A Multiobjective Approach to Locate Emergency Shelters and Identify Evacuation Routes in Urban Areas

Authors


João Coutinho-Rodrigues, Department of Civil Engineering, Faculty of Sciences and Technology, University of Coimbra—Polo II, 3030-194 Coimbra, Portugal
e-mail: coutinho@dec.uc.pt

Abstract

Evacuation planning is an important component of emergency preparedness in urban areas. The number and location of rescue facilities is an important aspect of this planning, as is the identification of primary and secondary evacuation routes for residents to take. This article introduces a multiobjective approach to identify these aspects of evacuation planning. The approach incorporates a multiobjective model into a geographical information systems–based decision support system that planners can access via the Internet. The proposed approach is demonstrated with a case study for the City of Coimbra, Portugal, for evacuation during major fires. Although presented in this context, this approach is applicable to other emergency situations such as earthquakes, floods, and acts of terrorism.

Abstract

El planeamiento de evacuaciones es un componente importante en la preparación contra emergencias en áreas urbanas. El número y ubicación de establecimientos de rescate es un aspecto clave de dicho planeamiento así como lo es la identificación de rutas de evacuación primarias y secundarias. El estudio presente utiliza un enfoque multi-objetivo para identificar los aspectos mencionados en la planeación de evacuaciones. Este enfoque incorpora un modelo multi-objectivo dentro del sistema de apoyo a la decisión de un Sistema de Información Geográfica. Este sistema puede ser accedido por los planificadores vía la Internet. Para demostrar la aplicabilidad del enfoque propuesto, el sistema es aplicado a estudio de caso de evacuación por motivo de incendios en la ciudad de Coimbra, Portugal. A pesar de ser un caso específico, el enfoque presentado puede ser aplicado a otros tipos de emergencia tales como sismos, inundaciones y actos de terrorismo.

Abstract

疏散计划是城市地区应急预案的重要组成部分。救援设施的数量和位置是疏散计划的重要内容,直接关系到主要的与次要的居民疏散路线的确定。本文介绍了一种多目标方法来确定疏散计划中救援设施的数量和位置。该方法将多目标模型集成到基于GIS的决策支持系统中,规划者可以通过网络访问该系统。以葡萄牙的科英布拉城市重大火灾撤离为例,证实了该方法的可用性。除本文所提及的应用外,该方法也能适用于地震,洪水和恐怖主义袭击等其他应急情况。

Introduction

Fires and other catastrophes are an important concern for fire departments and Emergency Medical Services (EMS) in urban areas. In this article, we present a Web-based decision support system to assist fire departments and EMS in the design of evacuation plans for an urban area. The plans include the determination of the number and location of rescue facilities (henceforth these will be referred to as “shelters”) as well as the routes that individuals should take to reach their assigned shelter. The core component of the system is a multiobjective extension of the p-Median model (ReVelle, Marks, and Liebman 1970; ReVelle and Swain 1970; ReVelle et al. 1977; Rosing, ReVelle, and Rosing-Vogelaar 1979; ReVelle 1997). In addition, it includes various multicriteria tools to aid decision makers in the selection of their most preferred option. Although the system was designed specifically for emergencies related to fires in Coimbra, Portugal, the basic framework and model could be adapted to other evacuation situations (e.g., floods, acts of terrorism, etc.) in other cities.

The underlying problem is a multiobjective location/routing problem. There is a long tradition of multiobjective location problems (see, e.g., Current, Schilling, and Min 1990b; Daskin 1995; Current, Daskin, and Schilling 2001 for reviews) and multiobjective routing problems (see, e.g., Current and Min 1986; Current and Marsh 1993 for reviews). The mathematical model at the core of our approach also follows a long tradition of location models addressing emergency situations (e.g., Toregas et al. 1971; Schilling et al. 1979; Church and Weaver 1980; Schilling et al. 1980; Daskin and Stern 1981; Daskin 1982; ReVelle 1989; ReVelle and Snyder 1995).

There are numerous historic examples of catastrophic fires (e.g., Chicago, October 9, 1871; Boston, November 9, 1872; Baltimore, February 7, 1904; San Francisco earthquake and fire, April 18, 1906). Various European and Asian cities (e.g., Dresden, London, Tokyo) were ravished by fires during World War II. Recent events have made emergency service planners in Coimbra particularly conscious of the possibility of a catastrophic fire. According to Reuters News Service, 2003 and 2005 were the worst years on record for fires in Portugal (http://www.planetark.org/dailynewsstory.cfm/newsid/37062/newsDate/30-Jun2006/story.htm). On August 24, 2005, Coimbra was surrounded by forest fires with more than 300 firefighters working to contain flames on the edge of the city (e.g., BBC News: http://news.bbc.co.uk/1/hi/world/europe/4175922.stm).

