Category Archives: Computers

Battle Lines, Commanders & Computers

When we look at maps of battles even the novice armchair general can quickly trace the battle lines of the armies. Recognizing battle lines is one of the most important skills a commander – or a wargaming Artificial Intelligence (AI) – can possess. Without this ability how will you identify the flanking units? And if you can’t identify the units at the end of a line, how will you implement a flanking attack around them? Equally important is the ability to identify weak points in a battle line.

The algorithm for detecting battle lines and flank units is one of the ‘building block’ algorithms of my TIGER / MATE tactical AI and first appeared in my paper, Implementing the Five Canonical Offensive Maneuvers in a CGI Environment¹⁾http://riverviewai.com/papers/ImplementingManeuvers.pdf. I will discuss how the algorithm works at the end of this blog. For now, just accept that it finds lines and flanks.

Let’s look at some examples of the General Staff AI ‘parsing’ unit positions. First, the battle of Antietam, situation at dawn (by the way, Antietam is one of the free scenarios included with the General Staff Wargaming System):

The battle of Antietam, dawn, September 17, 1863. Screen shot from the General Staff Sand Box program. Click to enlarge.

This is how a human sees the tactical situation: units on a topographical map. But, the computer AI sees it quite differently. In the next image, below, the battle lines and elevation are displayed as the AI sees the battle (note: the AI also ‘sees’ the terrain but, for clarity, that is not being shown in this screen capture):

The battle of Antietam, September 17, 1862 dawn, with computer AI battle lines and elevation displayed. Note: the identification of flank units. Both red and blue forces are assembling on the field. Click to enlarge.

What is immediately obvious is that Red (Confederate) forces are hastily constructing a battle line while Blue (Union) forces are beginning to pour onto the battlefield to attack. Let us now ask the question: what is the weakest point of the Red battle line? Where should Blue attack? This point is sometimes called the Schwerpunkt. German for point of maximum effort²⁾See also, “Clausewitz’s Schwerpunkt Mistranslated from German, Misunderstood in English” Military Review, 2007 https://www.armyupress.army.mil/Portals/7/military-review/Archives/English/MilitaryReview_20070228_art014.pdf. Where should Blue concentrate its forces?

Computer AI representation of battle lines for Antietam, dawn September 17, 1862. The AI is locating the Schwerpunkt or place to attack. Click to enlarge.

Now that the weakest points of Red’s battle line have been identified, Blue (assuming Blue is being controlled by the AI) can exploit it by attacking the gaps in Red’s battle line. The Blue AI can order either a Penetration or Infiltration Maneuver to exploit these gaps (the following images are from my paper, “Implementing the Five Canonical Offensive Maneuvers in a CGF Environment.” Note, in the TIGER / MATE screen shots below Range of Influence (ROI) is also visible:

From the paper, “Implementing the Five Canonical Offensive Maneuvers.”

Both of these maneuvers are possible because the AI has identified weak points in the OPFOR (Opponent Forces) battle lines. Equally important when discussing battle lines are the location of the flanks. The next two images use the original American Kriegsspiel (1882) map which is also included in the General Staff Wargaming System:

The original American Kriegsspiel map (1882) restored and now used in the General Staff Wargaming System. Screen shot from the General Staff Sand Box AI test program. Click to enlarge.

In this screen capture from the General Staff Wargaming System Sand Box AI test program battle lines are displayed by the AI. Note the flank units and especially the unanchored (or open) Blue flank. Click to enlarge.

Identifying flank units is vitally important in the Turning Maneuver and the Envelopment Maneuver:

Knowing the location of flank units is also important for classifying tactical positions (this will be the subject of an upcoming blog).

So, how does this algorithm work?

