Numerous works prove that existing neighbor-averaging graph neural networks (GNNs) cannot efficiently catch structure features, and many works show that injecting structure, distance, position, or spatial features can significantly improve the performance of GNNs, however, injecting high-level structure and distance into GNNs is an intuitive but untouched idea. This work sheds light on this issue and proposes a scheme to enhance graph attention networks (GATs) by encoding distance and hop-wise structure statistics. Firstly, the hop-wise structure and distributional distance information are extracted based on several hop-wise ego-nets of every target node. Secondly, the derived structure information, distance information, and intrinsic features are encoded into the same vector space and then added together to get initial embedding vectors. Thirdly, the derived embedding vectors are fed into GATs, such as GAT and adaptive graph diffusion network (AGDN) to get the soft labels. Fourthly, the soft labels are fed into correct and smooth (C&S) to conduct label propagation and get final predictions. Experiments show that the distance and hop-wise structures encoding enhanced graph attention networks (DHSEGATs) achieve a competitive result.
The unmanned aerial vehicle (UAV) swarm technology is one of the research hotspots in recent years. With the continuous improvement of autonomous intelligence of UAV, the swarm technology of UAV will become one of the main trends of UAV development in the future. This paper studies the behavior decision-making process of UAV swarm rendezvous task based on the double deep Q network (DDQN) algorithm. We design a guided reward function to effectively solve the problem of algorithm convergence caused by the sparse return problem in deep reinforcement learning (DRL) for the long period task. We also propose the concept of temporary storage area, optimizing the memory playback unit of the traditional DDQN algorithm, improving the convergence speed of the algorithm, and speeding up the training process of the algorithm. Different from traditional task environment, this paper establishes a continuous state-space task environment model to improve the authentication process of UAV task environment. Based on the DDQN algorithm, the collaborative tasks of UAV swarm in different task scenarios are trained. The experimental results validate that the DDQN algorithm is efficient in terms of training UAV swarm to complete the given collaborative tasks while meeting the requirements of UAV swarm for centralization and autonomy, and improving the intelligence of UAV swarm collaborative task execution. The simulation results show that after training, the proposed UAV swarm can carry out the rendezvous task well, and the success rate of the mission reaches 90%.
The anti-aircraft system plays an irreplaceable role in modern combat. An anti-aircraft system consists of various types of functional entities interacting to destroy the hostile aircraft moving in high speed. The connecting structure of combat entities in it is of great importance for supporting the normal process of the system. In this paper, we explore the optimizing strategy of the structure of the anti-aircraft network by establishing extra communication channels between the combat entities. Firstly, the thought of combat network model (CNM) is borrowed to model the anti-aircraft system as a heterogeneous network. Secondly, the optimization objectives are determined as the survivability and the accuracy of the system. To specify these objectives, the information chain and accuracy chain are constructed based on CNM. The causal strength (CAST) logic and influence network (IN) are introduced to illustrate the establishment of the accuracy chain. Thirdly, the optimization constraints are discussed and set in three aspects: time, connection feasibility and budget. The time constraint network (TCN) is introduced to construct the timing chain and help to detect the timing consistency. Then, the process of the multi-objective optimization of the structure of the anti-aircraft system is designed. Finally, a simulation is conducted to prove the effectiveness and feasibility of the proposed method. Non-dominated sorting based genetic algorithm-II (NSGA2) is used to solve the multi-objective optimization problem and two other algorithms including non-dominated sorting based genetic algorithm-III (NSGA3) and strength Pareto evolutionary algorithm-II (SPEA2) are employed as comparisons. The deciders and system builders can make the anti-aircraft system improved in the survivability and accuracy in the combat reality.
During extended warranty (EW) period, maintenance events play a key role in controlling the product systems within normal operations. However, the modelling of failure process and maintenance optimization is complicated owing to the complex features of the product system, namely, components of the multi-component system are interdependent with each other in some form. For the purpose of optimizing the EW pricing decision of the multi-component system scientifically and rationally, taking the series multi-component system with economic dependence sold with EW policy as a research object, this paper optimizes the imperfect preventive maintenance (PM) strategy from the standpoint of EW cost. Taking into consideration adjusting the PM moments of the components in the system, a group maintenance model is developed, in which the system is repaired preventively in accordance with a specified PM base interval. In order to compare with the system EW cost before group maintenance, the system EW cost model before group maintenance is developed. Numerical example demonstrates that offering group maintenance programs can reduce EW cost of the system to a great extent, thereby reducing the EW price, which proves to be a win-win strategy to manufacturers and users.
