University at Buffaloqinghe/papers/journal/2016 infiltration.pdf# Springer Science+Business Media New York 2016 ... setting and develop the corresponding optimization model. We then

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Journal of Transportation Security ISSN 1938-7741 J Transp SecurDOI 10.1007/s12198-016-0168-z

Optimal routing of infiltration operations

Mingyu Kim, Rajan Batta & Qing He

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Mingyu Kim1,2& Rajan Batta2 & Qing He2,3

Received: 1 February 2016 /Accepted: 21 March 2016# Springer Science+Business Media New York 2016

Abstract This paper suggests a method for routing military ground operations, focusedon conducting infiltration based on the shortest-path method. We model the problem infour parts. First, we estimate enemy locations by using public facility location model andmilitary data, and use these to define possible enemy scenarios. Second, for eachscenario, a shortest-path problem is solved, where each link’s cost is given by bothBSpeed^ (Travel time) and BSurprise^ (Detection probability). And the detection prob-ability is jointly determined by the distance from the enemy’s closest location, detectiondevice’s location and concealment probability from vegetation information. Third, thepreferred solution is selected by a robust optimization process. The fourth step involvesthe use of dissimilar paths to incorporate the impact of a deception operation. Themethodology is demonstrated by a case study that uses realistic data from South Korea.

Keywords Shortest path . Infiltration .Military operations research . Location problem

Introduction

Military operations consist of diverse movements not only in wartime but in peacetimeas well. Many types of movements exist in the military including convoys, mechanical

J Transp SecurDOI 10.1007/s12198-016-0168-z

* Mingyu [email protected]

Rajan [email protected]

Qing [email protected]

1 Republic of Korea Army, 564, Hwarang-ro, Nowon-gu, Seoul, Korea 018052 Department of Industrial and Systems Engineering, University at Buffalo (SUNY), Buffalo,

NY 14260, USA3 Department of Civil, Structural and Environmental Engineering, University at Buffalo (SUNY),

Buffalo, NY 14260, USA

Author's personal copy

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troops’ tactical maneuvers, personnel movement, and GOP patrol. Choosing appropri-ate routes for these movements is a critical procedure in the military. The focus of thispaper is on the infiltration movement.

Background

German General Oskar von Hutier astonished the whole world and raised his reputationas a military strategist by new tactics in Operation Michael in 1918 during the WorldWar I (WWI). His tactics were different than any existing tactics, which focused onattacking enemy’s frontal line. His tactics’ key factors were BSpeed^ and BSurprise^;after the Artillery units’ preparatory fires, the Light Infantry unit penetrated the enemy’sweak points quickly and furtively to bypass them. Then, he isolated heavily defendedpositions in the frontal line. With these tactics, von Hutier destroyed the British Armyand captured around 50,000 prisoners in March 1918 during the Spring Offensive. Thetactics became known as BHutier Tactics^ which represent infiltration operations. Afterthat time, infiltrations have been used in many ways in military operations. In navalhistory, German Submarine Forces (U-boats) conducted infiltration to attack in depthand carry out their mission in enemy territory. Special forces conduct infiltration to raidthe enemy’s core facility; intelligence agents also perform infiltration to get importantinformation or to support operations. Nowadays, infiltration is used in variouscircumstances.

Infiltration

Infiltration is a tactic where operating forces conduct covert movements into the enemyforces’ rear area, which is occupied by the enemy. The general goals of the tactic are to:Secure key terrain in support of the main effort; Attack lightly defended positions orstronger positions from the flank and rear; Secure the enemy’s rear area to envelopenemy forces; Prevent and destroy the enemy’s rear operations including combatservice support (CSS); Attack the core facilities of enemy forces from the flank orrear. Depending on the battlefield situation, infiltration operations have different fea-tures; however, the key components are the same: “Speed” (Travel time) and “Surprise”(Detection probability). To fulfill these factors, which play a central role in infiltration,there are many other aspects to consider. As mentioned before, one of the mostimportant considerations is concentrating efforts to find the optimal infiltration route,which is not a simple task that can be generated by solely using a commander’sexperience or by field manuals. To assist in such a situation, we introduce a standard-ized mathematical model for infiltration routing.