I’ve never been a fan of graph theory; or heavy mathematical lifting in general. One of the required classes in grad school was Design and Analysis of Algorithms and it got into graph theory quite a bit. The whole time I was thinking, “I’m never going to use any of this stuff, but I have to get at least a B+ to graduate,” so I took a lot of notes and studied hard. Later, when I was looking for a framework to understand tactics and to write a tactical AI it became obvious that graph theory was at least part of the solution. Maps are routinely divided into a grid, unit locations can be points (or vertices) at the intersections of these lines. Battle lines can be edges that connect the vertices. I need to publicly thank my doctoral advisor, Dr. Alberto Segre, for first suggesting that battle lines could be described using something called a Minimum Spanning Tree³⁾https://en.wikipedia.org/wiki/Minimum_spanning_tree (MST). An MST is the minimum possible distances (edge weights to be precise) to connect all the vertices in a tree (or a group, as I call them in the above screen shots).

I ended up implementing Kruskal’s algorithm⁴⁾https://en.wikipedia.org/wiki/Kruskal’s_algorithm for identifying battle lines. It is what is called a ‘greedy algorithm’ and it runs in O(E log V) which means it gets slower as we add more units but we’re never dealing with gigantic numbers of individual units in an Order of Battle (probably around 50 is the maximum) so it takes less than a second to calculate and display battle lines for both Red and Blue.

Lastly, and I guess this is my contribution to military graph theory, I realized that the flank units of any battle line must be the maximally separated units. That is to say, that the two units in a battle line that are the farthest apart are the flank units.

Obviously, this is a subject that I find fascinating so please feel free to contact me directly if you have any questions or comments.

References[+]

References
↑1	http://riverviewai.com/papers/ImplementingManeuvers.pdf
↑2	See also, “Clausewitz’s Schwerpunkt Mistranslated from German, Misunderstood in English” Military Review, 2007 https://www.armyupress.army.mil/Portals/7/military-review/Archives/English/MilitaryReview_20070228_art014.pdf
↑3	https://en.wikipedia.org/wiki/Minimum_spanning_tree
↑4	https://en.wikipedia.org/wiki/Kruskal’s_algorithm

Maps, Commanders & Computers

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How a map of the battle of Antietam looks to us humans. Screen shot from the General Staff Map Editor. Click to enlarge.

How the computer sees the same map (terrain and elevation). This is actually a screen shot from the Map Editor with the ‘terrain’ and ‘elevation’ layers turned on. Click to enlarge.

Computer vision is the term that we use to describe the process by which a computer ‘sees'¹⁾When describing various AI processes I often use words like ‘see,’ ‘understand,’ and ‘know’ but this should not be taken literally. The last thing I want to do is to get in to a philosophic discussion on computers being sentient. the world in which it operates. Many companies are spending vast sums of money developing driverless or self-driving cars. However, these AI controlled cars have had a number of accidents including four that have resulted in human fatalities.²⁾https://en.wikipedia.org/wiki/List_of_self-driving_car_fatalities The problem with these systems is not in the AI – anybody who has played a game with simulated traffic (LA Noir, Grand Theft Auto, etc.) knows that. Instead, the problem is with the ‘computer vision’; the system that describes the ‘world view’ in which the AI operates. In one fatality, for example, the computer vision failed to distinguish a white semi tractor trailer from the sky.³⁾https://www.theguardian.com/technology/2016/jun/30/tesla-autopilot-death-self-driving-car-elon-musk Consequently, the AI did not ‘know’ there was a semi directly in front of it.

In my doctoral research I created a system by which a program could ‘read’ and ‘understand’ a battlefield map⁴⁾TIGER: An Unsupervised Machine Learning Tactical Inference Generator http://www.riverviewai.com/download/SidranThesis.html. This is the system that we use in General Staff.

The two images, above, show the difference in how a human commander and a computer ‘see’ the same battlefield. In the top image the woods, the hills and the roads are all obvious to us humans.

The bottom, or ‘computer vision’ image, is a bit of a cheat because this is how the computer information is visually displayed to the human designer in the General Staff Map Editor. The bottom image is created from four map layers (any of which can be displayed or turned off):

The four layers that make up a General Staff map.

The background image layer in a General Staff map is the beautiful artwork shown in the top image. The place names and Victory Points layer are also displayed in the top image. The terrain and elevation layers are described below:

The next three images are actual visual representations of the contents of memory where these terrain values are stored (this is built in to the General Staff Map Editor as a debugging tool):

Screen shot from the Map Editor showing just terrain labeled as ‘water’. Click to enlarge

Screen shot from the General Staff Map Editor showing the terrain labeled as ‘woods’. Click to enlarge.

