Navigating Uncertainty in Weapon System-of-Systems Planning: A Hybrid Multiobjective Network-Based Optimization and Fuzzy Set Approach

The evaluation of the capability of network-based systems of systems has replaced the simple method that considers return on investment, becoming a new paradigm for planning national defence capabilities. However, the dual uncertainty of the key system attributes of scenes and weapons has brought great challenges for decision-making. Based on this, we developed a multiobjective optimization model with multiple stages and scenarios under uncertainty to determine plans. In this study, we consider planning risk and planning cost as the two objectives. To solve this problem, we propose a hybrid solution for a network-based optimization method integrated with fuzzy set theory. The network-based optimization method combines the NSGA-II-DE and complex network theory. We use the characteristics of the network to evaluate the capabilities of the WSoS, and the NSGA-II-DE is used to generate a development plan and finally output a set of Pareto optimal solutions. We use fuzzy sets to determine the fuzzy membership of each plan on the Pareto front and determine a satisfactory solution. Finally, we conduct simulation experiments to verify the rationality of the methods proposed in this article. The results can provide a set of efficient solutions for military planners, helping generate a variety of planning solutions and trade-offs according to their preferences. Graphical Abstract