Yukthi Opus: A Multi-Chain Hybrid Metaheuristic for Large-Scale NP-Hard Optimization

Yukthi Opus: A Multi-Chain Hybrid Metaheuristic for Large-Scale NP-Hard Optimization SB Danush Vikraman1, Hannah Abigail1, Prasanna Kesavraj1, and Gajanan V Honnavar∗2 1Department of ECE, PES University, Bengaluru, India 2Department of Science and humanities, PES University, Bengaluru, India 1Email: {pes2ug22ec049, pes2ug22ec058, pes2ug22ec099@pesu.pes.edu 2Email: gajanan.honnavar@.pes.edu January 27, 2026 Abstract We present Yukthi Opus (YO), a three-layer hybrid metaheuristic optimizer that systematically integrates Markov Chain Monte Carlo (MCMC) global explo- ration, greedy local search, and adaptive simulated annealing with reheating. YO addresses critical gaps in existing optimizers through structured burn-in explo- ration, blacklist mechanisms preventing revisits to poor regions, adaptive temper- ature reheating for escaping local minima, and multi-chain parallel execution for robustness. We evaluate YO on three challenging NP-hard benchmarks: the Ras- trigin function (5D) with comprehensive ablation studies, the Traveling Salesman Problem (50-200 cities), and the Rosenbrock function (5D) with state-of-the-art comparisons. Results demonstrate that YO reaches competitive or superior so- lution quality on complex problems while maintaining explicit evaluation budget control. Ablation studies quantify the contributions of each component, revealing that MCMC and greedy search are critical for solution quality (removing either causes 30-36% degradation), while simulated annealing and multi-chain execution ∗Corresponding author 1 arXiv:2601.01832v2 [cs.NE] 25 Jan 2026 primarily improve stability (reducing coefficient of variation by 32-55%). Compar- isons against CMA-ES, Bayesian Optimization, and APSO show YO achieves the fastest runtime while ranking second in solution quality on Rosenbrock 5D. 1 Introduction Combinatorial and continuous optimization problems with NP-hard characteristics re- main among the most challenging computational problems across scientific and engi- neering fields [1]. Classical optimization techniques often struggle with the fundamental trade-off between exploration and exploitation, where global search methods risk compu- tational inefficiency while local search heuristics frequently converge prematurely to sub- optimal solutions [10]. Markov Chain Monte Carlo (MCMC) methods provide powerful mechanisms for global exploration through probabilistic sampling of the search space [8], particularly effective in high-dimensional and multimodal landscapes. However, MCMC approaches alone lack the aggressive local refinement needed for rapid convergence to higher-quality solutions. Conversely, greedy local search methods excel at exploitation of promising regions but offer no systematic mechanism for escaping local optima. Simulated Annealing (SA) [6] addresses this problem through temperature-controlled stochastic ac- ceptance, though it requires careful parameter tuning and may fail to escape deep local minima without adaptive reheating techniques [5]. Existing state-of-the-art optimizers each address different aspects of this problem. Bayesian Optimization [9] excels in low-dimensional smooth landscapes but scales poorly. Covariance Matrix Adaptation Evolution Strategy (CMA-ES) [3] provides robust derivative- free optimization but incurs significant computational overhead. Accelerated Particle Swarm Optimization (APSO) [11] offers good exploration-exploitation balance but lacks mechanisms to avoid revisiting poor regions. Genetic Algorithms [4] introduce population- based evolutionary computation with selection, crossover, and mutation operators, while Tabu Search [2] employs memory structures to prevent cycling and encourage exploration. No single classical approach effectively combines global exploration, local exploitation, and adaptive escape mechanisms while maintaining computational efficiency across di- verse problem classes. We present Yukthi Opus (YO), a three-layer hybrid metaheuristic optimizer that sys- tematically integrates MCMC-based global exploration, greedy local search, and adap- tive simulated annealing with reheating, following the memetic algorithm paradigm [7] of combining population-based and local search methods. YO addresses several critical gaps: preventing premature convergence through structured burn-in exploration, avoid- ing computational waste via blacklist mechanisms that prevent revisiting poor regions, escaping local minima through adaptive temperature reheating, and maintaining solution robustness through multi-chain parallel execution with post-burnin selection. 2 Our key contributions include introducing a novel three-layer hybrid design that com- bines MCMC [8], greedy search, and SA [6] with adaptive reheating in a principled structure allowing explicit control over evaluation budgets, implementing a spatial black- list system that prevents repeated evaluation of demonstrably poor parameter regions, demonstrating through experiments that parall

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