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Application of RFID tracking to the optimization of function-space

assignment in buildings

Ren-Jye Dzeng

a,

, Chong-Wey Lin

b

, Fan-Yi Hsiao

c

a

Department of Civil Engineering, National Chiao Tung University, 1001, University Road, Hsinchu, Taiwan, ROC

bDepartment of Commutation and Technology, National Chiao Tung University, Taiwan, ROC c

Department of Civil Engineering, National Chiao Tung University, Taiwan, ROC

a b s t r a c t

a r t i c l e i n f o

Article history:

Accepted 28 December 2013 Available online 4 February 2014 Keywords: RFID Optimization Function–space assignment fmGA Genetic algorithm

Function–space assignment, which allocates a function for each space in a facility, is one of the most important factors in determining the usability performance of a building. Most architects renovate a building based on their personal perception of how the occupants might use the building instead of quantitatively analyzing their use behaviors. This study developed a function–space assignment optimization model based on the occu-pants' movement data as tracked by RFID technology. The model mines the movement data by constructing pat-terns and calculating the relation values between functions. The search for the best assignment is based on the fast messy genetic algorithm (fmGA) with the objective function incorporating the preference of space size and the minimization of the distance for movement required by the occupants during the performance of their daily activities. The proposed model incorporated building-blockfiltering mechanism in the fmGA problem-solving process to generate enough copies of the good building blocks so more copies would remain for subse-quent processing. The paper also describes two experiments that evaluate the performance of the model and compare the performances of the models with and without the building-blockfiltering mechanism.

© 2014 Elsevier B.V. All rights reserved.

1. Introduction

Function–space assignment, which allocates a function to each space in a facility, is one of the most important factors in determining the us-ability performance of a building. For example, in an educational build-ing, the layout of classrooms, the administration office, laboratories, etc., affects how occupants move and the distances required to fulfill their activities in the facility. Kalay[1]noted that function assignment only works in very limited areas of architectural design, primarily due to the lack of quantifiable data. Instead of relying on the facility administrator's trial and error tofind the optimum layout, mathematic optimization algorithms that have been applied in the layout of hospi-tals, factory assembly lines, and construction sites become feasible once quantifiable data about occupants' movements are available.

To collect quantitative data about occupants' movement, instead of relying on subjective experience or opinions, one may actually monitor the occupants' movement manually or by using currently available monitoring technologies, such as surveillance cameras and positioning technologies via radio frequency identification (RFID), wireless fidelity (Wi-Fi), etc. These positioning technologies have become more accurate and affordable in recent years and also have a variety of applications, as reviewed in the following section.

When quantitative data about occupants' movement behaviors are available, the layout may be optimized for certain specific objectives, such as the minimization of movement distances or preferred space size. In architecture, optimization techniques have been used primarily for solving problems of site layout, facility layout, structural design, and building performance[2–5]. Facility layout optimization involves find-ing feasible topology and the dimensions of interrelated objects that meet all of the design requirements and maximizing design preferences

[6]. Previous research has developed several formulations for the opti-mization of facility layout problem. For discrete formulations, the quadratic assignment problem (QAP)[7]is the most commonly en-countered in the literature.

The QAP is one of the most difficult problems in the NP-hard class. Exact approaches are generally unable to solve problems of size larger than n = 15[9]. Because exact solutions require large expenditures of time and money, it may not be worthwhile to search for the optimum solutions except in rare circumstances[10]. For this reason, several heu-ristics and meta-heuheu-ristics approaches have been developed to search sub-optimal solutions within a reasonable time limit.

There are two types of heuristic approaches, construction methods and improvement methods. Construction methods generate sub-optimal permutations from scratch by assigning functions to spaces one by one based on prioritized criteria. Examples are CORELAP[11], ALDEP[12], COFAD[13] and SHAPE [14]. Instead of starting from scratch, improvement methods begin with a feasible solution and try to systematically improve it by searching for other nearby solutions. ⁎ Corresponding author. Tel.: +886 916005996.

E-mail addresses:rjdzeng@mail.nctu.edu.tw(R.-J. Dzeng),cwlin@mail.nctu.edu.tw

(C.-W. Lin),minlove.xiao@gmail.com(F.-Y. Hsiao).

0926-5805/$– see front matter © 2014 Elsevier B.V. All rights reserved.

http://dx.doi.org/10.1016/j.autcon.2013.12.011

Contents lists available atScienceDirect

Automation in Construction

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / a u t c o n

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The process is continued until no improvement can be found. Examples of this method are CRAFT[15], FRAT[16]and DISCON[17].

Before the end of the 1980s, most of the proposed heuristic ap-proaches for combinatorial optimization problems were specific and dedicated to a given problem. Since that time, this paradigm has changed. More general methods have appeared, known as meta-heuristics[18]. Several of these methods are based on some type of sim-ulation of a natural process studied within anotherfield of knowledge. Recently, numerous researchers have developed meta-heuristics ap-proaches for the QAP. Solimanpur[19]developed an ant algorithm for a sequence-dependent single row machine layout problem. Yeh[8]

adopted annealed neural networks and Hopfield neural networks to solve preferences in a hospital building layout problem. Liang[20] de-veloped the multi-searching technique of tabu algorithms to improve facilities layout performance through several previous examples, including a pre-cast yard, construction site and hospital. Cheung[21]

developed the swap method of simple genetic algorithms to determine the least cost arrangement for a pre-cast yard layout. Jang[22]also employed simple genetic algorithms to optimize the layout of multi-floor construction material.

The simple genetic algorithm (sGA) is one of the meta-heuristic ap-proaches. First developed by Holland[23]in 1975, sGA is an efficient and commonly used algorithm[21,22,24,25]. Goldberg et al.[26] subse-quently developed the messy genetic algorithm (mGA) in 1989 to im-prove the sGA. Several experiments have im-proven that the mGA is much better at solving permutation problems than the sGA. In 1993, Goldberg[27]developed the fast messy genetic algorithm (fmGA) to re-duce the high memory consumption of operation processes. Over the years, mGA and fmGA have been used successfully in water distribution system design[28], the dispatching of ready mixed concrete trucks[29], the design of fuzzy control systems[30], solutions for clustering prob-lems[31], and learning classifier systems[32–35]. Because of its advan-tages, we used fmGA to search for the optimal solution in this research. The presented research aims to optimize function–space assignment by sensing the occupants' movement data. The proposed modelfirst tracks occupants' movements in a multi-floor building and then de-velops a systematic method which can analyze these movement data and optimize function assignment for the building. In addition, the fmGA is employed tofind the best assignment or improve the assign-ment according to the desired objectives, such as preferred space size and minimized movement distance. Finally, an experiment with a real case was conducted to evaluate the performance of the proposed model.

