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The routing cost of a spanning tree in a weighted and connected graph is defined as the total length of paths between all pairs of vertices. The objective of the minimum routing cost spanning tree problem is to find a spanning tree such that its routing cost is minimum. This is an NP-Hard problem that we present a GRASP with path-relinking metaheuristic algorithm for it. GRASP is a multi-start algorithm that in each iteration constructs a randomized greedy solution and applies local search to it. Path-relinking stores elite solutions and to find better solutions explores the paths between different solutions. Experimental results show the performance of our algorithm on many benchmark problems compared to the other algorithms.

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In the past decade, fuel consumption and CO₂ emission have increased in the airline industry. Large CO₂ footprint has a damaging effect on the environment. Global concerns over this issue has made the airline industry to be greener. Most efforts of the green airline industry are improving the fuel consumption to reduce the CO₂ emission and its environmental damage. Here, we use cruise speed control to control the fuel consumption and CO₂ emission. Each aircraft has a different speed level needing a different fuel consumption. Service quality is studied besides the energy consumption. We investigate two objectives including total energy consumption (TEC) and passenger service level (PSL). TEC and PSL are conflicting in nature. We develop a mixed-integer nonlinear programming model to integrate schedule design, aircraft assignment and maintenance routing problems. We make use of the augmented ε-constraint method to solve the problem. To evaluate the model, a real data based on the Emirates airline flights is used. The results are compared using four different scenarios

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We present a bi-objective model for a green truck scheduling and routing problem at a cross-docking system. This model determines three key decisions at the cross dock: (1) defining a sequence and schedule of inbound trucks at the receiving door, (2) specifying a sequence and a schedule of outbound trucks at the shipping door, and (3) determining the routes of the outbound truck while serving customers. The first objective function is related to responsiveness of the network that minimizes time window violations and the second objective function minimizes total fuel consumption of trucks in order to consider the environmental factor of the network. Also, a learning effect is considered in loading and unloading process times. To solve the bi-objective model, an archived multi-objective simulated annealing (AMOSA) is used and modified. Finally, a number of test problems are solved and the efficiency of the proposed AMOSA is compared with the e-constraint method.

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Capacitated vehicle routing problem (CVRP) is one of the most well-known and applicable issues in the field of transportation. It has been proved to be an NP-Complete problem. To this end, it is needed to develop a high-performance algorithm to solve the problem, particularly in large scales. This paper develops a novel mathematical model for the CVRP considering the satisfaction level of demand nodes. Then, the proposed model is validated using a numerical example and sensitivity analyses that are implemented by CPLEX solver/GAMS software. To solve the problem efficiently, a Genetic Algorithm (GA) is designed and implemented. The obtained results demonstrate that the proposed GA can yield high-quality solutions compared to exact solutions.

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This paper is concerned with presenting an exact algorithm for the Undirected Profitable Location Rural Postman Problem. This problem combines the profitable rural postman and facility location problems and also has some interesting real-life applications. Fixed costs are associated with end points of each profitable edge and the objective is to choose a subset of profitable edges such that the difference between the profit collected and the cost of opening facilities and traveling cost is maximized. A dominance relation is used to present an integer programming formulation for the problem and a branch and cut algorithm is developed for solving the problem and extensive numerical results on real-world benchmark instances are given to evaluate the quality of presented algorithms.
 

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Due to the importance of vehicle routing for delivering a large number of orders with different restrictions in the world, various optimization methods have been studied in past researches. In this article, a number of researches of recent years have been discussed, then the proposed model is described in 3 phases with the penalty index. This model has the ability to assign orders, route vehicles and determine the number of active vehicles dynamically with the aim of minimizing the total cost of distribution. By examining valid metaheuristic models and using their strengths and weaknesses, and considering multiple limitations, a new model of "dynamic 3-phase optimization" has been designed. The main application of the proposed model is for vehicle routing problems with capacity constraints of fleet number and capacity constraints (maximum and minimum number of orders). Finally, with simulation, the outputs of the model have been analyzed in different conditions . Although the limitation of maximum and minimum capacity is added to the problem, by dynamically considering the number of vehicles and using star clustering (initiative of this research), three social, environmental and economic dimensions were improved. The time for orders to reach customers decreased by 19.3%, fuel consumption and air pollution by 14.9%, and logistics costs by 8.7%. To calculate the final value of system stability, a unique 3D fuzzy model has been used. With the sensitivity analysis, we came to the conclusion that the 3-phase dynamic optimization model has led to a 14.58% improvement in system stability.

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One of the most important and widely used problems in the logistics part ‎of ‎any supply chain is the location-routing problem (LRP) of vehicles. The ‎‎purpose is to select distribution centers to supply goods for ‎‎customers and create suitable travel routes for vehicles to serve ‎customers.‎ Studies conducted in the field of supply chain logistics systems have shown that if vehicle travel routing is neglected when locating supply centers, the costs of the logistics system may increase dramatically. Therefore, in the LRP problem, the location of supply centers and the routing of vehicles are considered simultaneously. In this paper, we will present a multi-objective model for vehicle location-routing problems with a flexible fuzzy ‎approach. Its' goals are to make strategic decisions to deploy ‎candidate supply centers at the beginning of the planning horizon, as well as ‎form the vehicle travel at the tactical level to serve the customers in ‎short-term periods of time. Therefore, in ‎order to adapt the mathematical model to the real conditions, the ‎constraints related to the capacity of the vehicles have been considered in a ‎flexible fuzzy state, and also the problem has been modeled in a multi-period state along with the presence of the distance limit and the ‎accessibility factor for each vehicle. The evaluation criterion is to minimize costs related to the establishment of candidate supply centers, the fixed cost of using vehicles and transportation costs, as well as maximizing customer satisfaction by reducing shortage costs and reducing harmful environmental effects. To solve the model, it is first converted into a single-objective model using the weight method and then solved using the proposed algorithm. Finally, using a numerical example in the field of waste management, the effectiveness of the proposed solution method is shown. It should be mentioned that the model was solved using GAMS software and the results are shown.
 

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Enhancing the efficacy and productivity of transportation system has been on the most common issues in recent decades, noteworthy to the industrial managers and expert so that the products are delivered to the clients at right time and the least costs. Therefore, there are two important issues; one is to create hub as the as intermediaries for streaming from multiple origins to multiple destinations and also responding to the tours of every hub at the proper time. The other is a route where the vehicles should pay at time window of each destination node. On the other hand, these problems may cause cost differences between hub and interruption of their balance. Accordingly, this paper presents a model dealing with cost balancing among the vehicles as well as reducing the total cost of the system. Given the multi-objective and NP-Hard nature of the issue, a multi-objective imperialist competitive algorithm (MOICA) is suggested to provide Pareto solutions. The provided solutions are at small, average and large scales are compared with the solutions provided by Non-Dominated Sorting Genetic Algorithm (NSGA-II) algorithm. Then, its performance is determined using the index for evaluating the algorithm performance efficacy to solve the problem at large dimensions.