Optimal Solution of Neutrosophic Linear Fractional Programming Problems With Mixed Constraints

In this paper, Linear Fractional Programming (LFP) problems have been extended to neutrosophic sets (NSs) and the operations and functionality of these laws are studied. Moreover, the new algorithm is based on aggregation ranking function and arithmetic operations of triangular neutrosophic sets (TNSs). Furthermore, for the first time, in this paper, we take up a problem where the constraints are both equality and inequality neutrosophic triangular fuzzy number. Lead from genuine issue, a few numerical models are considered to survey the legitimacy, profitability and materialness of our technique. At last, some numerical trials alongside one contextual analysis are given to show the novel techniques are better than the current strategies.

Application of Water Cycle algorithm to Stochastic Fractional Programming Problem

This paper presents an application of Water Cycle algorithm (WCA) in solving stochastic programming problems. In particular, Linear stochastic fractional programming problems are considered which are solved by WCA and solutions are compared with Particle Swarm Optimization, Differential Evolution, and Whale Optimization Algorithm and the results from literature. The constraints are handled by converting constrained optimization problem into an unconstrained optimization problem using Augmented Lagrangian Method. Further, a fractional stochastic transportation problem is examined as an application of the stochastic fractional programming problem. In terms of efficiency of algorithms and the ability to find optimal solutions, WCA gives highly significant results in comparison with the other metaheuristic algorithms and the quoted results in the literature which demonstrates that WCA algorithm has 100% convergence in all the problems. Moreover, non-parametric hypothesis tests are performed and which indicates that WCA presents better results as compare to the other algorithms.

Application of Water Cycle algorithm to Stochastic Fractional Programming Problem

This paper presents an application of Water Cycle algorithm (WCA) in solving stochastic programming problems. In particular, Linear stochastic fractional programming problems are considered which are solved by WCA and solutions are compared with Particle Swarm Optimization, Differential Evolution, and Whale Optimization Algorithm and the results from literature. The constraints are handled by converting constrained optimization problem into an unconstrained optimization problem using Augmented Lagrangian Method. Further, a fractional stochastic transportation problem is examined as an application of the stochastic fractional programming problem. In terms of efficiency of algorithms and the ability to find optimal solutions, WCA gives highly significant results in comparison with the other metaheuristic algorithms and the quoted results in the literature which demonstrates that WCA algorithm has 100% convergence in all the problems. Moreover, non-parametric hypothesis tests are performed and which indicates that WCA presents better results as compare to the other algorithms.

A new Mean Deviation and Advanced Mean Deviation Techniques to Solve Multi-Objective Fractional Programming Problem Via Point-Slopes Formula

In this paper, we have proposed a new technique to find an efficient solution to fractional programming problems (FPP). The multi-objective fractional programming problem (MOFPP) is converted into multi-objective linear programming (MOLPP) utilizing the point-slopes formula for a plane, which has equivalent weights to the MOFPP. The MOLPP is diminished to a single objective linear programming problem (SOLPP) through using two new techniques for the values of the objective function and suggesting an algorithm for its solution. Finally, we obtained the optimal solution for MOFPP by solving the consequent linear programming problem (LPP). The proposed practicability is confirmed with the existing approaches, with some numerical examples and we indicated comparison with other techniques.

Fuzzy solution of fully fuzzy multi-objective linear fractional programming problems

In this study, we present a novel method for solving fully fuzzy multi-objective linear fractional programming problems without transforming to equivalent crisp problems. First, we calculate the fuzzy optimal value for each fractional objective function and then we convert the fully fuzzy multi-objective linear fractional programming problem to a single objective fuzzy linear fractional programming problem and find its fuzzy optimal solution which inturn yields a fuzzy Pareto optimal solution for the given fully fuzzy multi-objective linear fractional programming problem. To demonstrate the proposed strategy, a numerical example is provided.

An Efficient Branch-and-Bound Algorithm for Globally Solving Minimax Linear Fractional Programming Problem

This paper presents an efficient outer space branch-and-bound algorithm for globally solving a minimax linear fractional programming problem (MLFP), which has a wide range of applications in data envelopment analysis, engineering optimization, management optimization, and so on. In this algorithm, by introducing auxiliary variables, we first equivalently transform the problem (MLFP) into the problem (EP). By using a new linear relaxation technique, the problem (EP) is reduced to a sequence of linear relaxation problems over the outer space rectangle, which provides the valid lower bound for the optimal value of the problem (EP). Based on the outer space branch-and-bound search and the linear relaxation problem, an outer space branch-and-bound algorithm is constructed for globally solving the problem (MLFP). In addition, the convergence and complexity of the presented algorithm are given. Finally, numerical experimental results demonstrate the feasibility and efficiency of the proposed algorithm.