2. Location tracking technology

With the increasing use of location-based services (LBS) in mobile communication, GPS appears to be the most popular solution for out-door location systems. However, for inout-door location applications, other technologies are more common than GPS because of the limita-tion caused by indoor barriers that block satellite signals. Examples of other technologies for indoor applications are Wi-Fi based systems

[36], infrared systems[37], ultrasound[38], scene analysis[39], and radio frequency identification[40].

Based on Tesoriero et al.[41]and Li and Becerik-Gerber[40], the following section summarizes the strengths and weaknesses of these technologies. The Wi-Fi-based system uses existing IEEE 802.11 infra-structure and shows advantages in the cost of deployment. However, the performance of the Wi-Fi based system decreases in multi-floor or densely partitioned indoor environments because the signal reflections and dynamic network conditions may affect signal readings. The infra-red system has the advantages of low power consumption, low cost and compact size. Nevertheless, the infrared system is sensitive to sun-light so it is not suitable for non-enclosed spaces. Ultrasound technology is inexpensive, easy to install, and suitable for precise measurements. However, the installation and maintenance costs are comparatively high because of the requirement for dense deployment. The scene

analysis technique analyzes images of multi-cameras that monitor tar-get areas and is precise at room level but is high cost. RFID technology has the advantages of durability, rich data capacity, repetitive read/ write capabilities, and non-contact features[40,42]. However, active RFID tags usually require periodic battery replacement for approximate-ly every 5–10 years[43].

Our research required a location technology that is able to track oc-cupants' movement between multiple partitioned indoor spaces in a multi-floor building using corridors that can be exposed to sunlight. Thus, the Wi-Fi, infrared, ultrasound, and scene analysis technologies are not suitable. As Lionel et al. noted[44], the active RFID system for in-door location sensing is a viable and economical option; therefore, we chose RFID for our location technology.

RFID technology is a wireless sensor technology based on electro-magnetic signal detection[45]. As shown inFig. 1, a typical RFID system consists of two main components, a reader and a tag, and operates at a certain frequency. The tag, containing a microchip and an internal an-tenna, is attached to the object to be tracked. Each tag, with a unique ID, can store the object-related data, and send the data to a reader upon its request. A reader, containing a transceiver and an external an-tenna, reads/writes data from/to a tag via radio frequency and transfers data to a host computer for later retrieval and analysis.

While RFID technology has already seen significant beneficial appli-cations in manufacturing, retail, transport and logistics industries over the years, its potential applications in the construction industry have only begun to be explored. However, RFID technology is not completely new to the construction industry. Jaselskis et al.[46]envisaged its pos-sible applications in construction, including concrete processing and handling, cost coding for labor and equipment, and materials control. Recently, more RFID-related applications in the construction industry have become available. For example, by combining radio and ultrasound signals, Jang and Skibniewski[47]developed an embedded system for tracking construction materials and equipment. Goodrum et al.[48] ex-plored the applications of RFID for tool tracking on construction job sites. Dziadak et al.[49]developed a model for the 3D location of buried assets based on RFID technology. Domdouzis et al.[50]explored the ap-plications of RFID in the construction industry for the automated track-ing of pipe spools and valued items and in an on-site inspection support system. Tzeng et al.[51]explored the verification tests of interior decorating materials combining RFID system recognition. Wang[52]

explored how to improve construction quality inspection and manage-ment via RFID technology. To assist logistics and progress managemanage-ment, Chin et al.[53]combined RFID with 4D CAD to develop an information system. Yin et al.[54]developed a pre-cast production management system utilizing RFID technology. Li et al.[55]proposed an RFID-based location-sensing algorithm to perform a study on evaluation of indoor location sensing using RFID tags. In summary, all of the related research has tracked objects, and none have focused on the tracking of human movement to facilitate the functional layout of a building.

3. Research problem

Taking a real renovation project of an educational facility as an ex-ample, an existing public building with multi-floors requires renova-tion, and the owner and the architect plan to adjust the functions of the spaces in the building during renovation based on their usage expe-rience in order to accommodate the usability problems. The function provided by a space isfixed once the function–space assignment is final-ized. There are several types of occupants, and they move around the spaces in the building based on the activities which they have been for-mally assigned or in which they are personally interested. Some activi-ties occur periodically and some do not. Some activiactivi-ties require an occupant to participate at specific times, and some allow them to partic-ipate at will and at their preferred times. Each occupant has an identi fi-cation object so that their individual movement can be detected. The objective of the adjustment of space functionality is to minimize the

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total occupants' movement distance and tofind the best assignment based on preferred space size.

4. The proposed model

The proposed model consists of 3 modules, namely movement tracking and positioning, occupants' movement analysis, and optimiza-tion as illustrated inFig. 2. The three modules are described as follows.

4.1. Movement tracking and positioning

For tracking the occupants' movements, we used an active RFID po-sitioning approach, and the movement tracking devices included readers, tags, and gateways. As shown inFigs. 1 and 2, a reader was installed at each tracked space, and occupants carrying RFID-tagged ID cards were detected once they moved in and out of the space. The gate-way was responsible for acquiring the terminal data from the readers.

The number of required gateways, usually operating at 2.4 GHz, depended on the accessibility of the wireless signals. Based on our field test, we followed certain guidelines to determine the installation location of each reader. A reader was installed in each space we intended to monitor. We determined that the most suitable place to in-stall a reader was far from neighboring aisles and close to open windows on the same side as the associated gateway. Placing the reader far from neighboring aisles reduced the RSSI reading of tags merely passing through those aisles, allowing us to distinguish them from the tags that actually entered the monitored space.

The manufacturer's proprietary algorithm was used for detecting the RSSI of each tag to determine each tag's position. As shown inFig. 3, tags were detected by readers installed at various positions, and readers were configured to send tag position data to the server, through the gateways, every 5 s. Because a tag could be detected by multiple readers, each tag's associated reader was identified according to the reader that had the highest RSSI for that tag; the tag was then assumed

Sever

Tag

Tag

Reader

Reader

ZigBee

2F

Reader

Tag

Tag

Tag

Reader

Reader

ZigBee

Reader

Gatway

1F

3F

4F

Gatway

RJ-45 Network

Fig. 1. Tracking occupants' movement by the RFID technology.

