The main purpose of this paper is the optimization of Multiple categorical correlated responses. So, a heuristic approach and a log-linear model have been used to simultaneously estimate the responses of surface parameters. Parameter estimation has been performed with the aim of maximizing the amount of concordance. Concordance means that the joint probability of occurrence of dependent responses in each treatment is more than other probabilities in the same treatment. The second step of this research is the optimization of Multi correlated responses for categorical data using some practical metaheuristic algorithms, including simulated annealing, Tabu search and the genetic algorithm. Using each meta heuristic algorithm, the best controllable factors are selected to maximize the joint probability of success. Three simulated numerical examples with different sizes have been used to describe the proposed algorithms. Results show the superiority of joint success probability values in the Tabu search algorithm, compared to the other approaches.

The main objective of this research is to improve the design and performance of the polyurethane foam-filled thin-walled aluminum grooved circular tubes using Multi-response optimization (MRO) technique. The tubes are shaped with the inner and the outer circular grooves at different positions along the axis. For this aim, several numerical simulations using ABAQUS finite element explicit code are performed to study the energy absorption of these structures. The effects of the grooves distance, tube diameter, grooves depth, foam density, and tube thickness are investigated on the crash worthiness parameters of grooved circular tubes. Finite-element analysis is performed along the lines defined by design of experiments (DOE) technique at different combinations of the design parameters. The MRO is carried out using the mathematical models obtained from response surface methodology (RSM) for two crashworthiness parameters termed as the specific energy absorption (SEA) and the crushing force efficiency (CFE). Finally, by analyzing all the design criteria including the absorbed energy of tube, the mass of tube, the mean crushing load, and the maximum crushing load, the optimal density of polyurethane foam and geometric parameters were obtained through both Multi-objective optimization process and Pareto diagram. A comparison of the obtained results indicates the significance of grooves distance and the inner diameter of the tube as the most influential parameters.

In this paper, a novel approach to Multi response optimization is presented. In the proposed approach, response variables in treatments combination occur with a certain probability. Moreover, we assume that each treatment has a network style. Due to the probabilistic nature of the treatment combination, the suggested approach can compute the efficiency of each treatment under the desirable reliability.The approach has been constructed based on a network data envelopment analysis and the chance constraint method. Finally, a numerical example shows applicability of the proposed method to a Multi response problem. The results indicate that the proposed approach is a capable method for analyzing the best treatment and compared to other existing methods, it performs better in efficient treatment determination.

This paper presents a Multi-objective model for location-transportation problem under uncertainty that has been developed to respond to crisis. In the proposed model, humanitarian aid distribution centers (HADC), the number and location of them, the amount of relief goods stored in distribution centers, the amount of relief goods sent to the disaster zone, the number of injured people transferred to medical centers and the delivery of relief regarding the limits of capacity for transport, distribution centers and also available time and budget limits are all considered. This work aims at minimizing unfulfilled needs; that is meaning the number of people have not been transferred to medical centers. In order to take the inevitable uncertainty in some parameters into account, the primal deterministic model has been reformulated by applying the robust optimization approach. Also the performance of the both deterministic and robust models are investigated by solving a numerical example. The results of the study show that the robust counterpart of deterministic model will remain feasible with a high probability in reality.