Sharif Digital Repository

A new weighted order scheme is presented for finding alternative Pareto optimal solution of multi objective linear programming problems. In developing the weighted scheme, a big M model is proposed. We establish some properties of the ordering scheme and the proposed model and show how to determine proper values of the parameter M. Illustrative examples are worked out to show the effectiveness of the proposed approach and the competitiveness of the obtained solutions as compared to the ones obtained by the weighted maxmin and the weighted aggregation methods  

In this letter, both the number of participating nodes and spatial dispersion are incorporated to establish a bi-objective optimization problem for maximizing the quality of aggregation under interference and delay constraints in tree-based wireless sensor networks (WSNs). The formulated problem is proved to be NP-hard with respect to Weighted-sum scalarization and a distributed heuristic aggregation scheduling algorithm, named SDMAX, is proposed. Simulation results show that SDMAX not only gives a close approximation of the Pareto-optimal solution, but also outperforms the best, to our knowledge, existing alternative proposed so far in the literature  

A wind turbine transformer internal resonance, excited by high frequency transients i.e.; under its energization through a short length of cable, is considered to obtain a proper transformer design method. A multi-objective optimum design method (using TOC and inrush current energy factor as objective functions) is employed and the optimal Pareto solutions for this design are derived. Selected design from the Pareto optimal solutions are then modeled using the lumped RLC ladder network, valid over a wide frequency range. The obtained frequency responses are then compared with each other to investigate the effect of multi-objective design on different aspects of the transformer winding... 

A wind turbine transformer (WTT) is designed using a 3D wound core while the transformer's total owning cost (TOC) and its inrush current performance realized as the two objective functions in a multi-objective optimization process. Multi-objective genetic algorithm is utilized to derive Pareto optimal solutions. The effects of inrush current improvement on other operating and design parameters of the transformer such as: losses, dimensions, and weights are investigated. An approach is presented to select one design from optimal Pareto solutions based on relative improvement of the inrush current performance. Finally, this multi-objective optimum wind turbine transformer design is compared... 

We consider a multi-objective linear programming model with type-2 fuzzy objectives. The considered model has the flexibility for the user to specify the more general membership functions for objectives to reflect the inherent fuzziness, while being simple and practical. We develop two solution strategies with reasonable computing costs. The additional cost, as compared to the type-1 fuzzy model, is indeed insignificant. These two algorithms compute Pareto optimal solutions of the type-2 problems, one being based on a maxmin approach and the other on aggregating the objectives. Finally, applying the proposed algorithms, we work out two illustrative examples  

In this investigation, the multi-objective selection and optimization of a gantry machine tool is achieved by analytic hierarchy process, multi-objective genetic algorithm, and Pareto-Edgeworth-Grierson-multi-criteria decision-making method. The objectives include maximum static deformation, the first four natural frequencies, mass, and fabrication cost of the gantry. Further structural optimization of the best configuration was accomplished using multi-objective genetic algorithm to improve all objectives except cost. The result of sensitivity analysis reveals the major contribution of columns of gantry with respect to the crossbeam's contribution. After determining the most effective... 

In this paper, assuming porosity varies only along thickness direction, its optimal distributions in functionally graded porous (FGP) beams are tailored. Two multi-objective optimization problems are defined. In the first one, critical buckling load and mass are optimized simultaneously while in the second one, we concentrate on simultaneous optimization of mass and fundamental frequency. Employing Timoshenko beam theory, we present governing equations for a FGP beam. For the solution, we use Ritz method and propose appropriate trial functions according to the boundary conditions (Hinged-Hinged, Clamped-Clamped, Clamped-Hinged and Clamped-Free). Since the porosity distribution along... 

We present a linear programming based algorithm for a class of optimization problems with a multi-linear objective function and affine constraints. This class of optimization problems has only one objective function, but it can also be viewed as a class of multi-objective optimization problems by decomposing its objective function. The proposed algorithm exploits this idea and solves this class of optimization problems from the viewpoint of multi-objective optimization. The algorithm computes an optimal solution when the number of variables in the multi-linear objective function is two, and an approximate solution when the number of variables is greater than two. A computational study... 

Green and sustainability issues are being considered extensively in industry and in the literature. Most of the green-related effects in the manufacturing sector can be modeled by the costs associated with the production machines due to their resource consumption and/or pollutant emission, as a part of the operation cost. Accordingly, taking into account the machine processing costs alongside the other production criteria is one of the main approaches to consider green issues in the production management problems. In the same way, scheduling as one of the major operational problems in the factories can benefit this point of view to involve sustainability aspects. In this paper, the... 

Increasing rates of environmental and social concerns involved in various communities have recently attracted researchers’ attention to consider them in proper designs of sustainable supply chains (SSCs). In this paper, the planning problem of a multi-period multi-echelon sustainable closed loop supply chain (SCLSC) is investigated. A comprehensive model that seriously takes into account the social and environmental aspects of the supply chain (SC) decisions and measures their social and environmental effects using the GRI (Global Reporting Initiative) guideline indicators is proposed. The proposed planning model includes tactical decisions comprising the price of the product and logistic... 

In this paper, we develop a multi-objective stochastic programming approach for supply chain design under uncertainty. Demands, supplies, processing, transportation, shortage and capacity expansion costs are all considered as the uncertain parameters. To develop a robust model, two additional objective functions are added into the traditional comprehensive supply chain design problem. So, our multi-objective model includes (i) the minimization of the sum of current investment costs and the expected future processing, transportation, shortage and capacity expansion costs, (ii) the minimization of the variance of the total cost and (iii) the minimization of the financial risk or the... 

In the present study, considering two-dimensional porosity distribution through a functionally graded porous (FGP) beam, its optimal distributions are obtained. A multi-objective optimization problem is defined to maximize critical buckling load and minimize mass of the beam, simultaneously. To this end, Timoshenko beam theory is employed and equilibrium equations for two-dimensional functionally graded porous (2D-FGP) beam are derived. For the solution, we present generalized differential quadrature method (GDQM) and consider two symmetric boundary conditions (Clamped-Clamped and Hinged-Hinged). Solving generalized eigenvalue problem, critical buckling load for 2D-FGP beam is then obtained.... 

This paper presents a long-term dynamic multi-objective model for distributed generation investment. The proposed model optimizes three objectives, namely active losses, costs and environmental emissions and determines the optimal schemes of sizing, sitting of DG units and specially the dynamics of investment over the planning period. The Pareto optimal solutions of the problem are found using a GA algorithm and finally a fuzzy satisfying method is applied to select the optimal solution considering the desires of the planner. The solutions of Pareto optimal front are analyzed to extract general useful information for planners about the appropriate DG technologies and placement schemes. The...