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Multi-objective Based Road-Link Grading for Health-Care Access During Flood Hazard Management Omprakash Chakraborty (B ) , V. Yeshwanth, Pabitra Mitra, and Soumya K. Ghosh Indian Institute of Technology (IIT) Kharagpur, Kharagpur, West Bengal, India [email protected] , [email protected] , [email protected] , [email protected] Abstract. Health-care centers form a critical part in citizen services during disaster management. Road networks play an important role in facilitating access to such services from settlements. The importance of a road depends on its utility in this respect along with its geospatial characteristics. In this article, road importance measures are proposed that consider spatial properties as well as path utlizations. These met- rics are then utilized to identify optimal links of the network in terms of safety and sustainability towards relief-facility access even in severe hazard conditions. A case study is presented for a flood scenario in the Bankura district of West Bengal, India. The proposed approach provides a more realistic assessment of the road importance as compared to con- ventional link analysis. The identification of optimal road links help in several mitigation and rescue strategies for disaster management. 1 Introduction Amongst all natural hazards, floods pose one of the highest threats [1] to the pop- ulace and their properties in the Indian sub-continent. The entire coastal areas of the sub-continent are the most resource rich areas leading to high population density and drawing continuous stream of migrant population [1]. The increasing population density and the changing pattern of the monsoons pose a higher risk in these areas. A study on floods and their societal impacts has been carried out in Bangladesh [2]. Incidentally, Bangladesh lies in the Indian sub-continent and shares similar experience with flood related vulnerability. West Bengal has in past, experienced several large floods, most of these can be attributed to trop- ical cyclones or monsoonal rains [3]. The socio-economic characteristics of the flood prone areas are such that most of these floods have left behind irreparable losses. These losses can be characterized into direct losses - losses incurred due to mortality and morbidity of population, loss to physical property, damaging of standing crops, loss to livestock, and indirect losses - outbreak of epidemics, forced migration [3]. c Springer International Publishing AG, part of Springer Nature 2018 O. Gervasi et al. (Eds.): ICCSA 2018, LNCS 10960, pp. 277–293, 2018. https://doi.org/10.1007/978-3-319-95162-1_19

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Page 1: Multi-objective Based Road-Link Grading for Health-Care Access … · 2018-07-03 · Multi-objective Based Road-Link Grading for Health-Care Access During Flood Hazard Management

Multi-objective Based Road-Link Gradingfor Health-Care Access During Flood

Hazard Management

Omprakash Chakraborty(B) , V. Yeshwanth, Pabitra Mitra,and Soumya K. Ghosh

Indian Institute of Technology (IIT) Kharagpur, Kharagpur, West Bengal, [email protected], [email protected],

[email protected], [email protected]

Abstract. Health-care centers form a critical part in citizen servicesduring disaster management. Road networks play an important role infacilitating access to such services from settlements. The importance ofa road depends on its utility in this respect along with its geospatialcharacteristics. In this article, road importance measures are proposedthat consider spatial properties as well as path utlizations. These met-rics are then utilized to identify optimal links of the network in termsof safety and sustainability towards relief-facility access even in severehazard conditions. A case study is presented for a flood scenario in theBankura district of West Bengal, India. The proposed approach providesa more realistic assessment of the road importance as compared to con-ventional link analysis. The identification of optimal road links help inseveral mitigation and rescue strategies for disaster management.

1 Introduction

Amongst all natural hazards, floods pose one of the highest threats [1] to the pop-ulace and their properties in the Indian sub-continent. The entire coastal areasof the sub-continent are the most resource rich areas leading to high populationdensity and drawing continuous stream of migrant population [1]. The increasingpopulation density and the changing pattern of the monsoons pose a higher riskin these areas. A study on floods and their societal impacts has been carried outin Bangladesh [2]. Incidentally, Bangladesh lies in the Indian sub-continent andshares similar experience with flood related vulnerability. West Bengal has inpast, experienced several large floods, most of these can be attributed to trop-ical cyclones or monsoonal rains [3]. The socio-economic characteristics of theflood prone areas are such that most of these floods have left behind irreparablelosses. These losses can be characterized into direct losses - losses incurred dueto mortality and morbidity of population, loss to physical property, damagingof standing crops, loss to livestock, and indirect losses - outbreak of epidemics,forced migration [3].c© Springer International Publishing AG, part of Springer Nature 2018O. Gervasi et al. (Eds.): ICCSA 2018, LNCS 10960, pp. 277–293, 2018.https://doi.org/10.1007/978-3-319-95162-1_19

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278 O. Chakraborty et al.

