B. Behaviors inspired by the environmental management

Environmental management is a discipline created by humans in order to find the necessary resources to tackle the environmental problems, which, in principle, are caused either by the environmental intervention, exchanging its natural behavior by a behavior induced by nature itself or by people ¹². These behaviors are dynamic and source for multiple studies to analyze their causes and effects, as well as to model the environmental complexity ⁵.

Studies about the environment found a pattern in the natural disasters that is faced by environmental management. It occurs that in the sceneries presented, always four factors were intervening: a. An environmental entity, b. The natural behavior of that entity. c. Some variables or functions that affect the natural behavior. And d. the intervention result of those variables ¹³, defined, as "induced behavior" by the present study.

But, how to tackle such complex problem, called environmental management? We went to bio-inspired computing, in the multi-agents' field, where ¹⁴ and ¹⁵ affirm that the multi-agent systems are designed to solve the high complexity problems.

The multi-agent system, by itself, is not enough to face an environmental problem; therefore, incorporating the geometric aspects of the vector model and involving them into the agent modeling is necessary. It is noteworthy that the geographic vector agents already exist ⁸, but since they modify themselves, comparing their initial and final (induced) behaviors, main aspect of the environmental management to control the behaviors of the studied entities, is not allowed.

C. The vectorial model'geometry

The spatial entities geometric representation, from the basic elements stated by Euclid, such as the points, lines and polygons ¹⁶ allows to have a model, capable to support real worlds different objects in a referenced context.

The vector model' geometry use in the AVNG, is divided in two moments: 1) The studied environmental entity geometry, when presents its natural behavior, and 2) The agent created information, from the function or variable intervention, which induces the environmental entity. Starting from the mentioned elements, the agent assumes the geometry, and alters it, by the geographic function and takes the data to a new shapefile, where it keeps the induced behavior.

The function to modify the natural behavior points is shown in the equation (1)

where ^_Pnew is the point where the vector goes once the induced behavior occurs; P_t Is the initial point where the entity is, when it has its natural behavior; C_ind is the variable or function which generates the induced behavior; ^_Cnat is the variable or function that represents the entity natural behavior, and K is a constant obtained from the time in which the two behaviors are evaluated (sec); n is defined by the unity type (length, area or volume) that present the following behaviors: n is defined by the unity type (length, area or volume) that present the behaviors: If is in meters, then is n=1, if it is in m², then n=2, and if is in m³, then n=3.

1) Shapes construction: The vector model has three primitives, which are modeled by the AVNG following a point continuum algorithm in each one of them, for which it is applied the equation (1) en each geographic entity point, to modify its structure in a new shape, that allows to visualize the two behaviors. An example of this is shown in Fig 1, where the natural behavior is visualized in blue, and the possible induced behaviors, in red, within the same shape geometric structure. In Fig 1a, it is visualized the primitive point; in 1b, the primitive line and in 1c, the primitive polygon.

Fig.1. Graphic representation of a point (a), line (b), and polygon (c)' AVNG. 

As may be observed, the origin vector is not modified, given that represents the natural behavior in color blue, and the induced behavior, in red color, it is generated in a new shapefile, allowing to realize comparisons of longitudes, areas and volumes for a further analysis in the decision taken.

D. A geo-inspired (AVNC) natural vector agent's proposal

The AVNG is based on the environmental aspects integration, modeled in two behaviors and in the vector agents' theory ⁸ based on the Euclidian geometry.

As it was mention, an AVNG represent a geographic or environmental entity, in which can be modeled two behaviors: The natural and the induced ones. The first, correspond to the entity natural state, which can be modified by the physic variables, without showing significant changes. In the present study, these variables are modeled by an aleatory variable. The second behavior is the one which represents the entity, when it overrides the natural function, which occurs when it is affected by one or more generated physical variables. In this moment the natural behavior is transformed in a induced behavior, or by the human intervention.

After these types of behaviors it was established the geographic function, that helps to integrate the Geographic information systems' visual component, starting from the vector model that represents the entities through the primitives (points, lines or polygons.) Each geographic entity has an initial vector which represents it.

