Mathematical Problems in Engineering

Volume 2017 (2017), Article ID 9843735, 12 pages

https://doi.org/10.1155/2017/9843735

## Research on Multiaircraft Cooperative Suppression Interference Array Based on an Improved Multiobjective Particle Swarm Optimization Algorithm

^{1}Aeronautics and Astronautics Engineering College, Air Force Engineering University, Xian 710038, China^{2}Tianjin University, Tianjin 300072, China

Correspondence should be addressed to Huan Zhang

Received 26 October 2016; Revised 11 January 2017; Accepted 17 January 2017; Published 5 March 2017

Academic Editor: Thomas Hanne

Copyright © 2017 Huan Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

For the problem of multiaircraft cooperative suppression interference array (MACSIA) against the enemy air defense radar network in electronic warfare mission planning, firstly, the concept of route planning security zone is proposed and the solution to get the minimum width of security zone based on mathematical morphology is put forward. Secondly, the minimum width of security zone and the sum of the distance between each jamming aircraft and the center of radar network are regarded as objective function, and the multiobjective optimization model of MACSIA is built, and then an improved multiobjective particle swarm optimization algorithm is used to solve the model. The decomposition mechanism is adopted and the proportional distribution is used to maintain diversity of the new found nondominated solutions. Finally, the Pareto optimal solutions are analyzed by simulation, and the optimal MACSIA schemes of each jamming aircraft suppression against the enemy air defense radar network are obtained and verify that the built multiobjective optimization model is corrected. It also shows that the improved multiobjective particle swarm optimization algorithm for solving the problem of MACSIA is feasible and effective.

#### 1. Introduction

Under the condition of information warfare, the enemy air defense radar network often has a strong ability to resist “the four” [1, 2]. It increases the difficulty of combat aircraft penetration safely, so combat aircraft must have the aid of suppression interference against the enemy air defense radar network by the electronic support jamming aircraft. In this way it can provide a safe route planning space for subsequent route planning. Since the enemy air defense radar network is often deployed by a number of air defense radars, if only relying on a single electronic jamming aircraft to interfere with the enemy radar network, it is difficult to achieve the desired suppression effect due to the limited interference resources on a single jamming aircraft. Therefore, a solution of multiple electronic jamming aircraft cooperating with each other to interfere with the air defense radar network must be used. In order to make more reasonable distribution of interference resources in the process of cooperative interference, a reasonable array pattern should be used to determine the position of each jamming aircraft. This is the optimal problem of MACSIA in electronic warfare mission planning. For this problem, the domestic and foreign research are mainly focused on the operational efficiency and suppression interference effect of combat aircraft, and so on. But the study on the MACSIA is rare. In [3], Shi et al. analyzed the influence of electronic jamming on the path planning of combat aircraft. In [4], Wang et al. proposed a multiconstraint condition genetic algorithm to optimize the deployment of the enemy radar network. The calculation method of operational efficiency of combat aircraft against ground warning radar is studied under the condition of stand-off jamming [5]. Ruan et al. [6] have explored the influence of all kinds of factors on the suppression interference effect by taking the minimum interference distance as evaluation criterion. In a work by Tang et al. [7], the evaluation model of active suppression interference effect is built and the timing of interference is analyzed. In [8], Chen et al. have built a single objective optimal model of MACSIA, but the MACSIA is not considered as a multiobjective optimization problem (MOP) to solve. All the objective functions are aggregated into a single objective function by the weighted sum method, so a single objective optimization model for this problem is built. Different Pareto optimal solutions can be obtained by selecting different weight combinations. But the drawbacks of this method are obvious. Obviously the selection of weights is related to the relative importance of each objective function. If the user does not have sufficient prior knowledge of the problem, it is difficult to find the Pareto optimal solution that satisfies the decision maker. However, if the problem is regarded as a MOP to solve, it can avoid these drawbacks effectively.

In this paper, for the optimal problem of solving MACSIA, firstly, the calculation method of the enemy air defense radar detection range under the terrain masking condition is given, and the active interference model of electronic warfare is built. Secondly, the concept of route planning security zone is proposed and the mathematical morphology method is used to calculate the minimum width of route planning security zone. Thirdly, fully considering the characteristics of MOP for MACSIA, the minimum width of route planning security zone and the sum of the distance between each jamming aircraft and the center of the enemy air defense radar network are taken as objective functions, so the multiobjective optimization model of MACSIA is built. Finally, multiobjective particle swarm optimization (MOPSO) [9–17] has been widely used in multiobjective optimization based on its simple, fast convergence, easy to achieve in engineering [18–20], and so on. However, due to the disadvantages of particle swarm optimization algorithm [21], the distribution of nondominated solutions generated by MOPSO along the Pareto front is not very uniform and the computation time of MOPSO is not very fast enough. In order to solve these problems, the decomposition mechanism and the proportional distribution mechanism are introduced into the MOPSO algorithm. Therefore, an improved MOPSO algorithm is proposed which is used to solve the multiobjective optimization model of MACSIA. The optimal MACSIA schemes for the limit of the minimum width of route planning security zone and ensuring the safety of the jamming aircrafts are obtained by the simulation examples.

#### 2. Model Building

##### 2.1. Radar Detection Model under the Terrain Masking Condition

###### 2.1.1. Digital Elevation Model (DEM)

Digital elevation model (DEM) refers to a method of storing terrestrial elevation information in the form of specific data. There are two common representations of digital elevation models, which are the grid structure and the contour map. In this paper, the grid structure is used.

###### 2.1.2. Radar Detection Model

Radar detection model is generally characterized by radar equation which is defined asIn this equation, is the radar detection range (m), is the radar emitting peak power (), is the radar antenna gain, is the radar cross section (), is the radar wavelength (), is the signal to noise ratio of radar receiver, is the noise coefficient, is the Boltzmann constant (), is the radar working temperature (), is the noise bandwidth (), and is the system loss.

###### 2.1.3. Calculating the Radar Detection Range under Terrain Masking Condition

The calculation diagram of radar detection range under terrain masking condition is shown in Figure 1.