With a decentral and global economy, distributed scheduling problems are getting a lot of attention. This paper addresses a distributed flexible job shop scheduling problem (DFJSP) with minimizing makespan, in which three subproblems, namely operations sequencing, factory selection and machine selection must be determined. To solve the DFJSP, a novel mixed-integer linear programming (MILP) model is first developed, which can solve the small-scaled instances to optimality. Since the NP-hard characteristic of DFJSP, a hybrid algorithm (GA-VNS-CP) of genetic algorithm (GA), variable neighborhood search (VNS) and constraint programming (CP). Specifically, the GA-VNS-CP is divided into two stages. The first stage uses the hybrid meta-heuristic algorithms of GA and VNS (GA-VNS), and the VNS is designed to improve the local search ability of GA. In GA-VNS, the encoding only considers the factory selection and the operations sequencing problems, and the machine selection problem is determined by the decoding rule. Because the solution space may be limited by the decoding rule, the second stage uses the CP to extend the solution and further improve the solution. Numerical experiments based on benchmark instances are conducted to evaluate the effectiveness of the MILP model, VNS, CP and GA-VNS-CP. The experimental results show effectiveness of the MILP model, VNS and CP. Moreover, the GA-VNS-CP algorithm has better performance than traditional algorithms and improves 6 current best solutions for benchmark instances

In this paper, an electric vehicle routing problem with time windows and under travel time uncertainty (U-EVRW) is addressed. The U-EVRW aims to find the optimal proactive routing plan of the electric vehicles under the travel time uncertainty during the route of the vehicles which is rarely studied in the literature. Furthermore, customer time windows, limited loading capacities and limited battery capacities constraints are also incorporated. A new mixed integer programming (MIP) model is formulated for the proposed U-EVRW. In addition to the commercial CPLEX Optimizer version 20.1.0, a modified Clustering Search based Genetic algorithm (MCSGA) is developed as a solution method. Numerical tests are conducted on the one hand to validate the effectiveness of the proposed MCSGA and on the other hand to analyze the impact of travel time uncertainty of the electric vehicle on the solutions quality.

This paper investigates a novel problem concerning material delivery in a matrix manufacturing workshop, specifically the multi-automated guided vehicle (AGV) dispatching problem with unloading setup time (MAGVDUST). The objective of the problem is to minimize transportation costs, including travel costs, time penalty costs, AGV costs, and unloading setup time costs. To solve the MAGVDUST, this paper builds a mixed-integer linear programming model and proposes an improved genetic algorithm (IGA). In the IGA, an improved nearest-neighbor-based heuristic is proposed to generate a high-quality initial solution. Several advanced technologies are developed to balance local exploitation and global exploration of the algorithm, including an optimal solution preservation strategy in the selection process, two well-designed crossovers in the crossover process, and a mutation based on Partially Mapped Crossover strategy in the mutation process. In conclusion, the proposed algorithm has been thoroughly evaluated on 110 instances from an actual electronic factory and has demonstrated its superior performance compared to state-of-the-art algorithms in the existing literature.

Vehicle Routing Problem (VRP) is important in the transportation and logistics industries. Vehicle Routing Problem with Time Window (VRPTW) is a kind of VRP with the additional time windows constraint in the model and is classified as an NP-hard problem. In this study, we proposed Stas crossover in Genetic Algorithm (GA) to solve VRPTW by developing the problem with K-mean clustering. The experiments use the standard Solomon’s benchmark problem instances for VRPTW. The results with K-mean clustering are shown to perform better for minimum distance and average distance than without K-mean clustering. In the case of location and dispersion characteristics of the customer, the paths with K-mean clustering are arranged into groups and are orderly, but the paths without K-mean clustering are disordered. After that, this paper shows the comparison of the crossover operator performance on instances of Solomon benchmark, and appropriate crossover operators are recommended for each type of problem. The results of the proposed algorithm are better than the best-known solutions from the previous studies for some instances. Moreover, our proposed research will serve as a guideline for a real-world case study.

