A multi-objective military system of systems architecting problem with inflexible and flexible systems: formulation and solution methods

System of systems (SoS) architecting is the process of bringing together and connecting a set of systems so that the collection of the systems, i.e., the SoS is equipped with a set of required capabilities. A system is defined as inflexible in case it contributes to the SoS with all of the capabilities it can provide. On the other hand, a flexible system can collaborate with the SoS architect in the capabilities it will provide. In this study, we formulate and analyze a SoS architecting problem representing a military mission planning problem with inflexible and flexible systems as a multi-objective mixed-integer-linear optimization model. We discuss applications of an exact and an evolutionary method for generating and approximating the Pareto front of this model, respectively. Furthermore, we propose a decomposition approach, which decomposes the problem into smaller sub-problems by adding equality constraints, to improve both the exact and the evolutionary methods. Results from a set of numerical studies suggest that the proposed decomposition approach reduces the computational time for generating the exact Pareto front as well as it reduces the computational time for approximating the Pareto front while not resulting in a worse approximated Pareto front. The proposed decomposition approach can be easily used for different problems with different exact and heuristic methods and thus is a promising tool to improve the computational time of solving multi-objective combinatorial problems. Furthermore, a sample scenario is presented to illustrate the effects of system flexibility.