Lecture 9: Multi-Objective - Purdue University
Lecture 9: Multi-Objective Optimization
Suggested reading: K. Deb, Multi-Objective Optimization using Evolutionary Algorithms, John Wiley & Sons, Inc., 2001
Multi-Objective Optimization Problems (MOOP)
Involve more than one objective function that are to be minimized or maximized
Answer is set of solutions that define the best tradeoff between competing objectives
2
General Form of MOOP
Mathematically
min/max fm (x), m =1, 2,L, M
subject to g j (x) 0, j =1, 2,L, J
hk (x) = 0, k =1, 2,L, K
x x x , (L)
i lower
(U )
i
i upper
i =1, 2,L, n
bound
bound
3
Dominance
In the single-objective optimization problem, the superiority of a solution over other solutions is easily determined by comparing their objective function values
In multi-objective optimization problem, the goodness of a solution is determined by the dominance
4
Definition of Dominance
Dominance Test
x1 dominates x2, if
Solution x1 is no worse than x2 in all objectives
Solution x1 is strictly better than x2 in at least one objective
x1 dominates x2
x2 is dominated by x1
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