how to solve a multi objective optimization using genetic algorithm

MINIMIZE SR = -0.0841111 - 0.0006945 Speed - 11.9767 Feed + 4.48667 Depth of cut + 2.66833e-007Speed*Speed + 68.3333 Feed*Feed - 2.61867 Depth of cut*Depth of cut MAXIMIZE MRR = -2114.54 + 0.228237 Speed + 4571.23 Feed + 4132.55 Depth of cut +3.60467e-005 Speed*Speed + 14388.7 Feed*Feed - 2306.69 Depth of Cut*Depth of cut CONSTRAINTS SPEED:1000 TO 3000 rpm FEED :0.05 TO 0.15 mm/min DOC:0.5 TO 1 mm how to solve the above equations in genetic algorithm (which is multi objective)

[John D'Errico]

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[Alan Weiss]

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Alan Weiss

MATLAB mathematical toolbox documentation

Answer 1

[John D'Errico]

The standard solution to multi-criteria optimization is to optimize the sum of a linear combination of those competing objectives.

Thus, make them all minimization problems, by negating those that are maximization. Then choose a set of weights for the various objectives to make them of all comparable importance. Form the weighted sum, and at least in theory, you have ONE optimization problem that any optimization tool can handle.

You really cannot do much better than that, because no solution will make all of the objectives completely "happy". An intelligent choice of weights is of course crucial.