ABSTRACT
In the multiobjective optimization problem, two or more objective functions are to be simultaneously optimized. For example, the criteria in manufacturing a product could be cost minimization and efficiency maximization. The general form of a multiobjective optimization problem can be mathematically stated as
Minimize
fk(x) k = 1, 2,…, K (7.1)
subject to
gi(x) ≤ 0 i = 1, 2,…, m < n (7.2)
hj(x) = 0 j = 1, 2,…, r < n (7.3)
xl ≤ x ≤ xu (7.4)
where x is a vector of n design variables given by
x =
x
x
xn
The solution to a multiobjective problem results in a number of points in the objective function space referred to as Pareto optimal solutions. For a multiobjective problem with two objective functions (the first function is efficiency maximization and the second function is cost minimization), a typical Pareto optimal front is shown in Figure 7.1. The first objective ( f1) function “efficiency” is along the x-axis of this figure and the y-axis contains the second objective ( f2) function “cost.” The Pareto optimal front is obtained using the principle of domination. In this concept, each solution is compared to check whether it dominates another solution or not.
