Combining Max-min and Max-max Approaches for Robust SoS Architecting

A System of Systems (SoS) architecting problem requires creating a selection of systems in order to provide a set of capabilities. SoS architecting finds many applications in military/defense projects. In this paper, we study a multi-objective SoS architecting problem, where the cost of the architecture is minimized while its performance is maximized. The cost of the architecture is the summation of the costs of the systems to be included in the SoS. Similarly, the performance of the architecture is defined as the sum of the performance of the capabilities, where the performance of a capability is the sum of the selected systems' contributions towards its performance. Here, nevertheless, the performance of a system in providing a capability is not known with certainty. To model this uncertainty, we assume that the performance of a system for providing a capability has lower and upper bounds and subject to complete uncertainty, i.e., no information is available about the probability distribution of the performance values. To solve the resulting multi-objective SoS architecting problem with uncertainty, we propose and compare three robust approaches: max-min, max-max, and max-mid. We apply these methods on a military example and numerically compare the results of the different approaches.