Occupants' movement analysis Movement patterns determination Pattern decomposition Pattern counting Conditional probability transforming Movement relation of functions x and y (Rfifj)

Optimal function assignment

Function-space assignment optimization

Objective function Algorithm setting Functional assignment constraints

Reference data

Distance between spaces si and sj (Dsisj) Suitability preference

of function fi assigned to space si (Pfisi)

fmGA algorithm

Building floor plan

Movement tracking and positioning Occupants'movement database Sever Data screening Association determination Data merging

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6-1. Record the tag to be present in the

corresponding space

If the tag is associated

with a reader at least once

for each minute

8. Remove noises

(i.e., passing instead of using a space)

2. Determine the reader that has the

highest RSSI

3. Record the time and space for the tag

Tag i, i=1, 2,

, n

5. Reduce the data from every five

seconds to every minute

6-2. Record the tag to

be absent in the

corresponding space

9. Determine the entering and leaving

times for each tag with each space

Sever

Association determination

Data merging

RJ-45 Network

1. Readers detect tags at

various spaces and send

data to the server

Gatway

Gatway

Reader

Reader

Reader

Gatway

Z

igBee

ZigBee

4. Correct data for signal instability

Data screening

7. Eliminate data outside of the

tracking time range

No

Yes

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to be in that reader's space at the detected time. The server collected data on the tag and its associated space at 5-second intervals. Our pur-pose was to determine whether a tag was inside a particular space. We did not need to estimate the precise location of the tag according to the RSSI strengths from the three readers.

In the data merging, to accommodate the instability of signal, the tag would be determined to be present in the corresponding space during a particular minute if the tag was associated with a reader at least once during that minute (i.e., 1 out of 12 times). In the data screening, the server eliminated data outside of the tracking time range and only kept the data obtained within 8:00 AM and 10:00 PM on weekdays. And the data was furthered merged to determine the entering and leav-ing times of a tag for the associated space accordleav-ing to the minimum stay time specified by the user. In this step, the server removed noisy data such as in the situations where an occupant entered a space and left from it right away, or an occupant stood outside of but adjacent to a space instead of being actually inside the space. The minimum stay time required to be considered as using the space was set to 1 min for the library and administration office and 5 min for the rest of the func-tions. Thus, a tagged student who entered the administration office to retrieve mail and left after 2 min was considered to have used the office once. A student who entered a classroom to collect some textbooks he forgot during a previous lecture and left the classroom after 2 min was not considered to have used the classroom.

4.2. Occupants' movement analysis

The analysis of occupants' movement involves four steps, i.e., move-ment pattern determination, pattern decomposition, pattern counting, and conditional probability transforming, as shown inFig. 4. Movement pattern determination data mined an occupant's movement pattern be-tween spaces on each day. One can set up a threshold of maximum break time for a movement between two spaces to be considered as part of a pattern. For example, one may set the maximum break time to be 30 min. Thus, if the time interval of the detections of a tag at two differ-ent spaces is smaller than 30 min, the corresponding occupant's move-ment between the two spaces will be considered as a movemove-ment pattern; otherwise, the uses of two spaces will be considered as inde-pendent usages.

Pattern decomposition breaks down the daily movement pattern of an occupant into pairs of spaces for later counting purposes. For exam-ple, as shown in the movement pattern table inFig. 3, Tag 120 has used space a, a, b, c, c, and d on March 1st of 2011. The breakdown results in pairs of aa, ab, bc, cc, and cd.

Pattern counting counts the occurrence of each pair of spaces in the breakdown result of the previous step in preparation for constructing

the interactive preference table. As shown in the pattern counting table ofFig. 3, each number represents the number of occurrences of the corresponding pair (from a column space to a row space). For exam-ple, the use pattern aa (the use of space a following space a) occurs 4 times, ab occurs 1 time, and so on.

The fourth step is to calculate the conditional probability of a row space given a column space, as shown in the movement relation table ofFig. 4. For example, the likelihood of using spaces b, c, and d after using space c is 1/5 (0.2), 3/5 (0.6), and 1/5 (0.2), respectively.

4.3. Function–space assignment

The optimization module maximizes the objective function under defined constraints by finding the best assignment of functions to spaces. The objective function used in this research was based on the concept proposed by Koopmans and Beckman[7], which was previous-ly applied by Jo and Gero[56]in assigning functions to spaces of equal size in an office building. Yeh[8]modified the objective function to en-able the assignment of functions to spaces with different sizes in a hos-pital. We used the objective function proposed by Yeh[8]but with two primary differences. First, the objective function of this research was based on the interactive preference derived from the tracking of real oc-cupants' movements instead of subjective judgments. Secondly, while Yeh[8]optimized the objective function using an annealed neural net-work, this research used a newly developed algorithm called the fast messy genetic algorithm.

Eq.(1)is the objective function, which is a weighted average of two parts. First, (Xfisi× Pfisi) represents the assessment of the suit-ability of a function assigned to a space. For example, a classroom assigned to a large space is more suitable than to a small space. Sec-ondly, (Xfisi× Xfjsj× Dsisj× Rfifj) represents the assessment of a func-tion assigned to a space from the perspective of the moving distance (Xfisi× Dsisj) based on the movement relation (Xfjsj× Rfifj). For exam-ple, strong related functions assigned to neighboring spaces may have a higher assessment value than that to spaces at a distance.

Table 1is an example of Xfisi, where 5 functions (f1to f5) are to be assigned to 5 spaces (s1to s5). Xfisiindicates that f1is assigned to s1, f2to s3, f3to s2, f4to s5, and f5to s4. Max O¼ W1 X fi X si Xfisi Pfisi n ! þW2 X fi X si X fj X sj Xfisi Xfjsj Dsisj Rfifj n ! ð1Þ

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Subjected to

Xfjsi¼ 0 if Xfisi¼ 1 and fj≠fi; Xfisj¼ 0 if Xfisi¼ 1 and sj≠si: where O: objective function;

Xfisi: permutation matrix variable (i.e., the value is 1 if function fiis assigned to space si, and is 0 if not assigned to si);

Pfisi: suitability preference of function fiassigned to space si(e.g., the library function prefers large spaces, the value for the library function assigned to large, medium, and small spaces were 1, 0, and 0, respectively.);

Dsisj: distance between spaces siand sj;

Rfifj: movement relation of functions fiand fj(i.e., the value is between 0 and 1, where 0 represents no sequential movement pattern exists between functions fiand fj, and 1 represents the use of fi always followed by the use of fj);

n: total number of functions;

W1: the assessment weight of the suitability of a function assigned to a space (the weight between 0 and 1).

W2: the assessment of a function assigned to a space from the per-spective of the moving distance (the weight between 0 and 1).

5. fmGA for function assignment optimization

The fmGA can efficiently find optimal solutions for large-scale per-mutation problems. There are three distinct features that differentiate the fmGA from the sGA[29,35]: (1) chromosomes of variable length can be adopted in fmGA; (2) the optimization process contains both a primordial and a juxtapositional stage; and (3) competitive templates are adopted to retain the most outstanding gene building blocks in each generation. Because of the large number of functions and spaces usually involved in a building, the fmGA representation was used.

5.1. Problem-solving process

The function–space assignment is optimized using fmGA using the processflow shown inFig. 5. The required input data include the suit-ability preference of function fiassigned to space si(Pfisi), distance be-tween spaces siand sj(Dsisj), the movement relation of functions fiand fj(Rfifj), and fmGA parameters. The process consists of 4 primary steps described as follows.

