The p-compact-regions problem

WenWen Li, Richard L. Church, Michael Goodchild

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

The p-compact-regions problem involves the search for an aggregation of n atomic spatial units into p-compact, contiguous regions. This article reports our efforts in designing a heuristic framework-MERGE (memory-based randomized greedy and edge reassignment)-to solve this problem through phases of dealing, randomized greedy, and edge reassignment. This MERGE heuristic is able to memorize (ME of MERGE) the potential best moves toward an optimal solution at each phase of the procedure such that the search efficiency can be greatly improved. A dealing phase grows seeded regions into a viable size. A randomized greedy (RG of MERGE) approach completes the regions' growth and generates a feasible set of p-regions. The edge-reassigning local search (E of MERGE) fine-tunes the results toward better objectives. In addition, a normalized moment of inertia (NMI) is introduced as the method of choice in computing the compactness of each region. We discuss in detail how MERGE works and how this new compactness measure can be seamlessly integrated into different phases of the proposed regionalization procedure. The performance of MERGE is evaluated through the use of both a small and a large p-compact-regions problem motivated by modeling the regional economy of Southern California. We expect this work to contribute to the regionalization theory and practice literature. Theoretically, we formulate a new model for the family of p-compact-regions problems. The novel NMI introduced in the model provides an accurate, robust, and efficient measure of compactness, which is a key objective for p-compact-regions problems. Practically, we developed the MERGE heuristic, proven to be effective and efficient in solving this nonlinear optimization problem to near optimality.

Original languageEnglish (US)
Pages (from-to)250-273
Number of pages24
JournalGeographical Analysis
Volume46
Issue number3
DOIs
StatePublished - 2014

Fingerprint

heuristics
regionalization
inertia
regional economy
aggregation
efficiency
modeling
performance

ASJC Scopus subject areas

  • Geography, Planning and Development
  • Earth-Surface Processes

Cite this

The p-compact-regions problem. / Li, WenWen; Church, Richard L.; Goodchild, Michael.

In: Geographical Analysis, Vol. 46, No. 3, 2014, p. 250-273.

Research output: Contribution to journalArticle

Li, WenWen ; Church, Richard L. ; Goodchild, Michael. / The p-compact-regions problem. In: Geographical Analysis. 2014 ; Vol. 46, No. 3. pp. 250-273.
@article{b042f4b1038642d288b6f00f86852d5e,
title = "The p-compact-regions problem",
abstract = "The p-compact-regions problem involves the search for an aggregation of n atomic spatial units into p-compact, contiguous regions. This article reports our efforts in designing a heuristic framework-MERGE (memory-based randomized greedy and edge reassignment)-to solve this problem through phases of dealing, randomized greedy, and edge reassignment. This MERGE heuristic is able to memorize (ME of MERGE) the potential best moves toward an optimal solution at each phase of the procedure such that the search efficiency can be greatly improved. A dealing phase grows seeded regions into a viable size. A randomized greedy (RG of MERGE) approach completes the regions' growth and generates a feasible set of p-regions. The edge-reassigning local search (E of MERGE) fine-tunes the results toward better objectives. In addition, a normalized moment of inertia (NMI) is introduced as the method of choice in computing the compactness of each region. We discuss in detail how MERGE works and how this new compactness measure can be seamlessly integrated into different phases of the proposed regionalization procedure. The performance of MERGE is evaluated through the use of both a small and a large p-compact-regions problem motivated by modeling the regional economy of Southern California. We expect this work to contribute to the regionalization theory and practice literature. Theoretically, we formulate a new model for the family of p-compact-regions problems. The novel NMI introduced in the model provides an accurate, robust, and efficient measure of compactness, which is a key objective for p-compact-regions problems. Practically, we developed the MERGE heuristic, proven to be effective and efficient in solving this nonlinear optimization problem to near optimality.",
author = "WenWen Li and Church, {Richard L.} and Michael Goodchild",
year = "2014",
doi = "10.1111/gean.12038",
language = "English (US)",
volume = "46",
pages = "250--273",
journal = "Geographical Analysis",
issn = "0016-7363",
publisher = "Wiley-Blackwell",
number = "3",

}

TY - JOUR

T1 - The p-compact-regions problem

AU - Li, WenWen

AU - Church, Richard L.

AU - Goodchild, Michael

PY - 2014

Y1 - 2014

N2 - The p-compact-regions problem involves the search for an aggregation of n atomic spatial units into p-compact, contiguous regions. This article reports our efforts in designing a heuristic framework-MERGE (memory-based randomized greedy and edge reassignment)-to solve this problem through phases of dealing, randomized greedy, and edge reassignment. This MERGE heuristic is able to memorize (ME of MERGE) the potential best moves toward an optimal solution at each phase of the procedure such that the search efficiency can be greatly improved. A dealing phase grows seeded regions into a viable size. A randomized greedy (RG of MERGE) approach completes the regions' growth and generates a feasible set of p-regions. The edge-reassigning local search (E of MERGE) fine-tunes the results toward better objectives. In addition, a normalized moment of inertia (NMI) is introduced as the method of choice in computing the compactness of each region. We discuss in detail how MERGE works and how this new compactness measure can be seamlessly integrated into different phases of the proposed regionalization procedure. The performance of MERGE is evaluated through the use of both a small and a large p-compact-regions problem motivated by modeling the regional economy of Southern California. We expect this work to contribute to the regionalization theory and practice literature. Theoretically, we formulate a new model for the family of p-compact-regions problems. The novel NMI introduced in the model provides an accurate, robust, and efficient measure of compactness, which is a key objective for p-compact-regions problems. Practically, we developed the MERGE heuristic, proven to be effective and efficient in solving this nonlinear optimization problem to near optimality.

AB - The p-compact-regions problem involves the search for an aggregation of n atomic spatial units into p-compact, contiguous regions. This article reports our efforts in designing a heuristic framework-MERGE (memory-based randomized greedy and edge reassignment)-to solve this problem through phases of dealing, randomized greedy, and edge reassignment. This MERGE heuristic is able to memorize (ME of MERGE) the potential best moves toward an optimal solution at each phase of the procedure such that the search efficiency can be greatly improved. A dealing phase grows seeded regions into a viable size. A randomized greedy (RG of MERGE) approach completes the regions' growth and generates a feasible set of p-regions. The edge-reassigning local search (E of MERGE) fine-tunes the results toward better objectives. In addition, a normalized moment of inertia (NMI) is introduced as the method of choice in computing the compactness of each region. We discuss in detail how MERGE works and how this new compactness measure can be seamlessly integrated into different phases of the proposed regionalization procedure. The performance of MERGE is evaluated through the use of both a small and a large p-compact-regions problem motivated by modeling the regional economy of Southern California. We expect this work to contribute to the regionalization theory and practice literature. Theoretically, we formulate a new model for the family of p-compact-regions problems. The novel NMI introduced in the model provides an accurate, robust, and efficient measure of compactness, which is a key objective for p-compact-regions problems. Practically, we developed the MERGE heuristic, proven to be effective and efficient in solving this nonlinear optimization problem to near optimality.

UR - http://www.scopus.com/inward/record.url?scp=84904270075&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84904270075&partnerID=8YFLogxK

U2 - 10.1111/gean.12038

DO - 10.1111/gean.12038

M3 - Article

VL - 46

SP - 250

EP - 273

JO - Geographical Analysis

JF - Geographical Analysis

SN - 0016-7363

IS - 3

ER -