According to the United States Fire Administration (USFA), approximately 4000 Americans die and 20,000 are injured each year in fires with 83% of the civilian deaths occurring in residences (http://www.usfa.dhs.gov/statistics/quickstats/). USFA studies indicate that “[a]dults age 65 and older are 2.5 times more likely to die in fires than the overall population” and “[s]moking continues to be the number one cause of residential fire deaths” (http://www.usfa.dhs.gov/safety/) in the United States. USFA states that “… having a sound escape plan will greatly reduce fire deaths and protect you and your family's safety if a fire occurs” and that “… the best plans have two ways to get out …” (http://www.usfa.dhs.gov/safety/escape/).

As a consequence, Coimbra planners decided to start fire evacuation planning in the “downtown” (or “Baixa” region) as this is the area of Coimbra with the highest percentage of its population 65 years of age or older. In addition, the Baixa consists primarily of old buildings that are highly flammable and many streets that are too narrow for modern firefighting equipment or ambulances. Concentrating evacuation planning on areas with special conditions has also attracted the attention of modelers. For example, Cova and Church (1997) and Church and Cova (2000) introduce mathematical methods to identify and classify urban neighborhoods with high ratios of populations that might face transportation difficulties during an evacuation. Owing to the size of the study area and the well-known nature of its street network (mostly for pedestrian use only), methods such as these were not needed to identify the Baixa as an area of special problems.

The remainder of this article is organized as follows. The case study background is given in the next section. The modeling approach is presented in the third section. The underlying mathematical model is formulated in the fourth section and its implementation (with results of the initial application) is presented in the fifth section. The article ends with a summary and conclusions section.

Case study background

Coimbra is a city of about 150,000 residents with more than 2000 years of history. The Baixa is a section of the city with many narrow streets and old buildings (some dating to medieval times) that contain a considerable amount of wood in their construction. It covers about 15 ha that include: 749 buildings (376 are inhabited) with 1086 residential apartments (739 are inhabited) and 1450 commercial, services, or governmental units (1217 are occupied). A large percentage of the ground level of the buildings is occupied with retail activities (e.g., 487 buildings have commercial and/or service activities).

Since 2003 the University of Coimbra has been engaged with the city government in a multidisciplinary project to study the Baixa in order to plan the renovation of that part of the city. Three departments of the university (architecture, civil engineering, and sociology) have studied the buildings in this area. In 2004 and 2005, this study generated photographs and computer-aided design (CAD) drawings of the interiors and exteriors of the buildings, identified the pathologies of their construction, and recorded and analyzed the populations that inhabit them and economic activities that occur in them. A fourth team (decision support systems) has designed and implemented a Web-based spatial information and decision support system using geographical information systems (GIS) technology (see, e.g., Laurini 2001; Worboys and Duckham 2004; Longley et al. 2005). The system (SIGUrb) was developed by programming in the GIS ESRI ArcServer software (which provides GIS functions in a Web browser) and in SQL (for database implementing and management) in order to obtain an integrated system that also includes a decision support models base. It stores the gathered data and the CAD drawings produced as well about 90,000 digital photos of the buildings (e.g., roof, pavements, stairs, walls, windows and doors, water/sewage/electrical/gas/information networks, etc.). Authorized users can access SIGUrb via any Internet browser (sigurb.dec.uc.pt). The data used in the research presented in this article was imported from SIGUrb. (Note that the acronym for GIS is SIG in Portuguese.)

Problem and modeling approach

The overall goal of the research presented in this article was to determine the number and locations of shelters and the paths that people should take from their building to their assigned shelter in case of a fire. Given that the fire might make an evacuation path impassable or evacuation shelter unusable, a backup shelter and path were determined for each building. The planners identified four objectives of interest. These were the minimization of total travel distance for people to reach their shelter, the minimization of total risk of the primary path being impassable, the minimization of fire risk at the shelters, and minimization of the total time required to transfer people from their evacuation shelter to the University Hospital when necessary. These are similar to the efficiency and risk objectives presented in Current and Ratick (1995).

Several constraints were imposed upon the design. These included a lower (or threshold) population assigned to a shelter, as well as a maximum population assigned to a shelter. The minimum and maximum populations were based on “general” considerations and “specific” considerations based on conditions at each potential site (e.g., area available, accessibility, characteristics of surrounding buildings). Given that almost all people would need to walk to their shelter, it was determined by the planners that no path from building to shelter should be longer than 500 m.

