AUTOMATIC PARAMETERIZATION FOR EXPEDITIOUS

MODELLING OF VIRTUAL URBAN ENVIRONMENTS

A New Hybrid Metaheuristic

Filipe Cruz, Ant´onio Coelho and Luis Paulo Reis

Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias 4200-465, Portugal

Keywords:

Metaheuristics, optimization algorithms, optimization systems, expeditious modelling.

Abstract:

Expeditious modelling of virtual urban environments consists of generating realistic 3d models from limited

information. It has several practical applications but typically suffers from a lack of accuracy in the parameter

values that feed the modeller. By gathering small amounts of information about certain key urban areas, it

becomes possible to feed a system that automatically compares and adjusts the input parameter values to ﬁnd

optimal solutions of parameter combinations that resemble the real life model. These correctly parameterized

rules can then be reapplied to generate virtual models of real areas with similar characteristics to the refer-

enced area. Based on several nature inspired metaheuristic algorithms such as genetic algorithms, simulated

annealing and harmony search, this paper presents a new hybrid metaheuristic algorithm capable of optimiz-

ing functions with both discrete and continuous parameters and offer competitive results in a highly neglected

ﬁeld of application.

1 INTRODUCTION

There has been a growing need for expeditious mod-

elling systems for urban environments in recent years.

Applications include virtual city tours, georeferenced

services, urban planning.

Creating urban models that are accurate repre-

sentations of the real world can be extremely hard

in terms of information gathering and invested man

power. Close resemblances to the real world is often

an acceptable compromise for some applications. It

often occurs that it is quite impossible to gather in-

formation from the entire city you are trying to model

but it is somewhat easy to extract detailed information

from certain key-deﬁning small areas from within the

city. Generating expeditious modelling rules that will

match such information is an important requirement.

The artiﬁcial intelligence ﬁeld of optimum search in-

cludes meta heuristic algorithms that can determine

optimum parameter values.

The work described in this paper focuses on

solving this problem by creating a new hybrid

meta heuristic algorithm, competitive and capable of

handling both discrete and continuous parameters.

Adapting ideas from several other nature based meta

heuristic algorithms such as genetic algorithms, sim-

ulated annealing and harmony search.

This paper is divided into 5 sections: the ﬁrst serv-

ing as the introduction, the second section referring to

related work, the third describing the developed sys-

tem, the fourth presenting and discussing the results

achieved, and the ﬁfth presenting the conclusions and

future work.

2 RELATED WORK

2.1 Expeditious Modelling of Virtual

Urban Environments

The modelling of virtual urban environments has

many different applications including virtual city

tours (Schilling and Coors, 2003), georeferenced ser-

vices (Ito et al., 2005), cultural heritage preservation

(Hildebrand et al., 2000) (Zach et al., 2001) and urban

planning. Often there is a need for realistic or semi-

realistic models of cities, however, modelling accu-

334

Cruz F., Coelho A. and Paulo Reis L. (2008).

AUTOMATIC PARAMETERIZATION FOR EXPEDITIOUS MODELLING OF VIRTUAL URBAN ENVIRONMENTS - A New Hybrid Metaheuristic.

In Proceedings of the Fifth International Conference on Informatics in Control, Automation and Robotics - ICSO, pages 334-337

DOI: 10.5220/0001495603340337

 SciTePress

rate realistic models grows problematic considering

increasing needs in size and complexity.

Using principles of l-system (Lindenmayer, 1968)

(Prusinkiewicz, 1986), it is possible to deﬁne sets of

production rules to model all kinds of urban environ-

ment elements (Parish and Muller, 2001) based on

limited georeferenced data (Muller et al., 2006). It’s

often difﬁcult to acquire reliable data of an entire city

we are trying to model, however it is relatively easy

to gather information from certain key-deﬁning sec-

tions of a city and assign the data to a georeferenced

database. The production rules with the data collected

will enable the creation of models resembling the area

of gathered information.

2.2 Meta Heuristic Algorithms for

Solving Optimization Problems

The ﬁeld of artiﬁcial intelligence branchesmany areas

(Russel and Norvig, 2003), one of the most relevant

ones is the ﬁeld of optimum search. Meta heuristic

algorithms play an important role in this ﬁeld. Dif-

ferent meta heuristic variants and hybrid versions re-

fer to evolutionary computation or nature inspired be-

haviors: genetic algorithms (Holland, 1992) (Gold-

berg, 2002), simulated annealing (Kirkpatrick et al.,

1983) (Aarts et al., 2005) and harmony search (Lee

and Geem, 2005) (Mahdavi et al., 2007).

