Agent goals in NetLogo: the wolf, the goat, and the cabbage

The puzzle of the wolf, goat, and cabbage is an ancient one – it appears in the Propositiones ad acuendos iuvenes, attributed to Alcuin of York, and written around 800 AD. The NetLogo solution described here builds on a modified version of my Goals in NetLogo tutorial.

The goto goal here is the same as for the previous tutorial, and the meet goal differs only in containing a reference to an agent, rather than a string identifier.

The wait goal contains a reporter task, and succeeds when that task returns “true.” The instruct goal gives aditional goals to another agent or (with an empty list) erases another agent’s goals. The pickup and drop goals set the carrier variable of another agent to mark it as being carried. Agents being carried always follow the agent carrying them. The embark and disembark goals are used by the man to be carried by the boat.

Domain-specific goals include eat, satisfied by the wolf and goat if they succeed in devouring their favourite food, together with go-left and go-right, the first of which expands to the goal list ["meet" boat "embark" "instruct" boat ["goto" (1 - bank) 0] "wait" (task at-left) "disembark" "goto" (- (bank + 3)) 0)], and the second of which expands to something similar. Note the use of task to create a reporter task from the reporter at-left.

The problem is solved when the man has the goal list ["drop" wolf "drop" cabbage "go-left" "drop" goat "go-right" "pickup" wolf "go-left" "pickup" goat "drop" wolf "go-right" "pickup" cabbage "drop" goat "go-left" "drop" cabbage "go-right" "pickup" goat "go-left"]. The sequence of picking up and dropping entities ensure that the wolf and goat are unable to carry out their eating goals. The top-level goal procedure is:

to obey
  if (carrier != nobody) [
    move-to carrier
  ]
  if (goal != []) [
    let kind (item 0 goal)

    if-else (kind = "goto") [ if (obey-goto (item 1 goal) (item 2 goal)) [ drop3-goal ] ] [

    if-else (kind = "meet") [ if (obey-meet (item 1 goal)) [ drop2-goal ] ] [

    if-else (kind = "wait") [ if (runresult (item 1 goal)) [ drop2-goal ] ] [

    if-else (kind = "instruct") [ obey-instruct (item 1 goal) (item 2 goal)
                                  drop3-goal ] [

    if-else (kind = "pickup") [ obey-pickup (item 1 goal)
                                drop2-goal ] [

    if-else (kind = "drop") [ obey-drop (item 1 goal)
                              drop2-goal ] [

    if-else (kind = "embark") [ obey-embark
                                drop-goal ] [

    if-else (kind = "disembark") [ obey-disembark
                                   drop-goal ] [

    if-else (kind = "eat") [ if (obey-eat (item 1 goal)) [ drop2-goal ] ] [

    if-else (kind = "go-left") [ obey-go-left ] [

    if-else (kind = "go-right") [ obey-go-right ] [

    obey-unknown kind ] ] ] ] ] ] ] ] ] ] ] ]
end

Specific goal commands include:

to obey-disembark
  if (verbose?) [ show (list "disembarking") ]
  set carrier nobody
end

to obey-embark
  if (verbose?) [ show (list "embarking") ]
  set carrier boat
end

to obey-pickup [ him ]
  ask him [ set carrier myself ]
  if (verbose?) [ show (list "picking up" ([label] of him)) ]
end

to obey-drop [ him ]
  if-else ([ carrier ] of him = self)
    [ ask him [ set carrier nobody ]
      if (verbose?) [ show (list "dropping" ([label] of him)) ] ]
    [ show (list "CANNOT DROP" ([label] of him)) ]
end

to obey-instruct [ him g ]
  if-else (g = [])
    [ ask him [ set goal [] ] ]
    [ ask him [ set goal (sentence goal g) ] ]
  if (verbose?) [ show (list "instructing" ([label] of him) "to" g) ]
end

Initialisation code is as follows, with the entire program available at Modeling Commons. See also here for a video. For agents to develop the solution on their own, a planner is still needed.

turtles-own [
  speed   ;; agent speed in cells per tick
  goal    ;; goal list
  carrier ;; agent carrying this agent (or "nobody")
]

globals [
  wolf
  goat
  cabbage
  man
  boat
  verbose? ;; if true, agents print what they are doing
  bank     ;; location of river bank (+ or -)
]

to setup
  clear-all
  set bank 13
  set verbose? true
  ask patches with [ pxcor <= (- bank) or pxcor >= bank ] [set pcolor green ]
  ask patches with [ pxcor > (- bank) and pxcor < bank ] [set pcolor blue ]
  
  crt 5 [ setxy (bank + 3) 0
    set speed 0.01
    set size 3
    set carrier nobody
    set goal [ ] ]
  
  set wolf (turtle 0)
  set goat (turtle 1)
  set cabbage (turtle 2)
  set man (turtle 3)
  set boat (turtle 4)
  
  let labels [ "wolf" "goat" "cabbage" "" "boat" ]
  ask turtles [ set label (item who labels) ]
  
  ask man [ set shape "person"
    set size 4
    set goal (list "drop" wolf "drop" cabbage "go-left" "drop" goat "go-right" "pickup" wolf "go-left"
                   "pickup" goat "drop" wolf "go-right" "pickup" cabbage "drop" goat "go-left"
                   "drop" cabbage "go-right" "pickup" goat "go-left "instruct" wolf [] "instruct" goat [])
    set color red ]

  ask cabbage [ set shape "plant"
    set carrier man
    set color 53 ]

  ask boat [ set size 5
    set xcor (bank - 1)
    set speed (speed * 2)
    set color brown ]

  ask goat [ set shape "cow"
    set goal (list "eat" cabbage)
    set carrier man
    set color white ]

  ask wolf [ set shape "wolf"
    set goal (list "eat" goat)
    set carrier man
    set color black ]
  
  reset-ticks
end

XKCD has his own take on this problem: