the best agents (x is the size of the population). For rank-based selections there is no direct connection between selection probability and fitness value. Instead of this, agents of the population are ranked on the basis of their fitness values

and are issued a serial number. From this point selection is likely to be proportional to the rank number.

Competition-based selection method consider selection and election algorithms to be common. In this case agents amounting to z (2 ≤ z ≤ x) are selected from the population with the same selection probability, their fitness values are compared and the best agents are copied to the pool designated for replication. This step is repeated n times. The selection pressure can diretly be regulated by factor z: the higher value z has, the higher the selection pressure is. The risk of the competition-based selection process lies in the fact that in extreme cases several identical agents are selected to the pool designated for replication.

The most widespread selection algorithm is the so-called roulette method. It is similar to a roulette wheel, which is divided into n sections. The width of sections is in direct proportion to the selection probability of the agent belonging to it. The roulette wheel is rotated n times and parents for the next generation are selected. It is obvious that the higher the fitness value of an agent is, the better chance he has to be selected several times. In this type of selection, similar to the competition-based selection, there is a risk that all the selected agents will be identical. Although this method has a relatively high deviation between the targeted and the actual deviation, it is the most widely used method.

The stochastic sampling has lower deviation. Let us take the same roulette wheel again as in the roulette method to illustrate the idea. Here, the width of the sections is also directly proportionate to the probability of selection, but in this case n number of arrows are placed around the wheel (n is the amount of agents). The wheel can be turned only once and an agent is selected for recombination as many times as many arrows point at the agent. This method excludes the risk of selecting only one agent into the stock.

Figure7: The process of the stochastic sampling

Some models of genetic algorithms separate selection processes from election processes.

The basis of selection processes – not depending on their types- is the fitness value. It has already been mentioned that fitness functions are not linked to environmental burden. Consequently, during selection process the environmentally friendly variations are not ensured preferences - thus, do not have better chances for selection. This fact has an unfavourable impact on the expected operation of our model. There are two ways of avoiding

this negative effect: • by external regulations: an external intervention can change external factors (stronger

and stricter state control, better quality of the supplied raw material and so on) so that the genetic diversity of the population can also change. Thus, the system will shift towards optimum.

• by internal regulations: a discriminative method can increase the selection probability of environmentally friendly variations. Although the explanatory force of our model will decrease, the potential extent of the minimal burden on the environment can be defined, ensuring a base for comparison of actual (local) and global optima.

Two election algorithms have been introduced that select the actually remained variations from the pool designated for selection. . It is essential to maintain the variety and diversity of variations, since this type of economic system can better adapt to quickly and frequently changing economic conditions. From an environmental point of view economy is also characterised by a constantly changing economic, social and legal environment. Let us take the changing legal regulations, the ever increasing activity of social welfare campaigners, the state-of-the-art raw materials and the sophisticated production technologies. From the above mentioned considerations it can be stated that stochastic sampling is more widely used than the roulette method and fits in better with the model because a variation will not appear twice in the selected pool, and will always ensure the diversity of the system. 4.3. Recombination

Perhaps the most important step of genetic algorithms is recombination. The operator of recombination determines the method for reproducing a new agent from one or more old chromosomes, that is, from the chromosomes of parents. Parents are selected from the stock designated for replication. Recombination in our case mean combination and harmonization of possible environmentally relevant strategies, so that a completely new strategy is introduced that better complies with the criteria.

The starting point is two-parent recombination since a multi-parent recombination is of less importance. The recombination probability index number (pc) defines whether recombination between two parents will actually be performed. If this value is, for example 0.6, recombination is more likely to happen than not. In practice a number between 0 and 1 is selected at random and is compared with recombination probability. If the chosen number is greater than pc, recombination will be performed. Otherwise, the unchanged chromosomes of parents will enter the mutation process in the following evolutionary step. All recombination types follow a logical order, there is a deviation only in recombination itself. 4.3.1. One-point recombination

In the one-point strategy firstly a recombination point between 1 and L-1 (L is the length of the chromosome) is chosen and then the point (the boundary of two genes) is determined. The genes of one of the parents that are to the right of this point will go into the first offspring and the genes to the left from this point will go into the second offspring. In the case of the other parent the distribution of genes happens vice versa. 4.3.2. N-point recombination

The principle of n-point recombination is similar to the principle of one-point recombination, but instead of selecting one point, n points are chosen for breaking the chromosomes.