5.1.1. Step 1 Randomly generate a competitive template

Thefirst step is to randomly generate a competitive template, which is a problem-specific, fixed-bit string that is randomly generated or found during the search process[27]. The competitive template is used to make up for the missing genes in the latter process when chro-mosomes are under-specified.

The fmGA process consists of inner and outer loops. Each inner loop is called an era and each outer loop is called an epoch. Thus, the execu-tion of the maximum number of eras defined by era_max completes an epoch. The execution of the maximum number of epochs defined by epoch_max terminates the fmGA evolution process.

The inner loop consists of three phases[27]: (1) the initialization phase—a population with sufficient chromosomes is created to contain all possible building blocks (BBs) of the order k, where BBs refer to par-tial solutions of a problem; (2) the primordial phase—bad genes are fil-tered out to maintain only the chromosomes with goodfitness; and (3) the juxtaposition phase—those good alleles (BBs) are rebuilt by cut-splice and mutation operations to form a high quality generation, which tends to generate an optimal solution.

5.1.2. Step 2 Initialization phase

To ensure a sufficient quantity of chromosomes, the population size of each era is determined by Eq.(2), as suggested by Goldberg[27]. In addition, n chromosomes are randomly generated in this phase, so the fitness of each chromosome is evaluated based on the objective func-tion, defined by Eq.(1).

n¼ l λ   l−k λ−k   2c αð Þβ2 m−1 ð Þ2k ð2Þ where

l: the problem length; k: the order of BBs;

λ: a random value, generally set to be l − k, kbλ ≤ l;

c(α): the square of a normal random deviate corresponding to a tail-probabilityα;

β: the signal-to-noise ratio which is the ratio of the fitness deviation to the difference between two competing BBs (i.e., the ratio of a chromosome with the optimumfitness (O) to those with the second bestfitness (O′)in the same era, β = O/O′);

m: BBs coefficient. 5.1.3. Step 3 Primordial phase

There are two operations in the primordial phase, namely building-blockfiltering and threshold selection. Building-block filtering includes block selection and random gene deletion. The key to building-blockfiltering is to pump up enough copies of the good building blocks so that even after random deletion eliminates a number of copies, there remain one or more copies for subsequent processing[57].

According to Goldberg et al.[58], having enough good building blocks provides more good chromosomes for subsequent processing. Thus, they used a generic threshold mechanism, where the selection between two strings was only permitted if they shared a greater than expected num-ber of genes in common, which restricts the competition between build-ing blocks with little in common. However, the threshold was not needed in our case because all of the chromosomes share the same set of genes (i.e., the same set of functions are assigned to a set of genes).

5.1.4. Step 4 Juxtaposition phase

The purpose of the juxtaposition phase is to change chromosomes, and it includes the cut-splice and mutation operations. The cut-splice operator, similar to the crossover operator in the sGA, is used to recom-bine different strings to create new strings[29]. Atfirst the cut-splice operation is applied to a predetermined probability (i.e., cut and splice probability Pc, Ps) of the chromosomes. After performing the cut-splice operation, thefitness value of a chromosome may be higher or lower than (or equal to) that of the competitive template in the previous era. The mutation is applied to a predetermined probability (i.e., muta-tion rate Pm) of the chromosomes with lower (or equal)fitness values because they are less competitive solutions and vice versa.

The newly generated and existing chromosomes are stored in a pool, representing the population of the era. The best chromosome with the highestfitness value will be selected and replaces the competitive tem-plate if itsfitness is higher. In addition, a predetermined proportion of Table 1

Permutation matrix withfive functions.

Xfisi Space s1 s2 s3 s4 s5 Function f1 1 0 0 0 0 f2 0 0 1 0 0 f3 0 1 0 0 0 f4 0 0 0 0 1 f5 0 0 0 1 0

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the best population is kept and carried to the next era. Steps 2 to 4 are it-erated for a predetermined number of times, which completes an epoch. Such a process is iterated until thefitness value of the best chromosome converges or the predetermined maximum number of epochs is reached.

5.2. Problems with over-/under-specifications

In the fmGA, a chromosome is composed of two pairs of genes, i.e., an allele locus and an allele value.Fig. 6shows a chromosome example C0, in which each allele locus represents a space while an allele value represents a function assigned to the corresponding space. The length

of the chromosome determines the number of spaces to which func-tions are assigned. Thus, the example represents a problem of assigning five functions to five spaces, e.g., functions f3to space s1and f4to s2.

Because the messy chromosomes may have various lengths after the cut-splice process, they may be“over-specified” or “under-specified”.

Fig. 7shows an example that illustrates this problem. Before the cut, both chromosomes C1and C2 are valid strings, where each space is assigned to a unique function. After cutting and splicing, the two chro-mosomes switch the genes on the right-hand side of the randomly se-lected cut point. The switch results in over-specified chromosomes, e.g., space s2is assigned to functions f3and f4in C1′, and s4is assigned to f2and f4in C2′. It also results in under-specified chromosomes, e.g., no functions are assigned to s4in C1′ and s1in C2′.

The use of an integer in this research instead of a binary value for genes complicates the over- and under-specified problems. Fig. 8

shows the proposed process to solve the over- and under-specified problems existing in C1′. To fix the over-specified chromosome, the string is scanned from left to right with thefirst-come first-serve rule. In Step 1, genes (2 4) and (1 5) are removed from C1′ because functions for spaces s1and s2are already assigned in genes (1 2) and (2 3). Step 2

End

Start

1. Randomly generate

competitive template (CT)

No

Yes

epoch=

epoch+1

era=1

Randomly generate

n chromosomes of length l

Evaluate fitness function

2. Initialization phase

era=

era+1

Inner loop:

era

era_max

Outer loop:

epoch

epoch_max

Select optimal chromosome

to replace old CT

Evaluate fitness function

3.Primordial phase

4. Juxtaposition phase

Building block filtering

Pool

Reserve a predetermined proportion

of chromosomes with the best fitness

Yes

Non-mutation

Cut and spice

Evaluate fitness function

Mutation

Input data

(1) P

fisi

(suitability preference)

(2) D

sisj

(space distance)

(3) R

fifj

(movement relation)

(4) fmGA parameters

Output data

Optimal function-space

assignment

No

Fig. 5. Problem-solving process for function–space assignment optimization.

1 2 3 4 5 3 4 5 1 2 Chromosome C0:

(1 3) (2 4) (3 5) (4 1) (5 2)

Allele locus : Allele value : s1 f3 s2 f4 s3f5 s4 f1 s5 f2

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fills the removed genes with the genes at the corresponding spaces in the competitive template. However, although C1′ now has all of its spaces specified, the filling results in over- and under-specified func-tions. Step 3 removes the functions of genes (3 3) and (5 2) because functions 3 and 2 have already been assigned to space s2and s1. Step 4 filters out the genes with functions already specified in C1′ (i.e., (1 3), (4 1), and (5 2)) after the removal, assigns the leftover functions to the unspecified spaces in C1′ from left to right.

