1. Introduction
1.4 Organization of this dissertation
The structure of this dissertation is showed in Figure 1. The research motivation,
background, purposes, framework and methods are described in Chapter 1. Chapter 2 describes the history of The Ardennes Campaign and articles of military warfare analysis tools. We introduce the stream of its development, planning and some modeling. We summarize some comprehensive generalized version of Lanchester equations model in Chapter 3. Furthermore, following the main stream of evolutionary computation, we introduce mathematical formulation of Lanchester equations and evolutionary algorithms .And one empirical study for seeking the a much better qualitative analysis model for the explanation of modern combat in Chapter 4. Finally, concluding remarks, recommendations and future research are given in Chapter 5.
Figure 1. The research process and organization of the dissertation
2. Literature review
In this section we summarize related methodology and about development issues of military warfare analysis tools. We also want to describe the history of Ardennes Campaign,
Introduction
Literature Review
Generalized version of Lanchester equations model
Mathematical formulation
Conclusions and Recommendation
Model Building and Implementation
Empirical Study Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
a partial article from Thomas D. Morgan (LT. Col.USA Ret.) Army magazine Nov. 20042 quoted by us. And cite Sun Tzu Art of War, On War Carl von Clausewitz [31] to discuss the doctrines of military affairs.
2.1 Lanchester equations3
The Lanchester laws are perhaps the best-known models of combat. They were developed by F. W. Lanchester [36] just prior to U.S. involvement in World War I and were first published in his now famous book, Aircraft in Warfare: The Dawn of the Fourth Arm. In this section, we discuss the Square and Linear law as following:
2.1.1 Lanchester Square Law
The effect of concentrating the force is reflected by the fact that the casualty rate is assumed to depend only on the size of the shooting force. This is due to the firepower delivery available with modern weapons. If we let R and B represent the initial size of the Red and Blue forces (number of units) respectively, and N and M (0 ≤N, M ≤1) be the effectiveness of each Red and Blue unit respectively, the rate at which each of the two forces is depleted is given by the relations
( ) ( )
B. The attrition to each side depends on the effectiveness of the shooting side’s units and the remaining size of the shooting force. Dividing the two equations, we get( )
Integrating from time 0 to time t, we get
This formulation allows us to examine the requirements for Blue (or Red) to win. For Blue to win, we must have that at time T, r(t) = 0 and b(t) > 0. Rewriting the above
Solving the inequality, we get .
For Blue to win, the relative effectiveness of the two forces must exceed the square of the initial force ratio.
One type of battle described by a Lanchester square law occurs when both sides can employ constant fractions of their forces and have target-rich environments. The size of the force the friendly commander commits to the battle determines the amount of enemy attrition attained rather than the size of the enemy force committed [3].
2.1.2 Lanchester Linear Law
The linear law reflects the inability, or more accurately the futility, of either side to mass its forces effectively. Lanchester referred to this as a characteristic of ancient warfare:
In olden times, when weapon directly answered weapon, the act of defence was positive and direct, the blow of sword or battleaxe was parried by sword and shield. . . . Under [these] conditions, it was not possible by any strategic plan or tactical maneuver to bring other than equal numbers of men into the actual fighting line; one man would ordinarily find himself opposed to one man. Under these conditions, attrition depends solely upon the effectiveness of the individual combatant. Another, more modern interpretation of the linear law is that it represents area fires. That is, we assume that the attacker knows the enemy is located within an area, but that he is unable to target each combatant individually.
The best he can do is launch indirect fires into the area. In this case, the effectiveness of the attacker depends not only on the effectiveness of the weapon, but also on the number of attackers (number of weapons), the effectiveness of each attacker, and the number of targets in the area fired upon. Both of these cases result in a linear law. As above, we let M and N be the effectiveness of each combatant, with r(0) = R and b(0) = B, the original size
of the Red and Blue forces. The number of firing opportunities for Blue is proportional to b(t)r(t), and the number of Red firing opportunities is proportional to r(t)b(t):
( ) ( ( ) ( ) )
The effectiveness scores refer to the effectiveness of the individual combatant.
Dividing the two equations as above, we get
( )
Integrating from time 0 to time t, we get
( ) (
r( )
t R)
. the above equation with t = T and solving for b(T), we get( ) N 0.
b T B R
= −M f
Solving the inequality, we get
⎟.
In this case, to win, the effectiveness ratio need only exceed the initial force ratio. In the linear case, the impact of the force size on combat outcome is significantly less than in the square case. The area-fires interpretation results in the following attrition rates:
( ) ( ( ) ) ( )
reflecting the effects of force size, weapon effectiveness, and targets available. Here (b(t)M) can be interpreted as the firing effectiveness of Blue and (r(t)N) can be interpreted as the firing effectiveness of Red. Dividing the two equations as above, we get exactly the same results as above.
2.2 Sun Tzu (Art of War)
Sun Tzu [1] one of the earliest great military thinkers who realized that war, a matter of vital importance to the State, demanded study and analysis. His works are the first known attempt to formulate a rational basis for the planning and conduct of military operations. His purpose, according to Samuel B. Griffith [35], was "to develop a systematic treatise to guide rulers and generals in the intelligent prosecution of successful war". Sun Tzu was also convinced that careful planning based on sound information would contribute to speedy victory.4 His partial work was quoted by us to discuss in this article.
