tabu-based heuristic approach for optimization of network evacuation contraflow

In urban evacuations, especially in response to an expected disaster, capac-ity reversibility (also known as contraflow) has been considered a work-able strategy to reduce traffic congestion and to meet evacuation timedeadlines. Currently, contraflow strategies are mostly planned by relyingon engineering judgment because of the lack of appropriate large-scaledecision support tools. A tabu search-based heuristic approach is intro-duced here that can be applied on realistic-size networks. The approachrelies on insights from an analytical formulation of optimal reversibil-ity design that reduces total system travel time. Computational resultson a hypothetical and an urban network example network are presentedand discussed.

Traffic management during evacuations of urban locations is a chal-lenging task, especially if the network is already congested for every-day demand. The conditions can only worsen when demand patternschange drastically while a large mass of people are trying to evacu-ate an urban area; conditions can be further exacerbated by possibleloss of capacity during or after the disaster. Since it is not financiallyfeasible to design the transportation network for rare evacuationoccurrences, redesign of the available network capacity to serve adisaster demand pattern is an option considered in emergency plans.For example, reversing the direction of highway lanes during evac-uation and reentry, also known as contraflow, is a redesign optionand can greatly shorten associated delays. Contraflow option designshave already been deployed in U.S. coastal states threatened fre-quently by hurricanes (1). The benefit of contraflow became appar-ent during Hurricane Floyd after it was successfully used in Georgiaand South Carolina (2–4), whereas long evacuation times and grid-lock were observed in Florida, where it was not used because ofsafety concerns.

Evacuation is often necessary before hurricanes strike but may alsobe required in cases of earthquakes, floods, and accidents at nuclearor chemical plants and in the transportation of hazardous materials aswell as in response to terrorist attacks. The literature on disaster stud-ies is extensively reviewed by Tuydes (5). The first documentedexamples of evacuation traffic management were limited to empiri-cal solutions (6, 7). After the partial meltdown of a reactor at theThree Mile Island nuclear power plant in 1979, the mandate by the

Nuclear Regulatory Commission for evacuation plans around nuclearpower plants gave the first momentum to evacuation modeling, whichdeveloped in two main categories: microscopic simulation–basedmodels and macroscopic ones.

The main disadvantage of the simulations was the extensive dataand computer resource requirements, whereas the macroscopic sim-ulations, such as NETVAC1 (8, 9), did not have the capability ofkeeping track of individual driver decisions. Besides, applicationsat that time mainly focused on evacuation planning around nuclearpower plants (10–12) and lacked the capability to address othertypes of disasters. An adaptation of NETVAC1 for multimodal net-works introduced by Han (13) effectively addresses different evac-uation response actions such as rearrangement of gathering points,traffic signal improvement, and use of partially reversible lanes onsix-lane highways. Han observed that integrated solutions had a big-ger impact on decreasing evacuation time as opposed to the sum ofindividual effects gained by partial improvements alone. More re-cently, the evacuation problem for hurricanes and nuclear powerplants was addressed by Barrett et al. (14) and Sattayhatewa andRan (15), respectively, without provision of realistic implementationexamples.

Luo et al. (16) provide a detailed comparison of five evacuationmodels currently in use and evaluate a trip-based four-step traveldemand model, three major evacuation traffic models, and the Traf-fic Estimation and Prediction System (TrEPS) model currentlybeing developed and used by FHWA. Three major models in usetoday are (a) the ETIS model by PBS&J, Inc. (17 ); (b) the OakRidge Evacuation Modeling System (OREMS), developed by OakRidge National Laboratory (18); and (c) the DYNEV model devel-oped by KLD Associates Inc. (12). Among these models, OREMSis a traffic simulation–based model that can estimate evacuationtime and help evaluate evacuation strategies or scenarios, such ascontraflow and staggered departing time strategies, and appears tohave better output information (16, 18).

Tuydes and Ziliaskopoulos (19) introduced a network evacuationmodel with capacity reversibility optimization based on a system-optimal dynamic traffic assignment (SO-DTA) method developedby Ziliaskopoulos (20) and Li et al. (21) with the Cell TransmissionModel (22, 23). The mesoscopic and dynamic nature of the methodaddresses some of the problems observed in previous studies, suchas representation of vehicle-level movements, spatiotemporal changesin disaster conditions, and capability of optimal capacity reversibil-ity calculation. One shortcoming of the model is the high computa-tion cost associated with the analytical nature, which prevents its usefor actual urban networks. But the dual analysis of this analyticalmodel reveals an SO joint traffic and capacity reversibility assign-ment principle similar to that derived by Li et al. (21), which can be

Tabu-Based Heuristic Approach for Optimization of Network Evacuation Contraflow

Hediye Tuydes and Athanasios Ziliaskopoulos

H. Tuydes, Civil Engineering, Middle East Technical University, Inonu Bulvari 06531,Ankara, Turkey. A. Ziliaskopoulos, Department of Industrial and Mechanical Engineering, University of Thessaly, Pedion Areos, Volos 38222, Greece.

