Weapon target assignment(WTA)problem is a critical problem in multiplatform confrontation.This paper studies a static WTA problem with heterogeneous weapons in multi-platform air combat scenarios,called heterogeneous ...Weapon target assignment(WTA)problem is a critical problem in multiplatform confrontation.This paper studies a static WTA problem with heterogeneous weapons in multi-platform air combat scenarios,called heterogeneous WTA(HWTA)problem.Heterogeneous indicates that the engagement platforms carry multiple kinds of weapons for different tactical purposes.The targets assigned and the weapons used by one side’s platforms will affect the survival probability and capability of the other side’s platforms.The goal of each side in HWTA is to find a solution to determine the kind of weapon used and the target assigned for each platform,so as to maximize their combat effectiveness.The problem is formulated as a two-player noncooperative game model with considering the conflicts between the engaged sides.The Nash equilibrium is an effective solution to the game in which no player has an incentive to deviate.However,the number of pure strategies in HWTA increases exponentially with the engagement platforms.To improve computing efficiency,a double oracle algorithm with constructive heuristic(DOCH)is developed,within which the constructive heuristic is embedded to solve the oracle subproblems efficiently.Numerical experiments are conducted to verify the effectiveness of the DOCH.The results show that the DOCH can find effective strategies for platforms to improve combat effectiveness.Moreover,the DOCH can find high-quality solutions in seconds,significantly outperforming the state-of-the-art algorithms in terms of computational efficiency,especially for large-scale problems.展开更多
Efficient multiple unmanned aerial vehicles(UAVs)path planning is crucial for improving mission completion efficiency in UAV operations.However,during the actual flight of UAVs,the flight time between nodes is always ...Efficient multiple unmanned aerial vehicles(UAVs)path planning is crucial for improving mission completion efficiency in UAV operations.However,during the actual flight of UAVs,the flight time between nodes is always influenced by external factors,making the original path planning solution ineffective.In this paper,the multi-depot multi-UAV path planning problem with uncertain flight time is modeled as a robust optimization model with a budget uncertainty set.Then,the robust optimization model is transformed into a mixed integer linear programming model by the strong duality theorem,which makes the problem easy to solve.To effectively solve large-scale instances,a simulated annealing algorithm with a robust feasibility check(SA-RFC)is developed.The numerical experiment shows that the SA-RFC can find high-quality solutions within a few seconds.Moreover,the effect of the task location distribution,depot counts,and variations in robustness parameters on the robust optimization solution is analyzed by using Monte Carlo experiments.The results demonstrate that the proposed robust model can effectively reduce the risk of the UAV failing to return to the depot without significantly compromising the profit.展开更多
Air-to-air combat tactical decisions for multiple unmanned aerial vehicles(ACTDMU)are a key decision-making step in beyond visual range combat.Complex influencing factors,strong antagonism and real-time requirements n...Air-to-air combat tactical decisions for multiple unmanned aerial vehicles(ACTDMU)are a key decision-making step in beyond visual range combat.Complex influencing factors,strong antagonism and real-time requirements need to be considered in the ACTDMU problem.In this paper,we propose a multicriteria game approach to ACTDMU.This approach consists of a multicriteria game model and a Pareto Nash equilibrium algorithm.In this model,we form the strategy profiles for the integration of air-to-air combat tactics and weapon target assignment strategies by considering the correlation between them,and we design the vector payoff functions based on predominance factors.We propose a algorithm of Pareto Nash equilibrium based on preference relations using threshold constraints(PNE-PRTC),and we prove that the solutions obtained by this algorithm are refinements of Pareto Nash equilibrium solutions.The numerical experiments indicate that PNE-PRTC algorithm is considerably faster than the baseline algorithms and the performance is better.Especially on large-scale instances,the Pareto Nash equilibrium solutions can be calculated by PNEPRTC algorithm at the second level.The simulation experiments show that the multicriteria game approach is more effective than one-side decision approaches such as multiple-attribute decision-making and randomly chosen decisions.展开更多
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 l...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.展开更多
基金supported by the National Natural Science Foundation of China(72571094,71871079,72271076,72001004)Anhui Provincial Natural Science Foundation(2308085QG233)+1 种基金Anhui Province Postdoctoral Research Activities Funds(2022B587)Talent Research Fund of Hefei University(24RC75).
