# An Improved Simulated Annealing Technique for Enhanced Mobility in Smart Cities

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## Abstract

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_{2}emissions as compared to other algorithms; also, similar performance patterns were achieved for the Birmingham test scenario.

## 1. Introduction

_{2}emissions are due to inefficient vehicle management [1]. This has resulted in significant economic and productivity losses, making improvement of mobility a key challenge within smart cities. Solving such a problem can be aided by information obtained via sensors deployed as part of smart city initiatives, which then have to be communicated to vehicles/drivers to allow them to make a decision with regards to alternative routes. Once such a decision had been made, it would also be feasible to eventually see information regarding planned routes to be communicated back from the vehicles to the smart city infrastructure. Such information can then be used to predict the number of vehicles at each intersection within a smart city, which in turn could be used to adapt the sequences of traffic lights to allow a more overall optimal traffic flow for the city as a whole. A further example of how this can be used within smart cities would be related to reducing the concentrations of air pollution within the city. This would be achieved by redirecting heavily polluting vehicles away from areas with high pollution levels.

- A large portion of the previous or current vehicle routing algorithms attempt to identify the minimum TD or TT. Generally, they cannot attain an active trade-off.
- Utilizing just individual traffic information or a single cost function for the vehicle routing problem is not satisfactory. Different navigation criteria should be considered to find the optimal path of the driver. This will help drivers to have different navigation options, which can be the fastest route, the least congested, the least fuel consumption and the least air pollution.

## 2. Related Work

- ISATOPSIS allows transition from a good solution to a worse solution under a strict condition. This allows the algorithm to find the global optimal solution and avoid becoming stuck in local optimal solutions.
- ISATOPSIS can work for dynamic path planning by collecting real-time traffic data from IoV and efficiently finding alternative routes for the driver.
- ISATOPSIS can optimize more than one criteria using the MADM TOPSIS method, which allows alternative routes to be judged on different criteria.
- ISATOPSIS periodically detects and avoids congestion by selecting the paths that have the minimum traffic, CO
_{2}emissions, fuel consumption, as well as travel time. This is due to combining different navigation attributes in the cost function.

## 3. System Description

#### 3.1. Data Dissemination

#### 3.2. Road Network

_{j}periodically sends a message msg

_{j}that contains {roadId

_{j}, averagespeed

_{j}, position

_{j}, route

_{j}, destination

_{j}} to the neighbouring RSUs.

- Road length ${C}_{L}=\left\{{r}_{kj}\right|\phantom{\rule{0.166667em}{0ex}}k=1,\cdots ,n;\phantom{\rule{1.em}{0ex}}j=1\}$ represents the normalized length in a directed graph G for each alternative in A.
- Average velocity ${C}_{S}=\left\{{r}_{kj}\right|\phantom{\rule{0.166667em}{0ex}}k=1,\cdots ,n;\phantom{\rule{1.em}{0ex}}j=2\}$ represents the normalized average speed of each vehicle at a certain period in A.

#### 3.3. Simulated Annealing of SAWS and SATOPSIS

Algorithm 1 The simulated annealing algorithm for enhancing mobility. | |

1: | ${X}_{c}={X}_{{c}_{0}}$ Initial random solution |

2: | $T={T}_{0}$ An initial temperature |

3: | α = Cooling rate |

4: | ${s}_{b}$ = Current best solution |

5: | ${s}_{b}$ ← ${X}_{c}$ |

6: | While $T>{T}_{m}$ where ${T}_{m}$ is the minimum temperature |

7: | Generate a random neighbour solution ${X}_{n}$ from ${R}_{k}$ |

8: | If $N\left({X}_{n}\right)>C\left({X}_{c}\right)$ |

9: | Move to ${X}_{n}$ |

10: | Accept change ${s}_{b}\leftarrow {X}_{n}$ |

11: | Else If $N\left({X}_{n}\right)\le C\left({X}_{c}\right)$ Then |

12: | Move to ${X}_{n}$ with transition probability |

13: | ${P}_{t}=1/1+\mathbf{exp}(C\left({X}_{c}\right),N\left({X}_{n}\right),T)$ |

