Journal of Optimization

Volume 2017, Article ID 8063767, 12 pages

https://doi.org/10.1155/2017/8063767

## A Hybrid Multiobjective Discrete Particle Swarm Optimization Algorithm for Cooperative Air Combat DWTA

School of Aeronautics and Astronautics Engineering, Air Force Engineering University, Xi’an, Shaanxi 710038, China

Correspondence should be addressed to Guang Peng; moc.361@7034335441gp

Received 30 December 2016; Accepted 20 March 2017; Published 11 April 2017

Academic Editor: Maoguo Gong

Copyright © 2017 Guang Peng 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

A hybrid multiobjective discrete particle swarm optimization (HMODPSO) algorithm is proposed to solve cooperative air combat dynamic weapon target assignment (DWTA). First, based on the threshold of damage probability and time window constraints, a new cooperative air combat DWTA multiobjective optimization model is presented, which employs the maximum of the target damage efficiency and minimum of ammunition consumption as two competitive objective functions. Second, in order to tackle the DWTA problem, a mixed MODPSO and neighborhood search algorithm is proposed. Furthermore, the repairing operator is introduced into the mixed algorithm, which not only can repair infeasible solutions but also can improve the quality of feasible solutions. Besides, the Cauchy mutation is adopted to keep the diversity of the Pareto optimal solutions. Finally, a typical two-stage DWTA scenario is performed by HMODPSO and compared with three other state-of-the-art algorithms. Simulation results verify the effectiveness of the new model and the superiority of the proposed algorithm.

#### 1. Introduction

The weapon target assignment (WTA) is a typical NP-complete constrained combinatorial optimization problem [1], which can be classified into two categories: static WTA (SWTA) and dynamic WTA (DWTA) [2, 3]. In SWTA, all the weapons attack targets in a single stage. In contrast, DWTA is much more complicated than SWTA, which takes the time window and resource constraints into account [4]. Besides, DWTA needs to deal with the new incoming targets and assesses the outcome of each engagement.

Most of the previous researches on WTA are focused on SWTA [4]. However, DWTA has begun to gain more attention of researchers since it was put forward by Hosein and Athans in 1990 [3]. Cai et al. [4] provided a survey of the research on DWTA problem and introduced some basic concepts on DWTA. Khosla [5] proposed a hybrid approach, which combines genetic algorithm (GA) with simulated annealing (SA) to solve a target-based DWTA problem. Liu et al. [6] analyzed the time and space restriction of the mathematical model of DWTA and proposed an adaptive memetic algorithm to obtain the suboptimum solution step by step. Chen et al. [7] established a generic asset-based DWTA model which incorporates four categories of constraints, namely, capability constraints, strategy constraints, resource constraints, and engagement feasibility constraints. Based on the asset-based DWTA model, Xin et al. [8] proposed a new technique for constraint handling. Moreover, Xin et al. [9] proposed an efficient rule-based heuristic, which uses the domain knowledge of DWTA in the form of three crucial rules, to solve asset-based DWTA problems. The proposed method has obvious advantage over the Monte Carlo method (MCM) with regards to solution quality and computation time. Wang et al. [10] applied intuitionistic fuzzy entropy of discrete particle swarm optimization (IFDPSO) algorithm to solve DWTA problem. Wang et al. [11] firstly established a multicombat step DWTA game model of UAV aerial combat and then presented a clonal selection optimization algorithm to solve the model.

However, the above WTA problems are focused on one objective (i.e., operational effects), ignoring the operational cost, while in actual combat situations, apart from considering the maximum of the damage to targets, the ammunition consumption should be also taken into account. Clearly, the two competitive objectives are conflicting, which implies that the WTA problem is a multiobjective optimization problem. Up to now, there have been several studies on multiobjective optimization for DWTA problems. Liu et al. [12] and Zhou et al. [13] proposed an improved MOPSO algorithm to solve the multiobjective programming model of SWTA, respectively. Lötter and Van Vuuren [14] used NSGA-II to solve a triobjective DWTA model for surface-based air defense. Li et al. [15, 16] established deterministic and uncertain multiobjective optimization models of multistage WTA (MWTA) problem and modified two multiobjective optimizers, NSGA-II and MOEA/D, by adding an adaptive mechanism for solving the NWTA models. However, MOPSO easily falls into the local optimum; NSGA-II and MOEA/D have complex computation for DWTA. DWTA problem has higher requirements for the real-time performance and the convergence. In order to meet the real-time performance and the convergence accuracy simultaneously, this paper proposed an efficient HMODPSO algorithm to solve the DWTA multiobjective optimization problem. The proposed HMODPSO algorithm can generate obviously better DWTA decisions without the cost of overmuch extra computation time, which can improve the cooperative air combat effectiveness.

The rest of this paper is organized as follows. In Section 2, the cooperative air combat DWTA multiobjective optimization model based on the threshold of damage probability is formulated. Section 3 presents the structure of HMODPSO algorithm. The simulation results based on the proposed algorithm for a typical two-stage DWTA scenario are discussed in Section 4, and also the comparisons with three other state-of-the-art algorithms are conducted in this section. Conclusions and future work will be drawn in Section 5.

#### 2. The Cooperative Air Combat Multiobjective Optimization Model for DWTA

*Definition 1 (time window of target). *The time window of target () is the exposure time of a target which the weapon can attack efficiently.

*Definition 2 (time window of algorithm). *The time window of algorithm () is the running time for solving the DWTA.

A complete cooperative air combat is a multistage offensive and defensive process. So the DWTA model can be regarded as the repetition of the SWTA model with the damage assessment. There are at most stages of DWTA, which means no targets or weapons left after final stage assignment. In the cooperative air combat DWTA model, the “shoot-look-shoot” engagement policy is adopted. When entering the stage, it is necessary to determine a set of alive targets and remaining weapons. Therefore, it needs to observe the outcome of the stage engagement and reformulate air combat situation assessment. The schematic diagram of cooperative air combat DWTA model is shown in Figure 1.