Population diversity is essential for the effective use of any crossover operator. We compare seven commonly used diversity mechanisms and prove rigorous run time bounds for the (μ+1) GA using uniform crossover on the fitness function Jumpk. All previous results in this context only hold for unrealistically low crossover probability pc = O(k/n), while we give analyses for the setting of constant pc < 1 in all but one case. Our bounds show a dependence on the problem size n, the jump length k, the population size μ, and the crossover probability pc. For the typical case of constant k > 2 and constant pc, we can compare the resulting expected optimisation times for different diversity mechanisms assuming an optimal choice of μ: • O (nk-1) J for duplicate elimination/minimisation, • O (n2 log n) for maximising the convex hull, • O(n log n) for det. crowding (assuming pc = k/n), • O(n log n) for maximising the Hamming distance, • O(n log n) for fitness sharing, • O(n log n) for the single-receiver island model. This proves a sizeable advantage of all variants of the (μ+1) GA compared to the (1+1) EA, which requires Θ(n). In a short empirical study we confirm that the asymptotic differences can also be observed experimentally.
|Original language||English (US)|
|Title of host publication||GECCO 2016 - Proceedings of the 2016 Genetic and Evolutionary Computation Conference|
|Publisher||Association for Computing Machinery, Inc|
|Number of pages||8|
|State||Published - Jul 20 2016|
|Event||2016 Genetic and Evolutionary Computation Conference, GECCO 2016 - Denver, United States|
Duration: Jul 20 2016 → Jul 24 2016
|Name||GECCO 2016 - Proceedings of the 2016 Genetic and Evolutionary Computation Conference|
|Other||2016 Genetic and Evolutionary Computation Conference, GECCO 2016|
|Period||7/20/16 → 7/24/16|
Bibliographical noteFunding Information:
The research leading to these results has received funding from the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement no. 618091 (SAGE) and from the EPSRC under grant no. EP/M004252/1.
- Genetic algorithms
- Run time analysis