Nine potential shelter sites were identified. The shelters are temporary structures (e.g., tents, mobile units) that will be opened or set up at the time of an emergency, as there are no enclosed structures with available space to serve as a permanent shelter. Some components of the shelters will be prepositioned at, or near, the sites. The number of candidate sites was limited by the area needed for a shelter, the width of streets for evacuee access to the shelter, requirements for ambulances and other support vehicles to access the shelter, and the 500 m maximum distance constraint. As was mentioned earlier, the Baixa contains many extremely narrow streets with many of them too narrow for two people to walk side by side.

Three actions were undertaken to reduce the dimensionality of the problem. First, the streets were aggregated into sectors of about 40 m in length. All of the buildings and their residents in a sector were assumed to be located at the midpoint of the sector. Consequently, the original 749 buildings (i.e., path origins) were reduced to 199 sectors (i.e., path origins). Demand aggregation is a frequently used approach in location modeling (e.g., Current and Schilling 1987, 1990; Erkut and Bozkaya 1999; Francis et al. 1999; Francis et al. 2004a, b; Horner and O'Kelly 2005). Second, it was decided to identify the secondary or backup evacuation paths after the shelter locations and primary paths had been determined rather than to determine them simultaneously. Finally, the problem was decomposed into a “Nighttime” problem and a “Daytime” problem. Two versions of the problem were considered and analyzed because the population (and their locations) of the study area varies greatly from day to night.

Although the daytime population (5663) is greater than the nighttime population (1265), planners were more concerned with the nighttime population as this population is residential, and generally more elderly than is the daytime population. According to research in the United States (e.g., http://www.midland-mi.org/government/departments/fire/HomeEscape.htm), most residential fires occur between 8 p.m. and 8 a.m. and deaths (more than half are children and senior citizens) occur in greater numbers between midnight and 4 a.m. when most people are asleep. Consequently, a higher priority was given to the nighttime planning period. Additionally, it was considered unwise to assign different evacuation routes (i.e., night versus day) for the residents of the district. However, “day planning” was performed. This analysis considered the additional daytime population (e.g., shopkeepers and customers, minus residents who are elsewhere during the day) in the area.

The first step of the modeling process was to generate a sufficiently large set of candidate evacuation paths from the 199 sectors to the nine candidate shelter sites. Two criteria, path length and path risk, were considered. The evaluation of the risk associated with each street (arc of the network) was based on the “Fire Risk Index Method” for safety/risk analysis in fire situations (NFPA 1995, 2001; Larsson 2000; Dobbernack and Klingenberg 2005) using data on the structures obtained from SIGUrb. SIGUrb includes a report generator module, customizable by the user, which retrieves the required data and feeds a generic matrix-oriented model generator used to construct the final evacuation model.

Given that these two criteria (path risk and path length) might be in conflict, the bicriteria path approach presented in Current et al. (1990a) and Coutinho-Rodrigues, Clímaco, and Current (1999) was used to generate nondominated paths. These were generated by considering a weighted sum of the two criteria. For each sector, 11 pairs of weights were considered. These ranged from 0 to 1 on the length objective and from 1 to 0 on the risk objective. They were (1; 0) (0.9; 0.1) (0.8; 0.2) (0.7; 0.3) (0.6; 0.4) (0.5; 0.5) (0.4; 0.6) (0.3; 0.7) (0.2; 0.8) (0.1; 0.9) (0; 1). These weights generated evacuation paths with a wide range of lengths and risks. The Buckets “Basic Implementation” (Dial 1969; Zhan and Noon 1998) of the Dijkstra algorithm (Dijkstra 1959) was used, because of its coding simplicity and efficiency. The total CPU time (on a laptop equipped with Intel Pentium Mobile 1.6 GHz CPU, 512 MB RAM, running Windows XP) to generate 19,701 paths (11 weights × 9 candidate shelters × 199 sectors) was <3 s. Given these times, the more sophisticated “Approximate Buckets” implementation (Zhan and Noon 1998) was not used. Of these 19,701 paths, 4236 were unique as different weights often yielded identical paths.

The number of candidate paths was further reduced by eliminating paths with origins in a sector with no population. These empty sectors varied for the daytime and nighttime populations. This reduced the number of nighttime paths to 3069 and the daytime paths to 4079. Finally, all paths longer than 500 m were eliminated as they were deemed to be too long by the planners. This is similar to the maximum distance constraints introduced into the p-Median problem by Church and Meadows (1977). This reduced the final number of paths to be considered to 2641 for the nighttime population and 3561 for the daytime population.

