A GENETIC ALGORITHM FRAMEWORK IN CLOJURE

13 SEPTEMBER, 2009 — CHARLOTTESVILLE, VA

As my title suggests, I’ve built Gajure: a framework for constructing genetic algorithms in Clojure. The definition of framework is debatable, so excuse my pretension: I mean only that Gajure is something I can reuse.

Genetic algorithms apply an evolutionary model to complex problems, and so evolve solutions from an initial population of random states. Eliding a few details, the process boils down (in lisp notation) to this:

(defn genetic-algorithm [some-params]
  (initialize-population)
    (loop (generations-that-remain)
      (if (no-generations-left)
         (print-stuff-and-exit)
         (pass-again-to-loop
          (mutate-population
            (crossover-population
              (select-population
               (population))))))

We want to construct an algorithm that accepts functions for initializing, sorting, crossing over and mutating population members. It should also take population parameters (e.g. the number of generations to run, or the mutation rate). Here’s what I came up with:

(defn run-ga
  [func-map setting-map]
  (let [ipop ((:init-fn func-map) (:pop-sz setting-map))]
    (loop [pop ipop
           num (:gen setting-map)]
      (if (zero? num)
        (do
          (println (first (sort-by (:fit-fn func-map) > pop ))))
            (let [total-left (- (:pop-sz setting-map)
                                      (:children setting-map))]
              (do
                (println (first (sort-by (:fit-fn func-map) > pop ))))
              (recur
               (concat
                ((:mut-fn func-map)
                 (do-crossover
                  ((:sel-fn func-map)
                   pop
                   (:fit-fn func-map)
                   (* (:children setting-map) 2))
                  (:cross-fn func-map)
                  2)
                 (:mut-r setting-map))
                ((:init-fn func-map) total-left))
               (dec num)))))))

This function follows the basic algorithm I laid out earlier. It takes as input two maps, func-map and setting-map, which provide problem-specific functions and settings. The helper-function do-crossover takes a list of parents, and runs a problem-specific crossover function provided as one of the parameters. All this code lives on github, but I’ll display it here as well.

(defn do-crossover
  [p-list cross-fn num-parents]
  (map cross-fn (partition num-parents p-list)))

Let’s consider an example problem: evolving the string “helloworld”. First we need to define some aspects of the problem space. Simple enough. The ‘DNA’ of a string is nothing but a list of characters:

(def dna (map str
              ['q 'w 'e 'r 't 'y 'u 'i 'o 'p 'a 's 'd 'f 'g 'h 'j 'k 'l
               'z 'x 'c 'v 'b 'n 'm]))

I wrote a few other helper functions, rand-from-list and rand-pop, which are generally useful for creating random populations. The first will return a ‘random’ list from a list of elements, made up of the elements in that list. The second will return a list of these random lists.

(defn rand-from-list
  [lst num]
  (let [total-el (count lst)]
    (map (fn [x] (nth lst (rand-int total-el))) (range 0 num))))

And the other:

(defn rand-pop
  [lst num num-pop]
  (map (fn [x] (rand-from-list lst num)) (range 0 num-pop)))

Let’s apply them to dna. A function that initializes a random population of strings might look like this (supposing we limit our population to strings of 10 characters):

(defn some-strings [num]
 (rand-pop dna 10 num))

This is not precisely what I do in my github example (I end up using a partial) but it is effectively the same thing. On to crossover:

(defn list-crossover
  [[s1 s2]]
  (let [point (rand-int
               (min (count s1)
                    (count s2)))]
    (concat (take point s1)
            (drop point s2))))

The function list-crossover chooses a cross-point, x, on two lists, and creates a new list made up of the first x elements of one list, and the last (length – x) elements of the other. Now mutation:

(defn generic-mutation
  [list prob]
  (map
   (fn [s-list]
     (map
      (fn [test]
        (if (> prob (rand-int 100))
          (let [r-s (rand-int (count list))
                r-t (rand-int (count (nth list r-s)))]
            (nth (nth list r-s)
                 r-t))
          test))
      s-list))
   list))

Mutation is difficult to make ‘generic,’ but generic-mutation uses the base elements of other population members as an approximation for all the ‘genetic material’ that can be swapped in or out of a mutated member.

These functions work on most kinds of list populations, but you may need more complex behavior, so I abstracted them away from the algorithm itself.

Although nearly done, we still lack what is perhaps the most important part of the GA: the fitness function. For this example, I use a system of one point for every directly matching character in the string. As follows:

(defn hello-fitness
     [lst]
     (reduce
      +
      (map #(if (= %1 %2) 1 0)
           lst
           '("h" "e" "l" "l" "o" "w" "o" "r" "l" "d"))))

So now we can define the maps:

(def func-map {:fit-fn hello-fitness :mut-fn generic-mutation
               :sel-fn roulette-select :init-fn (partial rand-pop dna 10)
               :cross-fn list-crossover})
(def set-map {:pop-sz 100 :children 50 :mut-r 1 :gen 100})

Note that roulette-select is another framework helper-method. It selects population members with a likelihood proportional to the fitness.

(defn roulette-select
  [pop fit-fn num]
  (let [pop-fits (map fit-fn pop)
        inc-fits (iterate (fn [[pfit idx]]
                             [(+ (nth pop-fits (+ idx 1)) pfit) (+ idx 1)])
                          [(first pop-fits) 0])
        max-fitness (apply + pop-fits)
        pick-one (fn [num] (second (first (drop-while #(< (first %) num)
                        inc-fits))))]
    (map (fn [x] (nth pop (pick-one (rand-int max-fitness)))) (range num))))

Now, we’re finished, so we can run the algorithm:

(run-ga func-map set-map)

GAs are simple but elegant, and they work surprisingly well on some sorts of problems. All this code is available on github.