When the attributes of unknown targets are not just numerical attributes, but hybrid attributes containing linguistic attributes, the existing recognition methods are not effective. In addition, it is more difficult to identify the unknown targets densely distributed in the feature space, especially when there is interval overlap between attribute measurements of different target classes. To address these problems, a novel method based on intuitionistic fuzzy comprehensive evaluation model (IFCEM) is proposed. For numerical attributes, targets in the database are divided into individual classes and overlapping classes, and for linguistic attributes, continuous interval-valued linguistic term set (CIVLTS) is used to describe target characteristic. A cloud model-based method and an area-based method are proposed to obtain intuitionistic fuzzy decision information of query target on numerical attributes and linguistic attributes respectively. An improved inverse weighted kernel fuzzy c-means (IWK-FCM) algorithm is proposed for solution of attribute weight vector. The possibility matrix is applied to determine the identity and category of query target. Finally, a case study composed of parameter sensitivity analysis, recognition accuracy analysis. and comparison with other methods, is taken to verify the superiority of the proposed method.
As a generalization of fuzzy set, hesitant probabilistic fuzzy set and pythagorean triangular fuzzy set have their own unique advantages in describing decision information. As modern socioeconomic decision-making problems are becoming more and more complex, it also becomes more and more difficult to appropriately depict decision makers’ cognitive information in decision-making process. In order to describe the decision information more comprehensively, we define a pythagorean probabilistic hesitant triangular fuzzy set (PPHTFS) by combining the pythagorean triangular fuzzy set and the probabilistic hesitant fuzzy set. Firstly, the basic operation and scoring function of the pythagorean probabilistic hesitant triangular fuzzy element (PPHTFE) are proposed, and the comparison rule of two PPHTFEs is given. Then, some pythagorean probabilistic hesitant triangular fuzzy aggregation operators are developed, and their properties are also studied. Finally, a multi-attribute decision-making (MADM) model is constructed based on the proposed operators under the pythagorean probabilistic hesitant triangular fuzzy information, and an illustration example is given to demonstrate the practicability and validity of the proposed decision-making method.
Unmanned air vehicles (UAVs) have been regularly employed in modern wars to conduct different missions. Instead of addressing mission planning and route planning separately, this study investigates the issue of joint mission and route planning for a fleet of UAVs. The mission planning determines the configuration of weapons in UAVs and the weapons to attack targets, while the route planning determines the UAV’s visiting sequence for the targets. The problem is formulated as an integer linear programming model. Due to the inefficiency of CPLEX on large scale optimization problems, an effective learning-based heuristic, namely, population based adaptive large neighborhood search (P-ALNS), is proposed to solve the model. In P-ALNS, seven neighborhood structures are designed and adaptively utilized in terms of their historical performance. The effectiveness and superiority of the proposed model and algorithm are demonstrated on test instances of small, medium and large sizes. In particular, P-ALNS achieves comparable solutions or as good as those of CPLEX on small-size (20 targets) instances in much shorter time.
To strengthen border patrol measures, unmanned aerial vehicles (UAVs) are gradually used in many countries to detect illegal entries on borders. However, how to efficiently deploy limited UAVs to patrol on borders of large areas remains challenging. In this paper, we first model the problem of deploying UAVs for border patrol as a Stackelberg game. Two players are considered in this game: The border patrol agency is the leader, who optimizes the patrol path of UAVs to detect the illegal immigrant. The illegal immigrant is the follower, who selects a certain area of the border to pass through at a certain time after observing the leader’s strategy. Second, a compact linear programming problem is proposed to tackle the exponential growth of the number of leader’s strategies. Third, a method is proposed to reduce the size of the strategy space of the follower. Then, we provide some theoretic results to present the effect of parameters of the model on leader’s utilities. Experimental results demonstrate the positive effect of limited starting and ending areas of UAV’s patrolling conditions and multiple patrolling altitudes on the leader ’s utility, and show that the proposed solution outperforms two conventional patrol strategies and has strong robustness.