Screen shot from the General Staff Map Editor showing the terrain labeled ‘road’. Click to enlarge.

A heightmap for Antietam. This is a visual representation of elevation in meters (darker = lower, lighter = higher). Click to enlarge.

To computers, an image is a two-dimensional array; like a giant tic-tac-toe or chess board. Every square (or cell) in that board contains a value called the RGB (Red, Green, Blue⁵⁾Except in France where it’s RVB for Rouge, Vert, Bleu ) value. Colors are described by their RGB value (white, for example, is 255,255,255). If you find this interesting, here is a link to an interactive RGB chart. General Staff uses a similar system except instead of the RGB system each cell contains a value that represents various terrain types (road, forest, swamp, etc.) and another, identical, two-dimensional array, contains values that represent the elevation in meters. To make matters just a little bit more confusing, computer arrays are actually not two-dimensional (or three-dimensional or n-dimensional) but rather a contiguous block of memory addresses. So, the terrain and elevation arrays in General Staff which appear to be two-dimensional arrays of 1155 x 805 cells are actually just 929,775 bytes long hunks of contiguous memory. To put things in perspective, just those two arrays consume more RAM than was available for everything in the original computer systems (Apple //e, Apple IIGS, Atari ST, MS DOS, Macintosh and Amiga) that I originally wrote UMS for.

So, not surprisingly, a computer stores its map of the world in which it operates as a series of numbers ⁶⁾Yes, at the lowest level the numbers are just 1s and 0s but we’ll cover that before the midterm exams. that represent terrain and elevation. But, how does a human commander read a map? I posed this question to Ben Davis, a neuroscientist and wargamer, and he suggested looking at a couple of studies. In one article⁷⁾https://www.citylab.com/design/2014/11/how-to-make-a-better-map-according-to-science/382898/, Amy Lobben, head of the Department of Geography at the University of Oregon, said, “…some people process spatial information egocentrically, meaning they understand their environment as it relates to them from a given perspective. Others navigate more allocentrically, meaning they look at how other objects in the environment relate to each other, regardless of their perspective. These preferences are linked to different regions of the brain.” Another⁸⁾https://www.researchgate.net/publication/251187268_USING_fMRI_IN_CARTOGRAPHIC_RESEARCH reports the results of fMRI scans while, “subjects perform[ed] navigational map tasks on a computer and again while they were being scanned in a magnetic resonance imaging machine.” to identify specific, “involvement or non-involvement of the brain area.. doing the task.”

So, how computers and human commanders read and process maps is quite different. But, at the end of the day, computers are just manipulating numbers following a series of algorithms. I have written extensively about the algorithms that I have developed including:

“Algorithms for Generating Attribute Values for the Classification of Tactical Situations.”
“Implementing the Five Canonical Offensive Maneuvers in a CGF Environment.”
“Good Decisions Under Fire: Human-Level Strategic and Tactical Artificial Intelligence in Real-World Three-Dimensional Environments.”
“Current Methods to Create Human-Level Artificial Intelligence in Computer Simulations and Wargames”
Human Level Artificial Intelligence for Computer Simulations and Wargames.
An Analysis of Dimdal’s (ex-Jonsson’s) ‘An Optimal Pathfinder for Vehicles in Real-World Terrain Maps’

These papers, and others, can be freely downloaded from my web site here.

As always, please feel free to contact me directly if you have any questions or comments.