The disaster mitigation strategies for affected communities can be sub-divided into two parts, first is a pre-disaster strategy of moving population toflood reliefs and second being the provision of emergency response services [3].The flood reliefs have a catchment area and the population residing within thatcatchment moves in before the disaster strikes. It also has provisions for safe-guarding livestock during the disaster. However, post disaster response activi-ties, as considered in our case, involve emergency medical-care, medical support,threat of epidemic and other public health issues, mortuary services apart fromother relief operations like fooding provisions, drinking water, etc. It is evidentthat both the pre- and post-disaster operations is dependent on road connec-tivity. The pre-disaster connectivity is mostly limited to community level, fairweather conditions whereas, post disaster connectivity needs to be addressed atthe regional level.

Spatial analysis or statistics is a wide and interdisciplinary scientific topicincluding a variety of techniques, many still in their early development, usingdifferent analytic approaches and applied in diverse fields. Spatial analysis isapplied to structures at the human scale, most notably in the analysis of geo-graphic data. In case of disaster management also, Geographic Information Sys-tems (GIS) techniques have vast implementations which are still being exploredwith alternative perspectives and extensive approaches.

Urban and Regional Studies deal with large tables of spatial data obtainedfrom several heterogeneous sources. It is necessary to channelize the huge amountof detailed information through a fixed work-flow in order to extract the maintrends. As GIS based service oriented approach is needed to integrate social andenvironmental data as a map for carrying out the analysis. This study aims toimplement a framework to retrieve diverse spatial data and incorporate it toanalyze road networks and compute key measures such as node importance andedge importance of the network.

In our study, we aim to analyze the road network of a region to facilitate themitigation strategies during disasters. We utilize spatial properties of the regionto assess the vulnerability of the road links followed by its diverse utilization bythe affected populace in reaching different healthcare facilities. Road importancemeasures have been proposed for the same. We also provide a relevant case studyto depict the results of our approach.

2 Related Works

The analysis of roads from various perspectives and different disaster circum-stances have been carried out over a decade. [4] gives an overview of the roadreliability, various approaches towards vulnerability and effective risk analysisaimed to optimize the service provisions. The discussions can be related to mostof the present day road network with variable traffic flow and usages. [5] promotesthe approach of network robustness index of the edge links for improvement overthe congested critical links. The index is derived based on the change in the timecaused due to the re-routing of traffic within the system owing to the instability

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Multi-objective Based Road-Link Grading for Health-Care Access 279

of that road edge. The transport network resilience has been studied by [6], interms of the critical capacity of the network. The approach involves a geneticalgorithm based approach to analyze the resilience in the view of a maxminoptimization problem. [7] gives an approach to derive the safety criteria for thevehicles in roads subjected to urban flood risks.

[8] evaluates the impact and risk of pluvial flash flood in the city center ofShanghai, China. It depicts a method to measure the impact of pluvial flashflooding and its risk on intra-urban road networks. The results indicate the localorigination of road floods and synchronization with the timing of rainfall is gen-erally proportionate to the magnitude of precipitation. Our previous work, [9],also aimed at the risk mapping for critical flood affected regions utilizing variedheterogeneous sources. It proposed a service oriented framework for the depic-tion of risk zones in a disaster prone region. Some interesting results revealedlarger water-bodies possessing a great effect towards water level risk in terms offlood assessment. The final result depicted the division of final risk zones withvariation in regional elevation within the study region.

3 Road Importance Grading Framework

The overall framework is shown in Fig. 1. The system takes different spatial data(road network, elevation map, facility locations etc.) as inputs, and grades thelinks to identify the least vulnerable paths. The approach modules are illustratedin the respective sections later.

