whale optimization algorithm

Scheduling and timetabling for university system have been a source of attention and an important challenge for the people in charge of administrations. The regulations and infrastructures are very diverse between universities, making it impossible to come up with a universal model for all. We, in this research, focused on coming up with an algorithm to help with timetabling of class courses for Islamic Azad university of Robat Karim. Our goal was to define an algorithm that could improve teacher satisfaction, and overall efficiency of the university timetabling. Instead, we managed to come up with an efficient algorithm.This research considers different factors such as teacher satisfaction, knowledge and skillset, categorizes students based on undergraduate versus post graduate degree, their research background, their scores and finally student satisfaction as well. This multi-objective mathematic model accounts for all the rules, regulations, and limitations of the university setting while following challenging confinements that guarantee the feasibility of the solution. Using metaheuristic algorithm of Whale and Genetic, while avoiding any breach of the soft limitations, we managed to come up with a system that provides the most satisfaction between the teachers and students. In our research, we compared Whale and Genetic algorithm with 4 other metaheuristic algorithms. We concluded that the results of Whale and Genetic algorithm are superior to other algorithms in regards to: Improved function goals, less run time, more Pareto front averages, more efficient solutions and results.

This paper addresses the open shop scheduling problem, considering parallel machines within each stage and integrating job transportation times between stages, independent of job specifics. In this scheduling problem, all jobs traverse each stage, and once a job commences on a machine, it must complete without machine breakdowns. To meet this challenge, a mixed-integer linear programming (MILP) model is introduced to minimize the makespan, which represents the maximum job completion time. Given the NP-hard nature of the open-shop scheduling problem, this study employs the whale metaheuristic algorithm to solve instances across various dimensions, spanning small, medium, and large scales. The algorithm parameters are systematically optimized using the Taguchi Method. Results from comparing the whale algorithm with the linear model implemented in GAMS highlight its exceptional efficiency in handling randomly generated small and medium-sized instances. Moreover, in a comparative analysis with other algorithms such as PSO and DE, the whale algorithm not only competes effectively but, in some instances, outperforms its counterparts. This observation underscores the algorithm's prowess in maintaining efficiency and high performance, particularly when addressing large-scale open-shop scheduling challenges. It excels in achieving a delicate balance between exploration and exploitation, thereby avoiding local optimal solutions.

This paper provides an integrated model for a two-stage assembly flow shop scheduling problem and distribution through vehicle routing in a soft time window. So, a mixed-integer linear programming (MILP) model has been proposed with the objective of minimizing the total cost of distribution, holding of products, and penalties of violating delivery time windows. To solve this problem, an improved meta-heuristic algorithm based on whale optimization algorithm (WOA) has been developed. A comparison of the integrated and non-integrated model in a case study of industrial gearboxes production shows that the integrated model compared to the non-integrated model has saved 15.6% and 13.6% in terms of delay time and total costs, respectively. Computational experiments also indicate the efficiency of improved WOA in converging to optimal solution and achieve better solution in comparison to the genetic algorithm (GA).