## 1 Introduction  
The unprecedented spread of the Severe Acute Respiratory Syndrome Coronavirus 2 (Covid-19) epidemic across the world has pushed the healthcare systems to their limits [1, 2]. The main problem comes from having too many patients that need medical assistance at the same time [3]. Infected patients vary in their status regarding their stage in the infection and their previous illnesses, medically known as (comorbidities). Having an effective admission system for Covid-19 patients can alleviate the burden over hospitals through admitting patients to the most suitable hospital according to their status in real time. This can minimize the waiting time of patients and save patients with severe status. To our knowledge, few studies have been proposed to deal with this problem [4]. Identifying the most suitable hospital for a patient to be admitted automatically is not an easy task. This task has parameters that need to be considered, such as an assessment of patient status, assessment of hospital preparations, the time before admitting patients to hospitals, and time that patients need to reach the hospital. This transforms the admission problem into a Multi-Objective Problem (_MOP_). Solving _MOPs_ needs multiple solutionsthat vary the degree of satisfaction to different objectives [5]. Identifying the best solution to the problem can be determined according to the current status of the problem. Pareto Optimization (_PO_) has been one of the most common methods used to solve _MOPs_[6]. It tries to satisfy the whole objectives simultaneously. It generates a non-dominated set of solutions for _MOPs_, which cannot be further optimized. _PO_ has been applied to solve _MOPs_ in different fields, such as clustering [7; 8; 9] and hospital resource optimization [10; 11; 12]_PO_ can be employed to solve the admission problem considering the different objectives of the problem as it has been used before in [13]. In this paper, a multi-objective algorithm is proposed to provide automatic identification of the appropriate hospital for Covid-19 patients according to their medical condition in real time. The main contributions of this paper can be summarized in:  
* Develop an effective multi-objective admission system for Covid-19 patients that admits patients to the most suitable hospitals in real time and considers the comorbidities of the patients. * The method considers two main criteria in the admission process: (1) the patient status regarding the hospital preparations and (2) the admission time (reach time and admission time). This method can minimize the in-bed time of patients as it directs each patient to the most suitable hospital. * Provide a mathematical representation of the problem and the main constraints that affect it. * Implement the method using the _PO_ to vary among the conflicting objectives as admitting a patient to a non-suitable hospital in less time can result in transferring the patient to a different one. * Test the method over a dataset that combines a real-life part that has been provided by King Faisal specialist hospital in Saudi Arabia and a synthetic part. The real-life part had the clinical symptoms of the patients and their medical conditions when they arrived at the hospital. Meanwhile, the arrival rate, admission time, time to reach, and medical devices in different hospitals have been generated randomly to mimic the real-life situation. * Results show the efficiency of _PO_ in obtaining the correct hospital for patients over the Lexicographic method [7]. Also, the method showed its effectiveness in obtaining the correct hospital in real time despite the increase in the number of hospitals. The rest of the paper is organized as follows. Section 2 presents the recently published papers that focused on the problem under investigation. Section 3 presents a detailed description of _MOPs_, _PO_, and mathematical definitions of the admission problem and its constraints.