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Target maneuver trajectory prediction is an important prerequisite for air combat situation awareness and threat assessment. Aiming at the problem of low prediction accuracy in traditional trajectory prediction methods, combined with the chaotic characteristics of the target maneuver trajectory time series, a target maneuver trajectory prediction model based on chaotic theory and improved genetic algorithm-Volterra neural network (IGA-VNN) model is proposed, mathematically deducing and analyzing the consistency between Volterra functional model and back propagation (BP) neural network in structure. Firstly, the C-C method is used to reconstruct the phase space of the target trajectory time series, and the maximum Lyapunov exponent of the time series of the target maneuver trajectory is calculated. It is proved that the time series of the target maneuver trajectory has chaotic characteristics, so the chaotic method can be used to predict the target trajectory time series. Then, the practicable Volterra functional model and BP neural network are combined together, learning the advantages of both and overcoming the difficulty in obtaining the high-order kernel function of the Volterra functional model. At the same time, an adaptive crossover mutation operator and a combination mutation operator based on the difference degree of gene segments are proposed to improve the traditional genetic algorithm; the improved genetic algorithm is used to optimize BP neural network, and the optimal initial weights and thresholds are obtained. Finally, the IGA-VNN model of chaotic time series is applied to the prediction of target maneuver trajectory time series, and the experimental results show that its estimated performance is obviously superior to other prediction algorithms.

The multi-objective weapon-target assignment problem, which aims to generate reasonable assignment to meet the objectives, is a typical optimization problem with complex constraints. In order to get close to the actual air combat, the game process between both sides at war is introduced to construct a three objective mathematical model, which includes the damage of the enemy, the cost of missiles, and the damage value of fighting capacity. Considering the NP-complete nature of multi-objective weapon-target assignment problem, an improved intelligent algorithm (named as D-NSGA-III-A) on the basis of non-dominated sorting genetic algorithm III (NSGA-III) is proposed. In this improved algorithm, first, the non-dominated sorting based on dominance degree matrix is proposed to reduce the unnecessary or repetitive comparisons in ranking schemes, so as to further decrease the time consumption. Second, diversity and convergence are taken into account resorting to the niching information and the dominance ratio when selecting individuals. Third, the adaptive operator selection mechanism, which selects the operators adaptively according to the information of generations from a pool where single point crossover and all bits crossover operators are included, is employed to seek a balance between intensification and diversification within the decision space and to improve the quality of Pareto solutions. From the experiments, the combination of above technologies obtains better Pareto solutions and time performance for solving the static multi-objective target assignment (SMWTA) problem than NSGA-III, MP-ACO, NSGA-II, MOPSO, MOEA/D, and DMOEA-εC.

The Perron–Frobenius eigenvalue (PFE) is widely used as measurement of the number of loops in networks, but what exactly the relationship between the PFE and the number of loops in networks is has not been researched yet, is it strictly monotonically increasing? And what are the relationships between the PFE and other measurements of loops in networks? Such as the average loop degree of nodes, and the distribution of loop ranks. We make researches on these questions based on samples of ER random network, NW small-world network and BA scale-free network, and the results confirm that, both the number of loops in network and the average loop degree of nodes of all samples do increase with the increase of the PFE in general trend, but neither of them are strictly monotonically increasing, so the PFE is capable to be used as a rough estimative measurement of the number of loops in networks and the average loop degree of nodes. Furthermore, we find that a majority of the loop ranks of all samples obey Weibull distribution, of which the scale parameter A and the shape parameter B have approximate power-law relationships with the PFE of the samples.

We build a complex networks model of combat System-of-Systems (SoS) based on empirical data from a real war-game, this model is a combination of command & control (C2) subnetwork, sensors subnetwork, influencers subnetwork and logistical support subnetwork, each subnetwork has idiographic components and statistical characteristics. The C2 subnetwork is the core of whole combat SoS, it has a hierarchical structure with no modularity, of which robustness is strong enough to maintain normal operation after any two nodes is destroyed; the sensors subnetwork and influencers subnetwork are like sense organ and limbs of whole combat SoS, they are both flat modular networks of which degree distribution obey GEV distribution and power-law distribution respectively. The communication network is the combination of all subnetworks, it is an assortative Small-World network with core–periphery structure, the Intelligence & Communication Stations/Command Center integrated with C2 nodes in the first three level act as the hub nodes in communication network, and all the fourth-level C2 nodes, sensors, influencers and logistical support nodes have communication capability, they act as the periphery nodes in communication network, its degree distribution obeys exponential distribution in the beginning, Gaussian distribution in the middle, and power-law distribution in the end, and its path length obeys GEV distribution. The betweenness centrality distribution, closeness centrality distribution and eigenvector centrality are also been analyzed to measure the vulnerability of nodes.

The weapon-target assignment (WTA) problem, known as an NP-complete problem, aims at seeking a proper assignment of weapons to targets. The biobjective WTA (BOWTA) optimization model which maximizes the expected damage of the enemy and minimizes the cost of missiles is designed in this paper. A modified Pareto ant colony optimization (MPACO) algorithm is used to solve the BOWTA problem. In order to avoid defects in traditional optimization algorithms and obtain a set of Pareto solutions efficiently, MPACO algorithm based on new designed operators is proposed, including a dynamic heuristic information calculation approach, an improved movement probability rule, a dynamic evaporation rate strategy, a global updating rule of pheromone, and a boundary symmetric mutation strategy. In order to simulate real air combat, the pilot operation factor is introduced into the BOWTA model. Finally, we apply the MPACO algorithm and other algorithms to the model and compare the data. Simulation results show that the proposed algorithm is successfully applied in the field of WTA which improves the performance of the traditional P-ACO algorithm effectively and produces better solutions than the two well-known multiobjective optimization algorithms NSGA-II and SPEA-II.

Distributed UCAV combat plays a much more important role in the future war. However, it contains many different combat units which may increase the complexity when executing the combat management. This paper addresses the problem of simplifying and re-building the structure of the distributed air combat, the traditional platform-combat mode is expanded to distributed-node-combat platform. Then we propose a modified GPGP(Generalized) method to solve the task coordination problem under air-to-air networked (ANA) mode, the extended contract net is put forward to resolute the conflict when the partial order relationship between different tasks are taken into account. the simulation results show that the proposed method is efficient in to complete the combat pre-planning.