The paper presents a Markov chain-based approach to analyze the expected optimization time of Bivalent Ant Colony Optimization (BACO), a simplified variant of Ant Colony Optimization (ACO) that uses only two pheromone values.
For the problems Sorting and LeadingOnes, the analysis provides the following key insights:
The pheromone ratio t = τ_min/τ_max significantly governs the runtime behavior of BACO. The optimal choice of t leads to tight bounds on the expected optimization time.
For Sorting, the analysis yields a tight bound of Θ(n^3) on the expected optimization time, using the optimal pheromone ratio t = 1/n^2. This improves upon the previous upper bound.
For LeadingOnes, the analysis provides the missing lower bound Ω(n^2), resulting in a tight bound of Θ(n^2) on the expected optimization time, using the optimal pheromone ratio t = 1/n.
As a byproduct, the known bounds on the expected optimization time for OneMax (O(n log n)) and LeadingOnes (O(n^2)) can be reproduced using the Markov chain-based approach.
The theoretical findings are validated through experiments with an implementation of BACO.
To Another Language
from source content
arxiv.org
Thông tin chi tiết chính được chắt lọc từ
by Matt... lúc arxiv.org 05-07-2024
https://arxiv.org/pdf/2405.03353.pdfYêu cầu sâu hơn