Fig. 1. Overview of the road importance grading framework

4 Flood Risk Measure

In case of a road network, the identification of risk at the edge level can bedetermined by the spatial vulnerability of the individual links as well as the

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280 O. Chakraborty et al.

effects of the link disruption on the overall connectivity of the road system.These critical factors are addressed using two proposed measures namely: (i) LinkVulnerability Measure (LVM ) and (ii) Edge Aggravation Magnitude (EAM ).

The road network is modeled as a weighted undirected multi-graph G =(V,E), where the set of vertices V denote the population settlements (villagesor towns) and E, the set of edges represent the connecting roads between them.

4.1 Link Vulnerability Measure (LVM)

LVM is proposed to predict the likeliness of the road-links for getting disrupted.That would be the measure of how vulnerable that particular link is in the caseof floods. The flood based vulnerability is computed based on the elevation ofthe link and proximity of the edge to a water-body, that if an area is at higherelevation and far from a water-body, it is less likely to get submerged. Thereforethe link would stay intact and so has a lower risk. Thus we can say that theprobability of a link getting disrupted (vulnerability) is inversely proportionalto the elevation of that link and its proximity from a water-body,

Pr(ei) ∝ 1Elevation(ei) × Proximity(ei)

,

where Proximity(ei) is the shortest distance of the link from the closest water-body.

So, the vulnerability relative to the sample points can be computed usingEq. 1.

Pr(ei) =

1

1+√

Elevation(ei)×Proximity(ei)∑

e∈E1

1+√

Elevation(ei)×Proximity(ei)

(1)

Note that both elevation and proximity values are taken as positive val-ues. Usual elevation data is given with respect to sea level. So it is possibleto encounter negative values. These negative values were normalized. Since weare finding out relative probability, the choice of function used to calculate theprobability does not alter the results.

5 Edge Aggravation Magnitude (EAM)/Edge CriticalityIndex

Applying the proposed EAM concept to the road networks, we calculate thecriticality of an edge in terms of the overall connectivity for optimal functioningof the road network. This may seem to be straightforward that the probability ofthe link getting disrupted (LVM) is the direct measure of edge criticality indexas a link is more susceptible to disruption it is more critical. However, it is notthe case as shown using a sample a road network connecting six villages shownin Fig. 2.

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Multi-objective Based Road-Link Grading for Health-Care Access 281

Fig. 2. Toy example to show that vulnerability doesn’t necessarily imply criticality

Say, the edge E2 has highest probability of getting disrupted. We can’t plainlysay that edge E2 has the highest EAM index among all the edges. Because E2 isconnecting vertices V5 and V6 which are also connected by V5 −V4 −V6 path. Soeven if E2 gets disrupted we can reach V 6 from V 5. Now suppose the edge E1

that is connecting V3 and V4 gets disrupted, this would mean that the networkis disconnected. Suppose there is a district hospital in V4, if E1 gets disruptedthere is no way that people from V1, V2 and V3 can access that hospital in V4.Thus, we need to consider the population and resource flow while calculatingthe EAM index of an edge. Putting the above discrepancy in theoretical terms,the magnitude of aggravation associated with the link disruption in additionto the vulnerability of the link should also be considered in order to completethe formulation of criticality. To calculate the EAM mertic, the utilization ofthe links are getting analyzed. If a link that is very frequently used to access ahospital, then that particular link staying functional is very important and thereis an inconvenience to huge population caused with its disruption hence it canbe termed as critical.

For the study purpose, a facility is defined as a place equipped with providinga particular service. For example - Hospitals, Banks, Education Institutes. Now,to capture the data of population flow and resource flow, we initially considerthe catchment of particular facility. Catchment area of a facility refers to theregion that is being served by that particular facility. The whole network isdivided into different catchments with respect to a particular facility based onthe shortest path distances from the facilities. The concept of catchment mappingis illustrated in the toy example in Fig. 3.

Fig. 3. Toy example to illustrate the concept of catchment

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282 O. Chakraborty et al.