157

Transportation Research Record: Journal of the Transportation Research Board,No. 1964, Transportation Research Board of the National Academies, Washington,D.C., 2006, pp. 157–168.

a guideline for a heuristic approach capable of handling large-scaleevacuation problems provided that required measures are estimatedproperly from simulation results. Such an algorithm not only candetermine which part of the network capacity is not optimally uti-lized but also can calculate the direction of an optimal capacity re-versibility scheme. The amount of reversing in the proposed heuristicis determined by a neighborhood search and improved via tabu-basedsearch options.

The basic components of a heuristic approach can be categorizedas a feasible solution, a neighborhood, and a goal function (24). Ina heuristic search, a local optimum is proved if a feasible solutionproduces a better objective value than all possible solutions in aneighborhood around it. A local optimum can be improved withmetaheuristic approaches such as tabu-based algorithms, which mayor may not find the global one. Tabu search was first proposed byGlover (25) and has been successfully applied to a wide range ofproblems, since it is flexible in design and can be customized tofocus on desired trends or behaviors in the search (26–30). It ismostly a search strategy that tries to take advantage of the history ofthe search and the problem structure intelligently (31).

CONTRAFLOW DESIGN FOR URBAN NETWORK EVACUATIONS

The concept of reversing network capacity is not new and has the mainadvantage of increasing the working network capacity without addingnew capacity. Although there are some daily applications, such asreversible left-turning lanes used in the direction of the peak-hour flow(32–38), contraflow did not gain much popularity mainly because ofthe implementation costs and safety and control issues (39).

However, during disasters with severe congestion and long delays,the benefits of contraflow may surpass its cost; this makes it a work-able option. The concept was revisited after Hurricane Floyd, whenit was rejected by officials of the State of Florida despite its suc-cessful implementation in Georgia and South Carolina. The mainreason cited for the rejection was the safety of the overall region be-cause of the lack of preparedness for the application and monitor-ing. Capacity reversibility during the recovery phase after a disasteris used more commonly, since there is no imminent threat and moretime to plan and implement. The necessity and efficiency of capac-ity reversibility are discussed in the aftermath of the Mexico Cityearthquake by Ardekani and Hobeika (40).

The contraflow option in existing evacuation plans is mostlydecided on either by scenario analyses or on the basis of historicaldata and common sense. Its optimality was not studied before theanalytical models developed by Tuydes (5, 19). A scenario-basedcontraflow analysis can be easily incorporated with traffic assign-ment problems but would not provide any measure to search intel-ligently instead of randomly. However, the analytical models lackability to handle urban networks because of the high computationalcost. The gap between these two alternatives can be closed by aheuristic approach that can handle large-scale networks, which fol-lows an optimal assignment principle derived from analytical modelsand is the focus of this study.

Methodologically, the optimality conditions are simpler when thereis no total capacity reversibility in the network, but this assumptionis too strong and not practical in terms of implementation. It wouldrequire more personnel and resources to implement partial reversi-bility, such as a lane-based contraflow strategy. Even with a totalreversibility option, contraflow in an urban network with many

158 Transportation Research Record 1964

intersecting roads has two main challenging issues: control of traf-fic flow crossing the contraflow corridors and dissipation of infor-mation to guide the evacuees to the contraflow segments. In thisstudy, to explore the full potential of contraflow in decreasing sys-tem travel time, perfect compliance and practicality assumptions aremade; however, when a real evacuation plan is designed for a loca-tion, such implementation issues should be addressed properly. Also,unacceptably long evacuation times without the contraflow optionmay justify investment in the technology and methodology to makecontraflow a workable option for urban networks. Furthermore, oncedeveloped, contraflow procedures can be used as a network man-agement option for nonemergency traffic management problems,such as special events and sports events (41).

METHODOLOGY

First, the linear programming (LP) formulation of the SO-DTAmodel with capacity reversibility (SO-DTA-CR), which was previ-ously presented by Tuydes and Ziliaskopoulos (19), is briefly re-viewed. The dual analysis of this problem provides the optimalcapacity reversibility principle, which is used as the basis for theproposed heuristic approach. Later, a tabu-based heuristic algorithmthat uses traffic simulation results is presented.

SO-DTA Model with Capacity Reversibility

The SO-DTA problem using the cell transmission model for trafficflow is first formulated as an LP problem by Ziliaskopoulos (20) andlater modified by Tuydes to account for optimal capacity reversibil-ity distribution (19). A brief summary of the model and the con-straints is as follows: Constraint 1a is the total travel time spent inthe network by all the vehicles; Equation 1b represents the mass con-servation for each cell; Equations 1c through 1f show the limits onthe flow that can travel from cell i to j at time t; 1g, 1h, 1j, and 1krepresent the initial and nonnegativity conditions for the traffic flowin the network, respectively; 1i represents the demand generation atthe source cells; and 1l and 1m are the capacity conservation andnonnegativity constraints for the reversibility variables, respectively.The notation used is presented in Table 1.

subject to

y r QIJod t

I JdoI I I

t

a

,

( , )

* *( ) (∈∈∈

−∑∑∑ ≤ −ECC SR

1 1ee)

y xIJod t

I JdoJod t

ooa

,

( , )

,

∈∈∈ ∈∈∑∑∑ ∑+

ECC CCSR SR

∑∑ ≤ − −( ) ( )* *1 1r N dJ J Jt

y x cIJod t

I J

Iod t

a

,

,

, ( )( )∈∑ ≤

E

1

x x y yIod t

Iod t

IJod t

KIod t

K IJ

, , , ,

( )