References[+]

References
↑1	When describing various AI processes I often use words like ‘see,’ ‘understand,’ and ‘know’ but this should not be taken literally. The last thing I want to do is to get in to a philosophic discussion on computers being sentient.
↑2	https://en.wikipedia.org/wiki/List_of_self-driving_car_fatalities
↑3	https://www.theguardian.com/technology/2016/jun/30/tesla-autopilot-death-self-driving-car-elon-musk
↑4	TIGER: An Unsupervised Machine Learning Tactical Inference Generator http://www.riverviewai.com/download/SidranThesis.html
↑5	Except in France where it’s RVB for Rouge, Vert, Bleu
↑6	Yes, at the lowest level the numbers are just 1s and 0s but we’ll cover that before the midterm exams.
↑7	https://www.citylab.com/design/2014/11/how-to-make-a-better-map-according-to-science/382898/
↑8	https://www.researchgate.net/publication/251187268_USING_fMRI_IN_CARTOGRAPHIC_RESEARCH

Computational Military Reasoning (Tactical Artificial Intelligence) Part 1

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I coined the phrase ‘computational military reasoning’ in grad school to explain what my doctoral thesis in computer science was about. ‘Computational reasoning’ is a formal method for solving problems (technically, you don’t even need a computer). But, for our purposes it means a computer solving ‘human-level’ problems. A classic example of this would be calculating the fastest route on a map between two points. In computer science we call this a ‘least weighted path’ algorithm and I did my Q (Qualifying) Exam on this subject. I have also written extensively on the subject including these blog posts.

So, ‘computational military reasoning’ is a, “computer solving human-level military problems.” Furthermore, we can divide computational military reasoning into two subcategories: strategic and tactical (Russian military dogma also adds a third category, ‘grand strategy’); however, for now, let’s concentrate on tactical artificial intelligence; or battlefield decisions.

Tactical AI is divided into two parts: analyzing – or reading – the battlefield and acting on that information by creating a set coherent orders (commonly known as a COA or Course of Action) that exploit the weaknesses in our enemy’s position that we have found during our battlefield analysis.

It is said that as Napoleon traveled across Europe with his staff he would question them about the terrain that they were passing; “Where is the best defensive position? What are the best attack routes?” Where would you position artillery? What ground is favorable for cavalry attack?”

We take it for granted that such analysis of terrain and opposing forces positioned upon it is a skill that can be taught to humans. My doctoral research ¹⁾TIGER: An Unsupervised Machine Learning Tactical Inference Generator; This thesis can be downloaded free of charge here. successfully demonstrated the hypothesis that an unsupervised machine learning program could also learn this skill and perform battlefield analysis that was statistically indistinguishable²⁾Using a one sided Wald test resulted in p = 0.0001.In other words, it was extremely unlikely that TIGER was ‘guessing correctly’. from analyses performed by Subject Matter Experts (SMEs) such as instructors at West Point and active duty combat command officers.

Supervised & Unsupervised Machine Learning

Netflix recommendations are a supervised learning program. Every time you ‘like’ a movie the program ‘learns’ that you like ‘documentaries’; for example. Any program that has you ‘like’ or ‘dislike’ offerings is a supervised learning program. You are the supervisor and by clicking on ‘like’ or ‘dislike’ you are teaching the program.

TIGER is an unsupervised machine learning program. That means it has to figure everything out for itself. Rather than being taught, TIGER is ‘fed’ a series of ‘objects’ that have ‘attributes’ and it sorts them into like categories. For TIGER the objects are snapshots of battlefields.

Screen capture from TIGER. An ‘object’ has been loaded into TIGER for analysis; in this case a ‘snapshot’ of the battle of Antietam at 1630 hours on September 17, 1863. Click to enlarge.

How TIGER perceives the battlefield

When you and I look at a battlefield our brains, somehow, make sense of all the NATO 2525B icons scattered around the topographical map. I don’t know how our brains do it, but this is how TIGER does it:

Screen capture from TIGER: How TIGER converts unit positions into lines and frontages using a Minimum Spanning Tree (MST). Click to enlarge.

By combining 3D Line of Sight with Range of Influence (how far weapons can fire and how accurate they are at greater distances displayed, above, with lighter colors) with a Minimum Spanning Tree algorithm³⁾Kruskal’s algorithm, https://en.wikipedia.org/wiki/Kruskal%27s_algorithm the above image is how TIGER ‘sees’ the battlefield of Antietam. This is an important first step for evaluating object attributes.

