Weighted sum method

The options that carry higher marks would be carried for further analysis. Table 2 presents an option evaluation by weighted sum method. 

Table 2 Workout Example of Weighted-sum Method for Waste Audit...

Eor k objectives, there will be - 1 additional constraints, each with a different e variable. For obtaining one Pareto-optimal solution, the SOO problem has to be solved with suitable values for weights (in the case of weighted sum method) or e variables (in the case of -constraint method). Both these methods are classical methods for solving MOO... 

The above bi-objective optimization problem can be transformed into a SOO problem by the -constraint method via making OFj as an additional constraint. Besides this method, goal programming and the weighted-sum method can also be used to convert the MOO problem into a SOO problem. Interested readers are referred to Chapter 4 for more details... 

Another consideration concerns the shape of the fronts. They appear convex, and would not be determinable with conventional multi-objective optimization methods like, for example, the Weighted Sum Method. This last method is a linear combination of the objectives, and the application of an Evolutionary optimization problem approach in Pareto s fronts definition would be more appropriate. 

Table 2. The crisp multiobjective optimization problem using the weighted sum method.

Kim, I.Y. and De Week, O.L. 2005. Adaptive weighted-sum method for bi-ob-jective optimization pareto front generation. Structural and Multidisciplinary Optimization, 29, 149-158. 

Marler, R. and Arora, J. 2010. The weighted sum method for multi-objective optimization new insights. Structural and Multidisciplinary Optimization, 41, 853-862. 

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