= + −− − −

∈∑1 1 1

Γ∈∈ −∑

⎛

⎝⎜⎜

⎞

⎠⎟⎟ ∀ ∈ ∀ ∈

∀ ∈ ∀ ∈

Γ 1( )

, ,

,

I

aI o

d t

C C

C

R

S

G

T \\{ } ( )0 1b

min x t aIod,t

tIdo a

Δ∈∈ ∪∈∈∑∑∑∑

TC CCCG RR SS

( )1

where o and d represent a source cell and a sink cell for the originand destination nodes, respectively; od is a given origin–destination(O-D) pair between which there is some demand; and K and J are

r I mIa≥ ∀ ∈0 1CG ( )

r r I lI Ia+ = ∀ ∈* ( )1 1CG

y I J o

d t k

IJod t a, ( , ) , ,

, ( )

≥ ∀ ∈ ∀ ∈

∀ ∈ ∀ ∈

0

1

E C

C

R

S T

x I o

d t j

Iod t a, , ,

, ( )

≥ ∀ ∈ ∪ ∀ ∈

∀ ∈ ∀ ∈

0

1

C C C

C

R R

S

G

T

x x dy o o

ood t

ood t od t

oJod t

, , ,

, ( ,= +

− ∀ ∈ ∀

− −

−

1 1

1 CR , JJ t ia) \{ } ( )∈ ∀ ∈E , T 0 1

y I J o d hIJod a, ( , ) , , ( )0 0 1= ∀ ∈ ∀ ∈ ∀ ∈E C CR S

x I o d gIod a, , , ( )0 0 1= ∀ ∈ ∪ ∀ ∈ ∀ ∈C C C CR R SG

y r QIJod t

I JdoJ J J

t

a

,

( , )

* *( ) (∈∈∈

−∑∑∑ ≤ −ECC SR

1 1 ff )

Tuydes and Ziliaskopoulos 159

any cells in the network that are predecessor and successor cellssuch that ∀(I, J) ∈ Ea and ∀(K, I ) ∈ Ea.

The main attributes of the model and its assumptions are as follows:

• The continuous capacity redistribution variable rI is a short-coming, since it may result in optimality solutions that are not easilyimplemented or practical. This problem is addressed by lane-basedcapacity reversibility (LCR) and total-or-no-capacity reversibility(TCR) definitions introduced in modified analytical SO-DTA-CRmodels (5). The corresponding SO-DTA-LCR and SO-DTA-TCRmodels are still not applicable for large urban networks because ofthe high computational cost of LP models.

• In the redesigned network description, the maximum capacitythat a cell can have is not a fixed value but a variable that can take avalue between zero and the sum of capacities of the coupled cells inthe original design, called total coupled cell capacity.

• Every cell (road segment) has a coupling cell that can be re-versed to increase the capacity of the link. In the absence of a phys-ical coupling cell, such as in the case of a one-way street, an artificialcell with zero capacity is added in the opposite direction to repre-sent the reversibility potential. The number of links or road seg-ments in the augmented network may be increased, but the totalnetwork capacity is kept unchanged by assigning zero capacity tothe augmented parts.

• A set of links that are eligible for capacity reversibility Vrev canalso be defined as a subset of the total network links; the corre-sponding flow constraints on these links can be written with the vary-ing limits shown in Expressions 1d–1f, and fixed capacity limits canbe defined for the other links.

Optimal Capacity Reversibility Assignment Principle

The dual of the analytical LP formulation was developed by Tuydes(5). The study of the dual variables using the complementary slack-ness theorem reveals the following insights into the optimality con-ditions for capacity reversibility in a traffic assignment: If there isno total reversibility in one direction, the optimal capacity redistri-bution between two coupled cells is reached when the aggregated(over time) values of dual variables times the total coupled cell stor-age and flow values for each flow constraint are the same for bothcells. In other words, over the duration of the analysis, the total mar-ginal cost of reversing one more unit of capacity in the direction ofone cell will have the same marginal cost as that of reversing in thedirection of the coupled cell.

If two coupled cells (or links) bear approximately the same levelof congestion through the whole duration of the analysis, not neces-sarily at the same time, the capacity is distributed optimally. Other-wise, the system can be managed better by reversing some capacityfrom a less congested cell (link) to the more congested one. Thelevel of congestion depends on how severely and for how long thecells are congested. This capacity reversibility principle can be usedas the principle for a heuristic algorithm developed for capacityreversibility optimization in large urban networks, provided that dualvariable values can be estimated.

