Classical Methods

Classical Methods

1. Weighted Sum Method

   • Scalarizes a set of objectives into a single objective by pre multiplying each objetive with a user supplied weight
   • "The solution to the problem represented is Pareto optimal if the weight is positive for all objetives"
   • If x is a Pareto optimal solution of a conversion multi objetive optimization problem, then exist a non zero positive weight vector w such that x is a solution to the problem given by equation
   • Advantages
     • The simplest way to solve an MOOP

2. E- Constraint Method

   • The reformulating the MOOP by just keeping one of the objetives and restricting the rest of the objetives within user specified values
   • Advantages
     • Can be found by using different Em values, can also be used for problems having convex or non convex objetive spaces alike

3. Weighted Metric Method

   • weighted metrics such as lp and l infinity distance metrics are used. For non negative weights, the weighted lp distance measure of any solution c from the ideal solution z can be minimized
   • Let x be a Pareto optimal solution. There then exist a positive weighting vector such than xx is a solution of the weighted tchebycheff problem, where the reference point is the utopian observe vector z

4. Benson's Method

   • The reference solution is taken as a feasible non Pareto optimal solution. A solution z0 is randomly chosen from the feasible region.
   • Advantages
     • To avoid scaling problems, individual differences can be normalized before the summation

5. Value Function Method

   • In the value function method, the user provides a mathematical value function U:Rm -> R relating all M objetives.

6. Goal Programming Method

   • To find solutions which attain a predefined target for one or more objetive functions.