How to determine the attribute of anchored or unanchored flanks

Battlefields are ‘objects’ that are made up of ‘attributes’. One of these attributes is the concept of anchored and unanchored flanks. While anyone who plays wargames probably has a good idea what is meant by a ‘flank’, following formal scientific methods I had to first prove that there was agreement among Subject Matter Experts (SMEs) on the subject. This is from one of the double-blind surveys given to SMEs:

Screen shot from online double-blind survey of Subject Matter Experts on identifying the presence of Anchored and Unanchored Flanks. Click to enlarge.

And their responses to the situation at Antietam:

Subject Matter Experts response to the question of the presence of Anchored or Unanchored flanks at Antietam. Click to enlarge.

And another double-blind survey question asked of the SMEs about anchored or unanchored flanks at Chancellorsville:

Response to double-blind survey question asked of SMEs about anchored and unanchored flanks at Chancellorsville. Click to enlarge.

So, we have now proven that there is agreement among Subject Matter Experts about the concept of ‘anchored’ and ‘unanchored’ flanks and, furthermore, some battlefields exhibit this attribute and others don’t.

Following is a series of slides from a debriefing presentation that I gave to DARPA (Defense Advanced Research Projects Agency) as part of my DARPA funded research grant (W911NF-11-200024) describing the algorithm that MATE (the successor to TIGER) uses to calculate if a flank is anchored or unanchored and how to tactically exploit this situation with a flanking maneuver. This briefing is not classified. Click to enlarge slides.

How to generate a Course of Action for a flank attack

Once TIGER / MATE has detected an ‘open’ or unanchored flank it will then plot a Course of Action (COA) to maneuver its forces to perform either a Turning Maneuver or an Envelopment Maneuver. Returning to the previous DARPA debriefing presentation (Click to enlarge):

MATE analysis of the battle of Marjah (Operation Moshtarak February 13, 2010)

The following two screen captures are part of MATE’s analysis of the battle of Marjah suggesting an alternative COA (envelopment maneuver) to the direct frontal assault that the U. S. Marine force actually performed at Marjah. Click to enlarge:

Conclusions & Comments about Computational Military Reasoning (Tactical Artificial Intelligence) & Battlefield Analysis (Part 1)

Usually, at this point when I give this lecture, I look out to my audience and ask for questions. I really don’t want to lose anybody and we’ve got a lot more Tactical AI to talk about. So far, I’ve only covered how my programs (TIGER / MATE) analyze a battlefield in one particular way (does my enemy – OPFOR in military terms – have an exposed flank that I can pounce on?) and there is a lot more battlefield analysis to be performed.

It’s easy, as a computer scientist, to use computer science terminology and shorthand for explaining algorithms. But, I worry that the non computer scientists in the audience will not quite get what I’m saying.

Do you have any questions about this? If so, I would really like to hear from you. I’ve been working on this research for my entire professional career (see A Wargame 55 Years in the Making) and, frankly, I really like talking about it. As a TA said to me many years ago when I was an undergrad, “There are no stupid questions in computer science.” So, please feel free to write to me either using our built in form or by emailing me at Ezra [at] RiverviewAI.com

References[+]

References
↑1	TIGER: An Unsupervised Machine Learning Tactical Inference Generator; This thesis can be downloaded free of charge here.
↑2	Using a one sided Wald test resulted in p = 0.0001.In other words, it was extremely unlikely that TIGER was ‘guessing correctly’.
↑3	Kruskal’s algorithm, https://en.wikipedia.org/wiki/Kruskal%27s_algorithm

A Wargame 55 Years in the Making (Part 5)

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In June, 2009 I successfully defended my thesis and was awarded a doctorate of computer science by the University of Iowa. What followed were some of the most productive years of my professional career. I designed, programmed, project managed and was principal investigator on:

MARS: Military Advanced Real-time Simulator (2009)

OneSAF is the “Semi Automated Forces” wargame / simulator used for training by the US Army. It relies on ‘pucksters’ (see pucksters in this blog) who are usually retired military officers who make all the moves for OPFOR (Opposition Forces), MARS provided an intuitive Graphical User Interface (GUI) for the modification and running of OneSAF scenarios.