Modeling procedure

Very few previous studies can be found in the domain of infiltration routing. Bang et al.(2010) published a paper about infiltration route analysis. They developed the problemwith respect to Thermal Observation Device (TOD) detection probability in ageospatial information system (GIS). They modeled a situation in which two confron-tational countries exist across a Military Demarcation Line (MDL) and applied optimal-path-searching algorithms with a raster-based map. Using the A* algorithm, they

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implemented the model to determine optimal routes on the basis of geographicalfeatures and expected TOD locations.

We develop upon this work by dividing the model into four parts. First, we estimatethe enemy’s locations based on a public facility location problem (Batta et al. 2014).After we define the enemy unit’s locations, we model the enemy’s detection device’slocations. In this research we considered TOD as the enemy’s detection equipment. Themodel is constructed to account for the enemy unit’s location and viewshed analysis.

Second, we model the infiltration path as a shortest path problem. Throughgeospatial information, we create a cost map for the whole area of operation.Enemy location, concealment probability from vegetation layer and theACQUIRE model (Hong et al. 2003) of TOD create a detection probabilitymap. To develop the travel time map, obstacle layers, slope-surface configura-tion layers and distance matrices are used. The final travel cost map is createdfrom these two maps. After that, we generate the best route using Dijkstra’salgorithm.

Optimal routes could change by enemy location scenarios. Hence we compute eachroute’s cost for every scenario and find out the maximum cost of each route; the value isa robustness indicator. We select the route which has the minimum robustness indicator.This constitutes the third step.

In the fourth step, we analyze the effect of deception operations. We assume that thedeception operation could affect the enemy’s detection pattern. After we define dis-similar paths for deception, we modify scenarios to reflect the enemy’s expectedreaction. We computed the optimal route’s travel cost with these scenarios and com-pared the result with the original travel cost.

The rest of this paper is organized as follows: In the next section, we define the basicsetting and develop the corresponding optimization model. We then present a casestudy to verify and develop the model. This paper ends by stating our researchconclusions and suggested future research directions.

Basic modeling

Enemy location model

To estimate an enemy unit’s location, we apply the p-maxian model (Battaet al. 2014) that takes advantage of the fact that the search for the 1-maxiancan be restricted to a finite set of points. That paper focused on optimal publicfacility locations with the appropriate use of dispersion, population, and equitycriteria. We adopt this model to a military situation. The notation shown inTable 1 is introduced (Table 2).

The whole operation area consists of the network G= (N, L) in which N isthe set of nodes and L is the set of links. Let |N| = n and the elements of N belabeled 1, 2, …, n. Let l(i, j) denote the length of a link (i,j) ϵ L and d(a,b)denote the length of the shortest length path between two points a and b in G.There are p enemy units to be located on the area of operations (AO). Enemyunits can be stationed at nodes and at any point along a link. Enemy units areassumed to be of infinitesimal size.



Since there is a tendency to prevent duplicating detection areas and todispose units dispersedly, the distance between any pair of enemy units in acandidate solution is greater than or equal to a detection range radius (R).Furthermore, to focus on the objective of the operation, the constraint βs ≤Ds

is added; βs is the distance of the closest enemy unit to a node s. Ds is afactor of proportionality. If the node s is closely located to the goal, Ds willbe tight bound. Otherwise for a node distant from the goal, Ds will begenerous. Let Z represent the set of sites available for enemy locations, andlet dsj denote the length of a shortest distance path between site s and j. αj isa binary decision variable so that αj= 1 means one of the enemy units islocated at j and 0 otherwise, for j = 1,…,z. Then, we define the index setsHs = {j : dsj ≤Ds, j= 1,… z}, s = 1,…, n. Each set Hs contains the indices j of thepossible locations, which are to fulfill the distance constraint dsj ≤Ds of nodes. Next, we need to assume the number of enemy units at the main operatinglocation. In practice, military forces normally are concentrated in importantareas relative to their mission such as border lines, choke points, critical

Table 1 Mathematical notation for enemy unit location

Notation Description

dsj The length of the shortest distance path between s and j

p The number of enemy units

Cs Index set that contains the indices j of the possible locations which are located in the MBA (MainBattle Area)

b The number of enemy units inside the MBA

Ds Factor of proportionality; It is equal to (1 + distance between nodes and important facility)*f

f Effective range of personal arms

Hs Index set that contains the indices j of the possible locations which are within acceptabledistance (Ds)

R Enemy’s detection radius

Table 2 Mathematical notation for TOD location

Notation Description

det The length of the shortest distance path between enemy location e and t

T The number of TODs

Ge Index set that contains the indices t of the possible locations which are within acceptabledistance (g)

Qe Index set that contains the indices t of the possible locations which are out of acceptabledistance (q)

ht Altitude of site t

g Maximum distance of TOD to enemy unit

q Minimum distance of TOD to enemy unit

u Minimum distance of TOD to TOD

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points, etc. On the other side, opponent forces try to get this area’s informa-tion as a priority through intelligence operations. Therefore, we define anotherindex set Cs = {j : inside theMBA(Main Battle Area)}: to describe the enemylocation which is located in the MBA to assign a specific number of enemyunits in important operation areas.