The SO-DTA-CR model assigns traffic on the paths with theleast path marginal costs that can be found considering contraflow,which is similar to the optimality traffic assignment principles derived

TABLE 1 Notation

Symbol Description

T Set of discrete time intervals

C Set of cells; general (CG), source (CR) and sink (CS)

E Set of connectors; general (EG), source (ER) and sink (ES)

Ca Set of cells; general (CaG), source (CR) and sink (CS)

Ea Set of connectors; general (EaG), source (Ea

R) and sink (EaS)

i Cell in the original network

i* Coupling part of cell i in the original network

I Cell i with the extended capacity in the redesigned network

I* Cell i* with the extended capacity in the redesigned network

Γ(i) Set of successor cells to cell i

Γ−1(i) Set of predecessor cells to cell

x ti Number of vehicles in cell i at time interval t

N ti Maximum number of vehicles in cell i at time interval t

N ti-i* Maximum number of vehicles in coupled set of cells i and i*

at time interval t

y tij Number of vehicles moving from cell i to cell j at time interval t

Q ti Maximum number of vehicles that can flow in or out of cell

i during time interval t

Qti-i* Maximum number of vehicles that can flow in or out of

coupled set of cells i and i* during time interval t

d ti Demand generated in cell i during time interval t

δ ti Ratio of v/w in cell i at time t

v Link free flow speed

w Backward propagation speed

rI Ratio of redesigned capacity of cell I to coupled capacity(Nt

I/NtI-I*)

Revi Reversibility ratio for cell i

by Ziliaskopoulos (20) and Li et al. (21) for other SO-DTA prob-lems. In a heuristic, the traffic and contraflow assignments can beoptimized separately and iterated until a predefined stopping criterionis reached.

Heuristic Approach for Large-Scale Capacity Reversibility Optimization

An effective heuristic algorithm for urban networks can be designedby the optimal capacity reversibility principle stated earlier beingtaken advantage of and traffic simulation to capture the complexbehavior of the SO objective with respect to a reversing scheme. Thetraffic simulator has to provide the performance measures requiredto estimate the optimality condition. For the proposed heuristicapproach, the basic components are chosen as (a) the SO-DTA withthe original capacity design as the initial solution, (b) the neighbor-hood of all possible capacity reversibility schemes on the set of cou-pled links with uneven congestion levels, and (c) the SO objectiveas the goal function.

The main challenge is the exhausting neighborhood search, whichis combinatorial by nature, if every link with reversibility potentialis reversed randomly and the properties of the SO traffic assignmentin conjunction with capacity reversibility are disregarded.

The complexity of the problem and the behavior of the SO objec-tive with respect to capacity reversibility in addition to the combi-natorial nature of the feasible domain call for customized search andevaluation techniques, which are beyond the capability of a localneighborhood search and can be achieved by a metaheuristic suchas a tabu search, which can push the search beyond a local optimum.

Reversing Eligibility

The set of links eligible for reversibility, Vrev, can be defined at thepreprocessing stage on the basis of implementation and physicalroadway characteristics, but eventually the final design of an opti-mal contraflow plan depends on the traffic assignment, more specif-ically, congestion levels on the links. If no link is congested, nocontraflow design is necessary. If some links reach maximum capac-ity at some point whereas their coupled links do not, that is an indi-cation of lack of optimal capacity use, and a better network capacityutilization can be achieved by capacity reversibility.

In the absence of dual values, it is not easy to calculate the mar-ginal cost of reversing a unit capacity in a cell (or a link), which isthe sum of dual values of the constraints (1d–f ). However, these dualvalues are nonzero only when the corresponding constraints arebinding, in other words, when the storage or flow capacities are fullyused. Thus, the marginal cost of reversing a unit capacity in a link ican be roughly estimated by the total number of times link capaci-ties are used at the maximum levels, which can be used as a con-gestion measure �i. Then, for every couple of links (i, i*), thedifference in the congestion levels Δ�i−i* is calculated to determinethe need for contraflow: if the given capacity utilization is not opti-mal and Δ�i−i* ≠ 0, the optimality requires capacity reversing fromi to its coupled link i*, or vice versa.

This congestion measure implicitly assumes that all dual variablescontribute equally; this is a strong assumption. But with congestiondue to the capacity limits represented, it is still more accurate thanother measures, such as total number of vehicles using the links.


Reversing Amount

Once the links that need reversing are determined, the next issue ischoosing a reversing scheme: how much of a link capacity to reverseand how many links at a time. For the former, a total-or-no reversibil-ity that reverses all capacity on the candidate links—which wouldbe a rather drastic move—can be proposed; if there are no alterna-tive paths to those that use reversed links, some demand may beunserviceable. An alternative scheme would be to reverse linkcapacities partially and let the iterative traffic assignment processreroute demand on other paths before total reversal. For such agradual-reversibility option, the principle of reversing one lane at atime is proposed, considering the applicability of the reversingschemes. This principle narrows the theoretical feasible domaindown to all possible combinations of candidate links, which maystill be large in an urban network application.

Reversing Scheme

Reversing one congested link without increasing the capacity of theupstream ones may result only in the shift of the location of the con-gestion and may not improve the objective function significantly orat all. Instead, one lane can be reversed on all links with uneven con-gested levels along paths or links with certain criteria, such as onlythe links with no flow in the reverse direction or links beyond a cer-tain congestion level. Preliminary studies of different reversingschemes tested by the dual variables from the LP model resultsshowed that a scheme that reverses one lane on all the links withunderutilized capacity, Δ�i−i* < 0, at once (all-at-once scheme) hasa better chance to reach to an optimal (or a suboptimal) solutionfaster (5).

Early in the search process, the proposed reversing scheme findsthe major congestion corridors that will significantly benefit fromcontraflow in reducing the system travel time without causing toomuch delay or congestion to any flow in the opposite direction.However, it may not be that effective when finer capacity adjust-ments are needed later in the process. In such cases, reversingschemes can be modified to find effective partial ones as opposed toan all-at-once scheme.

