The vehicle routing problem is widespread in terms of optimization, which is known as being NP-Hard. In this study, the vehicle routing problem with capacity constraints is solved using cost- and time-efficient metaheuristic methods: an invasive weed optimization algorithm, genetic algorithm, savings algorithm, and hybridized variants. These algorithms are tested using known problem sets in the literature. Twenty-four instances evaluate the performance of algorithms from P and five instances from the CMT data set group. The invasive weed algorithm and its hybrid variant with savings and genetic algorithms are used to determine the best methodology regarding time and cost values. The proposed hybrid approach has found optimal P group problem instances with a 2% difference from the best-known solution on average. Similarly, the CMT group problem is solved with about a 10% difference from the best-known solution on average. That the proposed hybrid solutions have a standard deviation of less than 2% on average from BKS indicates that these approaches are consistent.

In this paper, we propose a hybrid metaheuristic algorithm to maximize the production and to minimize the processing time in the steel-making and continuous casting (SCC) by optimizing the order of the sequences where a sequence is a group of jobs with the same chemical characteristics. Based on the work Bellabdaoui and Teghem (2006) [Bellabdaoui, A., & Teghem, J. (2006). A mixed-integer linear programming model for the continuous casting planning. International Journal of Production Economics, 104(2), 260-270.], a mixed integer linear programming for scheduling steelmaking continuous casting production is presented to minimize the makespan. The order of the sequences in continuous casting is assumed to be fixed. The main contribution is to analyze an additional way to determine the optimal order of sequences. A hybrid method based on simulated annealing and genetic algorithm restricted by a tabu list (SA-GA-TL) is addressed to obtain the optimal order. After parameter tuning of the proposed algorithm, it is tested on different instances using a.NET application and the commercial software solver Cplex v12.5. These results are compared with those obtained by SA-TL (simulated annealing restricted by tabu list).