# Multiprocessor Fair Scheduling Based on an Improved Slime Mold Algorithm
###### Abstract  
An improved slime mold algorithm (IMSMA) is presented in this paper for a multiprocessor multitask fair scheduling problem, which aims to reduce the average processing time. An initial population strategy based on Bernoulli mapping reverse learning is proposed for the slime mold algorithm. A Cauchy mutation strategy is employed to escape local optima, and the boundary-check mechanism of the slime mold swarm is optimized. The boundary conditions of the slime mold population are transformed into nonlinear, dynamically changing boundaries. This adjustment strengthens the slime mold algorithm's global search capabilities in early iterations and strengthens its local search capability in later iterations, which accelerates the algorithm's convergence speed. Two unimodal and two multimodal test functions from the CEC2019 benchmark are chosen for comparative experiments. The experiment results show the algorithm's robust convergence and its capacity to escape local optima. The improved slime mold algorithm is applied to the multiprocessor fair scheduling problem to reduce the average execution time on each processor. Numerical experiments showed that the IMSMA performs better than other algorithms in terms of precision and convergence effectiveness. s +
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progress rates among all tasks [6]. Due to its ability to balance system throughput and fairness, proportionate fairness scheduling has gained widespread adoption in practice [7]. Ensuring a fair allocation of resources can significantly impact the performance of scheduling algorithms. While various fair scheduling algorithms have been emerging rapidly, research on fair scheduling on multiprocessors is relatively limited. It has been established that the job scheduling problem for processors is NP-hard, and ensuring fairness in scheduling can improve the utilization of processor resources to some extent. The typical objective of fairness scheduling problems is usually to minimize the maximum total processing time on machines. This paper, however, sets the fairness scheduling objective as minimizing the average execution time on each processor. Scheduling problems with the objective of minimizing the maximum average processing time can be applied to tasks such as taxi and courier dispatch, which require handling a large number of scheduling tasks in a short time, necessitating algorithms that are efficient and have short processing times. The fair scheduling issue for multiprocessor multitasking is addressed in this research using a modified slime mold method. Swarm intelligence algorithms are mainly inspired by the evolution of organisms in the natural environment and the hunting, foraging, and survival processes of populations [8]. Some common swarm intelligence algorithms include particle swarm optimization (PSO) [9], the whale optimization algorithm (WOA) [10], the sparrow search algorithm (SSA) [11], the butterfly optimization algorithm (BOA) [12], and so on. These swarm intelligence algorithms have been studied and used extensively in a variety of fields, such as photovoltaic maximum power point tracking [13], multiobjective optimization problems [14], and COVID-19 infection prediction [15]. They have demonstrated good performance in solving problems in specific domains. A recently developed metaheuristic algorithm called the slime mold algorithm (SMA), which was introduced by [PERSON] et al. [16] in 2020, simulates the behavior and morphological changes of slime molds during natural foraging. Compared with other intelligent optimization algorithms, slime mold algorithm has the advantages of a simple principle, few adjustment parameters, a strong optimization ability, and an easy implementation. The slime mold algorithm has been successfully applied in many fields, especially in engineering optimization. [PERSON] et al. [14] proposed a multiobjective slime mold algorithm based on elite undominated ranking.