A Multiobjective Approach for the Heuristic Optimization of Compactness and Homogeneity in the Optimal Zoning
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Abstract
This paper presents a multiobjective methodology for optimal zoning design (OZ), based on the grouping of
geographic data with characteristics of territorial aggregation. The two objectives considered are the minimization of
the geometric compactness on the geographical location of the data and the homogeneity of any of the descriptive
variables. Since this problem is NP hard [1], our proposal provides an approximate solution taking into account
properties of partitioning algorithms and design restrictions for territorial space. Approximate solutions are generated
through the set of optimum values (Maxima) and the corresponding minimals (dual Minima) [2] of the bi-objective
function using Variable Neighborhood Search (VNS) [3] and the Pareto order defined over this set of values. The
results obtained by our proposed approach constitute good solutions and are generated in a reasonably low
computational time.