constrained gravitational search algorithm

In the past decades, vehicle routing problem (VRP) has gained considerable attention for its applications in industry, military, and transportation applications. Vehicle routing problem with simultaneous pickup and delivery is an extension of the VRP. This problem is an NP-hard problem; hence finding the best solution for this problem which is using exact method, take inappropriate time, and these methods are not useful in real-world applications. Using meta-heuristic algorithms for calculating and computing the solutions for NP-hard problems is a common method to contrast this challenge. The objective function defined for this problem, is a constrained objective function. In previous algorithms, the penalty method was used as constraint handling technique to define the objective function. Determining the value of parameters and penalty coefficient is not easy in these methods. Moreover, the optimal number of vehicles was not considered in the previous algorithms. So, the user should guess number of vehicles and compare the result with other values for this variable. In this paper, a novel objective function is defined to solve the vehicle routing problem with simultaneous pickup and delivery. This method can find the vehicle routes such that increases the performance of the vehicles and decreases the processes’ costs of transportation. in addition, the optimal number of vehicle in this problem can be calculated using this objective function. Finding the best solution for this optimization problems is an NP-hard and meta-heuristic methods can be used to estimate good solutions for this problem. Then, a constrained version of gravitational search algorithm is proposed. In this method, a fuzzy logic controller is used to calculate the value of the parameters and control the abilities of the algorithm, automatically. Using this controller can balance the exploration and exploitation abilities in the gravitational search algorithm and improve the performance of the algorithm. This new version of gravitational search algorithm is used to find a good solution for the predefined objective function. The proposed method is evaluated on some standard benchmark test functions and problems. The experimental results show that the proposed method outperforms the state-of-the-art methods, despite the simplicity of implementation.