6. Case and experiment

We conducted an experiment based on a real case to prove the re-search concept and to evaluate the performance of the proposed sys-tem. The following sectionsfirst give a case overview, the RFID field test, the variables of function–space assignment, and then present the result of function–space assignment, followed by the comparison of fmGA performance with and without building-block selection.

Chromosome C2:

(5 1) (4 2) (3 3) (2 4) (1 5)

Chromosome C1:

(1 2) (2 3) (3 5) (4 4) (5 2)

Cut point

(3 3) (2 4) (1 5)

(3 5) (4 4) (5 2)

(a)

Before cut

(b)

After cut and spice

Chromosome C1' :

(1 2) (2 3)

Chromosome C2' :

(5 1) (4 2)

Fig. 7. Cut-splice process.

2 3 3 3 4 5 1 2 Functions Competitive template (1 2) (2 3) (3 3) (2 4) (1 5) Chromosome C1' : 2 3 1 (1 2) (2 3) (3 3) (4 1) (5 2) 2 3 4 1 5 (1 2) (2 3) (3 4) (4 1) (5 5) 2 3 3 1 2 (1 2) (2 3) (3 3) (4 1) (5 2) (1 3) (2 4) (3 5) (4 1) (5 2) Functions

Step 1 Step 2 Step 3 Step 4

Fig. 8. Evaluation of over-specified and under-specified chromosomes.

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6.1. Case

The case used in this experiment is the building of the Civil Engineer-ing Department of National Chiao Tung University in Hsinchu, Taiwan. The building is a 4-story courtyard building with a totalfloor area of 6616 m2, as shown inFig. 9. There are 3 main entrances on the ground floor and two staircases. The spaces of the building include a garden, a library, an auditorium, an administration office, classrooms, laborato-ries, meeting rooms, seminar rooms, faculty offices, mechanical rooms, and storage rooms. The building was renovated by an architect in 2010. Limited by the availability of RFID readers, we only tracked 10 key spaces (numbered from s1to s10), consisting of an administration office, a library, a seminar room, 2 laboratories, 2 meeting rooms, and 3 class-rooms, which were situated separately on the 4floors of the building. There were 98 students (23% of the total number of college and gradu-ate students) participating in this experiment. Each of them carried a Helicomm IP-Link 5110 active RFID tag while performing their daily activities in the building for 8 weeks during the middle and end of a se-mester in 2011. Although the movement was tracked 24 h a day during the experiment period, only the data obtained within 8:00 AM and 10:00 PM on weekdays (Monday to Friday) were used. The 10 tracked spaces were equipped with Helicomm IP-Link 2220 readers, and the data were transmitted wirelessly through two IP-Link 2220E gateways. The collected data were sent to another gateway, connected to the intra-net intra-network through RJ-45, to a computer server. The wireless intra-network operated on a 2.4-GHz global ISM (Industrial Scientific Medical) band. The maximum transmit range is 100 m for the tag, 400 m for the reader, and 1200 m for the gateway. In addition, the maximum data rate is 250 kbps for the reader, tag, and gateway.

6.2. Field test for RFID devices

To evaluate about the spatial location tracking of each tag pro-posed in this research, we conducted afield test to assess the data collection accuracy of this RFID device layout. Thefield test consisted of two experiments. Field Test I tested the ability of the readers to de-tect tags in spaces under various obstructive conditions. Field Test II tested the ability of the readers to detect tags carried by participants in different ways, some of whom also carried various amounts of metal. As shown inFig. 10, thefield test devices contained 50 tags, 10 readers, 3 gateways, and 1 server. The experimental results are shown as follows.

6.2.1. Field TestΙ

The location of the readers is crucial to ensuring the signal transmis-sion accuracy of active RFID devices. In active RFID, wireless communi-cation is used to collect data; signal transmission accuracy is therefore easily affected by various obstructive conditions. Thefield test was de-signed to test the performance of the readers in spaces obstructed by various obstacles, including walls, crowds, and chalk dust.Table 2 pre-sents the spaces under various obstructive conditions where the 10 readers were placed. Reader 4 was placed in space s4, where it was obstructed by crowds; Reader 6 was placed in space s6, where it was obstructed by walls, crowds, and chalk dust; Reader 7 was placed in space s7, where it was obstructed by chalk dust; and Reader 9 was placed in space s9, where it was obstructed by walls. The remaining readers (1, 2, 3, 5, 8, and 10) were located in unobstructed spaces s1, s2, s3, s5, s8, and s10,respectively. Each of the 50 participants in Field TestΙ carried a handheld tag and entered each of the 10 spaces

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sequentially (Fig. 11, s1to s10), remaining in each space for 5 min, 3 times total. In addition, the space of each reader had an antennafixed in the appropriate direction during thefield test.

Table 2presents thefield test results for the readers in spaces under various obstructive conditions. Readers 1, 2, 3, 5, 8, and 10, which were located in unobstructed spaces, exhibited read rates of up to 99.9%. Table 2

Results of Field Test I for readers in spaces under various obstructive conditions.

Reader no. Installationspace Obstruction Mean read rate (%) Variance of read rate (%)

Walls Crowd Chalk dust

1 s1 99.9 0.18 2 s2 100.0 0.00 3 s3 99.9 0.18 4 s4 ● 99.6 0.41 5 s5 100.0 0.00 6 s6 ● ● ● 97.1 0.63 7 s7 ● 100.0 0.00 8 s8 100.0 0.00 9 s9 ● 97.5 0.91 10 s10 100.0 0.00

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Readers 6 and 9 exhibited approximately 2% ~ 3% lower read rates than the readers in unobstructed spaces did. Readers 6 and 9 were located in spaces partially blocked by walls, which affected the signal transmission between the gateways and these readers. The read rate of Reader 4 was approximately 0.3% lower than that of readers in unobstructed condi-tions. Readers 4 and 6 were both located in crowded spaces (Reader 4 was placed in a medium-sized classroom surrounded by other class-rooms; Reader 6 was placed in a large classroom near a large auditori-um). Compared with readers in unobstructed spaces, Reader 7 was placed in a space where it was obstructed by chalk dust, and its read rate was not apparently affected.

6.2.2. Field TestΠ

Field Test II was conducted to determine the ability of readers to de-tect tags carried by participants in different ways, some of whom carried various amounts of metal; the results of this test are presented in

Table 3. The participants carried the active RFID tags in two ways: “naked” and “enclosed.” The naked tags were either held in the participant's hand or hung around the neck; the enclosed tags were placed in the participant's front pocket, back pocket, or backpack. To measure the effect of metal, certain participants who carried tags also carried various amounts of metal objects, such as keys. Certain partici-pants carrying tags in pockets or backpacks carried low amounts of metal (i.e., two bunches of keys), whereas only participants with back-packs carried middle amounts of metal (i.e., 14-inch laptop) and high amounts of metal (i.e., 2.5-kg dumbbells). To control for the effect of metal, some participants did not carry any metal objects. The tags (naked or enclosed) and amounts of metal carried by each of the 50 par-ticipants in Field Test II are listed inTable 3. The participants walked into the 10 spaces sequentially (Fig. 11, s1to s10) and remained in each space for 5 min, 3 times in total. Each reader was equipped with an antenna fixed in the appropriate direction during the test.

