The present study endeavors to show an application of the multi objective optimization on the basis of ratio analysis (MOORA) method and technique for order performance by similarity to ideal solution (TOPSIS) method to select optimal process parameters in sheet hydroforming process. The right choice of the process parameters is critical to produce a final part with proper quality. In order to meet this characteristic, the important properties are the cup final thickness (FT), required forming force (FF) and radial stress (RS) at cup wall region. Nine alternatives for selecting the process parameters were taken into consideration based on Taguchi L9 orthogonal array. The limit drawing ratio (LDR), maximum pressure and prebulge pressure were selected as input variables. To solve the problem of process parameters' selection, the two mentioned methods were used. A compromised weighting approach composed of Entropy and analytic hierarchy process (AHP) methods were used to weight all criteria. The alternatives ranking were performed using MOORA and TOPSIS methods and then the results were compared. The results achieved in both of the assessment represent that the alternative number 3, leads to the best multi performance features of the process among the 9 experiments. In this experiment LDR is 1.81, maximum pressure and prebulge pressure are 37 MPa and 15 MPa, respectively.

Abstract-This study first reviews fuzzy random Portfolio selection theory and describes the concept of portfolio optimization model as a useful instrument for helping finance practitioners and researchers. Second, this paper specifically aims at applying possibility-based models for transforming the fuzzy random variables to the linear programming. The harmony search algorithm approaches to resolve the portfolio selection problem with the objective of return maximization is applied. We provide a numerical example to illustrate the proposed model. The results show that the evolutionary method of this paper with harmony search algorithm, can consistently handle the practical portfolio selection problem.

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The problem of portfolio optimization is a standard problem in financial world and it has received tremendous attentions. Portfolio optimization plays essential role in determining portfolio strategies for investors. Portfolio optimization is intrinsically a discrete optimization problem whose decision criteria are in conflict and the proposed study of this paper considers a portfolio optimization problem involving fuzzy random variables. To solve the proposed model, we first present the possibility and necessity-based model to reformulate the fuzzy random portfolio selection model into linear programming models and using the resulted linear programs, a multi-objective problem is constructed. To solve the multi-objective problem we propose some methods to consider decision makers' optimistic and pessimistic views. A numerical example illustrates the whole idea on multiobjective fuzzy random portfolio optimization by possibility and necessity-based model.

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