MaximizeXn

s¼1

βs ð1Þ

Subject to constraints:

Xz

j¼1

α j ¼ p ð2Þ

Xz

j∈Cs

α j ¼ b b≤pð Þ ð3Þ

1−α j

� �Ds þ α jds j≥βs f or s ¼ 1;…; n; j∈Hs ð4Þ

Xj∈Hs

α j≥1 ð5Þ

M 2−α j−αl

� �þ α j−αl−1� �

d jl ≥2*R f or j ¼ 1;…; z−1ð Þ; l ¼ jþ 1;…; z ð6Þ

The objective function (1) is to maximize the distance from the nodes to theirclosest enemy unit. Constraint (2) ensures that only p enemy units are locatedamong the z sites, and (3) ensures that among p enemy units, b units are locatedinside the MBA. Constraints (4) and (6) are big-M constraints. Constraint (4)’s roleis to calculate the βs, which presents the distance of node s to the closet enemy. Inthis constraint, we set constraint set Hs to ensure enemy units are located withinDs for any node s. The role of the constraint (5) is to ensure that at least oneenemy unit will be located at one of the sites j∈Hs. The last constraint (6)ensures that the enemy units’ location j, l are located with the conditionthat djl ≥ 2 ∗ R. If we set M = 2 ∗ R, it would imply that at least one enemyunit exists between j and l. For computational purposes, to save time andmake tight boundaries, it is important to choose the M value as small aspossible within a range that can attain the objective.



Next, enemy’s detection equipment, TOD is normally operated inside military basesor at the front position from the base. Hence, associating enemy unit’s location withTOD is more practical than assuming the TOD’s location separately. Therefore, we fix eas one of the unit’s locations.

Like the enemy units’ location problem, we consider that the whole opera-tion area consists of the network G= (N, L). There are T numbers of TODs tobe located in the area of operations (AO). TOD can be stationed at nodes. LetZ represent the set of sites available for TOD location, and let det denote thelength of the shortest distance path between enemy location e and sites t. αt isa binary decision variable so that αt= 1 means one of TOD is located at t and 0otherwise, for t = 1, …, z.

Next, we define the index sets Ge={t :det≤g, t=1,…, z}, Qe={t :det≥q, t=1,…, z},e=enemy location . Each set Ge contains the indices t of the possible locations,which fulfill the distance constraint det≤ g of enemy location e. Also, each setQe contains the indices t of the possible locations, which fulfill the distanceconstraint det≥ q of enemy location e. To prevent duplicate detection areas withenemy units, the distance between TOD and enemy units is greater than orequal to TOD detection range radius (q). Similarly, to protect and keep contactwith TOD operating personnel, we can expect that the distance between theunit and TOD is restricted. Generally, this distance would be set depending onrange of radio waves (g). Furthermore, since a feature of the TOD equipment isoperated at a high point to prevent interference by topographical conditions,altitude should also be considered to locate TOD.

MaximizeXp

e¼1

βe ð7Þ

Subject to constraints:

Xz

t¼1

α j ¼ T ð8Þ

1−αtð ÞGe þ αtdet ≥βe f or e ¼ enemyunit location; t∈Ge ð9Þ

1−αtð ÞQe þ αtdet ≤βe f or e ¼ enemyunit location; t∈Qe ð10Þ

Xt∈Ge

αt ≥1 ð11Þ

M 2−αt−α0t

� �þ αt þ α

0t−1

� �dtt0 ≥u

f or t ¼ 1;…; z−1ð Þ; f or t0 ¼ t þ 1;…; zð12Þ

D* 1−α j

� �þ α jh j≥A ð13Þ

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The objective function (7) is to maximize the distance from enemy units to theirclosest TOD. Constraint (8) ensures that only T TODs are located among the z sites.Constraints (9), (10), (12) and (13) are big-M constraints. Constraint (9)’s role is tocalculate βe, which presents distance of enemy unit location e to the closet TOD. In thisconstraint, we set constraint set Ge to ensure TOD is located within range of radiowaves (g) with enemy unit e. In the same context, constraint (10) calculates the βe andusing constant Qe, it ensures that the TOD is located out of detection radius (q) fromenemy unit. The role of the constraint (11) is to ensure that at least one TOD will belocated at one of the sites t∈Ge. Constraint (12) ensures that distances between TODsare at least u. Constraint (13) ensures that the TOD is located at an area with an altitudeof at least A.