To define the concept of catchment mapping mathematically, the road net-work is considered as weighted undirected multi-graph G = (V,E). Let the vertexset V = v1, v2, . . . , vn be the set of all population settlements and edge set Ebe the connecting roads between them weighted based on the travel cost alongthe road. Let F i = f i

1, fi2, . . . , f

in be the set of facilities of type i such as hospi-

tals. It is reasonable to assume that for a given node vk, the nearest facility interms of travel distance is the one which serves it. We define a distance functiondist(vk, f i) as the cost of traveling from settlement vk to facility f i

j along theshortest path in the road network represented by the multi-graph G = (V,E).Then the Catchment CM of facility f i

j is the union of nodes that are served byf i

j and is represented as,

CMF (fi) = {⋃sk|sk ∈ V &

dist(sk, fi) = min(dist(sk, f1), dist(sk, f2), . . . , dist(sk, fm)} (2)

where 1 ≤ i ≤ m and 1 ≤ k ≤ nHowever, there is one fundamental assumption in the above approach that

we say that a particular settlement vk is served only by the facility f ij . But this is

not necessarily true in all cases. So instead of dividing the graph into catchments,we compute the probability with which a settlement vk is served by the facilityf i

j say Probabilistic Catchment (pCM). To calculate this probability we againconsider the distance function that was defined before and argue that higher thedist(vk, f i) lower the probability that people from the settlement vk are goingto choose f i

j as their primary facility. So inverse of the distance is considered forcalculating the probability. To handle the zero distance cases we add a bias term1 while calculating the probability. Now we define pCM as,

pCM(vk, f i) =1

1+dist(vk,fi)∑m

i=11

1+dist(vk,fi)

,

where 1 ≤ i ≤ m and 1 ≤ k ≤ npCM gives the probability of a particular settlement choosing a particular

facility. Next step would be reaching the facility starting from the settlement. Itcan be intuitively said that the people from a given settlement will choose theshortest available path from the settlement to the facility. But it is not necessarythat the people choose the shortest path to reach the facilities always. There canbe many other parameters such as safety, public transport service. So givingimportance only for the edges that come in the shortest path is not a good wayof looking at the problem. The alternate paths should be considered as well.People will usually go for first few alternatives and the rest can be discarded.Therefore, as a trade off, we consider the first K shortest paths to calculatethe edge aggravation magnitude. Now of course we can’t assume that all the Kshortest paths have equal effect in calculating edge aggravation. So based on thelength of the paths we assign weights to each of the paths and then add up tothe aggravation for each edge appearing in the paths.

Based on these analysis, the magnitude of aggravation associated with eachedge getting disrupted can be computed based on the following Algorithms 1–3.

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Multi-objective Based Road-Link Grading for Health-Care Access 283

Algorithm 1. EAM(u,v)

Input : G, F, pCM(v,f), k.

Output: Magnitude of aggravation associated with each edge getting disrupted withrespect to the accessibility of the facilities available in set F

1 Initialize the Edge Aggravation Magnitude EAM(u, v) = 0∀(u, v) ∈ E

2 for s in V do

3 for fiinF do4 P = GET K SHORTEST PATHS(s, fi, k)UPDATE EAM(EAM,P )

5 Return EAM

Algorithm 2. GET K SHORTEST PATHS(s, fi, k)

1 Initialize a set P = φ

2 Initialize Count[u] = 0∀u ∈ V

3 Insert Ps = s into Q with Cost[Ps] = 0

4 while Q �= φ and Count[fi] < k do

5 Let Pu be the root of the heap with Cost[Ps] = c

6 Pop the root from the heap. Q = Q − Pu

7 Increment the count of node u by 1. Count[u] = Count[u] + 1

8 If we have reached the destination i.e. u = fi : Update the set P. P = P ∪ Pu

9 if Count[u] < k then

10 for each vertex v adjacent to u do

11 if v /∈ Pu then

12 Let Pv be a new path with cost c + weight(u, v) formed by concatenating

the (u, v) to path Pu

13 Q = Q ∪ Pv

14 Return P

The algorithm calculates the Edge Aggravation Magnitude(or Edge Critical-ity) of each edge in the network with respect to one particular type of facility.In addition to EAM we have Link Vulnerability Measure(LVM). By combiningthese two parameters we calculate the risk associated with each edge.

Risk(ei) = LV M(ei) × EAM(ei) (3)

where LV M(ei) is the Link Vulnerability Measure that is given by the probabil-ity calculations of the relative probability of link, ei getting disrupted. EAM(ei)is the Edge Aggravation Magnitude i.e. the measure of impact associated withthe loss of that edge. The mapping of the link-risks along the road network is fol-lowed by the grading of the links based on the population flow along the roadsfor accessing the relief-facilities. This is computed using the Node ImportanceIndex.

