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

Abstract

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. 

DOI 10.5281/zenodo.17196320