2.2.1 Initial estimations ( Laying plans5 )
Sun Tzu said: The art of war is of vital importance to the State. It is a matter of life and death, a road either to safety or to ruin. Hence it is a subject of inquiry which can on no account be neglected. The art of war, then, is governed by five constant factors, to be taken into account in one's deliberations, when seeking to determine the conditions obtaining in the field. These are: (1) The Moral Law; (2) Heaven; (3) Earth; (4) The Commander; (5) Method and discipline. These five heads should be familiar to every general: he who knows them will be victorious; he who knows them not will fail. … Therefore, in your deliberations, when seeking to determine the military conditions, let them be made the basis of a comparison, in this wise: --
(a) Which of the two sovereigns is imbued with the Moral law?
(b) Which of the two generals has most ability?
(c) With whom lie the advantages derived from Heaven and Earth?
(d) On which side is discipline most rigorously enforced?
The general who loses a battle makes but few calculations beforehand. Thus do many calculations lead to victory, and few calculations to defeat: how much more no calculation at all! It is by attention to this point that I can foresee who is likely to w in or lose.
2.2.2 Planning offensives ( Attack by stratagem6 )
Sun Tzu said: In the practical art of war, the best thing of all is to take the enemy's country whole and intact; to shatter and destroy it is not so good. So, too, it is better to
4 http://www.ndu.edu/inss/siws/intro.html
5 http://www.kimsoft.com/polwar1.htm
6 http://www.kimsoft.com/polwar3.htm
recapture an army entire than to destroy it, to capture a regiment, a detachment or a company entire than to destroy them.
It is the rule in war:
(a) If our forces are ten to the enemy's one, to surround him;
(b) If five to one, to attack him;
(c) If twice as numerous, to divide our army into two.
(d) If equally matched, we can offer battle;
(e) If slightly inferior in numbers, we can avoid the enemy;
(f) If quite unequal in every way, we can flee from him.
Thus we may know that there are five essentials for victory:
(a) He will win who knows when to fight and when not to fight;
(b) He will win who knows how to handle both superior and inferior forces;
(c) He will win whose army is animated by the same spirit throughout all its ranks;
(d) He will win who, prepared himself, waits to take the enemy unprepared;
(e) He will win who has military capacity and is not interfered with by the sovereign.
Hence the saying: If you know the enemy and know yourself, you need not fear the result of a hundred battles. If you know yourself but not the enemy, for every victory gained you will also suffer a defeat. If you know neither the enemy nor yourself, you will succumb in every battle.
2.2.3 Military disposition (Tactical dispositions7)
Sun Tzu said: The good fighters of old first put themselves beyond the possibility of defeat, and then waited for an opportunity of defeating the enemy. To secure ourselves against defeat lies in our own hands, but the opportunity of defeating the enemy is provided by the enemy himself. Thus the good fighter is able to secure himself against defeat, but cannot make certain of defeating the enemy. Hence the saying: One may know how to conquer without being able to DO it. The consummate leader cultivates the moral law, and strictly adheres to method and discipline; thus it is in his power to control success.
In respect of military method, we have, firstly, Measurement; secondly, Estimation of quantity; thirdly, Calculation; fourthly, Balancing of chances; fifthly, Victory.
Measurement owes its existence to Earth; Estimation of quantity to Measurement;
Calculation to Estimation of quantity; Balancing of chances to Calculation; and Victory to
7 http://www.kimsoft.com/polwar4.htm
Balancing of chances. A victorious army opposed to a routed one, is as a pound's weight placed in the scale against a single grain. The onrush of a conquering force is like the bursting of pent-up waters into a chasm a thousand fathoms deep.
2.3 On War
Carl von Clausewitz [31], a Prussian military thinker, is widely acknowledged as the most important of the major strategic theorists. Even though he's been dead for over 170 year, he remains the most frequently cited, the most controversial, and in many respects the most modern.
2.3.1 What is war8
We shall not enter into any of the abstruse definitions of War used by publicists. We shall keep to the element of the thing itself, to a duel. War is nothing but a duel on an extensive scale. If we would conceive as a unit the countless number of duels which make up a War, we shall do so best by supposing to ourselves two wrestlers. Each strives by physical force to compel the other to submit to his will: each endeavours to throw his adversary, and thus render him incapable of further resistance. War therefore is an act of violence intended to compel our opponent to fulfill our will.
If there was only one form of War, to wit, the attack of the enemy, therefore no defence; or, in other words, if the attack was distinguished from the defence merely by the positive motive, which the one has and the other has not, but the methods of each were precisely one and the same: then in this sort of fight every advantage gained on the one side would be a corresponding disadvantage on the other, and true polarity would exist.
But action in War is divided into two forms, attack and defence, which, as we shall hereafter explain more particularly, are very different and of unequal strength. Polarity therefore lies in that to which both bear a relation, in the decision, but not in the attack or defence itself.
