# A Novel Genetic Algorithm for the Synthetical Sensor-Weapon-Target Assignment Problem
## 1 Introduction  
The sensor-weapon-target assignment (S-WTA) problem, as one of the most important issues in C4 ISR [1; 2], has attracted great attention in recent years. Its objective is to find an appropriate assignment scheme for sensors and weapons to enemy targets with the goal of maximizing the benefit of the scheme. This problem is a constrained combinatorial optimization problem, which can be regarded as a nondeterministic polynomial time complete (NP-complete) problem [3]. For certain cases, S-WTA can be considered as a composite of two independent parts, i.e., the sensor-target assignment (STA) [4; 5; 6; 7; 8] and the weapon-target assignment (WTA) [9; 10; 11; 12; 13; 14; 15; 16]. As the sensor is mainly used to obtain the information of the battlefield situation, the STA is performed in the mission of reconnaissance and surveillance to make decisions for the sensor management. As the weapon is used to protect the assets and obtain the superiority in the engagement, the WTA is implemented in the mission of attack to intercept and destroy the target. At present, as network-centric warfare (NCW) [17] and knowledge-centric warfare (KCW) [18] are the key operational architectures of the military operations, autonomy and cooperation are becoming more and more important. As a result, in this paper, we focus on the S-WTA problem, in which the sensors and weapons are allocated cooperatively. To be specific, the sensor can transmit the target information to the weapon in real-time and guide the weapon to attack the target accurately. In the last few decades, some scholars have paid attention to the S-WTA problem. The S-WTA model was established by [PERSON] and [PERSON] [19] for the first time. They deeply analyzed thecharacteristics of the S-WTA problem and proposed two types of S-WTA models: the independent S-WTA model and the dependent S-WTA model. Meanwhile, a heuristic algorithm based on auction algorithm was put forward in their paper to solve these S-WTA models. Afterwards, based on the proposed S-WTA model, [PERSON] further improved the auction algorithms named as Swt-opt [20], which has been proved that Swt-opt can generate complete optimal assignment. In order to improve the efficiency of the allocation schemes over many dynamic network topologies, [PERSON] et al. [21] proposed an improved Swt-opt, combining the consensus algorithm with Swt-opt. [PERSON] et al. [22] introduced the temporal and spatial constraints into the S-WTA problem to establish an improved dependent model. They considered this specific S-WTA problem as a kind of dynamic weapon-target assignment (DWTA) [23] problem and proposed an anytime algorithm based on decentralized cooperative auction to solve this problem. [PERSON] et al. [24] proposed an improved particle swarm optimization (PSO) to solve a similar dependent S-WTA problem. In this algorithm, some novel genetic operators were adopted to enhance the performance of the algorithm. [PERSON] et al. [25, 26] analyzed the integrated relationship between sensor, weapon, and target. They proposed four integrated formulations combining the sensor resource management and weapon-target assignment to further demonstrate the characteristics of the independent and dependent S-WTA problem. [PERSON] et al. [27] proposed an improved genetic algorithm (GA) to solve the dependent S-WTA problem, considering the situation where the kill probability of the weapons was modified to a formula with regard to the detection precision of sensors. Taking into account the synergic relationship between weapons and sensors as well as some specific constraints, [PERSON] et al. [28] established a novel dependent S-WTA model. Moreover, they proposed a marginal-return-based constructive heuristic (MRBCH) to solve the formulated S-WTA model, so as to generate the allocation scheme rapidly and accurately. The work has been discussed thus far only focus on one aspect of the S-WTA problem.