一個頂頂簡單的冷兵器近距離混戰的NetLogo模型

    NetLogo和StarLogo都是多主體(multi-agent)模拟平台，後者繼承自前者但功能更強大、開發程序也更活躍。它們都采用類Logo的模組化程式設計語言，并引入了大規模并發機制，是以特别适合用于構造由許許多多自主活動但互相影響的簡單個體組成的大規模系統(比如蟻群)。通過在電腦平台上模拟每個主體的行為，我們可以探索系統作為整體所表現出的宏觀現象和性質。

    本文介紹的模型是基于NetLogo的。這個模型有敵對的兩方(中國和羅馬)，每一方的士兵數量是可調參數。士兵隻會近戰，這意味着隻能攻擊與自己處于同一格子(NetLogo中叫patch)中的敵人。每個士兵都有血量(blood)和殺傷力(power)參數，血量為0士兵死亡，每個士兵每次攻擊打掉對手的血量等于自己的殺傷力。戰鬥開始時，雙發所有的士兵被随機地分布在一個矩形的戰場中，随後士兵開始搜尋一個敵對目标，找到一個後就逼近直到足夠近，然後開始攻擊直到對方或自己死亡。士兵搜尋敵人的政策是：先判斷自己所處的格子中有否敵人，如沒有且敵人總數大于20就随機地轉個角度并往前走1到3步，如果敵人少于20個就挑一個最近的敵人然後朝他逼近(每次随機地前進1到3步)，如果逼近過程中敵人死了就重新搜尋離自己最近的敵人。任何一方士兵全部死亡則戰鬥結束。

    模型運作開始時會估算哪方勝利以及剩餘的士兵人數，運作結束後會給出實際的勝利方以及剩餘的人數。這些資訊全都輸出在Command Center裡。

    衆所周知，蘭徹斯特線性律可以較好地描述冷兵器近距接觸戰和使用間瞄武器(比如炮)作戰的傷亡規律，而平方律則可以描述使用直瞄武器(比如步槍)的作戰過程。但是，通過多次用不同參數運作上述模型，發現這種簡單的冷兵器近距混戰中，雙方的傷亡數與蘭徹斯特平方律也還是比較吻合的。對于這種現象，我是這麼了解的：平方律的前提是雙方所有士兵都互相進入攻擊距離，每個士兵可以選擇任意一個敵人進行直接攻擊，這使得火力集中能産生效果，小範圍的直瞄武器戰鬥是滿足這個前提的；由于本文讨論的戰鬥是混戰，雙方是充分接觸，每個士兵的攻擊範圍内至少有一個敵人的機率是很大的(很少有士兵會無事可幹)，而且一個格子中雙方人數之比大緻等于雙方總人數之比，根據戰鬥規則，一個格子内人多一方火力也更集中，是以平方律也基本适用。

[1] StarLogo, http://education.mit.edu/starlogo

[2] NetLogo, http://ccl.northwestern.edu/netlogo

[3] 數理戰術學, 沙基昌 著, 科學出版社, 2003

附錄：

    下面是模型源代碼，将它複制粘貼到一個字尾名為nlogo的本地文本檔案中，然後從NetLogo中打開，調整好參數後點選"setup"按鈕初始化，再點"go"按鈕運作。

globals [final-winner final-survivors guess-winner guess-surviors battle-over]

breed [china]

breed [rome]

to setup

    ca

    create-china china-count

    create-rome rome-count

    ask-concurrent china [set color green setxy random world-width random world-height]

    ask-concurrent rome [set color red setxy random world-width random world-height]

    ask-concurrent china [init china-blood china-power]

    ask-concurrent rome [init rome-blood rome-power]

    let sososo guess

    set guess-winner first sososo

    set guess-surviors item 1 sososo

    show (list "guess" guess-winner guess-surviors)

    set battle-over false

end

to-report guess

    let winner china

    let surviors 0

    let china-left-sq (china-count ^ 2 - rome-count ^ 2 * rome-power / china-power)

    let rome-left-sq (rome-count ^ 2 - china-count ^ 2 * china-power / rome-power)

    ifelse 0 < rome-left-sq [

        set winner rome

        set surviors sqrt rome-left-sq

    ]