Screen capture of the MARS project for the US Army. MARS was a front end to facilitate creating and managing scenarios run on the Army’s OneSAF military simulator. The ‘Magic Bomb’ option is the puckster’s term for ‘magically’ removing a unit from the simulation. Click to enlarge.

CAPTURE: Cognitive and Physiological Testing Urban Research Environment (2010)

While on the surface CAPTURE appears to be a standard ‘shooting gallery’ program it was actually designed to test and store data about how returning veterans saw targets, ‘spiraled in’ on targets and reacted. There were two parts to CAPTURE: the first allowed the tester to set up any particular scenario they wanted (top image, below) and the second part (bottom image, below) was run using a projector, a large screen, an M16 air soft gun with Wii remote and laser mounted to the barrel and an IR camera. CAPTURE was done for the Office of Naval Research (Marines).

Two screens showing the CAPTURE program. The top screen shows the interface for creating target scenarios. The bottom screen is one of the the shooting ranges generated by CAPTURE. Click to enlarge.

NexGEN Behavior Composer (2011)

NexGEN Behavior Composer was another front-end project for OneSAF. Enemy units in OneSAF use scripted AI behavior written in XAML. These AI scripts often contained errors. NexGEN allowed the puckster to select a behavior from a hierarchical tree structure (top image, below) and click and drag it to a composing canvass where a series of behaviors could be joined together (bottom image, below). The artwork for the behaviors was done by my old friend, Ed Isenberg, who has worked with me on games since the ’80s.

Screen shot of NexGEN Behavior Composer which facilitated creating OneSAF behaviors by clicking and dragging behavior icons. Click to enlarge.

Screen shot of NexGEN Behavior Composer which facilitated creating OneSAF behaviors by clicking and dragging behavior icons. This is the hierarchical tree structure of behavior primitives. Click to enlarge.

And example of a OneSAF behavior composed of NexGEN behavior icons. Click to enlarge.

A series of behaviors have been placed together to create a complex behavior (a unit fires, conducts reconnaissance, waits for one minute, moves and then occupies a position). Click to enlarge.

MATE: Machine Analysis of Tactical Environments (2012)

Funded by a DARPA (Defense Advanced Research Project Agency) research grant (W911NF-11-200024) MATE added a new level of battlefield analysis to the TIGER project. Building on the previous nine years of research MATE had the capability of generating a series of ‘predicate statements’ that described the battlefield and then using them to construct a hypothetical syllogism that resulted in a precise Course of Action (COA) for BLUEFOR (US forces). MATE then output this COA as an HTML file and automatically launched a browser to view the COA. MATE was designed to be available to commanders in the field via a small handheld device like a tablet. It was able to perform battlefield analysis in less than 10 seconds.

Consider this real-world situation from the Battle of Marjah:

Given the same data that the commander had in the above video MATE returned this COA (complete with unit paths and ETAs):

MATE’s analysis and COA for the Battle of Marjah: a right-flank envelopment maneuver with two infantry platoons while a fixing force of the mortar platoon and a third infantry platoon kept the enemy’s attention. Click to enlarge.

To see the entire MATE analysis and COA results for the Battle of Marjah click here. (this will load a PDF of MATE’s HTML output on a new tab).

Unfortunately, about the time that I demonstrated MATE to DARPA a series of unfortunate events occurred that were to change my life. The United States Congress passed the Sequestration Transparency Act of 2012. This resulted in a 10% across the board cut in all federal spending. DARPA seemed especially hard hit and they stopped all funding for 4CI (Command, Control, Communications, Computers and Intelligence) research. Only a few years after receiving my doctorate, specifically so I could be the Principal Investigator on government funded 4CI research, I was out of a job.

Without any research funding, and not wanting to relocate I returned to the University of Iowa as a Visiting Assistant Professor teaching Computer Game Design and CS1. I love teaching. And I am extraordinarily proud of receiving the highest student evaluations in the department of Computer Science but I didn’t have as much strength as I used to have. I found myself out of breath and exhausted after a lecture. And then my kidneys began to inexplicably fail.