文摘Weapon target assignment(WTA)problem is a critical problem in multiplatform confrontation.This paper studies a static WTA problem with heterogeneous weapons in multi-platform air combat scenarios,called heterogeneous WTA(HWTA)problem.Heterogeneous indicates that the engagement platforms carry multiple kinds of weapons for different tactical purposes.The targets assigned and the weapons used by one side’s platforms will affect the survival probability and capability of the other side’s platforms.The goal of each side in HWTA is to find a solution to determine the kind of weapon used and the target assigned for each platform,so as to maximize their combat effectiveness.The problem is formulated as a two-player noncooperative game model with considering the conflicts between the engaged sides.The Nash equilibrium is an effective solution to the game in which no player has an incentive to deviate.However,the number of pure strategies in HWTA increases exponentially with the engagement platforms.To improve computing efficiency,a double oracle algorithm with constructive heuristic(DOCH)is developed,within which the constructive heuristic is embedded to solve the oracle subproblems efficiently.Numerical experiments are conducted to verify the effectiveness of the DOCH.The results show that the DOCH can find effective strategies for platforms to improve combat effectiveness.Moreover,the DOCH can find high-quality solutions in seconds,significantly outperforming the state-of-the-art algorithms in terms of computational efficiency,especially for large-scale problems.
基金supported by the National Natural Science Foundation of China(72571094,72271076,71871079)。
文摘Efficient multiple unmanned aerial vehicles(UAVs)path planning is crucial for improving mission completion efficiency in UAV operations.However,during the actual flight of UAVs,the flight time between nodes is always influenced by external factors,making the original path planning solution ineffective.In this paper,the multi-depot multi-UAV path planning problem with uncertain flight time is modeled as a robust optimization model with a budget uncertainty set.Then,the robust optimization model is transformed into a mixed integer linear programming model by the strong duality theorem,which makes the problem easy to solve.To effectively solve large-scale instances,a simulated annealing algorithm with a robust feasibility check(SA-RFC)is developed.The numerical experiment shows that the SA-RFC can find high-quality solutions within a few seconds.Moreover,the effect of the task location distribution,depot counts,and variations in robustness parameters on the robust optimization solution is analyzed by using Monte Carlo experiments.The results demonstrate that the proposed robust model can effectively reduce the risk of the UAV failing to return to the depot without significantly compromising the profit.
基金the National Natural Science Foundation of China(71971075,71871079,71671059)the Anhui Provincial Natural Science Foundation(1808085MG213).
文摘Air-to-air combat tactical decisions for multiple unmanned aerial vehicles(ACTDMU)are a key decision-making step in beyond visual range combat.Complex influencing factors,strong antagonism and real-time requirements need to be considered in the ACTDMU problem.In this paper,we propose a multicriteria game approach to ACTDMU.This approach consists of a multicriteria game model and a Pareto Nash equilibrium algorithm.In this model,we form the strategy profiles for the integration of air-to-air combat tactics and weapon target assignment strategies by considering the correlation between them,and we design the vector payoff functions based on predominance factors.We propose a algorithm of Pareto Nash equilibrium based on preference relations using threshold constraints(PNE-PRTC),and we prove that the solutions obtained by this algorithm are refinements of Pareto Nash equilibrium solutions.The numerical experiments indicate that PNE-PRTC algorithm is considerably faster than the baseline algorithms and the performance is better.Especially on large-scale instances,the Pareto Nash equilibrium solutions can be calculated by PNEPRTC algorithm at the second level.The simulation experiments show that the multicriteria game approach is more effective than one-side decision approaches such as multiple-attribute decision-making and randomly chosen decisions.
基金supported by the National Natural Science Foundation of China (71971075,71871079)the National Key Research and Development Program of China (2019YFE0110300)+1 种基金the Anhui Provincial Natural Science Foundation (1808085MG213)the Fundamental R esearch Funds for the Central Universities (PA2019GDPK0082)。
文摘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.
