Yukthi Opus A Multi-Chain Hybrid Metaheuristic for Large-Scale NP-Hard Optimization
We present Yukthi Opus (YO), a multi-chain hybrid metaheuristic designed for NP-hard optimization under explicit evaluation budget constraints. YO integrates three complementary mechanisms in a structured two-phase architecture Markov Chain Monte Carlo (MCMC) for global exploration, greedy local search for exploitation, and simulated annealing with adaptive reheating to enable controlled escape from local minima. A dedicated burn-in phase allocates evaluations to probabilistic exploration, after which a hybrid optimization loop refines promising candidates. YO further incorporates a spatial blacklist mechanism to avoid repeated evaluation of poor regions and a multi-chain execution strategy to improve robustness and reduce sensitivity to initialization. We evaluate YO on three benchmarks the Rastrigin function (5D) with ablation studies, the Traveling Salesman Problem with 50 to 200 cities, and the Rosenbrock function (5D) with comparisons against established optimizers including CMA-ES, Bayesian optimization, and accelerated particle swarm optimization. Results show that MCMC exploration and greedy refinement are critical for solution quality, while simulated annealing and multi-chain execution primarily improve stability and variance reduction. Overall, YO achieves competitive performance on large and multimodal problems while maintaining predictable evaluation budgets, making it suitable for expensive black-box optimization settings.