The natural behavior is associated to the initial vector, and from it are carried out the adjustments toward the induced behavior, in order to show its spatial variation. The last component is the environment management function, that supplies the control variable for the behavior or the agent induced function. In the Fig. 2 can be observed the proposed structure to the AVNG.

Fig. 2 Geo-inspired natural vector Agent's structure (AVNG). 

A. JADE

To develop the agents systems or multiagents, there are several platforms. JADE is one among the most known and used, due to its functionalities that allow to develop, among others, the agents application' development, that comply with FIPA' specifics for multi-agent systems ^19,4.

The JADE agents platform, allows a distributed agents system, which functions using the Jave language, According to the multi-agents systems focus, an application on the JADE platform base, is composed by a cooperants agents group, that are able to communicate between them, through the messages interchange ⁴.

Each agent is immersed in an environment on which can act and whose happenings may be noticed. The environment may evolve dynamically, and the agents appear and disappear in the system, according the necessities and the applications' requirements. JADE supplies the necessary basic services for the environment application distribution, allowing each agent to discover others in a dynamical way and communicate with them.

B. Geotools

Geotools is a free code library for the geographic information systems that allows to develop solutions adapted to the standards that run under the JAVA programing language. It supplies the Open Geospatial Consortium' Specifications implementation ²⁰.

The Geotools development allows to integrate the programing basic aspects to the SIG development, which had been restricted to some software developers' houses. This library fundamental aspect lies in that allows to manipulate the geographic entities implemented in the SIGs, enabling to modify and to edit the elements that already are the information system' passive part ²¹.

In the Multi-AVNG model, Geotools provides the fundamental code, to evaluate the initial vectors, which represent the entity and to model through JADE the studied entity' natural and induced behavior. This library used allows to visualize in a graphic way, the studied entity' induced behavior.

A. Variables and functions that should be taking account

Natural behavior. From the mathematic and computational point of view, the natural shape, can be defined as the function that represents the natural entity behavior, and for the present study we will call it N (g), whose value is represented according to the study objective, for instance, a river flow.

Induced behavior. For practical effects, this agent function is defined as the behavior, that it assumes once has been influenced by the variable or the surroundings function. This function is called I(g): Example, a river flooding flow,

Function or surrounding variable. This function or surrounding variable is the cause to alter the natural behavior and to establish the induced behavior in the studied environment entity. There may be one or several variables, that intervene in the behavior change of the environmental entity. For example, based on the initial environment problem, we are able to talk about pluviosity.

Memory. Is the variable that stores the induced behavior in a time (t) to be transmitted to the same AVNG or to other within its context.

Geographic Function: The geographic function is the one that allows to vectorize the induced behavior, from the difference between its two behaviors, in a defined time interval (see equations 2, 3, 4 and 5).

With (M) memory = 0 the equation is the followed presented one:

With (M) memory > 0 the equation assumes the form:

F(t) = The function or the time variable; N(g) = The natural behavior; I (q)= The induced behavior; ^{_{latn, longn}} = The latitude and longitude values in the stretch n; The altitude value in the point n; The C value is a constant obtained from the reference shaefile measure unit and is given in meters. It works with the vector model and it is defined as the primitive and the space reference system to analyze each vector agent. r Is the entire value that assumes the root, which will depend from the unities of induced behavior (longitude, area or volume), For example, for m, r=1; for m², r=2, and for m³, r=3.

Environment management function. The environment management function is the one which controls the behavior of the induced entity. This function tries to have tolerance degrees, between the natural behavior and the induced one, with the purpose to call alert when it is above the established limits.

B. Multi-AVNG System, to determine a flooded urban area

To use the Multi AVNG system, is presented a case study, in order to approach the flooded areas problem in an urban center. With that purpose, it is carried out the zone studied description, plus the functions and behaviors determination to be modeled, in order to use it in the proposed system.