The common principle is to ﬁnd the best combi-

nation of parameters of a given vector function such

that a related objective function is maximized or min-

imized. This process is iterated through educated ran-

dom guesses following the heuristic logic of the algo-

rithm. There is no best heuristic, performance varies

according to the constraints of problem. A big num-

ber of proposals for hybrid or customized adaptations

is found in recent literature (Deep and Thakur, 2007)

(Arumugama et al., 2005) (Kumar et al., 2007) (Lee

and Geem, 2005) (Mishra et al., 2005).

3 IMPLEMENTATION

3.1 Problem Statement

An l-systems based expeditious modeler for the gen-

eration of realistic urban environments becomes more

valuable with an optimum parameterization system.

The system must handle the input of boolean, in-

teger and real based parameters. The system must

allow a conﬁguration easily adaptable to the prob-

lem. When solving linear constrained problems the

system must out-perform simple random based algo-

rithms such as hill climber and random search. When

solving problems with multiple local maximums the

system is required to perform above par of classic

meta heuristic algorithms such as simulated anneal-

ing, genetic algorithm and harmony search.

3.2 Hybrid Optimizer Meta Heuristic

Algorithm

The hybrid meta heuristic is inspired by basic prin-

ciples of real based genetic algorithms and concepts

from simulated annealing and harmony search.

There are two families of populations resident in

memory at all times, the original parent family and

the top list family. Their dimensions can be conﬁg-

ured by XML. Each iteration step of the meta heuris-

tic algorithm consists on creating a new original par-

ent family generation. The top list family maintains

in memory the best solutions ever found so far, sorted

by quality.

Each solution stores values for all parameters be-

ing calibrated. Each parameter has information re-

garding its type (integer, boolean, real) and scope

(minimum and maximum values). The type and scope

for each parameter are pre-conﬁgured by XML. The

values for the ﬁrst generation of the original par-

ent family are calculated randomly within its scope

boundaries. The ﬁrst generation of the top list family

is obtained by sorting the ﬁrst generation of original

parent family. These values can also be loaded from

disk to test scenarios in same starting terms.

Each following original parent generation is ob-

tained by cross-breeding the original parent family

with a chosen member of the top list family. Ensur-

ing an elitist selection behavior inspired by genetic

engineering. Several threshold variables further in-

ﬂuence the selection of the new solution to ensure a

wider search space scope not limited to the ﬁrst gener-

ation. These variables incorporate monte carlo meth-

ods (Metropolis and Ulam, 1949) using probability

thresholds inspired by simulated annealing and har-

mony search. Some are, or can be, affected by what

is referred to as globalentropy, an internal value in-

creasing by each passing iteration as described in (1).

There are a total of ﬁve threshold parameters which

must be calibrated considering the problem.

Random New Struct Threshold (trns), affects the

probability of choosing a completely random new so-

lution. The higher this value the more probable it be-

comes to occur a total random creation of a new solu-

tion as seen in formula (3).

globalentropy = iterationstep/maxsteps (1)

trns = thresholdRandomNewStruct (2)

randSol = rand() ∗ globalentropy < trns (3)

AUTOMATIC PARAMETERIZATION FOR EXPEDITIOUS MODELLING OF VIRTUAL URBAN ENVIRONMENTS

- A New Hybrid Metaheuristic

335

Random New Type Threshold (trnt), affects the prob-

ability of choosing a completely random new value

for each of the solution parameter types. The higher

this value is the more probable it is to occur a totally

random new value for the current parameter type of

the solution as seen in formula (5).

trnt = thresholdRandomNewType (4)

randType = rand() ∗ globalentropy < trnt (5)

Toplist Dispersion Threshold (ttld), affects the prob-

ability of choosing lower ranking toplist parents to

cross the solution with. The higher this value the

wider the scope of choice as seen in formula (8).

ttld = thresholdToplistDispersion (6)

ttld > 1.0 : ttld = 1 − globalentropy (7)

victim = (rand() ∗ ttld ∗ maxFamilySize) (8)

Typevalue Dispersion Threshold (ttvd), affects the

parental gene inﬂuence for each value of the parame-

ter types of the solution as seen in formula (13).

tlv = topslistParentValue (9)

orv = originalParentValue (10)

ttvd = thresholdTypevalueDispersion (11)

ttvd > 1.0 : ttvd = 1− globalentropy (12)

newvalue = (ttvd ∗ orv) + ((1− ttvd) ∗tlv) (13)

Typevalue Entropy Threshold (ttve), affects the prob-

ability of scope jitter for each value of the parameter

types of the solutionas can be seen in formula (17).

ttve = thresholdTypevalueEntropy (14)

ttve > 1.0 : ttve = 1 − globalentropy (15)

scope = k(OParentValue− TLParentValue)k (16)

igl = (1.0F − globalentropy) (17)

ttvss = igl ∗ igl ∗ igl (18)

range = MaxParamValue− MinParamValue (19)

scope < ttvss∗ range : maxscope = range∗ igl (20)

scope > ttvss∗ range : maxscope = scope∗ ttve (21)

maxscope = scope∗ rand() (22)

newvalue = newvalue+ scope− (maxscope/2) (23)

4 RESULTS

A test-case was prepared involving the parameteriza-

tion of a set of production rules which would model

several buildings with certain height values missing.

