###### Abstract
Hence, alongside improving traditional algorithms, many scholars have introduced machine learning algorithms, e.g., the Pareto-set cluster genetic algorithm [2] and particle swarm optimization [2], the binary-code genetic algorithm [3] and integer-code particle swarm optimization [3], the simulated annealing algorithm [4], particle swarm optimization (PSO) [5], the genetic algorithm [6], the machine learning algorithm [7], Multi-Objective PSO [8], the artificial bee colony algorithm [9], the hybrid optimization algorithm [10], etc., to solve the job scheduling problem of the computing tasks of cloud computing. Numerous different objectives have been discussed to measure service performance, e.g., cost, reliability, makspan, and power consumption [1; 2; 3; 4; 5; 6; 7; 8; 9; 10]. However, when conducting research on the job assignment problem, most scholars emphasize the single-objective job scheduling problem and overlook job scheduling problems with more than one objective [11; 12; 13; 14; 15; 16; 17]. By doing so, they fail to acknowledge other goals that may influence the quality of the cloud-computing service. It is thus necessary to balance various aspects when evaluating job scheduling problems [15; 16; 17]; for example, the objective of minimizing total energy consumption and the objective of minimizing makspan are conflicting objectives in real-life applications [17]. With the ever-advancing development of cloud computing, more and more data centers have successively been established to run a large number of applications that require considerable computations and storage capacity, but this wastes vast amounts of energy [12; 15; 16; 17]. Reducing power consumption and cutting down energy costs has become a primary concern for today's data center operators. Thus, striking a balance between reducing energy consumption and maintaining high computation capacity has become a timely and important challenge. Furthermore, with more media and public attention shifting onto progressively severe environmental issues, governments worldwide have now adopted a stronger environmental protection stance [12; 15; 16; 17]. This puts increasing pressure on enterprises to pursue higher output and also to focus on minimizing power consumption [12; 15; 16; 17]. Stemming from real-life concerns, as mentioned above, our previous work considered a two-objective time-constrained job scheduling problem to measure the performance of a certain job schedule plan with two objectives: the quality of the cloud computing service in terms of the makspan and the environmental problem based on the energy consumption [12; 15; 16; 17]. There are two different types of algorithms used to solve multi-objective problems. While one converts multi-objective problems to ones that are single objective in nature through methods such as \(\varepsilon\)-constraint, LP-metrics, goal programming, etc., the other solves multi-objective problems based on the concept of Pareto optimality. The latter is the one we adapted, both here and in our previous study [10; 11; 12; 13; 14; 15; 16; 17]. Moreover, a new algorithm called the multi-objective simplified swarm optimization (MOSSO) was proposed to solve the above problem [17]. However, there are some errors in the MOSSO source code, which ignores the multi-objective problem; the number of temporary nondominated solutions is not always only one, and some temporary nondominated solutions may not be temporary nondominated solutions in the next generation. Therefore, the performance comparison is limited to MOSSO and MOPSO, despite both having an iterative local search [17]. In order to rectify our previous source code with new concepts based on the Pareto optimality to solve the two-objective time-constrained job scheduling, we proposed a new algorithm called two-objective simplified swarm optimization (tSSO).