As shown inTable 3, the read rates for tags carried in backpacks were lower than those for tags carried in other ways (i.e., held in the hand, hung around the neck, in the front pocket, and in the back pocket). The read rates for tags carried in backpacks with no metal (Type I), low amounts of metal (Type J), middle amounts of metal (Type K), and high amounts of metal (Type L) were 98.0%, 97.3%, 92.7%, and 67.3%, respectively; statistical hypothesis tests were performed to de-termine whether the differences in read rates among the tags carried in backpacks with various amounts of metal were significant.

The read probability that each tag is read for tag-carrying type i (i.e., the read rates for Types A to L inTable 3) is denoted by pi, and each tag type is assumed to have the same piin every test. Fifty

tags were read in each test of type i, and Yihas a binomial distribu-tion with parameters 50 and an unknown pi, represented by Yi~ Bin[50, pi]. The variable nidenotes the sample size of type i (i.e., the number of tests, nI= nJ= nK= nL= 3), and Yijis the num-ber of tags read in the jth test of type i. Therefore, YI1, YI2, and YI3yield a random sample of size ni. The variable Yijcan then be summed to represent the total number of tags read in tests of type i, and approx-imated to a normal random variable Zi, defined in Eq.(4).

X

Yij Bin 50n½ i; pi≈Zi N 50n½ ipi; 50nipið1−piÞ ð4Þ The standard normal variable denoted by Zijcan be used to test the null hypothesis H0: pI= pJ(no difference in the mean read rate be-tween Types I and J) against H1: pIb pJ(a significant difference in the mean read rate between Types I and J). The hypothesis test results indi-cate that H0is rejected at a significance level α if the sample value of the test statistic Zijis lower than a critical value Zα.Table 4shows the hy-pothesis test results of the differences between the mean read rates of Types I and J (α = 0.01). The results indicate that the test was expected to result in the acceptance of H0(ZIJN Z0.01). In addition, there was no significant difference in mean read probabilities between tags exposed to no metal (Type I) and low amounts of metal (Type J).Table 5

shows the hypothesis test results of the differences between the mean read rates of Types J and K (α = 0.01). Similarly, the results indicate that there was no significant difference in mean read probabilities be-tween tags exposed to low metal (Type J) and middle amounts of metal (Type K). However, the hypothesis test results of the difference between the mean read rates of Types K and L (α = 0.01) are presented inTable 6, suggesting that the test was expected to result in the rejec-tion of H0(ZKLb Z0.01). In other words, there was a significant difference in mean read probabilities between middle amounts of metal (Type K) and high amounts of metal (Type L).

The Field TestΙ results indicated that the read rates of partially blocked readers were approximately 2% ~ 3% lower than those of readers in unobstructed spaces; the read rates of readers placed in crowded spaces were approximately 0.3% lower than those of readers in unobstructed spaces. These read rate decreases were determined to be within an acceptable range (b5%) for this study; thus, this device lay-out of gateways and readers (shown inFig. 11) was used in an experi-ment designed to track RFID tags carried by participants. The Field Test II results indicate that read rates for tags carried by participants in backpacks were lower than those for tags carried in other ways, and the read rates of tags carried with no metal (Type I), low amounts of metal (Type J), and middle amounts of metal (Type K) did not Table 3

Results of Field TestΠ for tag-carrying types with various amounts of metal.

Tag-carrying types Types Metal effect Mean read rate (%) Variance of read rate (%)

Naked Holding in hand A No 100.0 0.0

B Low 100.0 0.0

Hanging around neck C No 100.0 0.0

D Low 99.3 0.3

Enclosed Front pocket E No 98.7 0.3

F Low 98.7 0.3 Back pocket G No 98.7 0.3 H Low 98.0 1.0 Backpack I No 98.0 0.0 J Low 97.3 0.3 K Middle 92.7 2.3 L High 67.3 1.3 Table 4

Hypothesis test results for Types I and J.

Types Metal effect Mean read rate (%) ZIJ Z0.01

I No 98.0 −0.382 N−2.326

J Low 97.3 Accept H0

Table 5

Hypothesis test results for Types J and K.

Types Metal effect Mean read rate (%) ZJK Z0.01

J Low 97.3 −1.854 N−2.326

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significantly differ from the mean read rates. However, a significant dif-ference was observed between the tags carried with middle amounts of metal (Type K) and tags carried with high amounts of metal (Type L). Therefore, during movement tracking RFID experiments, participants must be restricted to carrying a small amount of metal (less than 14-inch laptop).

6.3. Variables of function–space assignment

Eq.(1)is the objective function of function–space assignment, which includes two parts of weights. In this case, the two parts of weights were given the same importance by the decision maker (W1= 0.5, W2= 0.5), and the other variables of Eq.(1)were further explained as follows.

1. Suitability preference of function fiassigned to space si(Pfisi)

The spaces were divided into 3 groups, i.e., large (L: 90–135 m2), medium (M: 45–80 m2), and small (S: 15–20 m2) spaces. Different functions require difference sizes of space. The library and seminar rooms prefer large spaces. The administration office and 2 laboratories prefer medium spaces. The 2 meeting rooms prefer small spaces. In ad-dition, one of the classrooms prefers a medium space, and the rest of the two classrooms prefer large spaces.Table 7provides the types of space size and the functions' preferred size.

The suitability preference for each possible pair of function–space assignment was given based on the following principles. A function requiring a large space can only be assigned to large space. Thus, the suitability preferences (Pfisi) for the function assigned to large, medium, and small spaces were 1, 0, and 0, respectively. A function requiring a medium space can only be assigned to a large or medium (with less preference) space. Thus, Pfisifor the function assigned to large, medium, and small spaces was 0.5, 1, and 0, respectively. A function requiring a small space can be assigned to any space with different preferences. Thus, Pfisifor the function assigned to large, medium, and small spaces was 0.1, 0.5, and 1, respectively. The pref-erence values between 0 and 1 were arbitrary depending on the de-cision maker, who, in this case, is the head of the department. The proposed model treated the zero preference as a constraint and never assigned a function to a space with Pfisi= 0.

