A Neutrosophic Metaheuristic Algorithm: Integrating Probability, Measures, and Adaptive Strategies for Robust Optimization of Complex Computational Problems

Real-world optimization problems are frequently noisy, partially observed, and internally inconsistent. Classical metaheuristics deliver strong results, yet they implicitly assume crisp fitness values and unambiguous constraints. This paper introduces a neutrosophic metaheuristic framework that embeds the triplet (truth, indeterminacy, falsity) into the core mechanics of population-based and trajectory-based search. The framework supplies: (i) a neutrosophic fitness representation for candidate solutions, (ii) an aggregation layer based on neutrosophic measures and integrals to combine uncertain objectives and constraints, and (iii) an adaptive control policy that modulates exploration–exploitation in proportion to measured indeterminacy. We demonstrate the practicality of the approach through three fully worked examples: (1) unconstrained nonlinear minimization, (2) scheduling with vague task durations, and (3) a traveling-salesman instance with uncertain edges. The results show consistent improvements in robustness and decision stability under uncertainty, while preserving competitive performance when data are crisp.