14: | Endif |

15: | $T=\alpha T$ |

16: | Endwhile (if $T<{T}_{m}$) |

17: | Return ${s}_{b}$ |

#### 3.4. An Improved Simulated Annealing TOPSIS Algorithm

#### 3.4.1. Off-Line Computation of Path Planning

- An initial optimal path ${X}_{c}=\{{r}_{s},{r}_{1},\cdots ,{r}_{i},{r}_{i+1},\cdots ,{r}_{l-1},{r}_{l},{r}_{d}\}$ where ${r}_{i}$ means the i-th road segment.
- The perturbation (see Figure 3) consists of the following three steps.
- (a)
- Two roads ${r}_{i}$ and ${r}_{l}$, called base roads, are chosen randomly in the ${X}_{c}$ path.
- (b)
- A path is constructed, using ${r}_{i}$ as an origin and ${r}_{l}$ as a destination.
- (c)
- The path ${X}_{c}=\{{r}_{s},{r}_{1},\cdots ,{r}_{i},{r}_{i+1},\cdots ,{r}_{l-1},{r}_{l},{r}_{d}\}$ is replaced by (${r}_{i}$, $\stackrel{\xb4}{{r}_{i+1}}$, ⋯, $\stackrel{\xb4}{{r}_{l-1}}$) to give a new path ${X}_{n}=\{{r}_{s},{r}_{1},\cdots ,{r}_{i},\stackrel{\xb4}{{r}_{i+1}},\cdots ,\stackrel{\xb4}{{r}_{l-1}},{r}_{l},{r}_{d}\}$.

- Check the feasibility of the new path.
- If its not feasible, then repeat the process. Otherwise, use SA as in Algorithm 1 and compare the cost of the new path to the previous path.

#### 3.4.2. On-Line Computation of Path Planning

#### 3.5. Calculate the Weights of SAWS, SATOPSIS and ISATOPSIS

#### 3.6. Simulated Annealing Weighted Sum Method

#### 3.7. TOPSIS Cost Function of SATOPSIS and ISATOPSIS

- Calculate the weighted normalized ratings by using the normalized matrix from Equations (1) and (2):$${z}_{kj}={w}_{j}{r}_{kj}$$
- Calculate the positive and negative ideal solutions (PIS and NIS), which are the maximum and the minimum values of the criterion (j) in ${C}_{L}$ and ${C}_{S}$, respectively. We can formulate the normalized road matrix and obtain the positive and negative ideal solutions as follows:$$\begin{array}{}\mathrm{(9a)}& \hfill PIS={H}^{+}=\{{z}_{1}^{+},\cdots ,{z}_{j}^{+}\}\mathrm{(9b)}& \hfill NIS={H}^{-}=\{{z}_{1}^{-},\cdots ,{z}_{j}^{-}\}\end{array}$$
- Calculate the separation (${D}_{k}^{*}$ and ${D}_{k}^{-}$) from PIS (${H}^{+}$) and NIS (${H}^{-}$) for the alternative paths as follows:$$\begin{array}{}\mathrm{(10a)}& \hfill {D}_{k}^{*}=\sqrt{{\displaystyle \sum _{j=1}^{2}}{({z}_{kj}-{z}_{j}^{+})}^{2}}\phantom{\rule{1.em}{0ex}}\phantom{\rule{1.em}{0ex}}k=1,\cdots ,n\mathrm{(10b)}& \hfill {D}_{k}^{-}=\sqrt{{\displaystyle \sum _{j=1}^{2}}{({z}_{kj}-{z}_{j}^{-})}^{2}}\phantom{\rule{1.em}{0ex}}\phantom{\rule{1.em}{0ex}}k=1,\cdots ,n\end{array}$$
- Calculate the cost function of SA by finding the similarities to PIS using:$${Y}_{k}^{*}=\frac{{D}_{k}^{*}}{{D}_{k}^{*}+{D}_{k}^{-}}\phantom{\rule{1.em}{0ex}}\phantom{\rule{1.em}{0ex}}{Y}_{k}^{*}\in [0,1]\phantom{\rule{1.em}{0ex}}\forall k=1,\cdots ,n$$

## 4. Performance Evaluation

#### 4.1. Scenario of Sheffield City

- A large initial temperature T allows for an exhaustive search, but leads to a large computation time. Reducing this initial value will reduce the computation time required at the expense of making it less likely that the globally optimal solution will be achieved.
- As the value of α controls the rate at which Tdecreases, a larger value gives a quicker decrease. This results in a shorter computation. However, this will also result in the algorithm running for fewer iterations, making it less likely to reach the truly optimal solution.

_{2}emissions have been computed based on parameters that have been considered in the cost function (vehicle speed and road length).

