Yu (1973) and Zeleny (1974) define the ideal solution (Yu describes this solution as the “utopia point”) as any solution that would simultaneously optimize each individual objective. In objective function space this point has the coordinates Z(x*) = [Z1(x*), ..., Zk(x*)], where x* optimizes every Zh(x). It is an unusual case where there is a single solution wh ich simultaneously optimizes all of the objectives. However, a representation of the unobtainable ideal solution can be obtained for any properly bounded set of alternatives by optimizing each Zh(x) separately. The coordinates of this representation are then given by [Z1(x1 *), ..., Zk(xk *)], where xh * optimizes the hth objective. Should any Zh be unbounded, Zh * cannot be precisely specified. This case will be discussed in greater detail in Section 10.4. If the ideal solution is obtainable (x1 * = ... = xk *) it is dearly the solution to the multiobjective linear program.
KeywordsMULTIOBJECTIVE Optimization Ideal Solution Ideal Point Compromise Solution Multiple Criterion Decision
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