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This holds strictly in the sense that from the Pareto front, the solutions according to the other combinations can be extracted.
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If two populations are from different fronts, the lowest front number is selected and if they are belong to the same front, the solution with the highest crowding distance is selected to form a mating pool.
For instance, in NSGA and NSGA-II the population is sorted into different fronts (or levels): front 1 contains the non-dominated solutions, front 2 the solutions that are only dominated by solutions of front 1, and so on.
This Pareto front contains the solutions that are acceptable operation for all objective functions.
This WM-MOGA process returns a set of solutions that form a Pareto front on the solutions space formed by the two objective functions.
The final front of the solutions in NSGA-II presents a variety of solutions for decision makers, and they have opportunity to select a proper solution based on the available budget and appropriate time for the project.
In case of same fronts, the solution with greater crowding distance is chosen.
The binary tournament selects individuals of lower front; in case of same fronts, the solution with greater crowding distance is chosen.
At first, to investigate the performance of the developed AMOSA algorithm to reach optimal Pareto front, the efficient solutions obtained by ∈-constraint method as an exact method for the three numerical examples are compared with the best Pareto solutions obtained by AMOSA.
Furthermore, the obtained Pareto fronts contain the solutions found with the most recent published topological representations for the well-known Microelectronics Center of North Carolina benchmark sets, and, allowed an improvement of placement area up to 23% on a previously optimized folded cascode operational amplifier for the United Microelectronics Corporation 0.13 μm fabrication process.
It is well known that moving mesh and upwinding schemes are two kinds of techniques for tracking the shock or steep wave front in the solution of PDEs.
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