مقاله ترجمه شده بهبود سازی دقیق کارآمد مشکلات تخصیص افزونگی چند منظوره در سیستم های سری و موازی
قسمتی از متن انگلیسی:
Proof: Without loss of generality, we
demonstrate this through an example with two subsystems and two
objectives. Consider the following non-dominated solution sets for
subsystem 1 and 2: ðf n o1 ð Þ x1 ,f n o2 ð ÞÞ ¼ x1 ð Þ ۳,۵ ,ð Þ ۲,۶ ,ð Þ
۴,۱ and ðf n o1 ð Þ x2 ,f n o2 ð ÞÞ ¼ x2 ð Þ ۲,۵ , ð Þ ۴,۳ ,ð Þg 1,7 .
The Cartesian combination results in 9 solutions and 4 of these
solutions are dominated by the remainder. For instance, the solution
obtained by combining 1st solution of subsystem 1 (3,5) and 2nd solution
of subsystem 2 (4,3) is (7,8), which is dominated by the solution (6,6)
obtained by combining 3rd solution of subsystem 1 (4,1) and 1st
solution of subsystem 2 (2,5). Hence, the Cartesian combination of the
non-dominated solutions of multiple subsystems can result in dominated
solutions. In order to maintain the computational efficiency, the
decomposition based approach in Fig. 2 alternates between the Cartesian
combining and Pareto filtering steps, e.g., filtering out dominated
solutions in smaller sets rather than all at once (Phase 3, Fig. 2). The
following proposition establishes that this sequential combining and
filtering process does eliminate any non-dominated solution of the RAP. D
