This article paper presents a hybrid metaheuristic algorithm to solve the time-dependent vehicle routing problem with hard time windows. Time-dependent travel times are influenced by different congestion levels experienced throughout the day. Vehicle scheduling without consideration of congestion might lead to underestimation of travel times and consequently missed deliveries. The algorithm presented in this paper makes use of Large Neighbourhood Search approaches and Variable Neighbourhood Search techniques to guide the search. A first stage is specifically designed to reduce the number of vehicles required in a search space by the reduction of penalties generated by time-window violations with Large Neighbourhood Search procedures. A second stage minimises the travel distance and travel time in an ‘always feasible’ search space. Comparison of results with available test instances shows that the proposed algorithm is capable of obtaining a reduction in the number of vehicles (4.15%), travel distance (10.88%) and travel time (12.00%) compared to previous implementations in reasonable time.
In future electricity industry transferring high quality of power is essential. In this case, using Flexible AC Transmission System (FACTS) devices is inevitable. FACTS devices are used for controlling the voltage, stability, power flow and security of transmission lines. Therefore, finding the optimal locations for these devices in power networks is necessary. There are several varieties of FACTS devices with different characteristics, deployed for different purposes. Imperialist Competitive (IC) algorithm is a recently developed optimization technique, applied in power systems. IC algorithm is a new heuristic approach for global optimization searches based on the concept of imperialistic competition. In this paper, an IEEE 4-bus system is deployed as a case study in order to demonstrate the results of this novel approach using MATLAB.