Neutrosophic goal programming technique with bio inspired algorithms for crop land allocation problem.

In agriculture, crop planning and land distribution have been important research subjects. The distribution of land involves several multi-functional tasks, such as maximizing output and profit and minimizing costs. These functions are influenced by a variety of uncertain elements, including yield, crop price, and indeterminate factors like seed growth and suitable fertilizer. In order to address this problem, other researchers have used fuzzy and intuitionistic fuzzy optimization approaches, which did not include the indeterminacy membership functions. However, the neutrosophic optimization technique addresses the problem by using individual truth, falsity, and indeterminacy membership functions. So, to improve the optimal solution, the Neutrosophic Goal Programming (NGP) problem with hexagonal intuitionistic parameters is employed in this study. The membership functions for truth, indeterminacy, and falsity are constructed using hyperbolic, exponential, and linear membership functions. Minimizing the under deviations of truth, over deviations of indeterminacy, and falsity yields the NGP achievement function, which is used to attain optimal expenditure, production, and profit under the constraints of labour, land, food requirements, and water. Bio-inspired computing has been a major research topic in recent years. Optimization is mostly accomplished through the use of bio-inspired algorithms, which draw inspiration from natural behaviour. Bio-inspired algorithms are highly efficient in exploring large solution spaces, and helps to manage trade-offs between various goals, and providing the global optimal solution. Consequently, bio-inspired algorithms such as Grey Wolf Optimization (GWO), Social Group Optimization (SGO), and Particle Swarm Optimization (PSO) are employed in the current work to determine the global optimal solutions for the NGP achievement function. The data for the study was collected from the medium-sized farmers in Ariyalur District, Tamil Nadu, India. To illustrate the uniqueness and application of the developed method, the optimal solutions of the suggested method are compared with Zimmermann, Angelov, and Torabi techniques. The proposed technique demonstrates that the bioinspired algorithms' optimal solution to the neutrosophic goal is superior to the existing approaches.