1) A case study: The tributary stream "la Perdiz", located in the Amazonia region, in the Colombian southest, between the south latitude 00 ° 42' 17" and 02° 04' 17" north latitude and 74° 18' 39" and 79° 19' 35" west longitudes, which represent the 7.79 % of the Colombian territory, in which is located in the Florencia municipality, the Caquetá department Capital, and represent a clear damage example, that may cause a small affluent within the urban centers. The flood conditions exposed have been little studied in this world region, given the amazon piedmont conditions, where the rough mountain views converge with the smooth plains. This land deep variety is the ideal scenery to prove the AVNG model, for the floodable areas definition.

2) Data origen to apply the Multi-AVNG as a study case: This geographic work development, was based on several digital information sources, among them: i) The Caqueta Department, Territorial Control Plan (POT), from which there were overplaced the risk regions in the Florencia municipality, allowing us to obtain the risks hydrologic map, where can be observed the zones that show landslides, flooding and geological faults. ii) Satelital image, LANDSAT 7, window -stream "the Perdiz' basin"-, the images are from 1998 and 2003, were obtained from the Amazonia University, Basic Sciences School, and the Geographic Institute Agustin Codazzi -IGAG- which allowed to have the study area reconnaissance and to digitize the vector base. iii) Aerial photography's: 9 Flight Photos from the C-2173 IGAC. -4 photos (241 to 244) obtained from the Basic Sciences School, and 5 photos (262 to 266) obtained from the IGAC- that allowed to digitized vectors from the zones which were shadowed in the satellite image. And iv) Plates: 3 official plates from the IGAC (389-VI-C and 413-II-A and C) at scale 1:25000. In this way were obtained the level curves, the houses positions, the schools and the roads infrastructure. In this way were built the irregular triangles networks (TIN) and the vectors based capes, that represent the geographic entity (La Perdiz streem).

The hydrographic data from 1969 to 2014, were obtained in the region, from the Colombian Hydrology, Meteorology and Environmental Studies (IDEAM), located in the coordinates shown in Table 1.

From this data was consolidated the worst floods study, that has suffered the municipality, and was established the water flow that was generated, to finally find the one which allowed to proof the model in a known context, and in this way, to be able to validate the obtained data, with the registered historical data, and the flooded areas that were demarked by the rainfalls.

In May 24 of 2003, were inundated 10 town quarters, reaching an approximated number of 1500 persons affected by the floods. But the worst effect was caused to the roads infrastructure and to the water supply networks, whose services were suspended during more that 10 days in some of the city's quarters. Two months latter, on the July 14^th of the same year, occurred a new hydroclimatic event, from which were reported 1.030 families affected, for a total of 5.200 people harmed.

3) DataSetproof Definition: The DataSet test is built with the registered rainfalls in the meteorological station, and from it, is made a 12 hours consolidation, to determine the basing behavior, with some pre-established values, and one hour intervals. Given that historically the sudden flooding, caused by rainfalls are developed between three to six hours, it is kept a margin for the results consolidation.

Besides, there were integrated the basing physical parameters, such as the area and the stream speed, in the stipulated stretches, in order to define the natural function parameters The induced function is called when the rainfall is higher than 0, in an hour lapse. The DATASET basic structure is shown in Table 2.

The file can be built as an Excel table or a flat file, for which it should be, modified some libraries of the fountain codices. For the simulation, there were assigned fixed values, taken from one of the most severe flooding of the epoch history, which occurred on April the 28^th of 2000, when it rained during three hours and approximately fell 50, 65 and 150 mm of rain ²². But the file can be linked in the nextworks by sensors located along the basing, in order to translate the data into real time.

4) Geographic entity vectorization (Stream La Perdiz): Starting from the geographic information obtained from the date sources already signaled, it is defined a set of vectors, that represent the entity to be processed. In the present research it was defined the area and the basing shape, factors that are important to calculate the induced behaviour. In this case study, the stream la Perdiz, is the geographic entity, and was divided in 71 sectors, given that has 71 variations in its gradient, along its stream from his origen to where it flows into the Hacha river. That is important, with the purpose to count with minor changes in the form and the volumne of the water that travels trough its basing.