Underlying mathematical model

As stated earlier, one output of the analysis was the determination of the number of shelters to be established. Given the discrete nature of this decision and its importance to the overall evacuation network, we structured this component of the decision as a constraint and then solved the underlying multiobjective model with various values for the number of shelters. As a result, the underlying model is a multiobjective p-Median model (ReVelle, Marks, and Liebman 1970; ReVelle and Swain 1970; ReVelle et al. 1977; Rosing, ReVelle, and Rosing-Vogelaar 1979), which we refer to as MOpM.

Given the following variable, set, and parameter definitions:

inline imagebinary variable, 1 if the cth primary candidate path from sector i to shelter j is chosen, 0 otherwise;
inline imagelength of the primary candidate path inline image; real parameter;
inline imagerisk associated with primary candidate path inline image; real parameter;
xj,jbinary variable, 1 if shelter j is opened, 0 otherwise;
pnumber of shelters to be located. pE; integer parameter;
Snumber of sectors; integer parameter;
Enumber of candidate shelters; integer parameter;
Ci,jnumber of primary candidate paths from a sector i to a shelter j; integer parameter;
ainumber of individuals in sector i to be evacuated; integer parameter;
Kjcapacity (number of individuals) allowed in the jth candidate shelter; integer parameter;
kjminimum number of individuals required for opening the jth shelter; integer parameter;
tjevacuation time from shelter j to the University Hospital; it is measured (scaled) in meters by multiplying the average travel velocity by the actual time for this secondary evacuation;
rjrisk associated to the jth candidate shelter; real parameter.

The underlying multiobjective p-Median model (MOpM) can be formulated as follows:

image(1)
image(2)
image(3)
image(4)

s. to:

image(5)

(ensures one evacuation primary path is chosen for each sector, with S the number of sectors; S constraints)

image(6)

(ensures the maximum capacity for shelter j is not exceeded, with E the total number of candidate shelters; E constraints)

image(7)

(ensures the minimum number of individuals required to open shelter j are assigned to shelter j before it is opened, with E the total number of candidate shelters; E constraints)

image(8)

(ensures p of the E candidate shelters are opened)

image(9)
image(10)

Objective (1) minimizes the total distance required for all of the population to reach its primary evacuation shelter. Objective (2) minimizes the fire risk faced by the total population as it travels to its primary shelter. Objective (3) minimizes total fire risks associated with staying in the primary shelter and Objective (4) minimizes the total time for eventual evacuation from the shelters to the University Hospital.

After a solution to MOpM has been identified, the backup shelter and path (P2) for each sector must be identified. To do this, the downtown area was divided into 11 zones (see Fig. 1). These zones were identified by planners based on local conditions. These included: topology (many of the streets in the Baixa are laid out like a river drainage basin, and so the zones reflected these “natural flow patterns”); access (all zones needed access to two potential shelter sites and the hospital); and homogeneity (zones should have similar populations, geographic area, and distance to two potential shelter sites).

Figure 1.

Downtown Coimbra divided in 11 zones (Z1–Z11) under study.

In order to diversify the P2 path from the primary (P1) path for a given sector, the secondary evacuation path was determined by the following rules (Kuby, Zhongyi, and Xiaodong 1997):

  • (i)if possible, P2 should not include any arcs or nodes (except for the path origin node) on the primary path (P1), that is, P2 should not intersect P1 for a particular sector's evacuation routes;
  • (ii)if possible, P2 should not cross any zone (see Fig. 1) that includes P1 other than the one that includes the path origin;
  • (iii)P2 should have its termination at a different shelter than does P1; and
  • (iv)P2 should be the least length (or time) costly path that satisfies the above rules.

Model implementation

Implementation of the approach was complicated. First, the underlying mathematical model is complex and difficult to solve optimally for large problem instances. Second, the multiobjective nature of the decision increases the computational complexity of the analysis and comparisons of nondominated solutions. Third, the decision makers typically have no advanced training in mathematical programming or multiobjective decision techniques.

We addressed the first factor by reducing the problem complexity as described in “Problem and Modeling Approach” and by structuring the number of shelters as a constraint as is described in the previous section. The number of shelters to open, p, varied from 2 (the minimum number possible given that each sector required a backup shelter) to 7 (out of a possible maximum of 9). Certainly, 8 or 9 (a trivial problem) shelters could have been evaluated but they were not of interest for various reasons.