In this paper, a reinforcement learning-based multi-battery energy storage system (MBESS) scheduling policy is proposed to minimize the consumers ’ electricity cost. The MBESS scheduling problem is modeled as a Markov decision process (MDP) with unknown transition probability. However, the optimal value function is time-dependent and difficult to obtain because of the periodicity of the electricity price and residential load. Therefore, a series of time-independent action-value functions are proposed to describe every period of a day. To approximate every action-value function, a corresponding critic network is established, which is cascaded with other critic networks according to the time sequence. Then, the continuous management strategy is obtained from the related action network. Moreover, a two-stage learning protocol including offline and online learning stages is provided for detailed implementation in real-time battery management. Numerical experimental examples are given to demonstrate the effectiveness of the developed algorithm.
The distributed hybrid processing optimization problem of non-cooperative targets is an important research direction for future networked air-defense and anti-missile firepower systems. In this paper, the air-defense anti-missile targets defense problem is abstracted as a nonconvex constrained combinatorial optimization problem with the optimization objective of maximizing the degree of contribution of the processing scheme to non-cooperative targets, and the constraints mainly consider geographical conditions and anti-missile equipment resources. The grid discretization concept is used to partition the defense area into network nodes, and the overall defense strategy scheme is described as a nonlinear programming problem to solve the minimum defense cost within the maximum defense capability of the defense system network. In the solution of the minimum defense cost problem, the processing scheme, equipment coverage capability, constraints and node cost requirements are characterized, then a nonlinear mathematical model of the non-cooperative target distributed hybrid processing optimization problem is established, and a local optimal solution based on the sequential quadratic programming algorithm is constructed, and the optimal firepower processing scheme is given by using the sequential quadratic programming method containing non-convex quadratic equations and inequality constraints. Finally, the effectiveness of the proposed method is verified by simulation examples.
The occurrence of social security events is uncertain, and the distribution characteristics are highly complex due to a variety of external factors, posing challenges to their rapid and effective handling. The scientific and reasonable requirement evaluation of the emergency force to deal with social security events is very urgent. Based on data analysis, this paper uses the neural network, operational research, modelling and simulation to predict and analyze social security events, studies the usage rule of emergency force and deployment algorithm, and conducts simulation experiments to evaluate and compare the different force deployment schemes for selection.
The source location based on the hybrid time difference of arrival (TDOA)/frequency difference of arrival (FDOA) is a basic problem in wireless sensor networks, and the layout of sensors in the hybrid TDOA/FDOA positioning will greatly affect the accuracy of positioning. Using unmanned aerial vehicle (UAV) as base stations, by optimizing the trajectory of the UAV swarm, an optimal positioning configuration is formed to improve the accuracy of the target position and velocity estimation. In this paper, a hybrid TDOA/FDOA positioning model is first established, and the positioning accuracy of the hybrid TDOA/FDOA under different positioning configurations and different measurement errors is simulated by the geometric dilution of precision (GDOP) factor. Second, the Cramer-Rao lower bound (CRLB) matrix of hybrid TDOA/FDOA location under different moving states of the target is derived theoretically, the objective function of the track optimization is obtained, and the track of the UAV swarm is optimized in real time. The simulation results show that the track optimization effectively improves the accuracy of the target position and velocity estimation.