Tabu-Based Search Algorithm

In a tabu search, the main parameters to define are the goal function,search moves, tabu moves, and improved search actions (such asdiversification and intensification). For optimization of capacityreversibility, it is possible to choose a goal function that optimizesthe number of link couples with uneven capacity utilization or thechange in the system travel time as a function of link reversals. How-ever, the formulation of such complex behaviors requires equallycomplex formulations and increased computational power require-ments. In this study, a rather simple tabu search approach was usedas explained next (and shown in Figure 1).

Goal Function

The SO objective, which is the minimization of total network traveltime, ΞSO, is also selected as the goal function for the capacity re-versibility optimization step. In this way, the capacity reversibility

optimization actions do not produce solutions that contradict thetraffic assignment step solutions.

Initial Solution (Step 0)

The necessary initial solution is chosen as the base case networkcapacity design with the SO objective value of ΞSO−base; this solutionalso corresponds to the do-nothing option in terms of capacity re-versibility. In addition to the basic information, the network datahave to be updated to include the capacity reversibility information,sets of coupled links, and augmentation, which are discussed in detailby Tuydes and Ziliaskopoulos (19).

Neighborhood Search (Steps 1 and 2)

A reversing scheme that has the potential to improve the objective isdefined as a search node or move. To determine a reversing scheme,


for every couple of links (i, i*) eligible for reversing i ∈ Vrev, the dif-ference in the link congestion levels Δ�i−i* is calculated, and the linkless congested than its coupled one is put in a search list Sn. The searchlist in each iteration may change as the number of unevenly congestedlinks changes during the progress of the reversibility design; it isexpected to get smaller in the later iterations and converge to anoptimal (or a suboptimal) design.

The next task is to check the currently available links in the searchlist at the end of the previous iteration, Ω n−1

i , and the tabu moves. Iflink i* is still not totally reversed or it did not receive capacity fromthe coupled link i in a previous iteration (to avoid cycling in link-reversing schemes), one lane is reversed from link i and added to thecapacity of link i*, ρn

i* = +1lane, where ρni represents the lane rever-

sal scheme on link i at iteration n. If there is no more capacity in linki or the link is not in the search list Sn, no further lane reversibilityis possible; ρn

i = ρni* = 0. The final network capacity redesign to be tested

is the combination of the current best network capacity distributionand the recently suggested lane reversal schemes

Reverse 1-lane

ρni* = +1 lane

ρin = –1 lane

ρik;i ∈Vrev ]Rn = [

Step 3Decisio

∀(i, i* ) ∈ Vrev

Calculate the difference inlink congestion levels

Step 4Termination

No

No

Step 0Initialization

Step 1ReversibilityPotential

Step 2ReversibilityScheme

Step 3Decision

Network preparations: coupling and augmentation

Determine base case SO-DTA system travel time,

Set iteration n=0; =

Create empty lists: tabu list, ;search list, S0; intensification list

n=n+1

Calculate the difference inlink congestion levelsCalculate the difference inlink congestion levels

SO-DTA•Assignment•Simulation

Sn = { }

0ni

i Flow onlink i?

Intensificationsearch

n

k=0

Rn

Feasible?

Diversificationsearch

Rn

<•Accept reversingScheme•Put reversed links in•Current best ΞSO–Rn

ΞSO–Rn

ΞSO–R0 ΞSO–base

ΞSO–base

ΞSO–Rn–1

No

impr

ovem

ent

Yes

No

Yes

Yes

Yes

Yes

i ∈ Sn

i ∈∀i ∈ Sn

Δλi–i*

Δλi–i* < 0

ρin = ρn

i* = 0

∑

YesNo

Criteria

FIGURE 1 Tabu-based metaheuristic algorithm to find optimal capacity reversibilityby using simulation results.

ρni ’s; , where ρ0

i is the number of lanes in linki in the base case.

Decision Criteria (Step 3)

Once a reversibility scheme and the consequent network capacityredesign Rn are decided on, their feasibility and effectiveness mustbe tested by traffic being reassigned on the proposed redesignednetwork. If the SO-DTA assignment with Rn-capacity reversibil-ity scheme is feasible, the resulting system travel time of ΞSO−Rn iscompared with the current best solution of the previous iteration,ΞSO−Rn−1. If ΞSO−Rn < ΞSO−Rn−1, then the current best objective is ΞSO−Rn

and the redesigned network is the current best design; the recentlyproposed lane reversal scheme is accepted. No lane reversibilityscheme is accepted until the objective function is improved. If theobjective function does not improve while there are links in thesearch list, the decision criterion can be modified to accept tem-porarily reversing schemes that do not improve the goal functionbut decrease the number of unevenly utilized coupled links, as adiversification action.

Tabu List

Once a reversing scheme is accepted, the links that lose capacityare added to the tabu list, , to avoid rereversing capacity in thefollowing iteration, and they are kept there until either a pre-defined number of iterations or an improved search is performedvia intensification. Rereversal need may be observed when thecongestion levels of two links are close and a lane capacity ismore than the optimal reversing amount. With the first reversalmade a tabu move, the reversal is made in the favor of a slightlymore congested link.

