🤖 AI Summary
Competitive coevolutionary algorithms (CCEAs) suffer from unstable convergence in dynamic environments due to non-transitivity and the Red Queen effect. Method: This paper proposes a *tag-gene* approach: (i) employing evolvable tag genes as dynamic performance benchmarks; (ii) integrating an adaptive weighting mechanism to balance exploration and exploitation; and (iii) incorporating a memory pool to enhance utilization of historical information. Contribution/Results: We theoretically prove that the method establishes a strong attractor under strict competitive games, with convergence points asymptotically approaching Nash equilibria. Empirical evaluation across canonical dynamic benchmarks—including Rock-Paper-Scissors, ZDT multi-objective optimization, and Shapley-biased games—demonstrates significant improvements in stability, robustness, and convergence quality. The proposed framework provides a novel, interpretable, and theoretically grounded paradigm for dynamic coevolution.
📝 Abstract
Competitive Co-evolutionary Algorithms (CCEAs) are often hampered by complex dynamics like intransitivity and the Red Queen effect, leading to unstable convergence. To counter these challenges, this paper introduces the Marker Gene Method (MGM), a framework that establishes stability by using a 'marker gene' as a dynamic benchmark and an adaptive weighting mechanism to balance exploration and exploitation. We provide rigorous mathematical proofs demonstrating that MGM creates strong attractors near Nash Equilibria within the Strictly Competitive Game framework. Empirically, MGM demonstrates its efficacy across a spectrum of challenges: it stabilizes the canonical Rock-Paper-Scissors game, significantly improves the performance of C-RMOEA/D on ZDT benchmarks, and, when augmented with a Memory Pool (MP) extension, it successfully tames the notoriously pathological Shapley Biased Game. This work presents a theoretically sound and empirically validated framework that substantially enhances the stability and robustness of CCEAs in complex competitive environments.