We consider biobjective shortest path problems in networks with fuzzy arc lengths. Considering the available studies for single objective shortest path problems in fuzzy networks, using a distance function for comparison of fuzzy numbers, we propose three approaches for solving the biobjective problems. The rst and second approaches are extensions of the labeling method to solve the single objective problem and the third approach is based on dynamic programming. The labeling methods usually producing several nondominated paths, we propose a fuzzy number ranking method to determine a fuzzy shortest path. Illustrative examples are worked out to show the e ectiveness of our algorithms.

In this paper, recommended spiral passive micromixer was designed and simulated. spiral design has the potential to create and strengthen the centrifugal force and the secondary flow. A series of simulations were carried out to evaluate the effects of channel width, channel depth, the gap between loops, and flowrate on the micromixer performance. These features impact the contact area of the two fluids and ultimately lead to an increment in the quality of the mixture. In this study, for the flow rate of 25 μl/min and molecular diffusion coefficient of 1×10-10 m2/s, mixing efficiency of more than 90% is achieved after 30 (approximately one-third of the total channel length). Finally, the optimized design fabricated using proposed 3D printing method.

Application of the network equivalent concept for external system representation for power system transient analysis is well known. However, the challenge to utilize an equivalent network, approximated by a rational function, is to guarantee the passivity of the corresponding model. In this regard, special techniques are required to enforce the passivity of the equivalent model through a post processing approach that minimizes its impact on the original model characteristics. In this paper, the passivity is enforced by expressing the problem in terms of a convex Optimization problem that guarantees the global optimal solution. The convex Optimization problem is efficiently solved by recently developed numerical interior–point methods. This passivity enforcement is also global which indicates that the passivity enforcement in one region does not lead to passivity violation in other regions.

We apply a primal-dual simplex algorithm for solving the biobjective min imum cost-time network flow problem such that the total shipping cost and the total shipping fixed time are considered as the first and second objective functions, respectively. To convert the proposed model into a single-objective parametric one, the weighted sum scalarization technique is commonly used. This problem is a mixed-integer programming, which the decision variables are directly dependent together. Generally, the previous works have consid ered the linear biobjective problem with the traditional network flow con straints, while in this paper, corresponding to each flow variable, a binary variable is defined. These zero-one variables are utilized to describe a fixed shipping time for positive flows. The proposed method is successful in finding all supported efficient solutions of a real numerical example.

This paper considers a biobjective transportation problem with various fuzzy objective functions coefficients. Fuzzy coefficients can be of different types such as triangular, trapezoidal, (semi) L 􀀀 R, or at (semi) L 􀀀 R fuzzy numbers. First, we convert the problem to a parametric interval biobjective transportation problem using-cuts of fuzzy coefficients. Then, we consider a fix-cut and obtain a necessarily weak efficient solution to the yielded interval biobjective program by a new algorithm. It uses basic feasible solutions and the parametric simplex algorithm. Furthermore, we suggest another algorithm for finding a reasonable solution, called -necessarily weak efficient, to the main biobjective transportation problem. To illustrate the validity and performance of the proposed algorithms, we present some numerical examples.

In this paper, a new version of multi-objective differential evolution with dynamically adaptable mutation factor is used for Pareto Optimization of a 5-degree of freedom vehicle vibration model excited by non-stationary random road profile. In this way, non-dominated sorting algorithm and crowding distance criterion have been combined to differential evolution with fuzzified mutation in order to achieve multi-objective meta-heuristic algorithm. To dynamically tune the mutation factor, two parameters, named, number of generation and population diversity are considered as inputs and, one parameter, named, the mutation factor as output of the fuzzy logic inference system. Conflicting objective functions that have been observed to be optimally designed simultaneously are, namely, vertical seat acceleration, vertical forward tire velocity, vertical rear tire velocity, relative displacement between sprung mass and forward tire and relative displacement between sprung mass and rear tire. Furthermore, different pairs of these objective functions have also been chosen for biobjective Optimization processes. The comparison of the obtained results with those in the literature unveils the superiority of the results of this work. It is displayed that the results of 5-objective Optimization subsume those of Bi-objective Optimization and, consequently, this achievement can offer more optimal choices to designers.

Bilevel programming is the model for hierarchical Optimization problems in which there are two decision makers that have different objective functions, variables and constraints. Alves et al in [1], proposed a method for computing the Pareto frontier of bilevel linear problem with biobjective at the upper level and a single objective function at the lower level. In this paper, we extend their method for the situation in which there exists more than two objective function at both levels, and then by using a suitable exchange variable, we proposed a new method for computing the Pareto frontier of bilevel linear problem with fractional multi-objective at the upper level. Finally we will show the efficiency of the propsed approaches by solving a few numerical examples and comparing the results with other methods.