Global Journal of Computer Science and Technology, D: Neural & Artificial Intelligence, Volume 22 Issue 1

append it to the route, update the variables and go for the next node, using the updated variables. These changes in each iteration are all recorded in a solution set, which will then be used for finding the best solution from the set. When determining the optimal route for the best solution, pheromone update is used which includes pheromone deposition and pheromone evaporation. Pheromone update is used to elevate the pheromone values that are found on good solution paths and decrease those that are on bad solution paths. In pheromone deposition and evaporation, pheromone values either increase or decrease at a constant rate [29]. The pheromone evaporation equation is given as such, = � + �, ∀( , ) ∈ (15) Where trail persistence 1 ≥ ≥ 0 of the evaporation factor 1 ≥ � + � ≥ 0 and is a constant. In each iteration, number of ants find = ∑ =1 of average total distance. Then pheromone is updated by the elitist and best ants After the evaporation process, only the best and the elitist ants can update the pheromone deposits on the optimal path chosen, which is given by the equation = + ∆ ∗ +� −1 =1 (16) Where,(16) ∆ = { − ℎ ( , )0 0 ℎ (17) ∆ ∗ = { ( , )0 ℎ (18) Looking at equations 17 and 18, it can be concluded that there are two types of pheromone depositions that are deposited on the trails during the pheromone update process. First, if elitist ants have travelled a path, that path will be updated as the best solution so far ( ) , in accordance with the ACO+K- Means Clustering algorithm. ∆ ∗ denotes the pheromone update by the elitist ants. Second, out of the ants available, only ( − 1) best ants, in the current iteration, can deposit pheromone on the path they have traversed. The term is used to denote the pheromone quantity laid down on the trails that have been traversed by them and the amount of pheromone that have been deposited by the ants are determined by their solution quality and rank and the value is equal to . To summarize, the elitist ants need to increase the probability of the best-solution so far after each iteration as the values that are updated will act as reference values for the next iteration. The ranking methodology has been employed in [17] so as to reduce pheromone deposition on those routes that have relatively lesser favourability. V. C ase S tudy a) Dataset Used The dataset for this paper has been taken from the Solomon-100 standard test set which have 20 problem cases. It also includes x-y location coordinates, service time, demand by customers, due dates and ready time. This section will be in comparison with [30] as it has used the same data set. This comparison will help in proving that the proposed solution from this paper is the better method of solving the (MPMDVRPTWHF) as it gives better cost reduction with lesser percentage of carbon emissions, along with optimized fuel consumptions and lesser vehicles used. b) Parameters Defined The parameters defined in this paper are derived from [30] as this paper is in comparison with the latter. Similar to [30] the delivery vehicle used is a refrigerator car and the set of pre-defined parameters as shown in table 1 given below. Global Journal of Computer Science and Technology Volume XXII Issue I Version I 54 ( )D Year 2022 © 2022 Global Journals Vehicle Routing Problem with Time Window Constrain using KMeans Clustering to Obtain the Closest Customer