Stopping Rule

The tabu search, by nature, has an open-ended search option but canbe terminated on the basis of predefined criteria. In this implementa-tion, an empty search list means that the capacity of reverse-eligiblelinks is evenly utilized, and there is no further improvement poten-tial via reversibility. If the search list is not empty, there are somelinks that are underutilized compared with their coupled ones. Butthe net impact of an additional reversing scheme may be small, andthe search can be terminated on the basis of a predefined goal functionimprovement threshold value. Other commonly used terminationmeasures are maximum iteration number and maximum time limit.Before the search is terminated, it is possible to improve the bestsolution that can be obtained by the neighborhood search via improvedsearch options such as intensification.

Diversification Searches

If an aggregate reversing policy such as the all-at-once schemedescribed earlier does not improve the solution any further, ΞSO−Rn >

R in

im

m

n= ∈⎡⎣ =∑ ρ ;0 Vrev


ΞSO−Rn−1, or the proposed scheme results in an infeasible solution andthere are still link couples to optimize, the proposed scheme can bemodified to find a new one that reverses either only those links thatwill improve the objective or those that do not cause infeasibility inthe traffic assignment. This diversification from a given move canbe achieved in different ways. To correct a reversibility scheme thatcaused infeasibility, a partial reversibility, Rn

s, scheme is developedby simple exclusion of the links that carried flow in the previous iter-ation and lost total capacity with the latest lane reversals. To improvethe effectiveness of the reversing scheme, the subset of links thathave a negative impact on the objective function is determined andexcluded from the reversal. In this way, a reversing scheme of thelinks that surely improves the objective is found.

Of course, there are many combinations of links in the search listto consider in iteration Sn, which could be computationally costly.The adopted decision rule in the proposed design is to accept feasi-ble solutions that are close to the current best but not better by a tol-erance value being added to the right-hand term—that is, ΞSO−Rn−1 +T—where T can be defined as a percentage of the current best objec-tive value. Thus, even though ΞSO−Rn is accepted as the best solutionfor iteration n to continue the search, the overall current best will beΞSO−Rn−1. The current best is kept as the ΞSO−Rn−1 until it is improved byanother reversing scheme.

Intensification Searches

To check the effectiveness of total reversals, within the tabu list ,a second list of the links that lost their capacity totally but servedsome flow in previous iterations is created. A reversibility schemethat proposes one-lane rereversal on these links can be tested foreffectiveness. As another intensification search, consecutive linksalong paths that could work together can be assigned as partialreversibility schemes. If the intensification moves find a better solu-tion, it is assumed as the current best, and the tabu list is updatedaccordingly. If not, and there is no link in the search list, the searchis terminated. Since the traffic assignment and consequently linkusage are mostly governed by the demand pattern and networktopology, no special method is developed for the intensificationprocess other than a scenario-based trial-and-error approach.

Since the developed capacity reversibility models and heuristicapproaches have the SO objective, the proposed heuristic approachrequires a large-scale SO-DTA simulator as well. Because of theabsence of a reliable path-based SO-DTA formulation and software,a simulation-based SO-DTA model was developed by Tuydes (5).This formulation is later coded into the Visual Interactive Systemfor Transport Algorithms (VISTA) software, which is an integratedenvironment of traffic assignment and simulation algorithms usedin the steps of the proposed heuristic approach (42).

Although the presented LP formulation and the optimal capacityreversibility principle are link-based, most of the traffic simulatorsare path-based. The path-based SO-DTA formulation with capacityreversibility that confirms the optimal assignment principle, pre-sented in the subsection on optimal capacity reversibility assign-ment principle, is discussed in detail by Tuydes (5). Of course, theheuristic approach presented here can be used with link-based traf-fic simulation tools as easily as with the path-based ones, since therequired congestion measures can be estimated from the results ofany traffic simulator.

COMPUTATIONAL EXPERIENCE

To study the contraflow option for evacuation of an urban region, anumerical example with a realistic network size is created for a hypo-thetical evacuation scenario for the city of Evanston, Illinois. It isassumed that a disaster will hit the Evanston campus of NorthwesternUniversity and require evacuation within a zone with a 3-mi radius(Zone 1) around the campus, which includes most of the city ofEvanston, the southern part of the city of Wilmette, and a small part ofthe city of Chicago. The region outside a 5-mi radius zone (Zone 3),including the potential evacuation destination locations, is assumedto be out of danger. The 2-mi zone (Zone 2) between Zone 1 andZone 3 is a buffer zone, which does not include evacuation demandbut has to be cleared of the primary evacuees in case a secondaryevacuation is needed for some reason.

In the absence of an evacuation demand study for any possibledisaster at the selected location, the demand and the O-D pattern arederived from census population demographics. Certain assumptionsabout evacuation behavior such as response, compliance, and mobi-lization rates are made whenever needed. Although these assump-tions will certainly affect the outcome of an evacuation and needfurther study separately, the focus of this example is not to develop


a real evacuation plan of Evanston but to demonstrate the potentialimprovement with a contraflow option for a large-scale example.