In summary, we have chosen a recently analyzed location model (p-maxian withconstraints) and adapted it for generating enemy locations and TOD positioning. Itassumes logical grounds for making decisions.

Modeling shortest path

To model the problem as a shortest path problem, firstly, we analyze travel costs foreach link of AO. Additionally we use geospatial information.

GIS is widely used in many fields. Both routing analysis and military applications areclosely connected with GIS. Bang et al. (2010) introduced how we can analyze theinfiltration route with GIS particularly using vector product interim terrain data (VITD).VITD is defined by the National Geospatial-Intelligence Agency (NGA) (1996) militarystandard. It consists of 6 layers: Obstacles (OBS), slope and surface configuration (SLP),soil and surface materials (SMC), surface drainage (SDR), transportation (TRN), andvegetation (VEG). With GIS data, raster based probability maps were created by usingArcGIS 10.2.2. ArcGIS is a GIS tool for working with maps and geographic information.In this research, we used this program to analyze mapped information, managing geo-graphic information based on VITD and Shuttle Radar Topography Mission (SRTM)’sterrain data. ArcGIS can create maps that consist of fixed size cells. Once the map wascreated, we model the problem as a shortest path problem.

As the first step of modeling the shortest path problem, we need to specify the routenetwork. A shortest path problem is typically constructed in a network with nodes andlinks. As we mentioned in the previous step, we divided the whole AO into a gridnetwork that contains cells with a fixed size by ArcGIS. In each cell’s center point willbe nodes; every node is connected with its neighbor node in vertical, horizontal, anddiagonal ways which organize route networks.

Next, we assign travel cost for each link. Let the networkG= (N, L) in which N is theset of nodes and L is the set of links. Each i, j is an element of N and (i, j) present a linkthat is made up of node i, j. As we mentioned before, the objective is tominimize the sum of cost function. (Minimize∑ijcijxij). The travel cost ismade of a combination of two factors: probability of detection and distance(Cij =αPij + βDij

′ ,α + β = 1). xij is a binary variable that indicates whether alink (i, j) is part of the shortest path or not; 1 when it is, and 0 if it is not.For re-scaling the distance factor (Dij) to the range [0,1] (Dij

′ ), we use a

simple formula, x0 ¼ x−min xð Þ

max xð Þ−mi xð Þ. Then to block the obstacles and river area,



we allocated a big number to those Bdo not pass^ areas. We then gave theweight (α, β) to the factors. Depending on the features of the operation, thevalue of weight α and β can be changed. For example, in the case that thecommander’s intent is timely infiltration with fast advances, <β. Otherwise,if the key factor of the operation is secrecy, the weight would be α >β.

After we establish enemy location scenarios and create a final travel costmap, we now have to find the optimal route of infiltration. For infiltrationroute optimization, we have to find the path with the lowest cumulative travelcost. Therefore, in this step, we are computing the shortest path problemusing Dijkstra’s algorithm. The travel cost of each link is not fixed. It ischanged depending on the scenario of enemy locations and TOD locations. Inthe case of an uncertain value, a robustness approach is an appropriatemethod to solve such problem. We can now define optimal routes for eachscenario. Then, we take the absolute robust shortest path (ARSP) process. It isa process that finds one final route that minimizes the maximum travel costamong all the scenarios. It computes the route’s travel cost in every scenarioand finds out the worst-case cost for each route. If S is a set of enemylocation scenarios, the objective function is

MinMaxsesXi j

ci jxi j

Maximum cost is recorded as the robustness indicator for each route, andthen the minimum indicator among all the scenarios is selected for the finalinfiltration route.

