Multiobjective Linear and Integer Programming by Carlos Henggeler Antunes Maria João Alves & João Clímaco

Author:Carlos Henggeler Antunes, Maria João Alves & João Clímaco
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Step 4

The nondominated solutions obtained by optimizing the 2p + 1 weighted sums of the objective functions computed in step 3 are filtered to obtain a sample of size Q and the DM is asked to choose the most satisfactory one according to his/her preferences.

The filtering process has the purpose of selecting the Q most distinct points for integrating the solution sample. A specific technique is used. For further details see Steuer (1986, chapter 9), where the following filtering techniques are suggested: closest point outside the neighborhoods and furthest point outside the neighborhoods.

Then, the objective function coefficient matrix for the next iteration is built by multiplying the previous one by a T matrix, leading to a new contracted and dislocated gradient cone with respect to the previous iteration cone. The new contracted cone tends to be centered around the convex combination of the objective function gradients associated with the solution preferred by the DM in the last iteration. This cross-section of the contracted cone is of the cross-section of the previous cone.

If the number I of iterations specified by the DM was not yet performed, then set h ← h +1 and return to step 3.

Otherwise, go to step 5.

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