The second and third factors were addressed in the design of the decision support system that implements MOpM. The decision support system (SIGUrb) was set up so that planners can access it and the underlying data via the Internet. Problem parameters are entered using the editing module. This module manages the input data, generates the integer-programming model, and transfers it to an algorithm server where the solution is calculated. The system generates nine nondominated solutions to MOpM to give the planners a general understanding of the trade-offs among the objectives. The first four of these optimize the four objectives individually with very small weights on the other three objectives to identify a nondominated solution (Ehrgott 2005).

Table 1 presents the results for 10 solutions for each value of p (number of facilities) for p=2, …, 7. The first four rows for each value of p contain the values for the solution that optimizes objectives 1, 2, 3, and 4, respectively. These columns are labeled “Opt 1: Path Length,”“Opt 2: Path Risk,”“Opt 3: Shelter Risk,” and “Opt 4: Shelter Evac.” The optimal value for Opt 1 is reported in terms of the average length traveled by all individuals in meters. Opt 2 and Opt 3 are expressed in average individual risk units and were evaluated as described in Larsson (2000) using data on the buildings found in SIGUrb. Opt 4 represents the average distance that individuals must be transported from their primary shelter to the hospital. Undoubtedly, all evacuees will not need to go to the hospital. However, at present we have no way of estimating the proportion of residents in a demand zone that will require this service; consequently, we assume that they all will require it. In essence, we assume that there is no significant variation in the demand for this service across zones.

Table 1.  Summary of Initial Solutions
p SolutionsOpt 1: Path LengthOpt 2: Path RiskOpt 3: Shelter RiskOpt 4: Shelter Evac.ΔL1ΔL2ΔL∞Global ΔL1Global ΔL2Global ΔL∞P1 Max LengthP2 MedP2 Max Length
Value (m)Nr ResidLength (m)Value (m)Nr Resid
  1. For each value of p, p=2, …, 7, solutions are numbered from 1 to 9. Each row of this table corresponds to a solution. Minimum (best) values are in bold.

2Opt 11 159 106107187101696421111474307182985713
Opt 22179 88 10718710269642131209339573115798
Opt 33292225 43 20030119313741227220650013197175
Opt 4416610085 168 6144421711038137312815279
Weight (25, 25, 25, 25)5176917817864403417510691432122644902
Weight (50, 10, 10, 30)6160114781686243351721047531073437279
Weight (10, 50, 30, 10)7182907817868423417911097432122644902
Goal L181649783171 56 4140167997939622775279
Goal L∞9188117731739251 29 20212610249613367368
Ideal15988431680001118274 
3Opt 11 120 7614523417311897228129102254142565551
Opt 22145 67 15224520613210426114710946032515701
Opt 33296228 48 20837724217643227821150012856705
Opt 441458582 168 7746341327860335182514196
Weight (25, 25, 25, 25)514781731797641271317561335182514196
Weight (50, 10, 10, 30)614088791717543311307555335182494196
Weight (10, 50, 30, 10)715579721808346351388169335182504196
Goal L181438277174 73 41291277458335182494196
Goal L∞914491721798343 24 1377759335182314196
Ideal1206748168000553835 
4Opt 11 101 71236307332229183367239193254142365551
Opt 22119 59 13824617911584214127942601421143712
Opt 33297230 53 21040826419644328121250012715855
Opt 441458487 170 10361441388160335181973968
Weight (25, 25, 25, 25)513176831859248301286846335182244196
Weight (50, 10, 10, 30)61197696188955242130705226242244196
Weight (10, 50, 30, 10)7139758218710053381357354335182244196
Goal L181277588183 90 4834125674426242244196
Goal L∞9129868118810151 28 1377043295720940314
Ideal1015953170000352016 
5Opt 11 91 68230315321218169356238186254142014311
Opt 22101 54 224305300207163335226180260141894311
Opt 33254192 61 20432721516336322316950011833845
Opt 441478191 177 11369561488462335181953968
Weight (25, 25, 25, 25)512372911969851321337047260141883726
Weight (50, 10, 10, 30)611474100200104543913974562541419838414
Weight (10, 50, 30, 10)7131719019810656401417446305551893726
Goal L181257491188 95 513413069482601417935714
Goal L∞9120829019910754 29 14272462541418438414
Ideal915461177000352117 
6Opt 11 86 632323263142151643582461882541418538414
Opt 2295 51 2223162912001543362321782601417235714
Opt 33238174 68 20929719715234220215349781793845
Opt 441458294 187 11671591608660335181863968
Weight (25, 25, 25, 25)5119709820094503313974552601416735714
Weight (50, 10, 10, 30)61127210520299523714478612541417538414
Weight (10, 50, 30, 10)7127679920911058411548256310717435714
Goal L181217295196 92 503513772522601416535714
Goal L∞9116789820310253 30 14776552541417338414
Ideal865168187000453125 
7Opt 11 85 642393243012061623642501952541418238414
Opt 2295 51 2203112661831433292271762601417135714
Opt 33235168 77 21828819115035020015049781743845
Opt 4413474101 198 97604916085583351815835714
Weight (25, 25, 25, 25)5116691062139349311568563262417235714
Weight (50, 10, 10, 30)6110731112149750341598867262417938414
Weight (10, 50, 30, 10)7122651092139853371618865310716535714
Goal L1812472101201 88 51391518058266216035714
Goal L∞9113741052129348 28 1568461260417038414
Ideal855177198000634533     
 Global Ideal 855143168   000     

