Data structure for efficient fitness-proportionate selection.
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Roulette tree Build Status

A roulette tree

A roulette tree (abbreviated rtree) is a data structure which allows one to pick a random item based on relative frequency in logarithmic time. If you for instance have three items: A, B and C, and A has a frequency of 1, B has a frequency of 2 and C has a frequency of 3, then a random pick would pick A 1/6 of the time, B 1/3 of the time, and C 1/2 of the time. Note that an rtree is not a set, it is an unordered collection of elements, where each element has a fitness value.

The rtree is designed to do insertions, random picks and random pops in O(log n) time, and count and total frequency in O(1) time.

Project Status

The Roulette Tree is properly implemented, but small details related to autotools remains. Additionally, a proper explanation of the insertion and removal algorithms remains.

This project is currently inactive, but may be revived in short time to finish off remaining issues.


A roulette tree is an excellent data structure for picking random elements based on fitness in evolutionary algorithms, especially when the set of individuals is huge. Using an array-based roulette tree makes insertion O(1) and random lookup O(log n), but random popping will still be O(n). Using linked lists will give insertion in O(1), lookup is O(n) and random popping in O(n). The roulette tree has a O(log n) insertion, O(log n) lookup and O(log n) random pop, considerably better if random popping is frequently done.

If random popping is done to select individuals for the next generation, the roulette tree will give a O(n log n) update speed, compared to O(n^2) for the other structures.


A roulette tree is rather easy to use. As an example, consider an algorithm where you have an n+m-sized population, and you pick n individuals from the old generation and m individuals from the new one. Assuming that the old population is contained within a rtree and the new individuals in an array of size n+m, a function to create a new population may look like this:

void destroy_genotype_rtree(RTree *rt) {
    // If you don't need to free memory, you can skip this loop and just do
    // rtree_destroy(rt)
    while (rtree_size(rt)) {
      genotype *g = (genotype *) rtree_rpop(rt);

RTree *make_gen(RTree *old_gen, genotype *new_gen_arr, int n, int m) {
    RTree *combined = rtree_create();

    // Add n individials from old gen
    for (int i = 0; i < n; i++) {
        genotype *chosen = (genotype *) rtree_rpop(old_gen);
        rtree_add(combined, (void *) chosen, calc_fitness(chosen));

    // insert new gen into its own rtree
    RTree *new_gen = rtree_create();
    for (int i = 0; i < m+n; i++) {
        double fitness = calc_fitness(new_gen_arr[i]);
        rtree_add(new_gen, (void *) new_gen_arr[i], fitness);
    // pick m elements from new gen
    for (int i = 0; i < m; i++) {
        genotype *chosen = (genotype *) rtree_rpop(new_gen);
        rtree_add(combined, (void *) chosen, calc_fitness(chosen));
    return combined;


Copyright © 2013 Jean Niklas L'orange

Distributed under the MIT License (MIT).