Equipment development planning (EDP) is usually a long-term process often performed in an environment with high uncertainty. The traditional multi-stage dynamic programming cannot cope with this kind of uncertainty with unpredictable situations. To deal with this problem, a multi-stage EDP model based on a deep reinforcement learning (DRL) algorithm is proposed to respond quickly to any environmental changes within a reasonable range. Firstly, the basic problem of multi-stage EDP is described, and a mathematical planning model is constructed. Then, for two kinds of uncertainties (future capability requirements and the amount of investment in each stage), a corresponding DRL framework is designed to define the environment, state, action, and reward function for multi-stage EDP. After that, the dueling deep Q-network (Dueling DQN) algorithm is used to solve the multi-stage EDP to generate an approximately optimal multi-stage equipment development scheme. Finally, a case of ten kinds of equipment in 100 possible environments, which are randomly generated, is used to test the feasibility and effectiveness of the proposed models. The results show that the algorithm can respond instantaneously in any state of the multi-stage EDP environment and unlike traditional algorithms, the algorithm does not need to re-optimize the problem for any change in the environment. In addition, the algorithm can flexibly adjust at subsequent planning stages in the event of a change to the equipment capability requirements to adapt to the new requirements.
How to make use of limited onboard resources for complex and heavy space tasks has attracted much attention. With the continuous improvement on satellite payload capacity and the increasing complexity of observation requirements, the importance of satellite autonomous task scheduling research has gradually increased. This article first gives the problem description and mathematical model for the satellite autonomous task scheduling and then follows the steps of “satellite autonomous task scheduling, centralized autonomous collaborative task scheduling architecture, distributed autonomous collaborative task scheduling architecture, solution algorithm". Finally, facing the complex and changeable environment situation, this article proposes the future direction of satellite autonomous task scheduling.
Reconnaissance mission planning of multiple unmanned aerial vehicles (UAVs) under an adversarial environment is a discrete combinatorial optimization problem which is proved to be a non-deterministic polynomial (NP)-complete problem. The purpose of this study is to research intelligent multi-UAVs reconnaissance mission planning and online re-planning algorithm under various constraints in mission areas. For numerous targets scattered in the wide area, a reconnaissance mission planning and re-planning system is established, which includes five modules, including intelligence analysis, sub-mission area division, mission sequence planning, path smoothing, and online re-planning. The intelligence analysis module depicts the attribute of targets and the heterogeneous characteristic of UAVs and computes the number of sub-mission areas on consideration of voyage distance constraints. In the sub-mission area division module, an improved K-means clustering algorithm is designed to divide the reconnaissance mission area into several sub-mission areas, and each sub-mission is detected by the UAV loaded with various detective sensors. To control reconnaissance cost, the sampling and iteration algorithms are proposed in the mission sequence planning module, which are utilized to solve the optimal or approximately optimal reconnaissance sequence. In the path smoothing module, the Dubins curve is applied to smooth the flight path, which assure the availability of the planned path. Furthermore, an online re-planning algorithm is designed for the uncertain factor that the UAV is damaged. Finally, reconnaissance planning and re-planning experiment results show that the algorithm proposed in this paper are effective and the algorithms designed for sequence planning have a great advantage in solving efficiency and optimality.
Multi-carrier faster-than-Nyquist (MFTN) can improve the spectrum efficiency (SE). In this paper, we first analyze the benefit of time frequency packing MFTN (TFP-MFTN). Then, we propose an efficient digital implementation for TFP-MFTN based on filter bank multicarrier modulation. The time frequency packing ratio pair in our proposed implementation scheme is optimized with the SE criterion. Next, the joint optimization for the coded modulation MFTN based on extrinsic information transfer (EXIT) chart is performed. The Monte-Carlo simulations are carried out to verify performance gain of the joint inner and outer code optimization. Simulation results demonstrate that the TFP-MFTN has a 0.8 dB and 0.9 dB gain comparing to time packing MFTN (TP-MFTN) and higher order Nyquist at same SE, respectively; the TFP-MFTN with optimized low density parity check (LDPC) code has a 2.9 dB gain comparing to that with digital video broadcasting (DVB) LDPC. Compared with previous work on TFP-MFTN (SE=1.55 bit/s/Hz), the SE of our work is improved by 29% and our work has a 4.1 dB gain at BER=1×10?5.