For each value of p, p=2, …, 7, three “compromise,” nondominated solutions were identified via the weighting method (e.g., Cohon 1978; Ehrgott 2005) using the following relative weights: Solution 5, (w1w2w3w4)=(25, 25, 25, 25); Solution 6, (w1w2w3w4)=(50, 10, 10, 30), which places a higher importance on travel lengths and times; and Solution 7, (w1w2w3w4)=(10, 50, 30, 10), which places a higher importance on the path and shelter risks. These relative weights were selected to generate an approximation of the set of nondominated solution set. For each value of p, Table 1 presents the objective function values for these three solutions in the columns labeled “Opt 1: Path Length,”“Opt 2: Path Risk,”“Opt 3: Shelter Risk,” and “Opt 4: Shelter Evac.”

It should be noted that these weights, (w1w2w3w4), are not the actual weights that are used in the model, inline image. These are generated by SIGUrb using the optimal values (opt1,popt2,popt3,popt4,p) for Solutions 1–4 for each value of p as follows:

image(11)

Consequently, the relative weights, wi, reflect the relative importance that the planners attach to the four objectives; where inline image. SIGUrb automatically generates the solution where the relative weights on the objectives are equal, that is (w1w2w3w4)=(25, 25, 25, 25). Given these relative weights for say p=2, SIGUrb will generate the following actual weights used by MOpM:

image
image

Via the editing module, planners can input other relative weighting schemes based on their relative preference among the objectives and the system will automatically calculate the actual weights.

A useful benchmark for comparing and evaluating nondominated solutions in multiobjective problems is the “ideal solution” (Zeleny 1982). The objective function values for the ideal solution for some value of p are the best possible value for each objective for that value of p: (opt1,popt2,popt3,popt4,p). The objective function values for the ideal solutions are given in the row labeled “Ideal” in columns labeled “Opt 1: Path Length,”“Opt 2: Path Risk,”“Opt 3: Shelter Risk,”“Opt 4: Shelter Evac.” in Table 1 for p=2, …, 7. The ideal solution is not feasible unless a single solution is optimal for all of the objectives. The “anti-ideal solution” is also determined for each value of p. The four objective function values for this solution are the worst (i.e., maximum) values for each objective in Solutions 1–4. They are not presented in Table 1 but are used in other displays.

One way to compare nondominated solutions is to compare their distances from the ideal solution. SIGUrb calculates the distance of each solution from its ideal solution using three frequently adopted metrics:

image(12)
image(13)
image(14)

inline image(here, n=4 objectives). Distances of each solution to the ideal solution of the respective p family solutions are represented in columns “ΔL1,”“ΔL2,” and “ΔL∞.”

The decision support system also uses the ideal solutions to identify two additional nondominated solutions for each value of p using goal programming (e.g., Min and Storbeck 1991; Tamiz and Jones 1997) where the “goals” are the ideal solution value for each objective. Solution 8 measures the distances from the goals using the L1 metric and Solution 9 measures the distances using the L metric. The objective function values for these solutions are given in rows “Goal L1” and “Goal L∞” of columns labeled “Opt 1: Path Length,”“Opt 2: Path Risk,”“Opt 3: Shelter Risk,”“Opt 4: Shelter Evac.” in Table 1 for p=2, …, 7 and their distances to the ideal solution are represented in columns “ΔL1,”“ΔL2,” and “ΔL∞.”

SIGUrb also identifies the “global ideal solution” (gopt1gopt2gopt3gopt4). The objective function values for this infeasible benchmark solution are the minimum of the minima of each objective:

image(15)

The global ideal solution is presented in the last row of Table 1, labeled “Global Ideal.”