2. Distance between spaces siand sj(Dsisj)

The distance between spaces siand sjwas given based on the nor-malization of the sum of the actual geographical distance and weighted floor difference value of the two spaces. The weighted floor difference value was equivalent to 0 m if the two spaces are located on the same floor, such as s5and s10inFig. 9. The average user walking time for one-story staircase in this case is approximately 15 s, which is equiva-lent to 20-meter walking. Therefore, the weighted distance between

two spaces located on two different consecutivefloors, such as s5and s4, is the sum of the horizontal distances plus 20 m. Similarly, the weighted value is 40 m and 60 m for the spaces situated 2 and 3floors apart, respectively. Eq.(3)was used to normalize the weighted distance sum to ensure that the value falls between 0 and 1.Table 8shows the normalized distances between the 10 spaces.

Dsisj¼

Dx−Dmin

Dmax−Dmin ð3Þ

3. Movement relation of functions fiand fj(Rfifj)

The movement relationship plays an important role in the opti-mization process.Table 9shows the values of the interactive prefer-ence (Rfifj), which was based on the movement analysis of the RFID tracking data. It signifies a usage pattern of an occupant between two functions. Basically, two functions with a large Rfifjshould be located closer together to reduce the moving distance.

6.4. Function assignment results

The proposed model was installed on a Pentium 3.40 GHz PC with 512 MB RAM, with the parameters epoch_max and era_max set to 5 and 4, respectively.Table 10shows the different function–space assign-ments suggested by the architect (row A0), the proposed model (row R1) versions, and their corresponding performances in terms of objec-tive values. The R1version has a 14.80% higher objective value than the architect's version. The functions are also assigned to the space sizes most-preferred by the administrator (e.g., f1is assigned to the large spaces of s6, f5is assigned to the small spaces of s9). Additionally, the functions having larger Rfifjare also placed at least at the same floor (e.g., functions f8and f9and functions f7and f9are onfloor 4).

The fmGA took approximately 16 s with the maximum genera-tion equal to 20. As shown inFig. 12, it actually required only 10 generations to converge to the optimal assignment (R1). The perfor-mance is acceptable considering the problem has a combination size of 3,628,800 (=10!). In addition, with 10 generations of 448 popula-tions, the number of solutions searched for by the proposed model was 4480 (= 448 × 10), which was only 0.123% (= 4480/3,628,800) of the search space.

Table 6

Hypothesis test results for Types K and L.

Types Metal effect Mean read rate (%) ZKL Z0.01

K Middle 92.7 −5.485 b−2.326

L High 67.3 Reject H0

Table 7

Space size and functions' preferred size.

Space s1 s2 s3 s4 s5 s6 s7 s8 s9 s10

Size M M L M S L M L S L

Function f1 f2 f3 f4 f5 f6 f7 f8 f9 f10

Preferred size L L L S S M M M M L

Description Library Classroom Seminar room Meeting room

Adm. office Classroom Laboratory Classroom Table 8

Distance between space siand sj.

Dsisj s1 s2 s3 s4 s5 s6 s7 s8 s9 s10 s1 0.00 0.97 0.09 0.78 0.38 0.00 0.72 0.04 0.43 0.60 s2 0.97 0.00 0.11 0.80 0.40 0.02 0.74 0.06 0.44 0.58 s3 0.09 0.11 0.00 0.32 0.57 0.49 0.24 0.53 0.61 0.40 s4 0.78 0.80 0.32 0.00 0.61 0.22 0.75 0.26 0.66 0.45 s5 0.38 0.40 0.57 0.61 0.00 0.47 0.53 0.51 0.96 0.84 s6 0.00 0.02 0.49 0.22 0.47 0.00 0.14 0.90 0.51 0.30 s7 0.72 0.74 0.24 0.75 0.53 0.14 0.00 0.18 0.57 0.37 s8 0.04 0.06 0.53 0.26 0.51 0.90 0.18 0.00 0.55 0.34 s9 0.43 0.44 0.61 0.66 0.96 0.51 0.57 0.55 0.00 0.80 s10 0.60 0.58 0.40 0.45 0.84 0.30 0.37 0.34 0.80 0.00

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6.5. Non-BBs vs. BBs

The proposed model, following Goldberg's suggestion[57], incorpo-rated building-blockfiltering in its fmGA problem-solving process to generate enough copies of the good building blocks so more copies would remain for subsequent processing. To improve the efficiency, we removed the building-blockfiltering step from the model, in partic-ular, Step 3 in the problem-solving process ofFig. 5. Thus, the non-BBs model has nofiltering step, which consists of building-block selection and random gene deletion.

We conducted another experiment to compare the performance of the fmGA with and without building-blockfiltering (BBs vs. non-BBs) using 3 function assignment scenarios. Scenario I is the actual case de-scribed in the previous sections. Scenarios II and III are expanded from thefirst one to 20-story and 40-story buildings with 50 functions and 100 functions, respectively.

For building block selection, we selected 2, 10, and 20 pairs of func-tions with the highest movement relation values (Rfifj) out of the C2

10, C250, and C2100combinations as the BBs for the 4-, 20-, and 40-story build-ings, respectively. For example, for the 4-story building, (f9and f8) and (f7and f9) are the pairs with the highest Rfifjs, namely 0.75 and 0.38, respectively. We limited the search space by imposing two additional constraining rules. First, the chromosomes in one era were only retained if the two pairs of functions were assigned to neighboring spaces (with distance value Dsisj≥0:8). Second, the random gene deletion operation, which randomly replaced genes for each of the lower halves of the pop-ulations in each era with the competitive template, should not replace the BBs.

Tables 11, 12 and 13compare the performances between the fmGA with and without BBs in Columns (a), (b), and (c) for scenarios I, II, and III, respectively. For the 4-story building with 10 functions, there were no significant differences in terms of objective values. The converging generations for the BBs were decreased by 23.1% and 13.3%, but with 23.1% and 15.4% more total running time compared to the Non-BBs with 20 and 40 maximum generations, respectively. For the 20-story building with 50 functions, the BBs resulted in 7.8% and 5.8% higher ob-jective values, and 17.3% and 2.9% less converging generations but with 452.6% and 412.1% more total running time for 800 and 1000 maximum generations, respectively. Similarly, for the 40-story building with 100 functions, the BBs resulted in 19.2% and 19.5% higher objective values, and 1.5% and 19.5% less converging generations but with 435.3% and 423.5% more total running time for 1600 and 1800 maximum genera-tions, respectively.

To further compare the required additional running time for non-BBs and non-BBs when the problem complexity increased, we repeated the 3 scenarios with the maximum generationsfixed at 1000.Fig. 13 com-pares the required running times for non-BBs and BBs in scenarios with complexities of 50 to 250 functions.

