Introduce el texto aquí

Introduce el texto aquí

1. °No- Preference °Posteriori °A priori °Interactive

2. Weighted Sum Method

   • Simplest method and guarantees finding solutions on the entire Pareto.optimal front
   • Objectives have to be converted into one type (nomalization), difficulties at finding optimal solution fot weighted objective and difficulties at non convex problems
   • Scalarizes a set of objectives into a single objective by pre-multiplying each objective with a user supplied weight. If x is a Pareto optimal solution of a conversion multi objective optimization problem, then exist non-zero positive weight vector w such that x is a solution to the problem given by equation. The solution to the problem represented is Pareto optimal if the weight is positive for all objectives.

3. є-Constraint Method

   • Can be implemented for convex or nonconvex objective spaces
   • Solution depends on the є chosen where it has to lie with the minimum or maximum of the individual objective function, as more objectives more elements for the vector є therefore more information from the user.
   • The reformulating the MOOP by just keeping one of the objectives and restricting the rest of the objectives within user specified values. Can be found by using different є values, can also be used for problems having convex or non-convex objectives spaces alike.

4. Weighted Metric Methods

   • Weighted metric Tchebycheff metric guarantees finding each and every Pareto optimal solution for the utopian vector z and solution can change dinamically
   • Normalize due different orders value of the objectives, leading to know optimal values of each objective before optimizing the lp

5. Benson´s Method

   • Simplest process to normalize, finding different Pareto optimal solutions eiter on the convex or non convex Pareto optimal region.
   • For optimization an additional number of contraints is needed

6. Value Function Method

   • Risk by using an over simplified value function

7. Goal Programming Methods

   • To find solutions which attain a predefined target for one or more objective functions.
   • Weighted , Lexicographic and Min-Max Goal Programming