Figure8: The process of the n-point recombination 4.3.3. Uniform recombination

During the process of uniform recombination each gene is examined and a decision is made whether to change it or not. The process of decision taking is as follows: there is a given predetermined value pux, and a value characteristic to each gene Uz (where z=1,2,…,L). If pux> Uz, the gene is replaced. Otherwise, it is not replaced (Figure 19).

Figure9: Uniform recombination 4.3.4. Gene-mixed recombination

Gene-mixed recombination is a further developed variation of one- or n-point recombination. In this case two more steps (mixing and remixing) are added to the mentioned recombination processes. Firstly, the numbered genes are mixed, which is followed by one- or n-point recombination. In the last step the order of the genes is restored.

Figure 10: Gene-mixed recombination 4.3.5. Diagonal recombination

Diagonal recombination is also a further developed variation of the n-point recombination. However, now the deviation happens differently from that of earlier processes. In this case recombination can only work with more than two parents. The diagonal method, due to its character, produces i number of offsprings from i number of parents. In this respect, this variation does not follow the biological analogy, as few similar examples for this type of reproduction can be found in nature. The first step in the process is to chose i-1 number of breakpoints on both the i number of parental and offspring chromosomes. Then the offspring chromosomes are “filled up” as follows: the first offspring inherits in its first empty section the first chromosome section of the first parent, in its second section the second chromosome section of the second parent and in its third section the third chromosome section of the third parent. The process continues similarly with the second offspring, etc.

Figure 11: The process of the diagonal recombination

The most important, the widest spectrum of genetic algorithms, is provided by different recombination processes. This process is also the most important step for us since the character of new strategic variations, i.e. the feasible new ideas, are determined by this process. In our model, unlike biological recombination, when making a selection attention is to be paid to maintaining the controlled nature of our model to a certain extent.

This requirement is best met by uniform recombination, where each bit is examined separately, and then it is decided whether the members of the selected variations are to be changed or not. Special care is to be taken not to take the smallest chromosome unit, the bit, as basis but rather the genes (which mean a strategic unit), otherwise a process similar to mutation may occur, which is less controlled and with a less predictable outcome. 4.4. Mutation

When applying biological genetic processes to economics we defined mutation either as deliberate variations of strategic elements or as errors made in one’s own or copied strategies. Consequently, in our model, mutation means a deliberate change of element(s) of environmentally-oriented corporate strategy or unscheduled changes occuring during the execution of the strategy. Deliberate changes may be induced by circumstances produced by sudden changes in the external or internal micro- or macro environment, which may result in the change in the priority of environmental protection as a corporate aim. At this stage the corporation, due to factors such as lack of time, may be unable to change its complete strategy, and can only modify certain elements of it. Unscheduled changes or modifications may come from inadequacies of information flow or other corporate processes, or an inaccurate imitation of the strategy of another corporation.

At first sight, mutation may not seem to have a major role in genetic algorythms, as the mutation probability of a bit (pm) is low, usually between 0,01 and 0,001. However, considering also the process of biological evolution, its importance is not to be neglected. If mutation probability is low and the chromosome is relatively long, mutation will cause hardly any change in the value of the chromosome. Mutation probability is generally identical to a

single gene, apart from the case of the binary code, where the mutation probability of single genes is different in order to compensate for position-dependent code values

The importance of mutation is that it prevents populations from converging too soon towards a local optimum and it also increases their heterogeneous character. In this way it acts, to a certain extent, against selection pressure. Obviously, it is a positive effect of mutation that it helps maintain the diversity of strategy variations, thus contributing to the possible achievement of the global optimum.