Based on the experiment, the improvement in the objective value in-creased as the problem became more complicated (from 0.0% for the 4-story building to a 19.5% improvement for the 40-4-story building). The converging generations required for the BBs were always less than the non-BBs but appeared to be random without an obvious tendency. The total running time for the BBs was always more than for non-BBs. In addition, the proportions of additional time required due to the in-creased maximum generations were about the same for both non-BBs and BBs. For example, in Scenario I, the running times were approxi-mately double the original running times when the maximum genera-tion increased from 20 to 40 for both non-BBs and BBs. The increased proportion relationship also remains the same for Scenarios II and III. However, fromFig. 13, the benefit of time savings soon became obvious once the functions were greater than 100. Thus, for an assignment lem with less than 100 functions, we suggest the use of BBs. For a prob-lem with greater than 100 functions, users need to consider the tradeoff between efficiency and solution quality because the BBs did find better assignments but with a significant cost in running time.

7. Conclusion

Assigning appropriate functions to building spaces is one of the most important factors in determining the use performance of a building. However, in architectural practice, architects and building owners ren-ovate buildings based on their personal subjective perceptions of how occupants use the building instead of systematically analyzing their use behaviors. This research proposed a function–space assignment op-timization model based on the occupants' movement data that was tracked using RFID technology. The model consists of 3 modules, name-ly movement tracking and positioning, occupants' movement ananame-lysis, and function–space assignment optimization. The model has contribut-ed to the following several aspects: First, the movement tracking and positioning module is adopted to track the occupants' movement data in a building. Second, the occupants' movement analysis module is used to mine occupants' movement pattern and calculate the relation values between functions. Third, the function–space assignment mod-ule is employed to identify the optimal result of function assignment based on the derived relation values and the acceptable size for each space.

Table 9

Movement relation of functions fiand fj.

Rfifj f1 f2 f3 f4 f5 f6 f7 f8 f9 f10 f1 0.13 0.03 0.01 0.01 f2 0.16 0.02 0.11 0.01 0.02 0.06 f3 0.01 0.04 0.02 0.04 0.06 f4 f5 0.01 0.02 0.02 f6 0.08 0.07 0.01 f7 0.05 0.01 0.12 0.00 0.38 0.02 f8 0.01 0.05 0.02 0.04 0.04 0.72 f9 0.01 0.01 0.01 0.03 0.09 0.75 0.00 f10 0.03 0.05 0.02 0.05 0.02 Table 10

Result of function–space assignment.

Result Function–space assignment Objective value s1 s2 s3 s4 s5 s6 s7 s8 s9 s10 Value Improvement A0 f8 f9 f3 f7 f5 f2 f10 f1 f4 f6 1.1047 (A0− A0)/A0 0.00% R1 f8 f9 f10 f7 f4 f1 f6 f2 f5 f3 1.2682 (R1− A0)/A0 14.80% 0 2 4 6 8 10 12 14 16 18 20 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3

Generations

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In addition, an experiment with a real case also showed that the model canfind better assignments than an architect showing a 14.8% higher objective value. The second experiment compares the perfor-mances of the model with and without the building-blockfiltering (BBs) mechanism. When the problem changes from simple to complex, we found that assignments with BBs are always equal or better than those with non-BBs showing an increase as high as 19.5% in the objec-tive value; however, the running time increase as much as 4.35 times. With the maximum generationfixed at 1000, the difference in running time between the two models became obvious for assignments with greater than 100 functions.

Future research may include the following directions. First, the pro-posed model is demonstrated specifically for application of RFID tracking technology to the optimization of function–space assignment in an edu-cational building, but it can be modified to apply to other similar func-tion–space assignment problems for remodeling buildings, such as administration buildings, office buildings, general hospitals, museums, as well as membership wholesaler stores. Second, there are still several objectives that the proposed model did not address but are still consid-ered significant in practice. Further research can extend the present objec-tive function, such as thermal, visual, acoustics comfort, energy saving, cost, or safety perspectives, to gain a more comprehensive assignment. Table 12

Comparison of performance between Non-BBs and BBs in scenario II. Scenario II (20-story building with 50 functions)

Max. generations Performance (a) Non-BBs (b) BBs (c) Difference [(b)− (a)]/[(a)]

800 Objective value 1.2312 1.3268 7.8%

Converging generation 717 593 −17.3%

Total running time (s) 371 2050 452.6%

1000 Objective value 1.2546 1.3274 5.8%

Converging generation 953 925 2.9%

Total running time (s) 463 2371 412.1%

Table 13

Comparison of performance between Non-BBs and BBs in scenario III. Scenario III (40-story building with 100 functions)

Max. generations Performance (a) Non-BBs (b) BBs (c) Difference [(b)− (a)]/[(a)]

1600 Objective value 1.0713 1.2770 19.2%

Converging generation 1565 1541 −1.5% Total running time (s) 2252 12,054 435.3%

1800 Objective value 1.0896 1.3023 19.5%

Converging generation 1729 1392 −19.5% Total running time (s) 2592 13,568 423.5% Table 11

Comparison of performance between Non-BBs and BBs in scenario I. Scenario I (4-story building with 10 functions)

Max. generations Performance (a) Non-BBs (b) BBs (c) Difference [(b)− (a)]/[(a)]

20 Objective value 1.2681 1.2681 0.0%

Converging generation 13 10 −23.1%

Total running time (s) 13 16 23.1%

40 Objective value 1.2681 1.2681 0.0%

Converging generation 15 13 −13.3%

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The experimental results indicate the usability of the proposed model, exhibiting a 14.8% improvement in objective value compared with the architect's version. It may be argued that, because of the high setup cost involved, acquiring the numerous RFID readers and tags the model requires is not economically beneficial for an educational facility. However, in the commercial sector, businesses such as membership wholesale stores may have an incentive to apply the model, for exam-ple, to optimize product arrangement and enable customers tofind products easily. The model could also become more economically feasi-ble by reducing the cost of collecting data. The price of RFID readers and tags is decreasing, and simulation software can also be used to simulate, instead of track, the movement of participants. We are currently ex-tending the proposed system to include an activity simulation module that provides an alternative method for users to collect movement data.

Acknowledgments

This work was partially supported by the National Science Council grants (NSC 99-2221-E-009-133-MY3). Their support is greatly appreciated.

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0.13 0.39 0.72 1.00 1.60 0.66 2.00 4.34 6.32 10.21 y = 0.13x1.53 y = 0.65x1.69 0.00 2.00 4.00 6.00 8.00 10.00 12.00 1 2 3 4 5

(50 Functions) (100 Functions)(150 Functions)(200 Functions)(250 Functions)

Total running time (hour)

Number of functions

Non-BBs BBs Power (Non-BBs) Power (BBs)

(16)

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數據

Fig. 2. Function–space assignment.
Fig. 3. Spatial location tracking of each tag using RSSI.
Table 1 is an example of X f i s i , where 5 functions (f 1 to f 5 ) are to be assigned to 5 spaces (s 1 to s 5 )
Fig. 7 shows an example that illustrates this problem. Before the cut, both chromosomes C 1 and C 2 are valid strings, where each space is assigned to a unique function
+7

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