To cope with multi-directional transmission coupling, spreading, amplification, and chain reaction of risks during multi-project parallel construction of warships, a risk transmission evaluation method is proposed, which integrates an intuitionistic cloud model with a fuzzy cognitive map. By virtue of expectancy $ {\rm{Ex}} $ , entropy ${\rm{En}}$ , and hyper entropy ${\rm{He}}$ , the risk fuzziness and randomness of the knowledge of experts are organically combined to develop a method for converting bi-linguistic variable decision-making information into the quantitative information of the intuitionistic normal cloud (INC) model. Subsequently, the threshold function and weighted summation operation in the traditional fuzzy cognitive map is converted into the INC ordered weighted averaging operator to create the risk transmission model based on the intuitionistic fuzzy cognitive map (IFCM) and the algorithm for solving it. Subsequently, the risk influence sequencing method based on INC and the risk rating method based on nearness are proposed on the basis of Monte Carlo simulation in order to realize the mutual conversion of the qualitative and quantitative information in the risk evaluation results. Example analysis is presented to verify the effectiveness and practicality of the methods.
The spoofing capability of Global Navigation Satellite System (GNSS) represents an important confrontational capability for navigation security, and the success of planned missions may depend on the effective evaluation of spoofing capability. However, current evaluation systems face challenges arising from the irrationality of previous weighting methods, inapplicability of the conventional multi-attribute decision-making method and uncertainty existing in evaluation. To solve these difficulties, considering the validity of the obtained results, an evaluation method based on the game aggregated weight model and a joint approach involving the grey relational analysis and technique for order preference by similarity to an ideal solution (GRA-TOPSIS) are firstly proposed to determine the optimal scheme. Static and dynamic evaluation results under different schemes are then obtained via a fuzzy comprehensive assessment and an improved dynamic game method, to prioritize the deceptive efficacy of the equipment accurately and make pointed improvement for its core performance. The use of judging indicators, including Spearman rank correlation coefficient and so on, combined with obtained evaluation results, demonstrates the superiority of the proposed method and the optimal scheme by the horizontal comparison of different methods and vertical comparison of evaluation results. Finally, the results of field measurements and simulation tests show that the proposed method can better overcome the difficulties of existing methods and realize the effective evaluation.
The status of an operator’s situation awareness is one of the critical factors that influence the quality of the missions. Thus the measurement method of the situation awareness status is an important topic to research. So far, there are lots of methods designed for the measurement of situation awareness status, but there is no model that can measure it accurately in real-time, so this work is conducted to deal with such a gap. Firstly, collect the relevant physiological data of operators while they are performing a specific mission, simultaneously, measure their status of situation awareness by using the situation awareness global assessment technique (SAGAT), which is known for accuracy but cannot be used in real-time. And then, after the preprocessing of the raw data, use the physiological data as features, the SAGAT’s results as a label to train a fuzzy cognitive map (FCM), which is an explainable and powerful intelligent model. Also, a hybrid learning algorithm of particle swarm optimization (PSO) and gradient descent is proposed for the FCM training. The final results show that the learned FCM can assess the status of situation awareness accurately in real-time, and the proposed hybrid learning algorithm has better efficiency and accuracy.
The use of artificial intelligence (AI) has increased since the middle of the 20th century, as evidenced by its applications to a wide range of engineering and science problems. Air traffic management (ATM) is becoming increasingly automated and autonomous, making it lucrative for AI applications. This paper presents a systematic review of studies that employ AI techniques for improving ATM capability. A brief account of the history, structure, and advantages of these methods is provided, followed by the description of their applications to several representative ATM tasks, such as air traffic services (ATS), airspace management (AM), air traffic flow management (ATFM), and flight operations (FO). The major contribution of the current review is the professional survey of the AI application to ATM alongside with the description of their specific advantages: (i) these methods provide alternative approaches to conventional physical modeling techniques, (ii) these methods do not require knowing relevant internal system parameters, (iii) these methods are computationally more efficient, and (iv) these methods offer compact solutions to multivariable problems. In addition, this review offers a fresh outlook on future research. One is providing a clear rationale for the model type and structure selection for a given ATM mission. Another is to understand what makes a specific architecture or algorithm effective for a given ATM mission. These are among the most important issues that will continue to attract the attention of the AI research community and ATM work teams in the future.