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284 O. Chakraborty et al.

Algorithm 3. UPDATE EAM(EAM,P )

1 Initialize weight(Pi) = 0∀Pi ∈ P

2 Initialize sumcost = 0 for Pi ∈ P do

3 sumcost = sumcost + 1(1+P.cost)

4 for Pi ∈ P do

5 Calculate the weight of the path

6 weight(P ) =1

(1+P.cost)sumcost Initialize current index

7 curr = 0 Initialize vulenrable pop = 0 Initialize destination(dest) to the last vertex

in the path Pi while curr < length(Pi) do

8 Update the vulnerable population by adding the population of the current

settlement weighted by the probability that the people from the current

settlement choosing the facility destination vertex.

9 vulnerable pop = vulenrable pop + population[Pi[curr]] × pCM(Pi[curr], dest)

10 Update the edge aggravation magnitude of the edge joining the current vertex and

the next vertex

11 EAM(Pi[curr], Pi[curr + 1]) =

EAM(Pi[curr], Pi[curr + 1]) + vulenrable pop × weight(Pi)

12 Move to the next node by incrementing the current index

13 curr = curr + 1

6 Node Importance Index (NII)

The Node Importance Index (NII) is a modification of the Edge ImportanceIndex (EII) [10], in which the importance is analyzed not for the intermediateedges of the network, but for the end-nodes of the road links along the path setsbetween the village centroids and the facilities. It not only withholds the pathimportance indices from the villages to catchment facilities but the completenode set of the entire road network. Once the road features are converted to adi-graph revealing the corresponding edge and node sets, the individual nodesof the path are treated with the village population as weights. The analysis isproceeded based on the node’s significance towards its utilization by the peopleof different villages. More the number of people from different villages use thelinks of the path, and passes through the nodes, the greater importance it gets.Thus for calculations, the nodes are assigned weights, the values of which areincremented with the population of the particular villages that use it.

Let SPO→D denote shortest path from origin, O and destination, D

SPO→D = arg min{dist(P∗O→D)}, (4)

where, dist(P∗O→D) represents the distance function for length of the paths in P∗.

The resultant node importance for a given node n can be depicted as in Eq. 6.

NII(n) = Cc(n)∑

POD

PO, if n ∈ SPO→D (5)

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Multi-objective Based Road-Link Grading for Health-Care Access 285

where, POD is the population of O accessing facility, D. Cc(n), is the closenesscentralities of nodes n.

The closeness centrality of a node is the measure of its shortest path lengthsto other nodes of the corresponding layer. It is denoted as,

Cc(u) =

[n∑

v=1

dist(u, v)

]−1

The centrality measure helps in better access to the road networks for fasterdispersion and citizen check-outs.

As the road-link utilizations change with the increase in hazard-scale, theNII values for the individual links also get altered to address the dynamics ofthe population flow for relief-access. Let D = {ρ1, ρ2, . . . , ρn}, be the considereddisaster scales. These scales are represented by the observed percentage of road-link disruption which implicitly reflect the level of water. The NII correspond-ing to the respective scales can be represented as Let NIIρ1 , NIIρ2 , . . . , NIIρn

respectively. For identifying the overall node importances, the net NII is takenas an average over all the corresponding values as,

NII =1D

ρ=ρn∑

ρ=ρ1

NIIρn (6)

7 Optimization Towards Multiobjective Edge-Grading

The safety of the path traversals to access the respective relief-facilities are basedon the risk and utilization parameters of the links and nodes forming the paths.To identify paths with highest overall importance, the grading should satisfythe criteria of being safe even at adverse disaster scenarios while having mostutility in reaching the different relief facilities. This scoring can be formalized asa max-min multi-objective optimization (MOO) approach on a ranking function,say φ, to minimize Risk and maximize NII parameters as in Eq. 7.

max φ ={

min Risk(ei)max NII(n) =

{LV M(ei) × EAM(ei)1D

∑ρ=ρn

ρ=ρ1Cc(n)

∑POD

PO

(7)

We implement the concept of Pareto optimality to grade the edges in theMOO model. The optimal edges at a given iteration are identified through thecomputation of the Pareto frontier. These edges, intuitively, represent the solu-tions in which one of the attributes cannot be further maximized without wors-ening the other. The edges are ranked based on their location on the respectivePareto frontier grades, which are iteratively computed during the MOO opti-mization process.