The importance of mutation must not be neglected in our model, either. Mutation itself can be considered either a deliberate or a random process. Naturally, the effect of mutation is not always positive, - the value of a given chromosome does not necessarily increase in view of the objective function, i.e. the environmental load will not necessarily decrease due to the effect of mutation. Economic processes being controlled processes, this random process is to be controlled and regulated if necessary. 5. The condition of the interruption of genetic algorithms There are several possibilities to interrupt the process of genetic algorithms:

• After a predetermined number of steps (generation change) there is an examination of the extent the population to which has improved compared to the initial population (strategy variations). In our case this means asking whether there is another strategy with which a lower pollution value can be obtained. If the answer is yes, the feasibility of this strategy in the given conditions is to be examined ( if it has not been checked at each step). If it is not feasible, the model can be run again after reasonable changes in the initial conditions (selection and mutation probability value, or external factors broadening the initial population) have been made. After the predetermined number of steps the interruption procedure is worth using if time limitations, the extent or nature of the pollution urges the corporation to introduce an environmentally friendly strategy.

• When a predetermined pollution limit has been reached. Naturally, the optimum

condition would be if the pollution value were zero, but it is only a theoretical possibility. That is why limits that meet both regulations and expectations are to be set. It is also possible that no strategy generation including a suitable strategy is formed. In this case, the procedure described in the previous point is to be followed. This process, unlike the previous one, can be used if it is not urgent for us to obtain a lower level of pollution, in this way a lower pollution value might be obtained than previously.

• The interruption of the algorythm may depend on the convergence of the population or

its best member. Convergence can have several definitions. For instance, for binary chromosomes a gene converges if the value of the given gene is 95% identical throughout the whole population; a population converges if all the genes converge. Another solution is if the average, maximum fitness value of the present population is compared with a previous population by the algorythm.

6. Advantages of the model

The advantages of the intagrated environmental-economics model supported by genetic algorythms compared to the conventional corporate forcast models and optimization-models can be summarized as follows:

1. The structure of the model shows that algorythms contain several environment-oriented coroprate strategies that meet both external and internal economics demands, i.e. they register not one but a cluster of possible strategies. This gives way to the formation of new strategy variations that better adapt to new conditions.

2. The model manages several strategies at the same time, thus it may present several, nearly optimum strategies as a solution. As genetic operations continuously maintain the diversity of the system, the model is able to adapt to rapidly changing conditions. There are always strategies that fluctuate around the optimum point (the environmental load assigned to them is bigger, so they are not optimum at a given moment), and which, considering the micro- and macro environmental changes, may be more suitable later than the ones used. The system does not stop in a static optimum but it changes dinamically.

The integrated environmental-economics model integrates the tasks of environmental

management as well; in this way it supports the environmentally-relevant decisions more effectively. When determining environment-oriented corporate strategies, the model takes into account internal and external factors that have an impact on corporations. In this way the changes in input and output markets, in state interventions and in competitions can be interpreted to help the decision making process on different levels. Literature

1. Arifovic, J, .: Genetic Algorithm Learning and the Cobweb-Modell, in: Journal of Economic Dynamic and Control, 18, 3-28., 1994

2. Meffert,H., Kirchgeorg, M.: Marktorientiertes Umweltmanagement. Stuttgart: Verlag

C.E. Poeschel., 1992

3. Nissen, V.: Einführung in Evolutionäre Algorithmen. Braunschweig: Vieweg Verlag., 1997

4. Schöneburg, E., Heinzmann, F., Feddersen, S.: Genetische Algorithmen und

Evolutonsstrategien. Bonn: Addison-Wesley., 1994

5. Stengel, M., Wüstner, K. szerk.: Umweltökonomie – Eine interdiszciplinäre

Einführung. München: Verlag Vahlen, 35-66, 1997

6. Weise, P.: Der synergetische Ansatz zur Analyse der gesellschaftlichen Selbstorganisation. In: Ökonomie und Gesellschaft, Jahrbuch 8: Individuelles Verhalten und kollektive Phänomene. Frankfurt, New York: Campus., 1990

7. Weise, P.: Eine dynamische Analyse von Konsumtionseffekten. In: Jahrbuch für

Nationalökonomie und Statistik. 159-172, 1993

8. Wicke, L.: Umweltökonomie, 3. Kiadás. München: Vahlen, 1991

9. Zittel, T.: Marktwirtschaftliche Instrumente in der Umweltpolitik. Opladen: Verlag

Leske+Budrich, 51, 1996