VisualUVAM: A Decision Support System Addressing the Curse of Dimensionality for the Multi-Scale Assessment of Urban Vulnerability in Spain

Abstract

Many-objective optimization methods have proven successful in the integration of research attributes demanded for urban vulnerability assessment models. However, these techniques suffer from the curse of the dimensionality problem, producing an excessive burden in the decision-making process by compelling decision-makers to select alternatives among a large number of candidates. In other fields, this problem has been alleviated through cluster analysis, but there is still a lack in the application of such methods for urban vulnerability assessment purposes. This work addresses this gap by a novel combination of visual analytics and cluster analysis, enabling the decision-maker to select the set of indicators best representing urban vulnerability accordingly to three criteria: expert’s preferences, goodness of fit, and robustness. Based on an assessment framework previously developed, VisualUVAM affords an evaluation of urban vulnerability in Spain at regional, provincial, and municipal scales, whose results demonstrate the effect of the governmental structure of a territory over the vulnerability of the assessed entities.

Enhancing Sustainability and Resilience through Multi-Level Infrastructure Planning

“…Broadly, vulnerability can be understood as the susceptibility to suffer from, or the difficulty in coping with the negative effects of an event, and it has become a major concern for sustainable urban development [35][36][37][38]. In a prior work, Salas and Yepes [39] presented VisualUVAM, a software that affords the urban vulnerability assessment of cities, provinces, and regions of Spain. This software extended the scope of possible variables for the characterization of urban vulnerability (UV) from the three basic criteria adopted by the Spanish Observatory of Urban Vulnerability (OVU) to a wider set of 36 possible indicators, among which the method selected those most suitable according to several criteria.…”

“…In VisualUVAM, the selection among the 36 possible indicators for characterizing UV is addressed via a multi-objective optimization (MOO) problem in which expert judgment, statistical consistency, and robustness against data uncertainties are used as the criteria for the choosing of indicators ( Figure 2). Since MOO usually yields large sets of solutions, giving rise to the so called "curse of dimensionality" problem [40], the assessment process also implements a cluster-analysis-based methodology that synthesizes the initial space of 300 solutions into a smaller, manageable one of 5 representative solutions ( Figure 2) [39]. This enables the decision-maker to focus the analysis on the most promising alternatives and to select the most suitable, which affords a multi-scale evaluation of the risk of urban vulnerability of entities at city, province, region, and country scales [39].…”

“…Since MOO usually yields large sets of solutions, giving rise to the so called "curse of dimensionality" problem [40], the assessment process also implements a cluster-analysis-based methodology that synthesizes the initial space of 300 solutions into a smaller, manageable one of 5 representative solutions ( Figure 2) [39]. This enables the decision-maker to focus the analysis on the most promising alternatives and to select the most suitable, which affords a multi-scale evaluation of the risk of urban vulnerability of entities at city, province, region, and country scales [39]. Once the set of indicators has been selected, the method yields, for each of the cities, provinces, and regions being assessed, both the state of vulnerability (SV) at a given time and the risk of increasing vulnerability in the future.…”

“…In seeking to achieve these goals, the MOO problem operated over the "rights" and "duties", which therefore became the MOO's decision variables, and were formulated as the percentage in which entities are allowed to deviate from the baseline plan, in the case of rights, or from the expected performance in the case of duties [4]. Along with the quantitative information, we also gathered the qualitative information regarding experts' preferences for the indicators best representing urban vulnerability, required by the assessment process [39]. Based on the analytic hierarchy process (AHP) multi-criteria technique [46], we asked the experts to pairwise compare the 36 indicators of the quantitative database, which were structured in three levels so that only in one case was the number of indicators to be compared greater than five.…”

“…Further, to avoid the problem of inconsistent judgment elicitation [47], we developed a software application, programmed in Matlab, that provided experts with real-time feedback on their judgments' consistency, enabling them to interactively revise their judgements until they became acceptable [39]. As an outcome, we obtained the experts' relative preferences for indicators as weights, which were incorporated into the experts' preferences objective in the optimization process ( Figure 2).…”