Maximum Diversity Problem. A Multi-Objective Approach
DOI:
https://doi.org/10.19153/cleiej.21.2.2Abstract
The Maximum Diversity (MD) problem is the process of selecting a subset of elements where the diversity among selected elements is maximized. Several diversity measures were already studied in the literature, optimizing the problem considered in a pure mono-objective approach. This work presents for the first time multi-objective approaches for the MD problem, considering the simultaneous optimization of the following five diversity measures: (i) Max-Sum, (ii) Max-Min, (iii) Max-MinSum, (iv) Min-Diff and (v) Min-P-center. Two different optimization models are proposed: (i) Multi-Objective Maximum Diversity (MMD) model, where the number of elements to be selected is defined a-priori, and (ii) Multi-Objective Maximum Average Diversity (MMAD) model, where the number of elements to be selected is also a decision variable. To solve the formulated problems, a Multi-Objective Evolutionary Algorithm (MOEA) is presented. Experimental results demonstrate that the proposed MOEA found good quality solutions, i.e. between 98.85% and 100% of the optimal Pareto front when considering the hypervolume for comparison purposes.
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CLEIej is supported by its home institution, CLEI, and by the contribution of the Latin American and international researchers community, and it does not apply any author charges whatsoever for submitting and publishing. Since its creation in 1998, all contents are made publicly accesibly. The current license being applied is a (CC)-BY license (effective October 2015; between 2011 and 2015 a (CC)-BY-NC license was used).