Modeling dissimilar path

In this paper, we present the effect of deception operations by use of a decoyunit. To optimize the decoy path, we adopt dissimilar paths by the gatewayshortest path (GSP) method (Akgun et al. 2000). This is based on a constrainedshortest path problem. The shortest path between the origin and the destinationis constrained to go through a specified node, called a Bgateway .̂ For the GSPmethod, we create a specific passage node, which must pass to go to theobjective, and then block all other nodes.

After generating dissimilar paths with this method, we reflect the enemy’s reactionon the travel cost map. At last, we compute the optimal route’s travel cost on thischanging travel cost map and compare it with the original cost. From this process, wecan predict the effect of the deception operation.

Case study

To verify the methodology we developed in the previous section and illustrate itspractical applications, this case study was developed in a real-world area, DaeJeon,

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South Korea, with a virtual mission by a light infantry battalion. The whole AO for thecase study is presented in Fig. 1.

For the case study, the operation area is restricted in size by 33.5 km x 35 km. Thearea has a unique origin–destination pair and consists of small cells sized 500 m x500 m. Each cell’s center point is considered a node that takes the average value of eachcell. The full operation sector consists of 4690 nodes. Each vertical and horizontal arc

length is 500 m and every diagonal arc length is 707 ≈ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi500000

p� �m. As a basic

assumption, we consider that a light infantry battalion will conduct infiltration tocapture the key point, described as an objective in the map. In addition, there is a rivertraversing the full AO, and there are two bridges to cross the river. We assume thatwithout these bridges, friendly forces can’t cross the river.

On the enemy side, there are 3 enemy units and 1 TOD located in unidentifiedpositions. From intelligence sources, the friendly forces obtained information that theenemy’s personal arm effective range (R) is 800 m and that 2 frontal enemy units arecovering the main battle area.

The enemy unit’s main detection asset is an advance guard post. Normally, aguard post is located depending on the range of radio waves (ex: PRC-999 K :8 km), thus, we can assume that Detection Range (τ) is 8.5 km (Guard postlocation: 8 km+human eye sight: 500 m) with an instantaneous Detection Rate(η) of 0.004. Lastly, in this case study, we did not consider buildings or otherman-made features.

Fig. 1 Operation area of case study (Daejeon, South Korea)



Estimating enemy location

The first step is to find all possible enemy units’ locations. To do so, we need to find theoptimal location using the formulation introduced in the previous section. Note here,since there are too many nodes in operation area that it would take too much time tocompute. Therefore, finding approximate locations by heuristic analysis can be a moreefficient method.

For the heuristic analysis, we divide the operation area into big blocks. Each blockincludes the same number of nodes. Figure 2 shows these big blocks which make upthe whole operation area. Among these blocks, we can assume approximate enemylocations. After we solve the location problem, we found the optimal solution that theenemy’s units should be located in B10, B27, and B43. After obtaining the approximatelocation with a block as a unit, for the next step, using the same formulation, wecompute again to find locations with a node as a unit. Every node inside the blocks(B10, B27, B43) is a candidate for an enemy unit location. Note that after we obtainedresults by node unit, we need to investigate their locations’ geographical features usingVITD’s obstacle data. From this data, we can exclude obstacle and river areas, andreduce the number of scenarios. Table 3 represents the final results of enemy locations.Eventually, 7 different scenarios are determined from this procedure.

For the second step, we computed the TOD location using the formulation intro-duced in the previous section. As explained before, by that model, we can consideraltitude, unnecessary TOD overlaps, and minimum and maximum distance from enemyunits.

The TOD location model results in 16 possible TOD locations; node 1734,1801, 1868, 1935, 2002, 2003, 2135, 2201, 2202, 2268, 2069, 2335, 2472,

Fig. 2 Dividing operation area with big blocks

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2539, 2540, and 2674. Note that in this point, the TOD is working at an areathat affords a wide and open view. Hence, to select the TOD location reflectingactual conditions, we need to apply viewshed analysis to each potential TODlocation cell. Figure 3 represents all potential TOD locations’ through viewshedanalysis.

From the viewshed analysis, obviously, we define two final TOD positions whichcan detect friendly forces’ area: node 1734 and 2002. After this procedure, we can

Table 3 Possible scenarios depending on enemy location

Unit Scenario E1 E2 E3

Scenario 1 4623 2669 689

Scenario 2 4623 2401 689

Scenario 3 4623 2669 697

Scenario 4 4623 2401 697

Scenario 5 4623 2669 1292

Scenario 6 4623 2401 1292

Scenario 7 4623 2669 1300

Fig. 3 Viewshed analysis depending on TOD locations



model 11 different scenarios depending on both enemy units and TOD locations asshown in Table 4. Each scenario’s detection range is represented on Fig. 4 (Table 5).

