If the notion of optimality for single-objective LP is directly applied to this MOLP, we arrive at the following notion of a complete optimal solution.
IV. GIS-Multi-criteria integration
There are two methods proposed by Jankowski 1995, or architectures, for integrating GIS and Multicriteria techniques: the loose coupling strategy and the tight coupling strategy.
The main idea of the loose coupling strategy is to facilitate the integration using a file exchange mechanism. The assumption behind this strategy is that multi-criteria techniques already exist in
the form of stand-alone computer programs. The results of the decision analysis may be sent to GIS for display and spatial visualization. The loose coupling architecture is based on linking
three modules GIS module, Multi-criteria technique module and file exchange module, as seen in figure 1.
The tight coupling strategy uses multiple criteria evaluation functions fully integrated into GIS, a shared database and a common user interface figure 2. Differently from the previous
architecture, the data manipulations and transferences between the boxes Data input management functions - Spatial analysis functions - Display and data output functions and
the box Multicriteria evaluation functions are performed endogenously, with no need of a file exchange module. Under this approach, the GIS evaluation functions facilitate spatial decision-
making with multiple criteria. The multiple criteria evaluation functions can be seen as a part of the GIS toolbox, that is, one can select a function from the common GIS user interface. This
design facilitates the map views of alternatives and their criteria. The IDRISI http:www.clarklabs.org03PROD03prod.htm and SPRING Georeferenced Information
Processing System - http:www.dpi.inpe.brenglishindex.html GIS software have multi-criteria evaluation functions that use the Analytical Hierarchic Process AHP method and can be seen
as examples of the tight coupling strategy implementation.
In this paper the methodology adopted, presented in figure 3, is based on the integration method proposed by Jankowski and Richard 1994, similar to the loose coupling strategy. On the whole,
the integration involves three main stages. In the first stage, conducted in a GIS environment, there is a reduction in the number of alternatives, through physical andor qualitative constraints
imposed by the criteria. These constraints, in most cases, are related to topological operations andor to search operations known as spatial queries, which yield details or parameters about
the features themselves, where the data is stored in a GIS database; the information processing is through database manipulation and mathematical analysis functions, using logic operators
AND, OR, NOT, easily carried out in GIS.
With this reduced set of alternatives, the authors proceed with the multi-criteria analysis to select the best alternative among these. The Multi-Objective Linear Programming MOLP problem was
solved through the Pareto Race method Korhonen and Laakso, 1986; Korhonen and Wallenius, 1988, implemented by VIG software Korhonen, 1987. The authors chose this method on
account of its interactivity, good graphical interface, permitting the use of a great number of objective functions, availability and compatibility with the operational systems handled by the
authors. In the third stage, the MOLP results are introduced into GIS, for the final visualization of the choice of the decision-maker, so as to guarantee that the most correct decision is that which
best represents the interests of the decision-maker Graeml and Erdmann, 1998.
V. Case study
