# A Novel Genetic Algorithm for the Synthetical Sensor-Weapon-Target Assignment Problem
## 1 Introduction
Consequently, some details of the collaborative operations of the sensors and weapons, which involve the cooperative engagement mode and the capacity constraints, are neglected. Therefore, in this paper, we focus on designing a comprehensive S-WTA model to demonstrate a more realistic S-WTA scenario. In order to improve the solution of the S-WTA model, the optimization algorithm is also studied in this paper. The algorithms used to solve the S-WTA problem can be divided into two categories: The first category is the heuristic algorithm, such as Swt-opt and MRBCH. Heuristic algorithms can solve the S-WTA in real-time. It can be used in a dynamic environment and handle the uncertainties over the engagement. Although heuristic algorithms can solve the S-WTA problem in real-time, they are very difficult to achieve a satisfactory solution in such a NP-hard problem. This is because heuristic algorithms search for solutions using specific heuristic information, which traps them into the local optimal easily. The second category is the evolutionary algorithm (EA) [29, 30], such as GA and PSO. As EA-based algorithms use many flexible mechanisms that fully consider the prior knowledge, they can achieve a satisfactory solution. However, the running time of EA-based algorithms are relatively large; they cannot solve the S-WTA problems in real-time. In this paper, as we focus on obtaining a high-quality assignment scheme, the running time of the algorithm is not considered. Since EA has many significant advantages in finding the optimal solution, we believe that choosing EA to solve the S-WTA problem can achieve a satisfactory assignment scheme. EA has attracted massive interest from researchers for decades. At present, the well-known evolutionary algorithms are GA [31], PSO [32], ant colony algorithm (ACO) [33], and differential evolution (DE) [34]. Among these algorithms, GA is one of the most important algorithms. Because GA has a simple framework, high flexibility, and strong convergence ability, it has been successfully applied in many real-world problems [35, 36, 37], especially in the WTA problem [13, 23, 38]. For these reasons, we believe that choosing GA to solve the S-WTA problem is reasonable and promising. In this paper, we proposed a novel GA to solve the S-WTA problem named GA-SWTA. The contributions of this paper are described as follows. In the context that sensors and weapons are allocated cooperatively, a novel S-WTA model is presented. The traditional S-WTA model has only two frameworks: the dependent framework and the independent framework. In order to fully reflect the relationship between sensors and weapons, the S-WTA has been extended to the synthetical framework. 2. For the proposed S-WTA model, a novel GA framework is proposed. Based on the characteristic of S-WTA, we redefine the form of chromosome encoding. We also adaptively improved the crossover operator to better match the redefined encoding. In addition, a problem-specific chromosome initialization method is proposed. 3. In order to handle the constrains and improve the convergence ability of the algorithm, chromosome repair approaches are proposed. Based on the prior knowledge of S-WTA, two repair operations--R-STA operation and R-WTA operation--are designed to cooperatively repair the chromosome. The experiments validate the good performance of the proposed approaches. The rest of this paper is organized as follows. In Section 2, the frameworks of the S-WTA problem are analyzed first, then we present a mathematical optimization model for the synthetical S-WTA problem. In Section 3, a novel GA, i.e., GA-SWTA, is proposed to solve the S-WTA problem. Meanwhile, a problem-specific initialization and a chromosome-repair mechanism are designed to improve the performance of the algorithm. In Section 4, GA-SWTA is compared with three state-of-the-art S-WTA approaches, then the performance of the proposed initialization and a chromosome-repair mechanism are investigated. The conclusion and future work are described in Section 5.