Unified Approach to (1 + 1) Evolutionary Algorithm on Discrete Linear Functions
- 10.2991/jrnal.k.190602.001How to use a DOI?
- Evolutionary algorithm; discrete linear function; (1 + 1) EA; PO-mutation; PO-EA
We consider the runtime property of discrete linear functions in (1 + 1) Evolutionary Algorithms (EAs), Partially Ordered mutation (PO-mutation) and Jansen’s model, Partially Ordered Evolutionary Algorithm (PO-EA). We analyze the process of evolution. This study was motivated by the paper of Jansen treating the runtime property of (1 + 1) EA on monotonic functions by means of probabilistic theory. As linear functions are special cases of monotonic function, we analyze their behavior. We show that the (1 + 1) EA can obtain an optimum solution at a stable hitting time for discrete linear functions. When the mutation rate is weak, on the order of 1/l, most monotonic functions behave similarly and can be approximated well by the PO-mutation model.
- © 2019 The Authors. Published by Atlantis Press SARL.
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Kenji Aoki AU - Makoto Sakamoto AU - Hiroshi Furutani AU - Satoru Hiwa AU - Tomoyuki Hiroyasu PY - 2019 DA - 2019/06/25 TI - Unified Approach to (1 + 1) Evolutionary Algorithm on Discrete Linear Functions JO - Journal of Robotics, Networking and Artificial Life SP - 56 EP - 59 VL - 6 IS - 1 SN - 2352-6386 UR - https://doi.org/10.2991/jrnal.k.190602.001 DO - 10.2991/jrnal.k.190602.001 ID - Aoki2019 ER -