Towards a conceptual multi-agent-based framework to simulate the spatial group decision-making process

Abstract

Most spatial problems are multi-actor, multi-issue and multi-phase in nature. In addition to their intrinsic complexity, spatial problems usually involve groups of actors from different organizational and cognitive backgrounds, all of whom participate in a social structure to resolve or reduce the complexity of a given problem. Hence, it is important to study and evaluate what different aspects influence the spatial problem resolution process. Recently, multi-agent systems consisting of groups of separate agent entities all interacting with each other have been put forward as appropriate tools to use to study and resolve such problems. In this study, then in order to generate a better level of understanding regarding the spatial problem group decision-making process, a conceptual multi-agent-based framework is used that represents and specifies all the necessary concepts and entities needed to aid group decision making, based on a simulation of the group decision-making process as well as the relationships that exist among the different concepts involved. The study uses five main influencing entities as concepts in the simulation process: spatial influence, individual-level influence, group-level influence, negotiation influence and group performance measures. Further, it explains the relationship among different concepts in a descriptive rather than explanatory manner. To illustrate the proposed framework, the approval process for an urban land use master plan in Zanjan—a provincial capital in Iran—is simulated using MAS, the results highlighting the effectiveness of applying an MAS-based framework when wishing to study the group decision-making process used to resolve spatial problems.

Appendix

1.1 Enrichment factor

In this study, spatial metrics such as enrichment factor are used to prepare spatial evaluation metrics. Verburg et al. (2004) introduced the enrichment factor to characterize the neighborhood effect. The enrichment factor is defined as the over- or underrepresentation of a land use in the neighborhood of a particular location, relative to the average land use distribution. The enrichment factor of a location is calculated as follows:

$$ F_{ikd} = \frac{{{\raise0.7ex\hbox{${n_{ikd} }$} \!\mathord{\left/ {\vphantom {{n_{ikd} } {n_{id} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${n_{id} }$}}}}{{{\raise0.7ex\hbox{${N_{k} }$} \!\mathord{\left/ {\vphantom {{N_{k} } N}}\right.\kern-0pt} \!\lower0.7ex\hbox{$N$}}}} $$

(3)

where $F_{ikd}$ characterizes the enrichment of neighboring cells with LUT k in distance d of central cell i. $n_{ikd}$ is the number of neighboring cells with LUT k in distance d of central cell i, $n_{id}$ is the total number of neighboring cells in distance d, $N_{k}$ is the number of cells with LUT k in the entire study area, and finally, N is the number of all cells in the study area (van Vliet et al. 2013).

The average neighborhood characteristic for a particular land use type i $\overline{{F_{{{\text{lkd}}}} }}$ is calculated by taking the average of the enrichment factors for all grid cells belonging to a certain land use type l, as follows:

$$ \overline{{F_{{{\text{lkd}}}} }} = \frac{1}{{N_{l} }} \mathop \sum \limits_{i \in L} F_{ikd} $$

(4)

where L is the set of all locations with land use type l and $N_{\text{l}}$ the total number of grid cells belonging to this set. In present study, the enrichment factor is presented on a logarithmic scale in order to obtain an equal scale for all LUTs. This is done by using Eq. (5).

$$ \lg \overline{{F_{{{\text{lkd}}}} }} = {\text{Log}} \left( {\overline{{F_{{{\text{lkd}}}} }} } \right) ) $$

(5)

where $\lg \overline{{F_{{{\text{lkd}}}} }}$ represents the logarithmic value of $\overline{{F_{{{\text{lkd}}}} }}$.

1.2 Compactness

Compactness is an important issue in urban areas. Similar LUTs may have a supporting and attraction effect on each other. This indicator is already used by researchers in different ways (Stewart et al. 2004). In this study, the compactness metric is calculated as:

$$ C_{ik} = \frac{{n_{ik} }}{n} $$

(6)

where $C_{ik}$, $n_{ik}$ and n are compactness of cell i with respect to LUT k, number of neighboring cells with LUT k and the total number of neighboring cells, respectively. $C_{ik} = 0$ if every cell with land use k has no neighboring cell with land use k, while $C_{ik}$ tends to be at a maximum if all cells with land use k form a single square region.

1.3 Incompatibility

The possible negative effect of some neighboring land uses on the activity of a specific land use is called “incompatibility.” Each land use type has a certain level of incompatibility with each other land use type in its neighborhood (Taleai et al. 2007). The incompatibility value of a cell (denoted as $I_{i}$) is defined as:

$$ {\text{In}}_{i} = \mathop \sum \limits_{j} f_{1} (d_{ij} ) \times {\text{Inc}}_{{C_{i} C_{j} }} $$

(7)

where ${\text{Inc}}_{{C_{i} C_{j} }}$ is the level of incompatibility between two land use types $C_{i}$ and $C_{j}$ that is extracted from the incompatibility matrix. Taleai et al. (2007) provided a detailed incompatibility matrix by a surveying method (specifically Delphi method) in Iran. $f_{1} (d_{ij} )$ is a function that describes how distance influences the incompatibility between two land use types. This function is determined by using a combination of the negative part of enrichment factor diagram and experts’ judgment.

1.4 Dependency

In contrast to incompatibility, the possible positive effect of an LUT on another LUT, such as the effect of residential on green spaces, is called “dependency.” In other words, often, an LUT needs some other LUTs and activities in its vicinity, in order to operate properly (Taleai et al. 2014). Similar to incompatibility, the dependency value of a cell (denoted as $D_{i}$) is defined as:

$$ D_{i} = \mathop \sum \limits_{j} f_{2} (d_{ij} ) \times {\text{Dep}}_{{C_{i} C_{j} }} $$

(8)

where ${\text{Dep}}_{{C_{i} C_{j} }}$ is the dependency level of two land use types $C_{i}$ and $C_{j}$ extracted from the dependency matrix, and $f_{2} (d_{ij} )$ is the distance function for the dependency. This function is determined by using a combination of the positive part of enrichment factor diagram and experts’ judgment.

1.5 Accessibility

Accessibility to the transportation network is a main important factor for every land use. In this study, the shortest Euclidean distance to an urban transportation road is used for calculating the accessibility index. The accessibility index is calculated as (Karimi et al. 2012):

$$ A_{i} = \mathop \sum \limits_{k = 1}^{2} \frac{1}{{1 + {\raise0.7ex\hbox{${d_{ik} }$} \!\mathord{\left/ {\vphantom {{d_{ik} } {a_{k} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${a_{k} }$}}}} $$

(9)

where $A_{i}$ characterizes the accessibility value of a cell i, $d_{ik}$ is the shortest distance to transportation road (type k), $a_{k}$ is the importance of accessibility to road type k (in this study, two types of road are used, the main roads and streets).

The expert agent computes suitability of each cell i ($S_{i}$) by using a simple weighted linear combination (WLC) technique as follows:

$$ S_{i} = W_{C} C_{i} + W_{D} D_{i} + W_{A} A_{i} - W_{I} {\text{In}}_{i} $$

(10)

where $W_{C}$, $W_{D}$, $W_{A}$ and $W_{I}$ are the relative weights that are assigned to the metrics $C_{i}$, $D_{i}$, $A_{i}$ and ${\text{In}}_{i}$, respectively.