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286 O. Chakraborty et al.

8 Case Study

Bankura (Fig. 4) is one of the inland districts (area of 6882 km2) located on thewestern side of the state of West Bengal. It has been recognized as a major floodprone area in the state of West Bengal [11]. Bankura has a unique physiographywhere four rivers run across the district from west to east direction (Damodaron the northern periphery, Dwarekeshwar river below it, followed by Silai andriver Kasai at the southern end of the district), which incidentally is prevalentgradient of the land. There are zones of plateau between the undulating hillywestern side (covered by reserved forests) and gradually sloped eastern part ofthe district.

The hierarchy of roads reveals that the district is connected to its adjoiningdistricts by a system of state highways (SH). The SH-9 runs from south to thenorth connecting Bankura to Paschim Medinipur (in south) to Bardhhaman(in the north). Similarly, SH-2 runs from west to east connecting Puruliya toHugli via Bankura. The SH-5 joins the eastern part of the state to the northernpart, whereas the SH-4 primarily serves the south-western part of the district.There are other arterial/sub-arterial road system in the district, which connectto this network of SH. The network of the district (up to the collector street levelsystem) was taken up for this study (Fig. 5). The objective of this study is tounderstand the network connectivity at extreme weather conditions. However,the base case for a further scenario generation and simulation is assumed fromfair weather connectivity.

Fig. 4. Case study region: Bankura,West Bengal, India; area: 6,882

Fig. 5. National and state highways ofBankura. [Source: National InformaticsCenter, Bankura]

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Multi-objective Based Road-Link Grading for Health-Care Access 287

8.1 Results

The results of Link Vulnerability Measure calculated with elevation and prox-imity to water body data are shown in Fig. 7. To compute LV M values of theroad links, we need to identify the distribution of river-basins of the region, theportion of land being drained by a particular river, which encompasses the roadnetwork and the spatial aspect of the links. The entire district of Bankura lieswithin the basins of the rivers Damodar and Rupnarayan respectively [12], wherethe latter more prominently infamous for causing flash floods, monsoonal floodsin the region [13]. Simultaneously, its upper catchments consist of 12◦–21◦ slopeswhere as the slope in the middle portion is 7◦–12◦. That is the reason the waterin the middle part does not get back to its upper catchments. The upper catch-ment’s water level getting higher and higher than its lower potion give backwardonrush of water. The middle portion of the river gets flooded. That is the reasonof monsoonal flood in its middle portion. Although, the rivers significantly dryout during the summer months, they overflow each year during the monsoons.Bankura receives flooding conditions due to discharge from upper basin areasthrough these four rivers, large volume of surface runoff, build-up of water dueto heavy rainfall, and the unique elevation profile of the region (as in Fig. 6).

Fig. 6. Road network links graded based on the regional elevation profile

The Edge Aggravation Magnitude (EAM) of the road links to access therelief-facility, healthcare in this case are, as discussed in Algorithm1, based onthe connectivity of the vulnerable population flow paths along the probablecatchment maps. The EAM values for the individual facilities is depicted inFig. 8.

The road segment node importances, NII analyses the population traversalbased importance index of the all the 3839 intermediate node sets of the roadnetwork for the respective facilities across the considered hazard scales. We haveconsidered the percentage of edge-disruption owing to flood-level rise as the

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288 O. Chakraborty et al.

Fig. 7. The LVM grading of the road links

Fig. 8. Healthcare access routes graded by EAM levels

hazard scales initiating from fair weather conditions iteratively upto 16% edgedisruptions, post which the road network fails to provide access to any health-care centers. The results reflecting significant importance changes are reflectedin Figs. 9, 10 and 11. The figures portray a significant shift the node importanceswith the rise in flood adversity. Table 1 depicts the overall NII results for someof the nodes.

