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.