Neutrosophic Initial Basic Feasible Solution for Model I
Initial basic feasible solution and the optimum solution of Model II will be obtained by the procedure in Sections 4.
A basic feasible solution
(BFS) is a basic solution that satisfies the constraints of the LP.
In a recent paper, Ru, Shen and Xue  considered the problem of finding an initial basic feasible solution
(bfs) of the LP problem of the form
4] is a transportation type linear programming problem with upper bound restrictions on some variables, therefore its global maximum exists at a basic feasible solution of its constraints.
As none of the constraints in the original system is redundant, a basic feasible solution to the original system shall contain (m+n) basic variables.
To formulate the problem such that an initial basic feasible solution is readily available, and, thus avoid the computational effort involved in Phase 1 of the simplex method.
The third objective of finding an initial basic feasible solution can be easily achieved and the method for doing so is described in the Solution of the Optimization Problem Section.
Starting from a non-basic feasible solution, as obtained above, a basic feasible solution with a superior objective function value is obtained by following a sequence of pivotal steps which we call a purification procedure.
Since in each major cycle, we move from one basic feasible solution to a superior basic feasible solution, two basic feasible solutions separated by one major cycle are most unlikely to be adjacent.
The LMOPSO computes the basic feasible solutions using linear programming and finds a random set of feasible solutions (particles) based on linear combinations of basic feasible solutions so that the produced solutions never become infeasible.
In other words, the linear combinations of basic feasible solutions very likely produce infeasible solutions, and a post-repairing algorithm is still needed to preserve the feasibility of the produced solutions.