Supervision by University Paris Dauphine LAMSADE, Naval Group
A complex system is a collection of sub-systems linked by structural constraints and interacting to provide the overall performance of the system.
Complex system optimisation is a topic explored widely for functions with continuous and scalar values, especially through decomposition and coordination approaches. These approaches alternate between distributed optimisation of sub-systems, made independent by fixing a state of their interaction, and updating the state of their interaction.
We study the case of functions with vector values, without a unique optimum, but with a set of non-dominated solutions. No optimum state of interaction can therefore exist between the sub-systems and traditional approaches cannot therefore be transposed.
Nevertheless, we show that the notion of decomposable optimisation is generalised to the multi-objective case, with the difficulty that combinations of non-dominated solutions for the sub-systems can be dominated for the global system. We suggest several algorithms to filter them effectively. For functions with Boolean variables, a solution to the original optimisation problem could be to enumerate all the possible states of interaction between sub-systems and resolve the associated decomposable problems.
In addition, we define, for a fairly wide range of complex system optimisation problems, notions of lower and upper bounds of all non-dominated solutions, bounds that can be obtained by decomposition.