This paper proposes the cuckoo search (CS), central force optimization (CFO), chemical reaction optimization (CRO) and 3-Opt for solving the capacitated vehicle routing problem (CVRP). HCSCROCFO-3Opt, which is the parallel hybrid algorithm that is proposed, is a form of augmented HCSCROCFO with a local search process founded on CS that utilizes positive aspects of the other optimization approaches including CRO and CFO in order to enhance quality of initial population and improve local search, correspondingly. The work is motivated by the need to enhance the computational effectiveness through attainment of improved outcomes compared to previous popular solutions, to explore the features of different parameters of to seek some ideal solutions. The first stage entails solving of CVRP through setting a variety of values to tune parameters for the HCSCROCFO-3Opt proposed. Then initialization of algorithm CS, CRO, CFO parameters are accomplished through tuning parameters within a tuning cycle. Subsequently, a novel solution is swapped in a random manner through a levy flight within the central loop, followed by execution of the hybrid solution as well as new CRO, CFO and CS algorithm solutions, whose implementation is supposed to enhance results for the local 3-Opt. Ultimately, the most ideal solution for general hybrid model’s solution space is identified, after which the solution that is best-suited for the CVRP purposes is presented. Within the standard CVRP cases, reported computational tests in large scale in the literature demonstrate the efficiency of presented approach.

Capacitated Vehicle Routing Problem (CVRP) is considered as one of the most famous specialized forms of VRP that has attracted considerable attention from researchers. This problem belongs to complex combinatorial optimization problems included in the NP-Hard Problem category, which is a problem that needs difficult computation. This paper presents an improvement of Ant Colony System (ACS) to solve this problem. In this study, the problem deals with a few vehicles which are used for transporting products to specific places. Each vehicle starts from a main location at different times every day. The capacitated vehicle routing problem (CVRP) is defined to serve a group of delivery customers with known demands. The proposed study seeks to find the best solution of CVRP by using improvement ACS with the accompanying targets: (1) To decrease the distance as long distances negatively affect the course of the process since it consumes a great time to visit all customers. (2) To implement the improvement of ACS algorithm on new data from the database of CVRP. Through the implementation of the proposed algorithm better results were obtained from the results of other methods and the results were compared.

In this paper, an optimization model for the Charging Station Location Problem of Electric Vehicles for Freight Transportation CSLP-EVFT is presented. This model aims to determine an optimal location strategy of Electric Vehicle Charging Stations EVCSs and the routing plan of a fleet of electric vehicles under battery driving range limitation, in conjunction with the impact on the power distribution system. Freight transportation is modeled under the mobility patterns followed by the Capacitated Vehicle Routing Problem CVRP for contracted fleet, and Shortest Path SP problem for subcontracted fleet. A linear formulation of the power flow is used in order to consider the impact on the electric grid. Several costs are examined, i.e., EVs routing, installation and energy consumption of EVCSs, and energy losses. Although uncertainties related to temporal variation of some aspects (number of customers and their demands, fleet size, power network nodes and routes) are not addressed, the proposed model represents a useful approach to evaluate multiple scenarios or to be introduced within stochastic optimization. Instead, the mathematical model is studied under the variation of EVs travel range that accounts for the advance of battery technology and sensitivity analysis. Additionally, the problem is reduced to a mixed integer non-linear mathematical model, which is linearized by using multivariable Taylor’s series.

Electric Vehicles (EVs) represent a significant option that contributes to improve the mobility and reduce the pollution, leaving a future expectation in the merchandise transportation sector, which has been demonstrated with pilot projects of companies operating EVs for products delivering. In this work a new approach of EVs for merchandise transportation considering the location of Electric Vehicle Charging Stations (EVCSs) and the impact on the Power Distribution System (PDS) is addressed. This integrated planning is formulated through a mixed integer non-linear mathematical model. Test systems of different sizes are designed to evaluate the model performance, considering the transportation network and PDS. The results show a trade-off between EVs routing, PDS energy losses and EVCSs location.

In this paper, we introduce a unified mathematical formulation for the Capacitated Vehicle Routing Problem (CVRP) and for the Capacitated Location Routing Problem (CLRP), adopting radiality constraints in order to guarantee valid routes and eliminate subtours. This idea is inspired by formulations already employed in electric power distribution networks, which requires a radial topology in its operation. The results show that the proposed formulation greatly improves the convergence of the solver.