We study the weapon-target assignment WTA problem which has wide applications in the area of defense-related operations research. This problem calls for finding a proper assignment of weapons to targets such that the total expected damaged value of the targets to be maximized. The WTA problem can be formulated as a nonlinear integer programming problem which is known to be NP-complete. There does not exist any exact method for the WTA problem even small size problems, although several heuristic methods have been proposed. In this paper, Lagrange relaxation method is proposed for the WTA problem. The method is an iterative approach which is to decompose the Lagrange relaxation into two subproblems, and each subproblem can be easy to solve to optimality based on its specific features. Then, we use the optimal solutions of the two subproblems to update Lagrange multipliers and solve the Lagrange relaxation problem iteratively. Our computational efforts signify that the proposed method is very effective and can find high quality solutions for the WTA problem in reasonable amount of time.
Multiplicative relations are one of most powerful techniques to express the preferences over alternatives (or criteria). In this paper, we propose a wide range of hesitant multiplicative fuzzy power aggregation geometric operators on multiattribute group decision making (MAGDM) problems for hesitant multiplicative information. In this paper, we first develop some compatibility measures for hesitant multiplicative fuzzy numbers, based on which the corresponding support measures can be obtained. Then we propose several aggregation techniques, and investigate their properties. In the end, we develop two approaches for multiple attribute group decision making with hesitant multiplicative fuzzy information and illustrate a real world example to show the behavior of the proposed operators.
The weapon target assignment (WTA) problem that arises in defense related applications is to find a proper assignment of weapons to the enemy's targets with the objective of minimizing the total expected survival value of all targets. The WTA problem can be formulated as a nonlinear integer programming problem, and falls into the category of NP-Complete problems. This paper proposes an efficient approximation algorithm for this problem. The algorithm is to define new approximating subproblems on the original problem, which forms a feasible descent iteration scheme for finding a suboptimal solution. Numerical results demonstrate the effectiveness of the proposed algorithm.
This paper presents an improved genetic algorithm (IGA) for dynamic route guidance algorithm. The proposed IGA design a vicinity crossover technique and a greedy backward mutation technique to increase the population diversity and strengthen local search ability. The steady-state reproduction is introduced to protect the optimized genetic individuals. Furthermore the junction delay is introduced to the fitness function. The simulation results show the effectiveness of the proposed algorithm.
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