Once it is vectorized the entity becomes the entrance to the AVNG sytem. It sholuld be remembered, that the vectorial model flexibility in the GIS, allows to represent every entity through out his primitives, therefore, it is necessary to realize a previous analysis, in order to determine, which one of them, is the one which represents in the right way, and on the adecuated scale, the geographic entity of the realized work.

5) The Multi-AVNG system definition and processing: Once are defined the entries, the dataset and the geographic entity representative vector for the AVNG, it proceeds to realize its execution, with the purpose to obtain the vectors demarcated area, that be affected by the water overflow.

Once the data are introduced in the AVNG (DataSet), it proceeds to analyze each one of the entity sectors and to verify whether the entity is in its natural behavior or changes into its induced behavior, for which are verified the pluviosity values provided by the Dateset. Once carried out the comparison, it proceeds to store into the variable memory, the modified value in the sector, which is sent, through a message to the following AVNG, that is monitoring the following sector (See Figure 4).

Fig. 4 An AVNG internal data flow. 

The value obtained from the message sent, is turned flow, given the situation. In this way, all the AVNG are into an additional entry for the AVNG, that receives it, communicated in a fall way all the AVNG, since the and is accumulated in the Natural or Induced function La Perdiz streem's birth, until its flow.

With the values obtained in each sector, before being sent to the following AVNG that receives it, is initiated the Geographic function, that takes the original vector points values (Figure 5) and modifies them, adding the generated values for the induced function to create vectors, that are displaced from the original sector. The obtained result is an image with vectors at certain distance form the original vector (Figure 9).

The obtained area, once the AVNG execution is visualized in the Figure 8, where it is demarked from the vectors that are displaced from the original vector toward the left or the right according the induced function, that is affected by the slope, the pluviosity values and the flow generated by the rainfalls.

Fig. 5 Geographic entity division in Vectors and the Multi-AVNG system' construction. 

A. Comparing the areas between the Multi-AVNG and the flooded area

Florence city is located in the Figures 6 and 7, at higher scale is divided by living quarters, streets and avenues. The urban area is located to the South of the municipality, and is irradiated by multiple water sources, among them the La Perdiz streem.

Fig. 6 The Perdiz Stream. 

Fig. 7 the Flooded Zones. 

From the satellite image, that shows the flooded area, was obtained a shape file, which limits this area (see Figure 7) and was compared with the vectors generated by the MultiAVNG system that obtained a shape filed, with the generated sections (see Figure 8.), In the two results comparison is shown in the Figure 9, where the differences within the defined area and the one obtained by the AVNG, are evidenced.

Fig. 8 Marked zone by the AVNG. 

Fig. 9 Zones comparison. 

Once were obtained the generated areas by the Multi-ABNG system, it was proceeded to take the remotest vector from the original vector, both by the left side as by the right one, in order to obtain an area on the TIN or the generated raster. Departing form this information it was utilized the method employed by ⁷ calculate the flooded area and the generated area by the system approximation percentage, for which it was utilized de equation (6).

^_Smod y ^_Sobs are the dominion sets or subregions (pixels, elements or cells) shown as flooded by the model and the historical date, reflected in maps or satellite images, and Numb (*) notes the group's member numbers. Therefore it varies between 0, for the model without covert between the flooded areas, and 100, for a model, in which the prediction data fully coincide with the observed ⁷ obtaining the following results (Table 3).

As can be observed, when using the comparison method [7], it was obtained a 70.29% of flooded area, from the Multi-AVNG model, achieving to consolidate a clear area, where the agents induced behavior had influence. Besides the model was evaluated, when there were not catastrophic events' pluviosity data. The system reflected only the entity natural behavior, in this case with the 95.78% of the area, related to the environment entity normal course. It is due to clarify that it is necessary more trials with different events, but for this study object demonstration, the agents change their behavior and reflect in the vectorial model structure, an approximation to the environmental entity. Nevertheless, it can advance in the following works, by improving the new behaviors.