For all solutions, the L1, L2, and L distances to this global ideal are presented in columns “Global ΔL1” (distance L1), “Global ΔL2” (distance L2), and “Global ΔL∞” (distance L) of Table 1.

The maximum primary evacuation path (P1) lengths (“P1 Max Length”: “Value”) and the number of individuals using them (“P1 Max Length”: “Nr Resid”), the median secondary path (P2) lengths (“P2 Med Length”), the maximum P2 lengths (“P2 Max Length”: “Value”), and the number of individuals using them (“P2 Max Length”: “Nr Resid”) are given in the last five columns of Table 1. For example, for p=4, the minimum of the maximum P1 path lengths is 254 m, used by 14 residents. As the information in Table 1 indicates, analyzing the trade-offs among the four objectives and the value of p (i.e., number of shelters) for various nondominated solutions is complex. To facilitate this analysis, SIGUrb includes numerous data and graphical interfaces.

For comparison purposes, tables can be readily generated to display specific data for various solutions. For example, P1 path lengths for two and four shelters are presented in Table 2. Path lengths are separated into seven intervals ranging from less than 50 m to between 400 and 500 m. The table lists the number of individuals who must traverse a path in each category. In addition, the maximum path length and the number of people who must traverse it are also included in the table. As this table indicates, the p=4 solutions have several maximum P1 path lengths under 300 m, while none of the p=2 solutions do.

Table 2.  Number of Residents by Lengths of P1 Paths—Nighttime Situation, P=2, 4
  Number of residents by lengths (m) of paths home to shelterP1 Max Length
[0, 50[[50, 100[[100, 150[[150, 200[[200, 300[[300, 400[[400, 500[Value (m)Nr Resid
(a) p=2 (shelters) solutions
1Opt 1: Path Length9912731735435018030718
2Opt 2: Path Risk991232043334466003957
3Opt 3: Shelter Risk276449834373512545001
4Opt 4: Shelter Evac.1071622793073218903731
5Weight (25, 25, 25, 25)1071642413043091281243212
6Weight (50, 10, 10, 30)1091652713103783203107
7Weight (10, 50, 30, 10)1071642462583231551243212
8Goal L11071712703153465603962
9Goal L∞10914219425745294174961
(b) p=4 (shelters) solutions
1Opt 1: Path Length239445341166740025414
2Opt 2: Path Risk1923722752731530026014
3Opt 3: Shelter Risk276449834313192925001
4Opt 4: Shelter Evac.15621730030325633033518
5Weight (25, 25, 25, 25)18926331226721618033518
6Weight (50, 10, 10, 30)196324323275147002624
7Weight (10, 50, 30, 10)18925227727519973033518
8Goal L1189259338317162002624
9Goal L∞189262333273208002957

SIGUrb also includes numerous graphical tools to help users generate and compare various nondominated solutions. These tools facilitate the comparison and generation of solutions in “geographic space” and “solution space” (Cohon 1978). To compare solutions in geographic space, output from the MOpM solutions can be readily exported to the GIS component of SIGUrb to produce color-coded graphics such as those shown in Figs. 2 and 3. Fig. 2 represents a p=4 solution to MOpM (sol #8, Goal L1). The locations of the four opened shelters are identified with different colored circles. Buildings assigned to a shelter are marked with the shelter's color. These identifications are overlaid on an aerial photograph of Coimbra. Buildings that are not color-coded in Fig. 2 are not in the study area, and white buildings are empty (i.e., have no residents).

Figure 2.

Facility location and assignments for p=4, Solution 8 (Goal L1).

Figure 3.

Example of primary (solid lines) and secondary (dashed lines) paths for two structures.

Fig. 3 shows the primary and secondary evacuation paths for two sectors marked with a black dot (one with two structures with the blue shelter as its primary shelter and one with three structures with the green shelter as its primary shelter). The primary path is shown with a line the same color as its shelter and the secondary path is marked with a line the color of its secondary shelter. These sectors are identified with black dots in Fig. 3. From the figure, it appears that their primary paths are not to their closest shelter. However, in fact, the primary paths do lead to their closest/least-risk shelter as Coimbra is not flat and adjacent structures may have their entrance/exit on different streets.

Once a shelter location/evacuation scheme has been selected, the decision support systems can generate evacuation path maps for each structure as well as the mailing addresses to inform the residents. In addition, EMS crews can be notified of buildings housing residents with special evacuation needs.

