To overcome the limitations of conventional robot task allocation algorithms, which often converge to suboptimal solutions, suffer from low computational accuracy, and produce excessively long execution paths as problem scales increase, we propose a novel marine predator algorithm (NMPA). By redesigning the predator–prey encoding mechanism in the traditional marine predator algorithm (MPA) and integrating information-based environmental search strategies with local search techniques, the proposed method substantially improves global exploration capability and solution precision. The NMPA is then evaluated on multiple benchmark and practical scenarios, including the traveling salesman problem (TSP), multi-traveling salesman problem (MTSP), single-robot task allocation with rigid time windows, and multi-robot task allocation. Experimental results on TSP and MTSP indicate that NMPA achieves more stable convergence, higher accuracy, and stronger robustness than ant colony optimization (ACO), simulated annealing, genetic algorithms (GAs), and their variants. Moreover, validation on real-world factory data in both single-robot and multi-robot task allocation scenarios confirms that NMPA delivers superior solution quality and overall performance compared with ACO, GAs, and their variants.