###### Abstract  
System portfolio selection is a kind of tradeoff analysis and decision-making on multiple systems as a whole to fulfill the overall performance on the perspective of System of Systems (SoS). To avoid the subjectivity of traditional expert experience-dependent models, a model and data-driven approach is proposed to make an advance on the system portfolio selection. Two criteria of value and risk are used to indicate the quality of system portfolios. A capability gap model is employed to determine the value of system portfolios, with the weight information determined by correlation analysis. Then, the risk is represented by the remaining useful life (RUL), which is predicted by analyzing time series of system operational data. Next, based on the value and risk, an optimization model is proposed. Finally, a case with 100 candidate systems is studied under the scenario of anti-missile. By utilizing the Non-dominated Sorting Differential Evolution (NSDE) algorithm, a Pareto set with 200 individuals is obtained. Some characters of the Pareto set are analyzed by discussing the frequency of being selected and the association rules. Through the conclusion of the whole procedures, it can be proved that the proposed model and data-driven approach is feasible and effective for system portfolio selection. model and data-driven; system portfolio selection; value and risk; capability gap; remaining useful life; genetic algorithm +
Footnote †: journal: Applied  
increasing popularity in the field of weapon SoS construction, where the optimal system portfolio will be selected by evaluating system portfolio candidates through model-based methods. So far, there has been little research that measures weapon system portfolios without subjective criteria. Typical measurements in most literature, such as benefit-risk analysis [6], cost-efficiency analysis [7], and requirement-satisfaction analysis [8] are inaccurate and unconvincing to some extent because they usually require too much expert experience. Motivated by solving issues mentioned above, data-driven methods are combined with traditional model-based approaches to improve the accuracy and credibility of evaluation results on system portfolios, by reducing dependence on artificial expertise. In addition, data-driven methods are complements of model-based approaches, instead of substitutions, because pure data without models cannot construct the bridge connecting scheme variable inputs and evaluation outputs. In civilian fields, the portfolio selection theory has been mainly studied and applied on project portfolio problems [9]. From the perspective of modeling, the scenario-based models are frequently used to describe the boundary of possible cases, based on which, decision-makers evaluate and select the well-matched optimal system portfolio [10; 11; 12; 13]. Robust models are also widely studied and applied in project portfolio problems to solve the difficulties in determining probabilities of future scenarios, aiming to select an ideal system portfolio that performances well at almost all possible situations [14; 15; 16]. As for the evaluation and trade-off of project portfolios, variant methods are proposed and studied, such as risk analysis methods [17], value evaluation methods [18], cost-efficiency methods [19], fuzzy assessment methods [4], preference-based methods [20], game theory, interactive decision methods [21], etc. A common ground of those methods is determining the value and risk of a system portfolio to abstractly indicate what decision-makers expect or not expect. As regard to portfolio planning and optimization, the goal is to select the optimal project portfolio by analyzing and comparing candidate project portfolios. The mixed integer model [22], multi-objective optimization [23], hybrid and dynamic planning are the most popular optimization methods.