SIGUrb also includes numerous graphical tools to help planners generate and compare nondominated solutions and to determine if additional solutions might be of interest. For example, Fig. 4 displays the objective function values for the four solutions that optimize objectives 1–4 when p=4 as well as the ideal and the anti-ideal solutions via a “BAGAL” (e.g., Coutinho-Rodrigues et al. 1997).

Figure 4.

First four solutions for p=4 and the resulting BAGAL.

Planners can use such graphics to generate new solutions in the editing module of SIGUrb similar to the methods presented in Coutinho-Rodrigues et al. (1997).

Initial results of the study indicate that p=4 shelters are the most preferred for the nighttime population. This was largely determined by its performance vis à vis the “Global Ideal” solution. The analysis was also conducted for the daytime population using MOpM and SIGUrb. Sector populations and path distances were adjusted to reflect the daytime population (in general larger) and slower travel times (more congestion) on the primary and secondary paths. An interesting preliminary result for planners was that the most preferred solution for the nighttime population sited four shelters and that the most preferred solution for daytime population sited five shelters, of which four were included in the nighttime solution.

Summary and conclusions

Fires are important concerns for urban planners. The old parts of cities are of particular concern due to the fact that narrow streets make firefighting and evacuation more difficult and old buildings often are highly flammable. The location of evacuation shelters and the identification of efficient routes to reach them can reduce deaths and injuries in major fires in such areas. This is a multiobjective location/routing problem. In recent years, there has been a growing interest in using optimization techniques integrated into a GIS-based decision support system to analyze such problems (e.g., Simão, Coutinho-Rodrigues, and Current 2004; Maria, Coutinho-Rodrigues, and Current 2005; Farhan and Murray 2008; Alçada-Almeida, Coutinho-Rodrigues, and Current in press; Santos, Coutinho-Rodrigues, and Current 2008).

The purpose of the research presented in this article was to develop and test a user-friendly, Web-based, multicriteria, decision support system to analyze such decisions. The system integrates a Web-based model generator and algorithm server into a GIS-based decision support system. The system, SIGUrb, was tested in the downtown area (Baixa) of Coimbra, Portugal. Coimbra was chosen for several reasons. First, the Baixa is an area with many narrow streets and very old buildings. Second, a rich database for this area has been assembled recently. This database indicated that the area has a high risk of fire and an older than normal residential population who are at increased risk from fire.

SIGUrb was designed to assist planners in determining the number and location of evacuation shelters and the paths that people should take from their buildings to their assigned shelters in case of fire. Nine potential shelter sites were identified. An important component of SIGUrb is a multiobjective p-Median model (MOpM) with four objectives: the minimization of total travel distance for people to reach their primary shelter, the minimization of total risk of the primary path being impassable due to the fire, the minimization of fire risk at the shelters, and the minimization of the total time required to transfer people from their evacuation shelter to the University Hospital, when necessary.

Two constraint sets were added to the standard p-Median problem formulation. These enforced a minimum and a maximum population assigned to an opened shelter. Two versions of the problem were analyzed, one for the nighttime and the other for the daytime, due to the variation of the population (in number and location) for those two planning situations. According to the USFA, a sound escape plan will greatly reduce fire death and “… the best plans have two ways to get out ….” Consequently, the system identifies two evacuation paths for each building. These two paths are as dissimilar as is possible. The number of shelters to open, p, was structured as a constraint in the model and varied from 2 to 7.

The MOpM was solved within the framework of a Web-based decision support system that included a high-level interface to mathematically structure the model instances, an algorithm server, and a linkage to a Web-based GIS. Various graphical techniques allow users to analyze nondominated solutions already generated and to determine additional solutions that may be of interest. This is done in geographic space via the GIS and in solution space via various graphical techniques.

The implementation of the system in Coimbra indicates that sophisticated integer programming, multicriteria analysis, GIS, and database management techniques can be integrated into a Web-based decision support system that requires no specialized training in these areas in order to be used by urban planners. According to Church (2002), GIS-based decision support systems are particularly appropriate for the analysis of location-routing decisions like the one addressed in this article because they are a good source of input data, the data can be used for other applications, and they are an effective way to present model results (e.g., Figs. 2 and 3).

A potential fire's location and spread is not known in advance. The system presented in this article addresses this uncertainty in several ways. For example, objectives 2 and 3 respectively minimize the risk of a fire along the primary evacuation routes and at the shelters. Additionally, a secondary shelter and evacuation route is determined for each building. The secondary evacuation route is as dissimilar as possible from the primary one. This was done by dividing the region into zones. Future research may address the definition of these zones for other urban areas where they are not as natural as they are in the Baixa of Coimbra.

Ancillary