Finding the optimal route

As stated at the beginning of this paper, to model an infiltration route as ashortest path problem, we need to consider two factors. First is travel time. Inthis study, we consider that travel time is affected by geographical slope anddistance (dij).

In addition, it should be noted at this point that in this case study, since we model thewhole operation area’s network as a grid, we only allow travel between neighbor nodes:between horizontal, vertical, diagonal adjacent nodes. Total travel time from node i to jis defined as

Di j ¼ w*di j

Second, we compute the detection probability. In this paper, the AQUIREmodel was used to compute TOD detection probability. This is the current USArmy’s standard algorithm for Search and Target Acquisition (STA). The modelcontains a performance assessment model for night-vision systems that cancompute the detection probabilities of specific targets according to distanceand weather and is based on minimum resolvable temperature differences(MRTD).

Table 4 Possible scenarios depending on enemy location and TOD

Unit Scenario E1 E2 E3 TOD

Scenario 1 4623 2669 689 1734

Scenario 2 4623 2669 689 2002

Scenario 3 4623 2401 689 1734

Scenario 4 4623 2669 697 1734

Scenario 5 4623 2669 697 2002

Scenario 6 4623 2401 697 1734

Scenario 7 4623 2669 1292 1734

Scenario 8 4623 2669 1292 2002

Scenario 9 4623 2401 1292 1734

Scenario 10 4623 2669 1300 1734

Scenario 11 4623 2669 1300 2002

Table 5 Giving weight by slope

Slope (%) ~10 10 ~ 25 25 ~ 50 50 ~

Weight (w) 1 1.3 1.5 2

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To estimate enemy unit detection probability, as in Nie et al. (2007), weassert that

Pik j ¼ 1−e−ηlik j

where η is instantaneous detection rate.In addition, detection probability is integrated with concealment probability.

Concealment probability is defined depending on features of VEG coverage. We applythree feature tables. Table 6 represents the concealment probability based on VEGlayer. Each cell’s average VEG value was used to compute the concealment probability.

Then we compute detection probability of enemy units and the TOD. Eventually,total detection probability from node i to j is defined as

PTotali j ¼ PEnemyUnit

i j þ PTODi j

� �− PEnemyUnit

i j � PTODi j

� �� n o� 1−PConcealment

i j

� �

Scenario 1 Scenario 2 Scenario 3



Scenario10 Scenario11

Fig. 4 Possible scenario depending on enemy location



At last, we combine these two factors, travel time (Dij) and detection probability(Pij). Once the final cost matrix is created, compute the shortest path using Dijkstra’salgorithm. Figure 5 is the graphical representation of each route respectively. Note thatin this case study, the model results in 4 different optimal routes by different locationsof enemy 2.

Next, we have to find the best route from the 4 different routes by using absoluterobust optimization (Yu and Yang 1998). Therefore, each route’s total travel cost wasre-computed with every scenario.

Table 6 VEG features table

Layer Vegetation Vegetationforested

Vegetationforested

Vegetationforested

Vegetationforested

Vegetationwater

Density measure of tree/canopy cover (%)

- 0–25 25–50 50–75 75–100 –

Concealment probability 0.125 0.125 0.375 0.625 0.875 0.125

Fig. 5 Optimal route for scenarios

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Table 7 shows the result of robust optimization. As we explained in theliterature review, we need to find a route which has the minimum of themaximum value across all scenarios. The box plot in Fig. 6 makes it easy tocompare these 4 routes’ values. According to the results, we choose route 4’sinfiltration route that has the minimum value of maximum travel cost.

Deception operation

After we define the final optimal route, we model a dissimilar path for a decoyunit to find out the effects of a deception operation. For the purposes of thisstudy, we assume the probability of the deception operation’s success is 1, andignore the possibility of failure. In other words, we assume the enemy unitsdefinitely react against the decoy.