    [

        set winner china

        set surviors sqrt china-left-sq

    ]

    report (list winner surviors)

end

to go

    if battle-over [

      show (list "fact" final-winner final-survivors)

      stop

    ]

    ask-concurrent turtles [fight]

    tick

end

turtles-own [target blood power]

to fight

    hunt-for-enemy

    attack-enemy power

    if not any-enemy [

        set final-survivors count-self

        set final-winner breed

        set battle-over true

        stop

    ]

end

to init [init-blood init-power]

    set target nobody

    set blood init-blood

    set power init-power

end

to hunt-for-enemy

    if not (nobody = target) [stop]

    let temp-target one-of-enemy-here

    if not (nobody = temp-target)

       [set target temp-target stop]

    ifelse count-enemy > 20

    [wiggle]

    [

      set temp-target nearest-enemy

      if nobody = temp-target [stop]

      set heading towardsxy [xcor] of temp-target [ycor] of temp-target

      fd random 3 + 1

    ]

end

to wiggle

    fd random 3 + 1

    rt random 180

    lt random 180

end

to-report one-of-enemy-here

     ifelse breed = china [report one-of rome-here]

                          [report one-of china-here]

end

to-report nearest-enemy

    let x xcor

    let y ycor

    ifelse breed = china

      [report one-of (rome with-min [distancexy x y])]

      [report one-of (china with-min [distancexy x y])]

end

to-report any-enemy

    ifelse breed = china [report any? rome] [report any? china]

end

to-report count-enemy

    ifelse breed = china [report count rome] [report count china]

end

to-report count-self

    ifelse breed = china [report count china] [report count rome]

end

to attack-enemy [damage]

    if not (nobody = target)

      [ask target [suffer-attack damage]]

end

to suffer-attack [damage]

    set blood (blood - damage)

    if blood <= 0 [die]

end

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WHAT IS IT?

-----------

This section could give a general understanding of what the model is trying to show or explain.

HOW IT WORKS

------------

This section could explain what rules the agents use to create the overall behavior of the model.

HOW TO USE IT

-------------

This section could explain how to use the model, including a description of each of the items in the interface tab.

THINGS TO NOTICE

----------------

This section could give some ideas of things for the user to notice while running the model.

THINGS TO TRY

-------------

This section could give some ideas of things for the user to try to do (move sliders, switches, etc.) with the model.

EXTENDING THE MODEL

-------------------

This section could give some ideas of things to add or change in the procedures tab to make the model more complicated, detailed, accurate, etc.

NETLOGO FEATURES

----------------

This section could point out any especially interesting or unusual features of NetLogo that the model makes use of, particularly in the Procedures tab.  It might also point out places where workarounds were needed because of missing features.

RELATED MODELS

--------------

This section could give the names of models in the NetLogo Models Library or elsewhere which are of related interest.

CREDITS AND REFERENCES

----------------------

This section could contain a reference to the model's URL on the web if it has one, as well as any other necessary credits or references.

@#$#@#$#@

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NetLogo 4.0.2

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@#$#@#$#@

@#$#@#$#@

<experiments>

  <experiment name="battle" repetitions="1" runMetricsEveryStep="false">

    <setup>setup</setup>

    <go>go</go>

    <metric>guess-winner</metric>

    <metric>guess-surviors</metric>

    <metric>final-winner</metric>

    <metric>final-survivors</metric>

    <enumeratedValueSet variable="rome-blood">

      <value value="30"/>

    </enumeratedValueSet>

    <enumeratedValueSet variable="china-blood">

      <value value="30"/>

    </enumeratedValueSet>

    <steppedValueSet variable="china-count" first="1" step="1" last="5"/>

    <enumeratedValueSet variable="china-power">

      <value value="3"/>

    </enumeratedValueSet>

    <enumeratedValueSet variable="rome-power">

      <value value="3"/>

    </enumeratedValueSet>

    <steppedValueSet variable="rome-count" first="1" step="1" last="5"/>

  </experiment>

</experiments>

@#$#@#$#@

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