Markov Chain-based Optimization Time Analysis of Bivalent Ant Colony Optimization for Sorting and LeadingOnes

The expected optimization time of Bivalent Ant Colony Optimization (BACO) can be precisely calculated using a Markov chain-based approach, revealing the crucial role of the pheromone ratio on the runtime behavior. BACO achieves tight bounds of Θ(n^3) for Sorting and Θ(n^2) for LeadingOnes.