The known information from all of the buildings in-

cluded georeferenced location and the values of the

buildings perimeter, area and bottomzvalue. The un-

known information from some of the buildings com-

prised solely the topzvalue.

The production rule used to estimate the unknown

topzvalue from the buildings is described mathemati-

cally in formula (27).

av = (cra − 1) ∗ fca∗ area (24)

ab = (crb− 1) ∗ fcb ∗ bottomzvalue (25)

ap = (crp− 1) ∗ f cp∗ perimeter (26)

topzvalue = avgz+ disp∗ (av+ ab+ ap) (27)

The formula implies a relation between the building’s

area (24), perimeter (26) and bottomzvalue (25) with

the building’s height to estimate a realistic topzvalue

for input to the expedite modeler.

Our formula has a total of 8 unknown ﬁelds to

be parametrized: avgz [100.0 .. 120.0], the average

height for all the buildings. disp [0.0 .. 1.0], the dis-

persion rate from the average height. cra [0 .. 3], area

correlation. crb [0 .. 3], bottomzvalue correlation. crp

[0 .. 3], perimeter correlation. fra [0.0 .. 1.0], the area

value correlation factor. frb [0.0 .. 1.0], the bottomz-

value correlation factor. frp [0.0 .. 1.0], the factor of

the perimeter correlation.

Different conﬁgurations of the meta heuristic al-

gorithm were tested with a ﬁxed toplist family size of

20. The different tested conﬁgurations include the be-

haviorof some classic algorithms: random search, hill

climber and simulated annealing. A few additional

conﬁgurations were also tested for comparative per-

formance results. Each test iterated 50 generations

with a family size of 8 and were labeled as follows:

h1r8, hybrid random search. h1n8, hybrid new con-

ﬁguration. h2n8, hybrid second new conﬁguration.

h3n8, hybrid third new conﬁguration. hhc8, hybrid

hill climber. hsa8, hybrid simulated annealing.

The calibration parameters of each conﬁguration

tested can be consulted in Table 1.

Table 1: Threshold parameters of the different conﬁgura-

tions.

conﬁg trns trnt ttld ttvd ttve

h1r8 1.0 1.0 0.0 0.5 0.5

h1n8 0.01 0.01 0.1 1.1 1.1

h2n8 0.001 0.001 0.4 0.15 1.1

h3n8 0.001 0.001 0.1 0.1 1.1

hhc8 0.01 0.01 0.0 1.0 0.1

hsa8 0.01 0.01 0.0 1.0 1.1

The quality function for the test case is calculated as

a weighted sum of the height from the involved build-

ings. All simulations were performed three times to

present some insight on how deeply the performance

of the meta heuristics algorithm stochastic nature is

ICINCO 2008 - International Conference on Informatics in Control, Automation and Robotics

336

affected. Table 2 displays the progressive results ob-

tained from our test case. It shows the quality value

of the best solution found at 2%, 40%, 80% and at the

end of the iteration process and allow us to speculate

on how each conﬁguration depend on the initial state

and perform comparatively to known random search,

hillclimber and simulated annealing algorithms.

Table 2: Progressive solution quality results from the differ-

ent conﬁgurations.

conﬁg 2% 40% 80% ﬁnal

h1r8-1 163.95 54.254 44.854 44.854

h1r8-2 373.90 98.338 14.557 14.557

h1n8-1 272.53 9.319 9.319 9.319

h1n8-2 29.479 10.910 8.972 8.972

h2n8-1 438.53 24.047 14.425 14.425

h2n8-2 1038.61 1.758 1.758 1.758

h3n8-1 22.164 6.418 0.175 0.175

h3n8-2 288.56 3.934 0.798 0.798

hhc8-1 117.35 47.728 47.728 32.145

hhc8-2 1069.77 427.75 232.77 104.08

hsa8-1 1207.92 75.354 40.354 40.354

hsa8-2 315.95 137.05 42.689 9.804

5 CONCLUSIONS AND FUTURE

WORK

An automatic parameterization system for expedi-

tious modelling of virtual urban environments has

been developed with a successful ﬁeld application.

Our test case, despite its relatively low complexity

and linear constraints, demonstrates the potential of

our new hybrid meta heuristic algorithm in ﬁnding

optimum parameters for rule sets of expeditious mod-

elling competitively to common optimum search al-

gorithms. Further test results are required to statis-

tically compare the performance of the new hybrid

meta heuristic algorithm with other meta heuristic al-

gorithms and parameter optimization problems.

An envisioned improvement to the system in-

volves applying principles of nested partition and lin-

ear regression to strengthen performance.

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- A New Hybrid Metaheuristic

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