The accuracy of target threat estimation has a great impact on command decision-making. The Bayesian network, as an effective way to deal with the problem of uncertainty, can be used to track the change of the target threat level. Unfortunately, the traditional discrete dynamic Bayesian network (DDBN) has the problems of poor parameter learning and poor reasoning accuracy in a small sample environment with partial prior information missing. Considering the finiteness and discreteness of DDBN parameters, a fuzzy k-nearest neighbor (KNN) algorithm based on correlation of feature quantities (CF-FKNN) is proposed for DDBN parameter learning. Firstly, the correlation between feature quantities is calculated, and then the KNN algorithm with fuzzy weight is introduced to fill the missing data. On this basis, a reasonable DDBN structure is constructed by using expert experience to complete DDBN parameter learning and reasoning. Simulation results show that the CF-FKNN algorithm can accurately fill in the data when the samples are seriously missing, and improve the effect of DDBN parameter learning in the case of serious sample missing. With the proposed method, the final target threat assessment results are reasonable, which meets the needs of engineering applications.
An economic dispatch problem for power system with wind power is discussed. Using discrete scenario to describe uncertain wind powers, a threshold is given to identify bad scenario set. The bad-scenario-set robust economic dispatch model is established to minimize the total penalties on bad scenarios. A specialized hybrid particle swarm optimization (PSO) algorithm is developed through hybridizing simulated annealing (SA) operators. The SA operators are performed according to a scenario-oriented adaptive search rule in a neighborhood which is constructed based on the unit commitment constraints. Finally, an experiment is conducted. The computational results show that the developed algorithm outperforms the existing algorithms.
In order to solve the current situation that unmanned aerial vehicles (UAVs) ignore safety indicators and cannot guarantee safe operation when operating in low-altitude airspace, a UAV route planning method that considers regional risk assessment is proposed. Firstly, the low-altitude airspace is discretized based on rasterization, and then the UAV operating characteristics and environmental characteristics are combined to quantify the risk value in the low-altitude airspace to obtain a 3D risk map. The path risk value is taken as the cost, the particle swarm optimization-beetle antennae search (PSO-BAS) algorithm is used to plan the spatial 3D route, and it effectively reduces the generated path redundancy. Finally, cubic B-spline curve is used to smooth the planned discrete path. A flyable path with continuous curvature and pitch angle is generated. The simulation results show that the generated path can exchange for a path with a lower risk value at a lower path cost. At the same time, the path redundancy is low, and the curvature and pitch angle continuously change. It is a flyable path that meets the UAV performance constraints.
To address the issue of rule premise combination explosion in the construction of the traditional complete conjunctive belief rule base (BRB), this paper introduces an orthogonal design method to reduce the conjunctive BRB. The reasoning method based on reduced conjunctive BRB is designed with the help of the conversion technology from conjunctive BRB to disjunctive BRB. Finally, the operational mission effectiveness evaluation is taken as an example to verify the proposed method. The results show that the method proposed in this paper is feasible and effective.
In recent years, high-altitude aerostats have been increasingly developed in the direction of multi-functionality and large size. Due to the large size and the high flexibility, new challenges for large aerostats have appeared in the configuration test and the deformation analysis. The methods of the configuration test and the deformation analysis for large airship have been researched and discussed. A tested method of the configuration, named internal scanning, is established to quickly obtain the spatial information of all surfaces for the large airship by the three-dimensional (3D) laser scanning technology. By using the surface wrap method, the configuration parameters of the large airship are calculated. According to the test data of the configuration, the structural dimensions such as the distances between the characteristic sections are measured. The method of the deformation analysis for the airship contains the algorithm of non-uniform rational B-splines (NURBS) and the finite element (FE) method. The algorithm of NURBS is used to obtain the reconfiguration model of the large airship. The seams are considered and the seam areas are divided. The FE model of the middle part of the large airship is established. The distributions of the stress and the strain for the large airship are obtained by the FE method. The position of the larger deformation for the airship is found.
The multilayer satellite network has high spatial spectrum utilization, flexible networking, strong survivability, and diversified functions. The inter-satellite links (ISLs) and cross-layer ISLs (CLISLs) enable direct communication paths between satellites, which improves the spatial autonomy of the constellation. Due to the existence of perturbation, ISLs are affected for a long time, which impacts reliable inter-satellite transmission. The stability and complexity of ISL establishment are related to the static and dynamic characteristics of range and azimuth. This paper presents a model of ISLs in a perturbed multilayer constellation. Series of theoretical derivation, simulation, and numerical calculation are carried out. A more comprehensive multilayer constellation ISL model is obtained. The work of this paper provides some theoretical foundations for constellation networking research.
