breed [ agents agent ]
breed [ tasks task ]
;breed [ links link ]

;my-skills: Vector which contains a number (0-1) that depicts an agent's performance with a specific skill.
;           *Skills are enumerated.
;W*: list of values from other agents
;S*: list of coalitions from other agents
;joined: the coalition the agent is associated with
agents-own [ my-skills W S joined ]

;requirements: Vector of requirements for a task that identifies the need of each skill.
;              *Size determined by num-skills and enumerated in the same manner as my-skills.
;coalition-in-use: As coalitions are associated with a task, they are added to this list for record-keeping
tasks-own [ requirements coalition-in-use ]

;L: global list of coalitions
globals [ L ]

to setup
  ca
  create-agents num-agents
  create-tasks num-tasks
  setup-agents
  setup-tasks
  setup-L
end

to find-co
  foreach ([who] of tasks) [ ask agents [ find-coalition who ? ] ]
end

to setup-agents
  output-show "my-skills:"
  ask agents [ 
    set my-skills build-list-randomly num-skills 1
    set W []
    set S []
    set label who
    set joined []
    set shape "airplane"
    set size 3
    set xcor -13
    set ycor (30 / num-agents) * ceiling(who / 2) * (-1)^(who)
    output-show my-skills ]
end

to setup-tasks
  output-show "requirements:"
  ask tasks [
    set coalition-in-use []
    set label coalition-in-use
    set requirements build-list-randomly num-skills max-need
    set shape "box"
    set size 3
    set color (color - 20) ;make it darker for readability
    set xcor 13
    set ycor (30 / num-tasks) * ceiling((who - num-agents) / 2) * (-1)^(who)
    output-show requirements ]
end

to setup-L
  set L []
  ask agents [ set L lput (list who) L ] ;add the single agent sets to L
  repeat num-agents [
    ask agents [
      without-interruption [
        foreach L [ 
          if( (not member? who ?) ) [ set L lput (sort(lput who ?)) L ]
          set L remove-duplicates L] ] ] ]
end

to-report add-to-list [ i lst ]
  report lput i lst
end

to-report build-list-randomly [ sz limit ]
  ;lst: The list returned.
  let lst 0
  
  set lst []
  ifelse (limit <= 1) [ repeat sz [ set lst lput (((random (limit * 100 - 1)) + 1) / 100) lst ] ] ;need to normalize if limit is less than 1
  [ repeat sz [ set lst lput (random limit) lst ] ]
  report lst
end

;find-coalition algorithm.
to find-coalition [ agent-i task_i ]
  ;L_i: list of coalitions containing agent-i
  ;Max_i: [S_i* w_i*] retrieved after evaluating all coalitions in L_i
  ;w_max: the maximum value in W*
  ;S_max: the coalition corrisponding to w_max (W*)
  let L_i 0
  let Max_i 0
  let w_max 0
  let S_max 0
  

  set L_i coalitions agent-i

  while [ not( empty? L_i ) ] [
    if ( trace ) [
      show (word "trace> L_i: "  L_i )]
    set W []
    set S []
    set Max_i  max-coalition L_i task_i
    if( trace ) [
      show (word "trace> S*(" agent-i "): " item 0 Max_i)
      show (word "trace> w*(" agent-i "): " item 1 Max_i)]
    broadcast Max_i
    set w_max item (find-index-of-max [W] of (agent agent-i)) W
    set S_max item (position w_max W) S
    if ( trace ) [
      show (word "trace> w_max list: " W)
      show (word "trace> coalitions: " S) ]
    foreach S_max [ ;look at members of the coalition
      if( ? = agent-i ) [ 
        set joined S_max
        if ( trace ) [
          show (word "trace> Agent " agent-i " added to the coalition.")]
        create-link-with (task task_i) [ set color (((position S_max L_i) mod 7) * 10 + 35) ]
        set heading towards task task_i 
        ask task task_i [ 
          set coalition-in-use lput S_max coalition-in-use
          set coalition-in-use remove-duplicates coalition-in-use ;a coalition of n-size will add to the list n times, cleanup
          set label coalition-in-use ] ] ] ;if current agent is in the coalition, join it
    set L_i remove S_max L_i
    foreach S_max [
      let i ?
      foreach L_i [
        if( member? i ? ) [ 
          if ( trace ) [
            show (word "trace> Removing (" ? ") from L_i") ]
          set L_i remove ? L_i ] ] ] ]
end

;Fetches the coalitions that contain member i
to-report coalitions [ i ]
  ;lst: the list returned
  let lst 0
  
  set lst []
  foreach L [ if( member? i ? ) [ set lst lput ? lst ] ]
  report lst 
end