Conveying the products to the customers under optimized circumstances is as crucial for the companies as the production itself. One optimization strategy to consider is transportation with the minimum quantity of vehicles and the selection of courses with the minimum distance between the locations. In other words, it is the examination of the solution to the Vehicle Routing Problem (VRP), particularly the Capacitated VRP (CVRP), which is a more realistic modelization approach. For businesses that perform distribution to customers frequently, such as management work with the coordination of daily distribution, finishing the distribution on time is of great importance. In big cities with complicated roads and many dropping points, this can be achieved by benefiting from the systematic modeling of the CVRP. In this study, the delivery network investigation for one production facility of the Istanbul People's Bread positioned on the Asian side of Istanbul, Türkiye that distributes three times a day will be the focus of interest. The corresponding Asymmetric CVRP (ACVRP) for the facility network and 215 bread-selling buffets with authentic driving distances will be solved with the Genetic Algorithm (GA), and an optimized transportation network will be presented.

The Multiple Traveling Salesman Problem (MTSP) was able to model and solve various theoretical and real-life applications. This problem is one of the many difficult issues that have no perfect solution yet. In this paper, on the one hand genetic algorithms with different combinations of operators and simulated annealing were used to solve the MTSP. On the other hand, the genetic algorithm with the combination of operators that gave the best solutions of the MTSP was hybridized with a Simulated Annealing algorithm. The simulation results showed that the hybrid algorithm significantly outperforms most of the comparable methods in obtaining the best-fitness solutions compared to the other methods in most of the test cases. In addition, by scaling the fitness function according to the amplitude of tours, it was obvious that the non-dominated front obtained by the hybrid algorithm was better than the non-dominated front obtained by the other algorithms.

The multiple travelling salesman problem (MTSP) extends the classical travelling salesman problem (TSP) by involving multiple salesman in the solution. MTSP has found widespread applications in various domains, such as transportation, robotics, and networking. Despite extensive research on MTSP and its variants, there has been limited attention given to the open close multiple travelling salesman problem (OCMTSP) and its variants in the literature. To the best of the author's knowledge, only one study has addressed OCMTSP, introducing an exact algorithm designed for optimal solutions. However, the efficiency of this existing algorithm diminishes for larger instances due to computational complexity. Therefore, there is a crucial need for a high-level metaheuristic to provide optimal/best solutions within a reasonable timeframe. Addressing this gap, this study proposes a first meta-heuristic called multi-chromosome-based Genetic Algorithm (GA) for solving OCMTSP. The effectiveness of the developed algorithm is demonstrated through a comparative study on distinct asymmetric benchmark instances sourced from the TSPLIB dataset. Additionally, results from comprehensive experiments conducted on 90 OCMTSP symmetric instances, generated from the renowned TSPLIB benchmark dataset, highlight the efficiency of the proposed GA in addressing the OCMTSP. Notably, the proposed multi-chromosome-based GA stands out as the top-performing approach in terms of overall performance. Further, solutions to symmetric TSPLIB benchmark instances are also reported, which will be used as a basis for future studies.

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.

The genetic algorithm (GA) is a natural selection-inspired optimization algorithm. It is a population-based search algorithm that utilizes the concept of survival of the fittest. This study creates a new crossover operator called “Stas Crossover” that is a combination of four crossover operators, including Single point crossover, Two points crossover, Arithmetic crossover, and Scattered crossover, and then presents the performance of this crossover operator. The area size and probability of Stas crossover can be adjusted.GA is used to find the optimal solution for this multi-product and multi-period aggregate production planning (APP) problem, which was used to test the algorithm, which provides optimal levels of inventory, backorders, overtime and regular production rates, and other controllable variables. According to the findings of this study, the benefit of stable crossover is that it allows for more variety in the way offspring are created and increases the opportunity for offspring to obtain good genetic information directly.

In this article, the application of the Multi-Skilled Resource-Constrained Flow Shop Scheduling Problem (MSRC-FSSP) in preventive maintenance as a case study has been investigated. In other words, to complete each maintenance order at each stage, in addition to the machine, a set of required human resources with different skills must be available. According to human resources skills, each of them can perform at least one order or at most N orders, and each maintenance order must be done by a set of human resources with different skills. To carry out a maintenance order, different human resources must be in communication and cooperation so that a preventive maintenance order can be completed. In this article, these resources are considered as technical supervisors, repairmen and maintenance managers who complete all maintenance orders in a flow shop environment as a job. For this problem, a new Mixed Integer Linear Programming (MILP) model has been formulated with the two-objective functions, minimizing total orders completion time and the human resources idle time. To solve the model on a small scale, CPLEX is used, and to solve it on a large scale, due to the fact that this problem is NP-Hard, a meta-heuristic algorithm named Genetic Algorithm (GA) is presented. Finally, the computational results have been done to validate the model, along with the analysis of the human resources idle time.