In 2013, because of the efforts of superb doctors Kelly Skelly and Joel Gordon at the University of Iowa Hospital, I was diagnosed with a very rare and usually fatal blood disease, AL amyloidosis. In 2014, thanks to the Affordable Care Act, I was hospitalized for 32 days, my immune system was purposely destroyed and I received an autologous bone marrow / stem cell transplant. This was followed up by a year of chemotherapy. Being severely immunocompromised I have contracted pneumonia six times in the last two years. Now, against the odds (and I’m a guy that deals with probabilities a lot so I’m being literal) I’ve completely recovered. My kidneys and lungs are permanently damaged but I’m not going to die from this disease. But, it also means I can’t teach anymore, either.

Luckily, I can still sit at a desk and write computer code. General Staff is my return to writing a commercial computer wargame and it will be the first commercial implementation of my tactical AI algorithms that I have been developing since 2003.

I need to produce a game that you grognards want. And, that means next week I will be posting a new gameplay survey to pin down exactly what features you want to see in the new game. As always, please feel free to contact me directly (click here) if you have any questions or comments.

A Wargame 55 Years in the Making (Part 3)

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The goal of my doctoral research was to create a suite of algorithms that were capable of making ‘human-level’ tactical and strategic decisions. The first step is designing a number of ‘building block’ algorithms, like the least weighted path algorithm that calculates the fastest route between two points on a battlefield while avoiding enemy fire that we saw in last week’s post. Another important building block is Kruskal’s Minimum Spanning Tree algorithm which allows the computer to ‘see’ lines of units.

I use terms like ‘see’ and ‘think’ to describe actions by a computer program. I am not suggesting that current definitions of these terms would accurately apply to computer software. However, it is simply easier to write that a computer ‘sees’ a line of units or ‘thinks’ that this battlefield situation ‘looks’ similar to previously observed battlefields. What is actually happening is that units are represented as nodes (or vertices) in a a graph and some basic geometry is being applied to the problem. Next week we will use probabilities. But, at the end of the day, it’s just math and computers, of course, don’t actually ‘see’ anything.

Examples of how Kruskal’s Minimum Spanning Tree algorithm can be used to separate groups of units into cohesive lines. These figures are taken from, “Implementing the Five Canonical Offensive Maneuvers in a CGF Environment.” by Sidran, D. E. & Segre, A. M.

When you and I look at a map of a battle we immediately see the opposing lines. We see units supporting each other, interior lines of communication, and lines of advance and retreat. The image, below, shows how the program (in this case, TIGER, the Tactical Inference Generator which was written to demonstrate my doctoral research) ‘sees’ the forces at the battle of Antietam. The thick black line is the ‘MST Spine’. You and I automatically perceive this as the ‘front line’ of the Confederate forces, but this is a visual representation of how TIGER calculates the Confederate front line. Also important is that TIGER perceives REDFOR’s flanks as being anchored (that is to say, BLUE does not have a path to the flanking objective, the tip of the green vector, that does not go through RED Range of Influence, ROI, or Zone of Control).

Figure 1. TIGER screen shot of ‘flanking attribute’ calculations for the battle of Antietam (September 17, 1862, 0600 hours). Note the thick black line that repres ents the MST spine of REDFO R Group 0, the extended vectors th at calculate the Flanking Goal Objective Point and BLUEFOR and REDFOR ROI (red and blue shading). REDFOR (Confederate) has anchored flanks.

TIGER screen shot of ‘flanking attribute’ calculations for the battle of Antietam (September 17, 1862, 0600 hours). Note the thick black line that represents the MST spine of REDFOR Group 0, the extended vector that calculates the Flanking Goal Objective Point and BLUEFOR and REDFOR ROI (red and blue shading). REDFOR (Confederate) has anchored flanks. From, “Algorithms for Generating Attribute Values for the Classification of Tactical Situations,” by Sidran, D. E. & Segre, A. M.