;Fetches the coalition with the highest value in a given set
;c_lst: list of possible coalitions
;task_i: current task
to-report max-coalition [ c_lst task_i ]
  ;maximum-value: v(S*)
  ;maximum-col: S*
  ;sum_vector: temporary space to hold the sum of my-skills for each agent in the coalition
  ;index: for moving through the elements in the my-skills vector
  let maximum-value 0
  let maximum-col 0
  let sum_vector 0
  let current_skills 0
  let index 0
   

  set maximum-value -1000 ;preset low

  foreach c_lst [  ;iterate through each coalition
    set sum_vector []
    repeat num-skills [ set sum_vector lput 0 sum_vector ] ;reset summation vector

    ;fetch the my-skills vector from each agent
    foreach ? [
      set index 0
      set current_skills [my-skills] of (agent ?)
      repeat num-skills [ ;sum up the values in the my-skills vectors for each agent in the current coalition
        set sum_vector replace-item index sum_vector precision ( (item index sum_vector) + (item index current_skills) ) 2
        set index ( index + 1 ) ] ]
      set index 0

    ;calculate the value for the coalition
    repeat num-skills [
      set sum_vector replace-item index sum_vector (-1 * abs( precision ( (item index [requirements] of (task task_i)) - (item index sum_vector) ) 2 ))
      set index ( index + 1 ) ]
    if ( ((sum sum_vector) / (length ?)) >= maximum-value ) [  ;check v(S)/|S| against current maximum
      set maximum-value precision ((sum sum_vector) / (length ?)) 2
      set maximum-col ? ] ] 

    report list maximum-col maximum-value
end

to broadcast [ pair ]
  ask agents [ 
    set W lput (item 1 pair) W
    set S lput (item 0 pair) S ]
end

to-report find-index-of-max [ lst ]
  let index 0
  let t 0
  
  set t -1000
  
  foreach lst [
    if( ? > t ) [
      set t ?
      set index (position ? lst) ] ]
  
  report index
end
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@#$#@#$#@
Title: Task Allocation
Author: William Wiles
Description:

Solves a task allocation problem with the coalition formation algorithm from
<ul><li>Onn Shehory and Sarit Kraus. <a href="http://jmvidal.cse.sc.edu/lib/shehory98a.html">Methods for Task Allocation via Agent Coalition Formation</a>. <i>Artificial Intelligence,</i> May; 101(1-2):165--200, 1998.</li></ul>

------

HOW IT WORKS
------------
From the problem set description,

There are num-skills (slider) available to the agents. Each agent (there are num-agents of them) is born with a my-skills vector which contains a number between 0 a 1 for each one of these skills. These vectors represent how well the agent can perform each one of the skills.

There is also a breed of tasks, of which there are num-tasks. Each task has a requirements variable which is a vector of size num-skill where each entry is a number randomly chosen between 0 and max-need. 

L is the list of all possible coalitions, and is found by each state adding the possible combinations of itself to the current sets in L, while pruning duplicates.  Since each member of a coalition will add itself, the number of duplicates increases linearly as the coalition size increases.  However, the code is direct and short.


Once this initialization takes place, the v(S) is calculated by each agent for its related coalitions, i.e. all possible coalitions it can be involved with, against each task.  The v(S) are calculated during the find-coalition implementation instead of beforehand to cut down on global variables, since message-passing will take care of any agent's information needs.

find-coalition is executed after setup.

HOW TO USE IT
-------------
To visualize the algorithm, links indicate an association between an agent and a task.  Tasks are in column formation on the right (Q1/Q4) hemisphere of the world; while, agents are arranged similarly on the left (Q2/Q3) hemisphere of the world.  

Agents in the same coalition for a task will have the same color link connecting them to that specific task.

The requirements and my-skills vectors are displayed in the output window to the right of the world.  

The tasks show their coalition solution as their label.  The agents show their ID.

The trace toggle will allow you to view the find-coalition algorithm in a step-by-step basis.  Expect alot of output for more than 3 agents or tasks.

THINGS TO NOTICE
----------------
If the max-need of the tasks is set above the number of agents, the problem becomes super-additive.


THINGS TO TRY
-------------
Setting the max-need above the number of agents.

Setting the mas-need to zero.


EXTENDING THE MODEL
-------------------
Performance analysis of the L constructor and find-coalition's max-arg (max-coalition in the implementation) for large agentsets.  Possible future pruning and optimization in these areas


CREDITS AND REFERENCES
----------------------
Problem Set Description:
http://jmvidal.cse.sc.edu/csce782/index.html

Fundamentals of Multiagent Systems:
http://jmvidal.cse.sc.edu/library/vidalfmas.pdf

Netlogo Handbook:
http://ccl.northwestern.edu/netlogo/docs/
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