Multiobjetivo

MULTIOBJETIVO

Algorithms classification:

Generating methods

Preference-based methods

Weighted Sum Method: scalarizes a set of objectives into a simple objective by pre-multiplying each objective with a user

Advantages: intuitive and easy to use

Disadvantages: all objectives have to be converted into one type

Constraint Method: this method is used in order to alleviate the difficulties faced by the weight sum approach in solving problems having non-convex objectives.

Advantages: different Pareto-optimal solution can be found by using different Em values.

This method can also be used for problems having convex or nonconvex objective spaces alike

Disadvantages: the solution to the problem largely depends on the chosen E vector.

Weighted Metric Methods: other means of combining multiple objective into a single objective

Advantages: this method guarantees finding each and every Pareto-optimal solution

Disadvantages: It is advisable to normalize the objective function

Benson´s Method: the reference solution in this method is taken as a feasible non-Pareto-optimal solution

Advantages: to avoid scaling problems, individual differences can be normalized before the summation

Disadvantages: the optimization problem formulated above has an additional number of constraints need it to restrict the search in the region dominating the chosen solution z^0

Value Function Method: in this method the user provides a mathematical value function, this must be valid over the entire feasible search space

Goal Programming Methods: the main idea of this method is to find a solutions attain a predefined target for one or more objectives functions

Advantages: this method is simple and ideal, if adequate value function information is available.

Disadvantages: the obtained solution entirely depends on the chosen value function

This method has different approaches:

- Weighted Goal Programming

- Lexicographic Goal Programming

- Min-Max Goal Programming

The decision-maker is involve in the optimization process, these techniques are becoming popular in practice

Interactive Methods: the main idea in those approaches is that from time to time during the optimization process the decision-makers is involved in providing some information about the direction of search, weight, vector and other factors

Classical Methods: some difficulties appear in the classical multi-objetive optimization algorithms

-Only one Pareto-optimal solution can be expected to be found in one simulation run of a classical algorithm

-Not all Pareto-optimal solutions can be found by some algorithms in non convex MOOPs

-All algorithms require some problems knowledge, such as suitable weights or E or target values

All the methods require some knowledge about the problem.