# Deriving Controllable Local Optimal Solutions through an Environment Parameter Fixed Algorithm
## 1 Introduction
EPFA-CLS is a useful approach for determining the optimal course of a ship when evading infrared guided missiles [13]. To evade these missiles, the first step is to change the missile's locked-on target [14]. Flares are commonly used as a deceptive measure, emitting a higher temperature than the ship and diverting the missile's attention [15]. As shown in Figure 3, the ship fires the flare to change the locked-on object from the ship to the flare. After deploying a flare, the ship needs to navigate an optimal course, considering its direction, velocity, and specific conditions. The course must be reachable based on the ship's top speed, such as the FFG-2 large class ship with a maximum speed of 15.4 m/s [16]. Additionally, the miss distance, which represents the distance between the ship and the missile when the missile hits the flare, should be increased [17]. This miss distance is influenced by wind conditions, and an optimization problem needs to be formulated to determine the ship's course. The objective function takes inputs such as ship direction, velocity, wind direction, and wind velocity, with the output being the miss distance (MD). Figure 3 illustrates miss distance. In summary, EPFA-CLS provides advantages for modeling the problem, including non-ideal factors such as wind information, and enables precise control over the ship's direction and velocity to navigate the optimal path. A similar approach is presented in several prior works [18; 19; 20; 21]. The work by [18] addresses the problem of finding the global optimum by employing a convex approach to transform the ICNN problem. However, our focus is on solving the problem of CLS derivation, which is distinct from their work. On the other hand, [19] does not adequately reflect the current point as it only considers a uniform initial condition and lacks the incorporation of control concepts. A structured prediction is achieved by leveraging the concept of an energy function commonly used for training neural networks. Furthermore, both [20] and [21] introduce the notion of a control variable and an uncontrollable variable. However, they establish a dependent relationship between these variables, where the past control variable becomes the present uncontrollable variable due to the inclusion of time conditions. In contrast, our method employs a different optimization approach by defining a new loss function as the objective function. Our contributions in this paper can be summarized from three aspects:  
First, we raise another problem of constraint optimization, named trained DNN objective optimization, and we define terms that fit the context of the problem. Second, we propose the EPFA-CLS method, which enables the representation of a trained DNN under a specific environment parameter, effectively capturing the  
Figure 3: An illustration of miss distance and the locked-on object as defined when deriving an optimal course. desired constraints. By fixing the environment parameter, we transform the original optimization problem into a problem of optimizing control parameters in the DNN defined objective function. Subsequently, well-established optimization algorithms such as Gradient Descent are employed to solve this problem. Once the environment parameter is fixed, the CLS can be obtained by capturing the current state of the trained DNN under the specific environment. Third, the EPFA-CLS algorithm verifies feasibility with the optimal course dataset and with the Boston housing dataset. This paper is structured as follows. Section 2 provides background on the optimization; the problem covered in this paper is explained in detail and the terms and concepts are organized. In Section 3, the proposed method is explained in detail with a flow chart of the algorithm. Section 4 shows whether the EPFA-CLS is valid by experimenting with the datasets. We verify that the CLS can be derived with the EPFA'CLS by using the Boston Housing Dataset and the optimal course dataset. Section 5 summarizes the results.