Experiment Design for a Multi-objective Partitioning Problem

  • Bernábe-Loranca, María B.
  • Ruiz-Vanoye, Jorge A.
  • Bustillo-Díaz, Mario
  • González-Velázquez, Rogelio
  • Ochoa-Zezzatti, Alberto
  • Martínez-Guzmán, Gerardo
Abstract:
This work presents a factorial statistic experiment for a bi-objective combinatory optimization problem, which optimizes two functions in conflict: geometric compactness and homogeneity for variables from a population problem, which belongs to the Territorial Design (DT) area. This kind of problems invest their biggest effort on the bi-objective clustering to build groups of zones under partitioning properties where the territorial partitions must be as compact and as homogeneous as possible. At this point, the resolution of the compromise between two objectives has to be approached with a multi-objective technique to find non-dominated solutions that at the same time form the set of solutions encompassed in a Pareto Frontier (FP). The method proposed to find the set of non-dominated solutions is supported on basic aspects from the order theory, in particular from the Hasse diagram to obtain the Minima, and to manage the computational cost we have incorporated the Variable Neighborhood Search metaheuristic (VNS). To calibrate the VNS parameters we have employed a factorial experiment known as Box Benhken (BB) and Response Surface, in this way we have achieved an ideal combination of parameters to find satisfactory solutions to the multi-objective problem under study.
Research areas:
Year:
2016
Type of Publication:
Article
Keywords:
Compactness; Homogeneity; Experiment Design; Pareto Frontier; Partitioning
Journal:
Latin America Transactions
Volume:
14
Number:
5
Pages:
2389-2401
ISSN:
1548-0992
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