Multi-objective collaborative optimization using linear physical programming with dynamic weight

The multi-objective collaborative optimization problem with multi-objective subsystems has a bi-level optimization architecture, that consists of the system and subsystem levels. Combining the multi-objective optimization algorithm with a bi-level optimization structure can obtain a satisfactory solution. Given that the preference-based algorithm requires minimal running time, the Linear physical programming (LPP) method, one of the typical preference-based algorithms, is adopted. Considering that setting the preference values for the incompatibility function is difficult, the weighted incompatibility function is added to the piecewise linear function of the LPP model. An expression of dynamic weight is also presented according to the inconsistency among the subsystems, which is caused by the sharing and auxiliary variables relative to the different subsystems. Using an engineering example, this study reveals that the interdisciplinary consistency is satisfactory when the dynamic weight is used in the LPP model, which thereby demonstrates the effectiveness of the presented method.