# Internet of Things-Assisted Vehicle Route Optimization for Municipal Solid Waste Collection
## 4 Proposed Technique  
In our proposed mechanism, multiple parameters related to waste is considered such that the route is selected keeping in mind all those parameters. For that, TOPSIS, known as the Technique for Order of Preference by Similarity to Ideal Solution, is used. It is a multi-criteria decision analysis method. TOPSIS is useful in situations where decision makers need to consider multiple criteria with varying importance. It provides a systematic approach to rank and select alternatives based on their overall performance, taking into account the preferences of decision makers. In waste collection, TOPSIS is utilized to choose the most efficient route by considering factors like volume, toxicity, time, and distance. The detailed algorithm is presented in Algorithm 1. Figure 1: Waste collection scenario. ```
Inputs:  A graph \(G=(n,e)\) with nodes \(n\) and edges \(e\)  Data regarding waste attributes as weights of \(G\) (toxicity \(\
u\), volume \(V\), time \(t\), \(d\)) Algorithm Steps: Step 1: Normalize the data for each waste attribute (\(\
u\), \(V\), \(t\), \(d\)) between 0 and 1. The goal is to maximize \(\
u\), \(V\), and \(t\) while minimizing \(d\). Normalized Value \(=\frac{\text{Actual Value}}{\sqrt{\sum\text{Actual Value}^{2}}}\) Step 2: Calculate the weighted normalized values for each route based on the waste attributes. WeightedValue = \((\
u\times W_{\
u})+(V\times W_{V})+(t\times W_{t})+(d\times W_{d})\)  where \(W_{\
u}\), \(W_{\
u}\), \(W_{t}\), and \(W_{d}\) are the assigned weights. Step 3: Determine the ideal and negative-ideal solutions for each attribute. Ideal solution: Maximum normalized value for toxicity, volume, and time; minimum normalized value for distance. Negative-ideal solution: Minimum normalized value for toxicity, volume, and time; maximum normalized value for distance. Step 4: Calculate the proximity of each path to the ideal and negative-ideal solutions using a distance measure. - Calculate the distance of each path from the ideal solution and the negative-ideal solution. \(D_{i}^{+}=\sqrt{\sum_{j=1}^{m}(\text{NormalizedValue}_{ij}-\text{IdealSolution} _{ij})^{2}}\) \(D_{i}^{-}=\sqrt{\sum_{j=1}^{m}(\text{NormalizedValue}_{ij}-\text{Negativeldeal Solution}_{j})^{2}}\) Step 5: Compute the TOPSIS score for each path: \(TOPSIS_{i}=\frac{D_{i}^{-}}{D_{i}^{+}+D_{i}^{-}}\) Step 6: Rank the paths based on their TOPSIS scores. The routes with higher accumulated TOPSIS scores are more favorable for waste collection as they match the criteria of higher toxicity, volume, time, and lower distance. Output:  The prioritized route(s) for waste collection based on TOPSIS scores. ```  
**Algorithm 1** Route Selection Algorithm using TOPSIS  
Algorithm 1 provides the steps involved in determining the prioritized routes in a graph \(G\), with nodes \(n\) representing the bins and edges \(e\) representing the paths between the nodes. The aim is to calculate or obtain a path between starting and ending nodes that is optimum for all the waste attributes that we are considering as weights of the edges. The data are normalized for each waste attribute (toxicity, volume, time and distance) individually to ensure that each attribute is on the same scale for a fair comparison. The normalization is performed as given below:  
\[\text{Normalized Value}=\frac{\text{Actual Value}}{\sqrt{\sum\text{Actual Value}^{2}}} \tag{1}\]  
Next, the algorithm calculates the weighted normalized values for each path. The weighted value is obtained by multiplying each normalized attribute (toxicity, volume, time, and distance) by its assigned weight and summing these values. The formula is given by:  
\[\text{WeightedValue}=(\
u\times W_{\
u})+(V\times W_{V})+(t\times W_{t})+(d \times W_{d}) \tag{2}\]  
where, \(W_{\
u}\), \(W_{V}\), \(W_{t}\), and \(W_{d}\) are the weights assigned for toxicity, volume, time, and distance, respectively. Then, in the next step, the ideal and negative-ideal solutions for each attribute are identified.