Now that TIGER can see the opposing lines and recognize their flanks we can calculate the routes for implementing the Course of Action (COA) for various offensive maneuvers. U. S. Army Field Manual 3-21 indicates that there are five, and only five, offensive maneuvers. The first is the Penetration Maneuver (note: the algorithms for these and the other maneuvers appear in, “Implementing the Five Canonical Offensive Maneuvers in a CGF Environment.” by Sidran, D. E. and Segre, A. M.) and can be downloaded from ResearchGate and Academia.edu.

The Penetration Maneuver is described in U.S. Army Field Manual 3-21 and as implemented by TIGER. Note how TIGER calculates the weakest point of REDFOR’s line. From, “Implementing the Five Canonical Offensive Maneuvers in a CGF Environment.” by Sidran, D. E. and Segre, A. M. Click to enlarge.

The next maneuver is the Infiltration Maneuver. Note that to implement the Infiltration Maneuver, BLUEFOR must be able to infiltrate REDFOR’s lines without entering into RED’s ROI:

The Infiltration Maneuver as described in U.S. Army Field Manual 3-21 and as implemented by TIGER. Note how TIGER reaches the objectives without entering into REDFOR ROI. From, “Implementing the Five Canonical Offensive Maneuvers in a CGF Environment.” by Sidran, D. E. and Segre, A. M. Click to enlarge.

The next maneuver is the Turning Maneuver. Note: in order to ‘turn an enemy’s flanks’ one first must be able to recognize where the flanks of a line are. This is why the earlier building block of the MST Spine is crucial.

The Turning Maneuver as illustrated in U. S. Army Field Manual 3-21 and in TIGER. From, “Implementing the Five Canonical Offensive Maneuvers in a CGF Environment.” by Sidran, D. E. and Segre, A. M. Click to enlarge.

Certainly the most complex offensive maneuver is the Envelopment Maneuver which requires two distinct movements and calculations for the attacking forces: first the attacker must decide which flank (left or right) to go around and then the attacker must designate a portion of his troops as a ‘fixing force’. Think of an envelopment maneuver as similar to the scene in Animal House when Eric “Otter” Stratton (played by Tim Matheson) says to Greg Marmalard (played by James Daughton), “Greg, look at my thumb.” Greg looks at Otter’s left thumb while Otter cold-cocks Marmalard with a roundhouse right. “Gee, you’re dumb,” marvels Otter. In an envelopment maneuver the fixing force is Otter’s left thumb. Its purpose is to hold the attention of the victim while the flanking force (the roundhouse right) sweeps in from ‘out of nowhere’. In the next post I will show a real-world example of an Envelopment Maneuver created by my MATE (Machine Analysis of Tactical Environments) program for DARPA.

The Envelopment Maneuver as shown in U. S. Army Field Manual 3-21 and as implemented in TIGER. From, “Implementing the Five Canonical Offensive Maneuvers in a CGF Environment.” by Sidran, D. E. and Segre, A. M. Click to enlarge.

Lastly, and obviously the maneuver of last resort, is the Frontal Assault:

The Frontal Assault Maneuver from, “Implementing the Five Canonical Offensive Maneuvers in a CGF Environment.” by Sidran, D. E. and Segre, A. M. Click to enlarge.

All that I’ve done in this post is show some of the things that the TIGER program does. What I haven’t done is show how the algorithms work and that’s because they are described in the papers, below. Obviously, this is a subject that I find pretty interesting, so feel free to ask me questions (you can use the Contact Us page).

It is my intention to incorporate these algorithms into the General Staff wargame. However, I’ve been told by a couple of game publishers that users don’t want to play against a human-level AI. What do you think? If you’ve read this far I would really appreciate it if you would answer the survey below.
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Papers that were cited in this post with download links:

“An Analysis of Dimdal’s (ex-Jonsson’s) ‘An Optimal Pathfinder for Vehicles in Real-World Terrain Maps'”

In PDF Format

“Algorithms for Generating Attribute Values for the Classification of Tactical Situations.”

In PDF Format

“Implementing the Five Canonical Offensive Maneuvers in a CGF Environment.”

In PDF Format