Evanston Evacuation Example

Network Data

The traffic network imported in VISTA (see Figure 2) is extractedfrom the Chicago Area Transportation Study regional six-county net-work. The study region is bordered by Lake Michigan to the east; byWillow Road, Winnetka, to the north; by Interstate 94 to the west; andby Addison Street, in Chicago, to the south. It includes 2,127 links(road segments and ramps) and 728 nodes (intersections and inter-changes). The current network does not include signal informationfor the evacuation scenario.

Demand Data

The demand data and locations of evacuation O-D points are esti-mated on the basis of Census 2000 housing characteristics and vehi-

FIGURE 2 Traffic network for example urban evacuation.

cle availability data provided at the census-tract and block levels (43).The disaster region (Zone 1) includes a total of 28 census tracts inEvanston and Wilmette. When a tract is not included fully within thedisaster zone, block-level information is used to decide which blockswill be contributing to the evacuation demand. A portion of Chicagothat falls into the disaster region is left out of the Evanston evacuationplan, since the number of census blocks included is small.

The total number of evacuation trips is estimated by the numberof households with vehicles in the selected 28 tracts, which totals32,715 vehicles: 29,651 from Evanston and 3,064 from Wilmette.The origin nodes are assumed as the internal centroids of the censustracts, which are connected to the traffic network by centroid con-nector links created in addition and do not contribute to the traveltime calculations. Six evacuation destinations (D1–D6) beyond the5-mi safety limit are selected as shown in Figure 2. These destina-tion nodes are connected to as many nodes along the periphery ofthe network as possible. No background traffic is considered.

The demand generation duration is assumed as 3 h, during which thevehicles are assigned to depart in twelve 15-min intervals. Theresponse to the evacuation order is represented by a normal cumula-tive curve with a mean of 1.5 h and a standard deviation of 30 min. Thedynamic demand profile used for the simulations is shown in Figure 3.

Trip Distribution

Although trip distribution is by itself a separate step in the evacua-tion modeling process, for the sake of simplicity it is assumed thatevacuation demand at an origin is assigned to the nearest destina-tion. The static O-D trip distribution data are given in Table 2. Inreality, there might be a more dispersed trip distribution pattern, inwhich some of the evacuees choose not to comply with the nearestdestination assignment and go to a further destination.

Base Case: Evacuation of Evanston Without Contraflow

Base case traffic assignment is performed with the VISTA SO-DTAmodule. The summarized results in Table 3 show a total system travel


time of 25,488 vehicle-h with a system average of 47 min/vehicle. Thenetwork clearance time is calculated as 5 h 12 min, with the latestarrivals at destination D6, which is the destination in the direction ofdowntown Chicago and is assigned the highest number of evacuees.The arrival and travel time statistics decomposed by the departuretime show that evacuees departing early travel in an uncongested net-work because of the empty-network assumption for the initial con-ditions. The later the departures times are, the longer the travel timesthat evacuees experience. The evacuees of high-population regionssuch as northern and southern Evanston departing in the last hourspend approximately 9 to 10 times longer in the network than thosein the uncongested case.

Evacuation of Evanston with Contraflow

To improve evacuation traffic conditions, a contraflow option alonga set of arterials is considered. The corridors eligible for reversal areshown in Figure 4. Although these corridors include most arterialsin the network, some arterials are left out to serve both directionsand accommodate possible emergency vehicle traffic in and out ofthe region.

The heuristic approach proposed in the subsection on tabu-basedsearch algorithm is implemented, starting with the base case with nocontraflow presented earlier as the feasible initial solution. A briefsummary of the iterations is presented in Table 4. Three iterationsof reversibility schemes are performed. Although a local optimumis found at the end of the second iteration, the analysis is continuedsince there was still reversibility potential in the selected contraflowcorridors.

The search is terminated when there are no more eligible links tobe reversed, and a better local optimum evacuation trip assignmentis achieved with a system travel time of 19,609 vehicle-h. The valueof this measure is 20.64% less than the one in the base case.

The network design at the end of all reversibility schemes isassumed to be the best network redesign, although it is likely to be alocal optimum. It is possible to get better solutions by an intensifica-tion process around the current best solution, but the details of theseimproved searches are not included here. The network segments that

0

0.05

0.1

0.15

0.2

0.25

0 3 6 9 12 15

Demand Assignment Intervals (x15 minutes)

% D

eman

d

FIGURE 3 Dynamic demand profile selected for evacuation.

are totally reversed in the opposite direction are shown in Figure 5.The six partially reversible links are located at the beginning or endof the total reversibility corridors.

Discussion of Results

In addition to the significant reduction in system travel time viacapacity reversibility, the results for the redesigned case are studiedfurther to gather information about the change in average travel timeand exit times, as presented in Table 5. The improvement in trafficconditions can be observed especially among vehicles assigned toD3, D4, and D5, which experience almost uncongested traffic condi-tions compared with the base case, with delays up to three or fourtimes the uncongested travel times. The average travel times of theevacuees destined to the other exit points are also improved, but thechanges are not that significant.

Although system travel time shows a significant 20% reduction,this improvement is not reflected in the latest exit time (a measureof network clearance time), which is reduced by only 3 min com-pared with that in the base case. This result is mainly because theobjective function in both the traffic assignment, and the heuristic


approach is chosen as the minimization of system travel time, notthe latest exit times. Also, the demand is generated in 3 h; it con-tributes to the network clearance time significantly compared with themuch shorter travel times. Network capacity is still large enoughto handle the evacuation demand, and there is no gridlock or longdelays in the base case, which would be a more suitable situation inwhich to consider the contraflow option. For more severe cases withlonger queues, capacity reversibility proves to be more effective (5).If the objective is defined as reduction of network clearance time, amodified model that minimizes the latest exit time with or withoutthe SO objective should be developed.

