Multi-objective decision support system in numerical reliability optimization of modern electronic packaging

摘要

Nowadays, numerical prototyping methods in electronic packaging are widely used. This is mainly due to cost and time reduction and improved functionality and reliability of final products. Recently, there has been a lot of interest and work conducted on advanced numerical optimization, which can be directly applied to prototyping. So far, the optimization is focused on one criteria while neglecting problem of multi-objectivity, which is not the best approach from practical point of view. Nevertheless, such an approach is jusitified from the point of view of complex analysis, interdisciplinary issues and reduced accuracy of numerical models. In reality, there are usually many criteria which, in order to solve the problem, have to be taken into consideration. There are many multi-objective methods, of which the Pareto set approach is mostly cited in the literature. The “problem” of multi-objective optimization is that not a single optimal solution has resulted but the set of equivalent optimal solutions. This set of equivalent optimal solutions is referenced as “the Pareto set”. From the mathematical point of view, every value from this set can be treated as optimal for certain assumed constraints. However, there could be some additional conditions which cannot be applied to optimization process and some of the results from the Pareto set are more likely (i.e., the fabrication process will be more repeatable) then the others. So, the question is: which value from the Pareto set should be taken to further processing? There are two possibilities: asking an expert for the advice or use the decision making system. Decision making methods based on multi-objective optimization could be referenced as “Multiple criteria decision making” (MCDM) or “Multiple criterial decision aid” (MCDA) systems. There are several groups of these methods: (a) mathematical multi-objective programming, (b) artificial intelligence methods, (c) simple arithmetic methods, and (d) advanced mathematical methods. The current paper will focus on designing and application of the decision support system for multi-objective numerical reliability optimization of electronic packaging. The work will be based on the self developed numerical tool based on Python Scrippting language and will present its application to selected microelectronic packages based on its numerical model elaborated in ABAQUS.