Finally, these results are utilized for grading the road links for sustainablerelief-facility access during disaster times as discussed in Sect. 7. The Paretobased grading can be conceptualized using Fig. 12. The plots contain all theroad link-nodes of the region that participate in forming paths for health-careaccess. The roads having same grade values are marked using a common andunique color band. The color-coded edges in the graph denote the min-maxPareto frontiers for the respective grades. Figure 13 portrays the road networkof the study region consisting of top four graded links which form the safest pathfor health-care access from the respective settlements.

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Multi-objective Based Road-Link Grading for Health-Care Access 289

Table 1. NII Analysis of all intermediate path nodes of the road network

SL No Longitude Latitude NII

1 86.85690308 22.86751938 14616

2 87.03074646 23.15146446 0

3 86.76268768 23.12214851 12687

. . . . . . . . . . . .

68 87.25009918 23.20824242 0

69 87.11117554 23.10203362 21016

. . . . . . . . . . . .

134 87.05408478 22.99751091 18699

136 87.17552948 23.11337852 0

. . . . . . . . . . . .

1000 87.23303223 23.31071472 0

1500 86.84412384 23.11271477 0

. . . . . . . . . . . .

2000 87.17552948 23.45362663 142800

2500 87.00985718 23.53209496 0

. . . . . . . . . . . .

3000 87.44976807 23.14036751 0

3839 86.93696594 23.16602707 0

Fig. 9. Highest NII valued nodes for healthcare access in normal conditions

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290 O. Chakraborty et al.

Fig. 10. Highest NII valued nodes for healthcare access at 7% edge disruption

Fig. 11. Highest NII valued nodes for healthcare access at 16% edge disruption

8.2 Discussion

Besides the primary results of the work, the approach also reveals some inter-esting inferences. The LVM values (Fig. 7) reflect the high overall proximityof the roads in the region that lead to their higher natural propensity to dis-rupt. The road network dissected almost at equal intervals by the main rivers ofthe region. Furthermore, majority of the region lies in low elevation area (referFig. 6), except the north-western part causing higher flood adversities. Withinthe road layout, the central part plays a critical part in holding sustainable con-nectivity (Fig. 8) and this may be one of the reasons for centralized location ofthe health-care centers. Based on the available locations, it is found that the

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Fig. 12. Road link grading based on min-max Pareto optimality (Color figure online)

Fig. 13. Top four ranges of highest graded road-links within the region. The grade 1(green path) links serve as the optimal links that provide the highest utilizations forhealth-care access and also have low risk from flood adversities. (Color figure online)

utilization of the roads by the populace to access the health-cares are mostlyconcentrated in the northern region (as in Figs. 9 and 11) which indeed hold thesafer paths to the facilities. Also, an extensive migration of the highest nodeimportances is observed from the central (Fig. 9) to the northern region post7% edge disruptions within the network. The Pareto optimal plots reveal themoderate utilization as well as risk of most of the common road links. However,the min-max frontiers highlight the importance of few yet low utilized roads(left-most frontier nodes of Fig. 12) that may facilitate safer health-care accessroutes. Finally, the optimal links (refer Fig. 13) emphasize the utilization of themajor roads in the central region. The results significantly coincide with some of

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the major state and national highways of the region (as in Fig. 5). This also actsas a validation as usually these roads are of the superior quality and preferredduring disaster management.

9 Conclusion

The identification of vital roads links for relief accesses by the populace alongwith alternate travel strategies, is a crucial factor for disaster managementschemes. It also promotes the safeguarding of the links for better service usabil-ities in disaster cases. In our study, we carry out an analysis of the road seg-ments in terms of its spatial layouts, contribution towards reliable paths forfacility access and alternate routes. We illustrate the road network based onthree importance factors of link vulnerability, edge criticality and resilience ofthe auxilary paths. The approach considers most of the aspects influencing thecapability of roads to provide the emergency services during disasters. How-ever, the work can be extended to encompass other vulnerability influencingparameters to enhance the efficiency further more. in the future, we also aimto implement the framework in larger flood regions and also explore the spa-tial attributes to a more detailed scale. The multi-objective based optimizationof the road-network enhances the analytical capabilities by identifying only thefacility-relevant link properties to be considered within the different input setsof importance measure evaluations.

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