Verification of Approach

Since there are no other approaches to optimize capacity reversibil-ity, the proposed model is verified by the results of the analytical LPmodel. Because of computational resource limitations, the LP SO-DTA-CR model is run on a test network of 25 nodes and 70 links,serving an evacuation demand of 606 vehicles, and is analyzed for500 s at 10-s time intervals. The tabu-based heuristic was able to findan SO objective, which is only 3% more than the optimal solution.

TABLE 2 Trip Distribution Data for the Evanston Evacuation Example

OriginDestination

(census tract) D1 D2 D3 D4 D5 D6 Total Demand

8,012 1,380 — — — — — 1,380

8,011 1,586 — — — — — 1,586

8,013 1,552 — — — — — 1,552

8,087 429 — — — — — 429

8,088 1,370 — — — — — 1,370

8,089 — 1,662 — — — — 1,662

8,090 — 1,371 — — — — 1,371

8,091 — 1,305 — — — — 1,305

8,093 — 1,557 — — — — 1,557

8,067 — — 1,544 — — — 1,544

8,071* — — 1,055 — — — 1,055

8,072** — — 1,261 — — — 1,261

8,092 — — 1,165 — — — 1,165

8,095 — — 650 — 651 — 1,301

8,096 — — 1,042 — — — 1,042

8,097 — — — 603 604 — 1,207

8,103.01 — — — 666 667 — 1,333

8,103.02 — — — 597 597 — 1,194

101 — — — — — 1,219 1,219

8,094 — — — — — 1,773 1,773

8,098 — — — — — 1,035 1,035

8,099 — — — — — 1,067 1,067

8,100 — — — — — 2,454 2,454

8,101 — — — — — 1,853 1,853

Total demand 6,317 5,895 6,717 1,866 2,519 9,401 32,715

* For Tract 8071, data from only Block Groups 1–3 are included.** For Tract 8072, data from only Block Groups 1–4 are included.— stands for the case of no demand between the given O-D pair.NOTE: Values are given in numbers of vehicles.


TABLE 3 Base Case Evacuation Time Statistics for UrbanNetwork Example

Number of vehicles: 32,715System travel time : 25,488 veh/hAverage travel time : 47 min/veh

Average Travel Times(min/veh)

Destination Latest Exit Times Evacuation Uncongested

D1 4 h 20 min 51 minDepartures

0–1 h 1 h 15 min 8 min 8 min1–2 h 3 h 58 min 46 min2–3 h 4 h 20 min 1 h 12 min




0–1 h 1 h 13 min 9 min 8 min1–2 h 3 h 0 min 20 min2–3 h 3 h 24 min 29 min





D6 5 h 12 min 1 h 9 minDepartures


Network clearance time: 5 h 12 min

NS1NS2

NS8

NS5

NS4

NS3

NS7

NS6

NS9

ES1

ES2

ES3

ES4

ES5

ES6

ES7

Lake MichiganNS1NS2

NS8

NS5

NS4

NS3

NS7

NS6

NS9

ES1

ES2

ES3

ES4

ES5

ES6

ES7

Corridor Arterial Start Point End PointNS1 Sheridan Rd-North Lake St (Wilmette) Willow RdNS2 Greenbay Rd Colfax St Willow RdNS3 Crawford AveNS4 McCormick Blvd Church St Devon AveNS5 Dodge Ave/California Ave Lawrence AveNS6 Asbury Ave/Western Ave Pratt AveNS7 Ridge AveNS8 Chicago Ave/Clark St Grove St Howard StNS9 Sheridan Rd-South Church St Devon AveES1 Wilmette Ave/Glenview Rd Sheridan Rd Harms RdES2 Old Orchard Rd/Colfax St Ridge Ave Harms RdES3 Church St Ridge Ave

Devon Ave

Devon Ave

Harms RdES4 Howard St Sheridan Rd McCormick BlvdES5 Devon Ave-West

Church St

Church StOakton StMain St

McCormick Blvd NLehigh Ave ES6 Pratt Blvd Sheridan Rd Kedzie AveES7 Devon Ave-East Sheridan Rd Ridge Blvd

FIGURE 4 Selected potential capacity reversibilitycorridors.

TABLE 4 Summary of Tabu Search for Local OptimalCapacity Reversibility

Number of

System Travel TimeReversed Links

Iteration (veh h) Partial Total

0 25,488 0 0

1 20,006 18 40

2 20,107 8 53

3 19,609 6 55

D1

D4

D3

D2

D6

D5

FIGURE 5 Network redesign with total capacityreversibility links.

The step-by-step performance of this verification example can befound elsewhere (5).

CONCLUDING REMARKS

This study is concerned with development of an approach to find anoptimal contraflow design for urban evacuations. A heuristicapproach is developed that approximately follows the optimal capac-


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The Transportation Network Modeling Committee sponsored publication of thispaper.

tabu-based heuristic approach for optimization of network evacuation contraflow

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