If the one Commander wishes the solution put off, the other must wish to hasten it, but only by the same form of action. If it is A’s interest not to attack his enemy at present, but four weeks hence, then it is B’s interest to be attacked, not four weeks hence, but at the
8 http://www.marxists.org/reference/archive/clausewitz/works/on-war/book1/ch01.htm
present moment. This is the direct antagonism of interests, but it by no means follows that it would be for B’s interest to attack A at once. That is plainly something totally different.
2.3.2 On the signification of the combat9
As war is nothing else but a mutual process of destruction, then the most natural answer in conception, and perhaps also in reality, appears to be that all the powers of each party unite in one great volume, and all results in one great shock of these masses. There is certainly much truth in this idea, and it seems upon the whole to be very advisable that we should adhere to it, and that we should on that account look upon small combats at first only as necessary loss, like the shavings from a carpenter's plane. Still however, the thing is never to be settled so easily.
That a multiplication of combats should arise from a fractioning of forces is a matter of course, and the more immediate objects of separate combats will therefore come before us in the subject of a fractioning of forces; but these objects, and together with them, the whole mass of combats may in a general way be brought under certain classes, and the knowledge of these classes will contribute to make our observations more intelligible.
Destruction of the enemy's military forces is in reality the object of all combats; but other objects maybe joined to that, and these other objects may be at the same time predominant; we must therefore draw a distinction between those in which the destruction of the enemy's forces is the principal object, and those in which it is more the means.
Besides the destruction of the enemy's force, the possession of a place or the possession of some object may be the general motive for a combat, and it may be either one of these alone or several together, in which case still usually one is the principal motive.
Now the two principal forms of War, the offensive and defensive, of which we shall shortly speak, do not modify the first of these motives, but they certainly do modify the other two, and therefore if we arrange them in a scheme( see Table 1 ) they would appear thus:
Table 1. The difference between Offensive and Defensive Offensive. Defensive.
9 http://www.marxists.org/reference/archive/clausewitz/works/on-war/book4/ch05.htm
1. Destruction of enemy's force.
2. Conquest of a place.
3. Conquest of some object.
1. Destruction of enemy's force.
2. Defence of a place.
3. Defence of some object.
These motives, however, do not seem to embrace completely the whole of the subject, if we recollect that there are reconnaissance and demonstrations, in which plainly none of these three points is the object of the combat. In reality we must, therefore, on this account be allowed a fourth class. Strictly speaking, in reconnaissance in which we wish the enemy to show himself, in alarms by which we wish to wear him out, in demonstrations by which we wish to prevent his leaving some point or to draw him off to another, the objects are all such as can only be attained indirectly and under the pretext of one of the three objects specified in the table, usually of the second; for the enemy whose aim is to reconnoitre must draw up his force as if he really intended to attack and defeat us, or drive us off, etc., etc. But this pretended object is not the real one, and our present question is only as to the latter; therefore, we must to the above three objects of the offensive further add a fourth, which is to lead the enemy to make a false move, or, in other words, engage him in a sham fight. That offensive means only are conceivable in connection with this object, lies in the nature of the thing.
On the other hand we must observe that the defence of a place may be of two kinds, either absolute, if as a general question the point is not to be given up, or relative if it is only required for a certain time. The latter happens perpetually in the combats of advanced posts and rear guards.
That the nature of these different intentions of a combat must have an essential influence on the dispositions which are its preliminaries, is a thing clear in itself. We act differently if our object is merely to drive an enemy's post out of its place from what we should if our object was to beat him completely; differently, if we mean to defend a place to the last extremity from what we should do if our design is only to detain the enemy for a certain time. In the first case we trouble ourselves little about the line of retreat, in the latter it is the principal point, &c.
But these reflections belong properly to tactics, and are only introduced here by way of example for the sake of greater clearness. What strategy has to say on the different objects of the combat will appear in the chapters which touch upon these objects. Here we have only a few general observations to make, first, that the importance of the object decreases nearly in the order as they stand above, therefore then, that the first of these objects must always predominate in the great battle; lastly, that the two last in a defensive
battle are in reality such as yield no fruit, they are, that is to say, purely negative, and can, therefore, only be serviceable, indirectly, by facilitating something else which is positive.
2.4 Game theory
The concepts and tools of game theory is a branch of microeconomics. Game theory has been widely used not only in business but also to analyze the effects of selecting alternative strategies to achieve a military objective.
2.4.1 The concept of game theory
For games of opposed interests, the basic concepts of maxmin and equilibrium strategies are defined and illustrated. Moving to general noncooperative games, the concepts of Stackelberg equilibrium and disequilibrium are presented in a duopoly game, and two logically consistent foundations for the competitive solution are given. The credibility of threats is discussed, and perfect equilibrium defined. Gaming is used by researchers interested in how people learn and play games and by other analysts interested in exploring strategies and policies, as a vehicle for helping understand complex issues [33].
People learn from gaming by designing games, playing them, or analyzing game
People learn from gaming by designing games, playing them, or analyzing game