In order to improve our military’s level of intelligent accusation decision-making in future intelligent joint warfare, this paper studies operation loop recommendation methods for kill web based on the fundamental combat form of the future, i.e., “web-based kill,” and the operation loop theory. Firstly, we pioneer the operation loop recommendation problem with operation ring quality as the objective and closed-loop time as the constraint, and construct the corresponding planning model. Secondly, considering the case where there are multiple decision objectives for the combat ring recommendation problem, we propose for the first time a multi-objective optimization algorithm, the multi-objective ant colony evolutionary algorithm based on decomposition (MOACEA/D), which integrates the multi-objective evolutionary algorithm based on decomposition (MOEA/D) with the ant colony algorithm. The MOACEA/D can converge the optimal solutions of multiple single objectives non-dominated solution set for the multi-objective problem. Finally, compared with other classical multi-objective optimization algorithms, the MOACEA/D is superior to other algorithms superior in terms of the hyper volume (HV), which verifies the effectiveness of the method and greatly improves the quality and efficiency of commanders’ decision-making.
The threat sequencing of multiple unmanned combat air vehicles (UCAVs) is a multi-attribute decision-making (MADM) problem. In the threat sequencing process of multiple UCAVs, due to the strong confrontation and high dynamics of the air combat environment, the weight coefficients of the threat indicators are usually time-varying. Moreover, the air combat data is difficult to be obtained accurately. In this study, a threat sequencing method of multiple UCAVs is proposed based on game theory by considering the incomplete information. Firstly, a zero-sum game model of decision maker ( $\mathcal{D}$ ) and nature ( $\mathcal{N}$ ) with fuzzy payoffs is established to obtain the uncertain parameters which are the weight coefficient parameters of the threat indicators and the interval parameters of the threat matrix. Then, the established zero-sum game with fuzzy payoffs is transformed into a zero-sum game with crisp payoffs (matrix game) to solve. Moreover, a decision rule is addressed for the threat sequencing problem of multiple UCAVs based on the obtained uncertain parameters. Finally, numerical simulation results are presented to show the effectiveness of the proposed approach.
This paper addresses the open vehicle routing problem with time window (OVRPTW), where each vehicle does not need to return to the depot after completing the delivery task. The optimization objective is to minimize the total distance. This problem exists widely in real-life logistics distribution process. We propose a hybrid column generation algorithm (HCGA) for the OVRPTW, embedding both exact algorithm and metaheuristic. In HCGA, a label setting algorithm and an intelligent algorithm are designed to select columns from small and large subproblems, respectively. Moreover, a branch strategy is devised to generate the final feasible solution for the OVRPTW. The computational results show that the proposed algorithm has faster speed and can obtain the approximate optimal solution of the problem with 100 customers in a reasonable time.
Anti-ship missile coordinated attack mission planning is a complex multi-objective optimization problem with multiple combinations of platforms, strong decision-making constraints, and tightly coupled links. To avoid the coupling disorder between path planning and firepower distribution and improve the efficiency of coordinated attack mission planning, a firepower distribution model under the conditions of path planning is established from the perspective of decoupling optimization and the algorithm is implemented. First, we establish reference coordinate system of firepower distribution to clarify the reference direction of firepower distribution and divide the area of firepower distribution; then, we construct an index table of membership of firepower distribution to obtain alternative firepower distribution plans; finally, the fitness function of firepower distribution is established based on damage income, missile loss, ratio of efficiency and cost of firepower distribution, and the mean square deviation of the number of missiles used, and the alternatives are sorted to obtain the optimal firepower distribution plan. According to two simulation experiments, the method in this paper can effectively solve the many-to-many firepower distribution problem of coupled path planning. Under the premise of ensuring that no path crossing occurs, the optimal global solution can be obtained, and the operability and timeliness are good.
