## 1 Introduction
We have updated the model to represent an abstracted DDOS attack. Single-objective optimization often fails to reflect the variety of complex real-world scenarios [8]. Most of the problems in real life involving decision-making depends on multiple objectives [9; 10]. Multi-objective decision-making has been a widely explored area [11]. Multi-objective problems are also known as multi-criteria optimization, or vector minimization [12]. Traditional methods, such as linear programing and gradient descent, are too complex for solving multi-objective Pareto-optimal fronts [13; 14]. Multi-Objective Reinforcement Learning has been actively researched in various fields [11]. In traditional reinforcement learning an agent learns and takes action based on receiving a scalar reward from the dynamic environment. The quality of estimate improves over time as the agent tries to maximize the cumulative reward [15]. [PERSON]'s [15] reward hypothesis states that goals and purposes can be thought of as maximization of the cumulative single scalar reward. Thus, a single scalarized reward is adequate to represent multiple objectives [11]. Since traditional RL focuses on a single objective, the algorithm requires a modification to accommodate multi-objective problems. The most common approach to deal with multi-objective problems is scalarization. Scalarization of multi-objective RL involves two steps. First, we specify the scalarization function \(f\), such that the \(V^{\pi}\) state value vector is projected into a scalar value \(V^{\pi}_{\overline{w}}(x)=f(V^{\pi}(x),\mathbf{w})\), where \(\mathbf{w}\) is the weight vector parametrizing \(f\). Then, we define an objective function with an additive scalar return, such that for all policies \(\pi\) and states \(x\), the expected return equals the scalarized value of \(V^{\pi}_{\overline{w}}(x)\). The simplest and most popular, as well as, historically, the first proposed scalarization technique,is linear scalarization [16]. In linear scalarization, \(\mathbf{w}\) represents the relative weight of the objectives. Since it is a convex combination of all objectives, linear scalarization lacks the ability to find all solutions in a non-convex Pareto set [17]. [PERSON] et al. [12] proposed an offline algorithm that uses linear function approximation. Although the method reduces the asymptotic space and complexity of the bootstrapping rule, generalizing the concept into higher dimensions is not straightforward. Commonly known non-linear scalarization, among others, includes the Hiriart-Urruty function [18] and Gerstewitz functions [19]. Another class of algorithm for solving multi-objective problems are evolutionary algorithms (EA). Multi-objective EA (MOEA) uses an evolving population of solutions to solve the Pareto fronts in a single run. [PERSON] and [PERSON] [20] proposed non-dominated sorting in a genetic algorithm (NSGA) to solve multi-objective problems. Despite NSGA being able to capture several solutions simultaneously, it has several shortcomings, such as high computation complexity, lack of elitism, and specification of sharing parameters. NSGA-II improves by addressing these issues [21]. Other EA algorithms includes Pareto-archived evolution strategy (PAES) [20] and strength Pareto EA (SPEA). For a thorough survey of multi-objective evolutionary algorithms, the interested reader is referred to [22]. In [23], [PERSON] and [PERSON] studied two categories of scalarization functions: classification and reference point-based scalarization functions. In classification, the current solution is compared to the desired value, whereas in reference point-based scalarization functions a reference point is used to represent the aspiration level of the decision-maker (DM) and can be specified irrespective of the current solution. [PERSON] et al. [24] used a step method (STEM) in which the DM classifies the current solution points into two classes, \(I^{<}\) and \(I^{\geq}\). The DM defines the ideal upper bounds for each objective function. This method requires global ideal and nadir points.