The Travelling Salesman Problem (TSP) is a well-known combinatorial optimization problem that belongs to a class of problems known as NP-hard, which is an exceptional case of travelling salesman problem (TSP), which determines a set of routes enabling multiple salesmen to start at and return to home cities (depots). The penguins search optimization algorithm (PeSOA) is a new metaheuristic optimization algorithm. In this paper, we present a discrete penguins search optimization algorithm (PeSOA) for solving the multiple travelling salesman problem (MTSP). The PeSOA evaluated by a set of benchmarks of TSP instance from TSPLIB library. The experimental results show that PeSOA is very efficient in finding the right solutions in a reasonable time

The spotted hyena optimization algorithm (SHOA) is a novel approach for solving the flow shop-scheduling problem in manufacturing and production settings. The motivation behind SHOA is to simulate the social dynamics and problem-solving behaviors of spotted hyena packs in order to identify and implement optimal schedules for jobs in a flow shop environment. This approach is unique compared to other optimization algorithms such as WOA, GWO, and BA. Through extensive experimentation, SHOA has been shown to outperform traditional algorithms in terms of solution quality and convergence speed. The purpose of this study is to present the details of the SHOA algorithm, demonstrate its effectiveness, and compare its performance with other optimization approaches. The method used in this study includes extensive experimentation and comparison with other algorithms. The findings of this study show that SHOA is a promising tool for optimizing production processes and increasing efficiency. The implications of this study are that SHOA can be used as an effective tool for solving flow shop-scheduling problems in manufacturing and production settings.

In this paper, we present the Rat Swarm Optimization with Decision Making (HDRSO), a hybrid metaheuristic algorithm inspired by the hunting behavior of rats, for solving the Traveling Salesman Problem (TSP). The TSP is a well-known NP-hard combinatorial optimization problem with important applications in transportation, logistics, and manufacturing systems. To improve the search process and avoid getting stuck in local minima, we added a natural mechanism to HDRSO through the incorporation of crossover and selection operators. In addition, we applied 2-opt and 3-opt heuristics to the best solution found by HDRSO. The performance of HDRSO was evaluated on a set of symmetric instances from the TSPLIB library and the results demonstrated that HDRSO is a competitive and robust method for solving the TSP, achieving better results than the best-known solutions in some cases.

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This paper presents a new hybrid algorithm that combines genetic algorithms (GAs) and the optimizing spotted hyena algorithm (SHOA) to solve the production shop scheduling problem. The proposed GA-SHOA algorithm incorporates genetic operators, such as uniform crossover and mutation, into the SHOA algorithm to improve its performance. We evaluated the algorithm on a set of OR library instances and compared it to other state-of-the-art optimization algorithms, including SSO, SCE-OBL, CLS-BFO and ACGA. The experimental results show that the GA-SHOA algorithm consistently finds optimal or near-optimal solutions for all tested instances, outperforming the other algorithms. Our paper contributes to the field in several ways. First, we propose a hybrid algorithm that effectively combines the exploration and exploitation capabilities of SHO and GA, resulting in a balanced and efficient search process for finding near-optimal solutions for the FSSP. Second, we tailor the SHO and GA methods to the specific requirements of the FSSP, including encoding schemes, objective function evaluation and constraint handling, which ensures that the hybrid algorithm is well suited to address the challenges posed by the FSSP. Third, we perform a comprehensive performance evaluation of the proposed hybrid algorithm, demonstrating its effectiveness in terms of solution quality and computational efficiency. Finally, we provide an in-depth analysis of the behavior of the hybrid algorithm, discussing the roles of the SHO and GA components and their interactions during the search process, which can help understand the factors contributing to the success of the algorithm and provide insight into potential improvements or adaptations to other combinatorial optimization problems.