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.

翻译：本文提出Yukthi Opus（YO），一种专为显式评估预算约束下的NP难优化问题而设计的多链混合元启发式算法。YO在一个结构化的两阶段架构中整合了三种互补机制：用于全局探索的马尔可夫链蒙特卡洛（MCMC）、用于局部开发的贪婪搜索，以及带有自适应再加热机制的模拟退火以实现从局部极小值的受控逃逸。一个专用的预热阶段将评估资源分配给概率性探索，随后一个混合优化循环对具有潜力的候选解进行精细化改进。YO进一步引入了空间黑名单机制以避免对劣质区域的重复评估，并采用多链执行策略以提升鲁棒性并降低对初始化的敏感性。我们在三个基准测试上评估YO：包含消融实验的Rastrigin函数（5维）、包含50至200个城市的旅行商问题，以及包含与CMA-ES、贝叶斯优化和加速粒子群优化等成熟优化器对比的Rosenbrock函数（5维）。结果表明，MCMC探索和贪婪精细化对解的质量至关重要，而模拟退火与多链执行主要提升了算法的稳定性并降低了方差。总体而言，YO在保持可预测评估预算的同时，于大规模多模态问题上取得了具有竞争力的性能，使其适用于昂贵的黑盒优化场景。