Artificial intelligence (AI) has surpassed top human players in a variety of games. In imperfect information games, these achievements have primarily been driven by Counterfactual Regret Minimization (CFR) and its variants for computing Nash equilibrium. However, most existing research has focused on maximizing payoff, while largely neglecting the importance of strategic diversity and the need for varied play styles, thereby limiting AI’s adaptability to different user preferences. To address this gap, we propose Preference-CFR (Pref-CFR), a novel method that incorporates two key parameters: preference degree and vulnerability degree. These parameters enable the AI to adjust its strategic distribution within an acceptable performance loss threshold, thereby enhancing its adaptability to a wider range of strategic demands. In our experiments with Texas Hold’em, Pref-CFR successfully trained Aggressive and Loose Passive styles that not only match original CFR-based strategies in performance but also display clearly distinct behavioral patterns. Notably, for certain hand scenarios, Pref-CFR produces strategies that diverge significantly from both conventional expert heuristics and original CFR outputs, potentially offering novel insights for professional players.

Counterfactual Regret Minimization (CFR) and its variants are widely recognized as effective algorithms for solving extensive-form imperfect information games. Recently, many improvements have been focused on enhancing the convergence speed of the CFR algorithm. However, most of these variants are not applicable under Monte Carlo (MC) conditions, making them unsuitable for training in large-scale games. We introduce a new MC-based algorithm for solving extensive-form imperfect information games, called MCCFVFP (Monte Carlo Counterfactual Value-Based Fictitious Play). MCCFVFP combines CFR’s counterfactual value calculations with fictitious play’s best response strategy, leveraging the strengths of fictitious play to gain significant advantages in games with a high proportion of dominated strategies. Experimental results show that MCCFVFP achieved convergence speeds approximately 20\%$\sim$50\% faster than the most advanced MCCFR variants in games like poker and other test games.

System-of-systems architecture is an important factor leading to successful system integration and capability delivery. However, current architecture model development based on architecture frameworks places heavy reliance on expert experiences. The lack of quantitative decision support not only increases human work burden, but also misses the chance of modeling better. Thus this paper proposes to identify and use decision patterns during the process of developing architecture description models. Five decision patterns built upon meta-model and associated decision points are identified, including the downselecting, partitioning, connecting, permuting, and assigning patterns. Each provides a mathematical framework to shape the important decision-making elements. A mixed use of decision patterns for an air and missile defense SoS architecture design is simply illustrated in the end. As a preliminary study, this paper demonstrates the potential of developing decision patterns to support and ease the architecture model development.

Dynamic complex environment requires resilient system-of-systems (SoS) architecture that can effectively deal with uncertainty. However, increasing resilience could affect other evaluation metrics, such as cost and effectiveness. To simplify the trade-off analysis process in the early design phase, this paper explores the use of a representative index that directly illustrates a balanced range of effectiveness, cost, and resilience. Specifically, this paper compares the combat SoS to an ecological network and develops a functional dependency network based effectiveness, resilience, and order-degree analysis method. Compared with the previous order-degree research, the proposed combat SoS architecture modeling and calcuation based on fucntional dependency network can reflect the rules of data exchanging more realistically. Based on the application to a notional anti-ship combat SoS, the order-degree is able to reflect the relationship between SoS resilience index and cost-effectiveness index (CEI) in the given scenarios. This implies that the order-degree has a good opportunity to serve as an indicator for supporting balanced resilient SoS design.

Architecture design that lays out the structure of components and their relationships plays a critical role in the combat system-of-systems (SoS) development. When the number of systems and their interactions keeps increasing in the future mosaic warfare oriented combat SoS, optimal architecture selection becomes very important due to the large number of possible design alternatives. However, in the optimal architecture selection problems, the dependency relationship between component systems has not been well captured. Thus, this paper developed a functional dependency incorporated architecture optimization formulation through a non-linear capability aggregation model. The architectural decisions include the allocation of physical systems to given functions and the determination of dependency parameters. Differential evolution algorithm is employed to solve this non-linear optimization problem. An application to a synthetic naval air and missile defense example in the end demonstrates that the proposed method can pick out the optimized architecture decisions for the combat SoS development.

Most System-of-Systems (SoS) problems face a highly dynamic, volatile, and uncertain environment. How to cope with the unpredictable and volatile changes is one of the key challenges for SoS practitioners. Agility, as an informative feature indicating an SoS's capability of effecting, coping with and exploiting changes, has not received sufficient attention in the context of SoS. This paper proposes a dynamic reconfiguration method that aims to improve the SoS agility from the perspectives of responding quickly to failures and recovering some amount of the SoS capability. This paper employs approximate dynamic programming method to compute the dynamic reconfiguration decisions that allow failed or degraded systems to be removed and the function-capability allocation to be changed quickly. A naval warfare SoS example takes a preliminary step towards demonstrating the effectiveness of the dynamic reconfiguration method, along with flexible architecture, in achieving the SoS agility in terms of responsiveness and resilience.