Table 7 Each route’s cost by scenario

Route Scenario R1 R2 R3 R4

Scenario 1 25.3 25.7 27.4 31.9

Scenario 2 25.3 25.7 27.4 31.9

Scenario 3 25.3 25.7 27.4 31.9

Scenario 4 28.1 26.1 32.1 33.1

Scenario 5 28.1 26.1 32.1 33.1

Scenario 6 28.1 26.1 32.1 33.1

Scenario 7 33.3 32.7 31.5 31.9

Scenario 8 33.3 32.7 31.5 31.9

Scenario 9 33.3 32.7 31.5 31.9

Scenario 10 34.7 34.1 34.6 33.6

Scenario 11 34.7 34.1 34.6 33.6

Fig. 6 Box plot of each route’s total travel cost



To model the decoy’s path as a dissimilar shortest path, we adopt thegateway shortest path method. Therefore, we block the bridge, which is partof the original optimal path, and then create a new shortest path of eachscenario using another bridge. Eventually, we result in 2 different optimalroutes according to enemy 3’s location. Figure 7 presents the dissimilar shortestpath for the decoy unit.

Similar to the previous stage, by using robust optimization process we canselect one dissimilar path (Route 2) that has the minimum value of maximumtravel cost. The computational result is shown in Table 8.

For the next step, to describe the enemy’s reaction against the decoy, weassume that the enemy 3’s instantaneous detection rate is partially decreased(η = 0.004→ 0.002), and increased (η = 0.004→ 0.006); half of the detectionrange circle (on the opposite side of the decoy’s first contact point withdetection circle) is decreased, and reversely, half of the circle (toward the

Fig. 7 Dissimilar path for scenario 1, 2, 4, 5, 7, 8, 10, 11 (left) and 3, 6, 9 (right)

Table 8 Each dissimilar path’scost by scenario

Route Scenario R1 R2

Scenario 1 34.5 35.1









Scenario 10 34.5 35.1

Scenario 11 34.5 35.1

M. Kim et al.


decoy) is increased. In addition, E1 is changing its detection range with thesame detection range size, toward the bridge that the decoy unit passed.Figure 8 graphically represents our assumption about the enemy’s reactionagainst the decoy in scenario 1.

After modifying the enemy status, the original optimal route’s cost is re-computed and updated. Table 9 compares the original cost and modified costfrom the decoy.

According to these results, we can say that this deception operation iseffective within our assumptions and that the decoy unit can be suggested forthis mission.

Fig. 8 Expected decoy’s influence to enemy (Scenario 1)

Table 9 Each dissimilar path’scost by scenario

Route Scenario R4 R4’










Scenario 10 33.6 32.0

Scenario 11 33.6 32.0



Conclusion and future work

For conducting military operations, operating forces should prepare against manyuncertainties in the operation area. In this paper, we propose a method to minimizeuncertainty in a specific military mission, infiltration. To model this problem, this studypresent an optimal routing technique combined with a location problem.

In the location problem, we focused on expecting enemy units and TOD locations tocreate possible scenarios. After building these scenarios, travel cost maps were createdby geospatial analyses. According to the final travel cost of each node, Dijkstra’salgorithm was applied to find the optimal infiltration route that minimizes the objectivefunction. Once we obtained an optimal route by using robust optimization, we com-pared optimal routes of each scenario and determined one final route, which has theminimum value of maximum travel cost. Lastly, we demonstrated the impact ofdeception operations with decoy deployment, assuming certain enemies’ reactions.

One of the difficulties in modeling the problem is that there are too many influencefactors in the real world. Also, military operations can be changed by multiple externalfactors. For example, for the computation of enemy locations, we assumed that wealready had information about the enemy’s features. Also, we considered just one typeof enemy unit and detector (TOD). However, there are actually many different types ofunits with different characteristics of operation method and capacity.

Furthermore, due to lots of uncertainty, there is not enough existing data which isessential to accurately make estimates. Therefore the computation of the optimal routefor infiltration including uncertain data remains an intricate and challenging issue thatstill needs to be addressed. Particularly in this paper we assumed the success probabilityof decoy deployment is 100 % and described its influence to enemy very simplistically.In the real world, there could be reverse effects of the decoy and various enemyreactions. Hence, in modeling this problem, appropriate assumptions of the situationand reasonable data are very critical to address this modeling enhancement.

One future research direction would be to develop a more detailed case study withaccumulated data which can accurately describe a military unit’s specific behaviors orpatterns. Also, to study applicability on other military operations or different fields suchas transportation problems can be another possible future direction of this study.

References

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Documents

University at Buffaloqinghe/papers/journal/2016 infiltration.pdf# Springer Science+Business Media New York 2016 ... setting and develop the corresponding optimization model. We then