# Clustering-Based Modified Ant Colony Optimizer for Internet of Vehicles (CACOIOV)
## 3 Proposed CACOIOV Architecture
### Protocol Description of CACIOV
The probability of the vertex being selected as a CH increases due to with the high heuristic \((He)\) and pheromone \((\tau)\) values. The edge selection is executed by the selection of a roulette wheel which has low computational complexity as O (1) to prevent algorithms becoming stuck in the local optimum [30]. Since we are using this approach (roulette wheel selection) for constructing a solution (transition rule), therefore, \(\tau_{i,j}\) and \(He_{i,j}\) are not raised to alpha and beta parameters as in the conventional ACO. The ant tour is finished when two main constraints are applied during the process of vertex selection. The first rule is the vertex, which does not exist in the current tour/solution but can be added into the tour. This rule assures CMs belong to only one cluster. The second rule is any vertex in the transmission range of another vertex in the current solution is not permitted to contribute to the selection process. This rule is to guarantee every cluster has only one CH. The solution construction/selection process will be continued until there are no more vertices available to be added into the tour. Consequently, to decrease the communication overhead, the tours which consist of fewer clusters or CH number will be preferred. \[P_{i,j}=\frac{\tau_{i,j}\cdot He_{i,j}}{\sum_{k\in s}\tau_{i,j}\cdot He_{i,j}} \tag{7}\]  
_(c) Fitness Evaluation:_  
As a result of the multi-objective nature of the clustering of the VANET, the equations that follow are used to evaluate the ant tour by the normalization of the objective function. Equation (8) is used to calculate both heuristic value and objective function [7]. \[f_{t}=W_{1}\cdot f_{1}+W_{2}\cdot f_{2} \tag{8}\]\[f_{1}(\Delta difference)=\sum_{i=1}^{|t|}ABS(D-|CM_{i}|) \tag{9}\] \[f_{2}(Dist-sum)=\sum_{i=1}^{|t|}(\sum_{j=1}^{|CM_{i}|}ED(CH_{i},CM_ {i,j})) \tag{10}\]  
_(d) Dynamic Strategy of Evaporation Factor:_  
The algorithm of conventional ACO consists of static evaporation rate (\(\rho\)) with the value of 0.05, which has a direct impact on the convergence rate and capability of global search. Sufficiency of search for ACO algorithm is determined by the evaporation rate, which decreases the pheromone value on an ant tour to zero. If this phenomenon occurs for an unvisited vertex then the ACO algorithm will not be successful in terms of the ability for global search to find the best tour. Hence, tuning evaporating and pheromone value is the controlling key to evaporate and release pheromone. In [43] the aim is establishing a dynamic evaporation rate with a huge value at the start of the ACO process for enhancement ability of the global search. This technique accelerates the convergence to some extent. To explore the decay model better, for the rate of evaporation, there are 3 decay model types: the model of curve decay, scale decay, and line decay. Based on the implementing of a set of experiments, the curve decay is selected by [PERSON] [46]. In this context, we proposed a novel method for finding the effective pheromone evaporation. By considering Dynamic Pheromone Effectiveness (_DPE_) value as zero at the first step, the evaporation rate can be initiated as follows in Equation (11), which is used in (line # 18) of Algorithm 1. Due to the interval evaporation rate, which is [0-1], _DPE_ should be multiplied to a constant value of 0.1 (\(\rho_{initial}\)). \[L_{D}=[\frac{(1-T_{D})}{\lambda^{\prime}}+1]^{-1} \tag{2}\]0  
_(i) Dynamic Pheromone Effectiveness (DPE):_  
The other important factor that is suggested by this work is _DPE_. This factor has a critical impact on updating a pheromone and the decision for the next node selection depends directly upon the evaporation rate of ants. This parameter has a change range of [0-1] which changes by time. At first, the coefficient is zero to give adequate time to ants to conduct a better search between existing nodes and, as time passes, this coefficient increases slowly to reach to one.