A Hybrid Discrete Grey Wolf Optimizer to Solve Weapon Target Assignment Problems

Jun Wang,Pengcheng Luo,Xinwu Hu,Xiaonan Zhang

doi:10.1155/2018/4674920

Abstract

We propose a hybrid discrete grey wolf optimizer (HDGWO) in this paper to solve the weapon target assignment (WTA) problem, a kind of nonlinear integer programming problems. To make the original grey wolf optimizer (GWO), which was only developed for problems with a continuous solution space, available in the context, we first modify it by adopting a decimal integer encoding method to represent solutions (wolves) and presenting a modular position update method to update solutions in the discrete solution space. By this means, we acquire a discrete grey wolf optimizer (DGWO) and then through combining it with a local search algorithm (LSA), we obtain the HDGWO. Moreover, we also introduce specific domain knowledge into both the encoding method and the local search algorithm to compress the feasible solution space. Finally, we examine the feasibility of the HDGWO and the scalability of the HDGWO, respectively, by adopting it to solve a benchmark case and ten large-scale WTA problems. All of the running results are compared with those of a discrete particle swarm optimization (DPSO), a genetic algorithm with greedy eugenics (GAWGE), and an adaptive immune genetic algorithm (AIGA). The detailed analysis proves the feasibility of the HDGWO in solving the benchmark case and demonstrates its scalability in solving large-scale WTA problems.

Highlights

As a classic military operational problem, the purpose of weapon target assignment (WTA) is to find an optimal or a satisfactory assignment solution, which determines the target attacked by each weapon, so as to maximize the total damage expectancy of hostile targets or minimize the loss expectancy of own-force assets
We propose a hybrid discrete grey wolf optimizer (HDGWO) in this paper to solve the weapon target assignment (WTA) problem, a kind of nonlinear integer programming problems
In order to examine the scalability of HDGWO, we first employ the above four algorithms to solve ten different scale WTA problems produced by a test case generator, and compare the results of all algorithms from three aspects, that is, the comparison of the solution quality, the comparison of the

Summary

Introduction

As a classic military operational problem, the purpose of weapon target assignment (WTA) is to find an optimal or a satisfactory assignment solution, which determines the target attacked by each weapon, so as to maximize the total damage expectancy of hostile targets or minimize the loss expectancy of own-force assets. Exact algorithms are developed according to the specific mathematical properties of WTA problems and can gradually eliminate the nonlinearity of the problem through transformation, decomposition, and other processing means [16] By this way, the model is translated to a linear one, and classical operations research methods can apply, such as the dynamic programming method [12], the branch and bound method [20, 21], the branch and price method [22], the mixed integer linear program (MILP) algorithm [17], and the Lagrange relaxation method [14].

Problem Formulation

Simulation Results and Analysis

Conclusion and Future Research

Conflicts of Interest