The fuzzy primal-dual simplex method is a new and efficient method for solving LINEAR programming problems with fuzzy variables. This algorithm is based on duality results and, similar to the dual simplex method, begins with dual feasibility and proceeds to primal feasibility. An important difference between the dual simplex method and the primal-dual method is that in the primal-dual algorithm, it is not required that the dual feasible solution to be basic. In this paper, we develop the primal-dual simplex method for solving fuzzy MULTIOBJECTIVE LINEAR programming problems. To this end, we utilize the fuzzy weighted sum scalarization method to present a fuzzy single objective OPTIMIZATION problem related to the fuzzy MULTIOBJECTIVE LINEAR programming problem. Then, by partitioning the weights of the weighted sum problem, we generalize the single objective primal-dual algorithm to fuzzy MULTIOBJECTIVE problems. By using the presented algorithm, we can find a set of fuzzy Pareto optimal solutions. Presenting a set of fuzzy Pareto optimal solutions to the decision maker, enables him\her to select the best solution based on his\her preferences. Finally, we apply the proposed algorithm for solving a three-objective OPTIMIZATION problem with fuzzy variables and compare the results with some existing methods.

In this paper, we focus on the utilization of the feasible value constraint technique to address MULTIOBJECTIVE OPTIMIZATION problems (MOPs). It is attempted to overcome certain drawbacks associated with this method, such as restrictions on functions and weights, inflexibility in constraints, and challenges in assessing proper efficiency. To accomplish this, we propose an improved version of the feasible value constraint technique. Then, by incorporating approximate solutions, we establish connections between $\varepsilon$-(weakly, properly) efficient points in a general MOP and $\epsilon$-optimal solutions to the scalarization problem.

In this paper, the artificial neural network based multi-objective OPTIMIZATION of twist extrusion process is carried out. The target purpose functions are equivalent plastic strain, strain distribution and extrusion force. The design variables are twistangle, friction factor and loading rate. The FEM model of the process is first created and used to create training cases for the ANN, and the well-trained ANN is used as a quick and exact model of the process. Then the OPTIMIZATION of the design variables is conducted by an integrated genetic algorithm and ANN modelto create a set of optimal solutions (Pareto front). Leveldiagrams are then used to select the best solution from the Pareto front. Finally the response surface methodology has been used to study the interaction between the design parameters. The obtained results show that the best range of twist angle is from 0.7 to 45 degree, friction factor from 0.65 to 0.7 and loading rate from 6.5 to 7 mm/s. Also variables with the largest effect on the process are twist angle and friction factor.