_{2}emissions) that are used in this paper. The obtained result of the proposed method has been compared to the SAWS, SATOPSIS and DA algorithms.

_{2}emission). The ISATOPSIS combines the SA algorithm and TOPSIS method as a cost function to optimize different conflicting criteria, such as the length and the average speed. It has successfully minimized the average travel time, fuel consumption and CO

_{2}emission. However, this has led to a slightly increased average travel distance that has not affected the overall traffic efficiency.

**Mean travel time (MTT)**: the average travel time of all vehicles.**Mean travel distance (MTD)**: the average travel distance taken by vehicles.**Fuel consumption (FC)**: the average fuel consumption of vehicles.**CO2 emission**: the average CO_{2}emission of all vehicles.

_{2}emissions because most vehicles travelling with DA are stuck in congestion. On the other hand, SATOPSIS attempts to minimize all of the matrices by considering multiple attributes in the cost function. It has better performance compared to SAWS, except for the travel time, which converges to some extent with SAWS. In comparison, ISATOPSIS decreases the MTT, FC and CO

_{2}emissions when compared to DA, SAWS and SATOPSIS. This reduction is due to the re-routing of all vehicles once the congestion is detected. In addition, these results demonstrate the benefits of considering the multiple attribute cost function performed by the ISATOPSIS algorithm to avoid the congestion. However, this re-routing slightly increased the MTD compared to DA and SATOPSIS, respectively. This increase is due to the dynamic re-routing of vehicles, and thus, an extra path has been added to the original route.

_{2}due to its ability to consider multiple pieces of traffic information. However, this reduction leads to a slight increase in the travel distance compared to DA and SATOPSIS, since ISATOPSIS utilizes the traffic information and re-routes the vehicles to avoid the congested roads, where DA and SATOPSIS have a constant travel distance that is not affected when congestion occurs.

_{2}emissions recorded from all of the algorithms. The results of CO

_{2}emissions are directly related to the results of fuel consumption. The longer travel distance, the larger waiting time and the more fuel consumed by the engine result in higher CO

_{2}emissions. High vehicle densities or traffic congestion lead to longer waiting times on the roads, so the fuel consumption, as well as CO

_{2}emissions are increased. It is clear from the figure that ISATOPSIS has the lowest average CO

_{2}emissions compared to the other algorithms. This is due to it having the best average travel speed and the optimal path (multi-attribute cost function) being obtained by ISATOPSIS. The SATOPSIS comes in second place in terms of CO

_{2}emissions compared to SAWS and DA. Both SAWS and DA have the worst CO

_{2}emissions due to a large amount of fuel consumed by the vehicles using them.

_{2}emissions of vehicles are optimized, in order to reach the destination via the optimal path.

#### 4.2. Scenario of Birmingham City

_{2}emissions.

## 5. Conclusions

_{2}emissions. The proposed method has been implemented and tested using an OpenStreetMap and the SUMO simulator. Results from the Sheffield scenario show that the simulated annealing weighted sum method can reduce the travel time by an overall average of 19.93% compared to DA and SATOPSIS. This is due to choosing the path with the highest average speed. However, it has a worse performance compared to ISATOPSIS. Simulation results show that our proposed ISATOPSIS method can successfully find a trade-off between different navigation attributes, in order to provide each driver with the least congested path according to the road condition. As reported from the Sheffield test scenario, it is shown that ISATOPSIS can improve the traffic flow by an overall average of 19.22% in terms of travel time, fuel consumption and CO

_{2}emissions when compared to the Dijkstra, simulated annealing weighted sum and SATOPSIS algorithms. Moreover, similar performance patterns were achieved for the Birmingham-based simulation. In future work, we envisage the route selections being communicated back to intelligent traffic light controls to help adaptively control their sequences to aid in achieving the overall optimal traffic flow for a smart city.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 5.**The city centre of Sheffield and the SUMO map. (

**a**) The city centre of Sheffield; (

**b**) SUMO map of Sheffield city centre.

**Figure 6.**The zoomed places showing traffic congestion on some roads. (

**a**) Traffic Congestion Area 1; (

**b**) Traffic Congestion Area 2; (

**c**) Traffic Congestion Area 3.

**Figure 12.**The section of Birmingham city centre and the SUMO map. (

**a**) The section of Birmingham city centre under consideration; (

**b**) The SUMO section of Birmingham city centre under consideration.

Simulation Parameters | Value |
---|---|

Map dimension | 4 km × 3.5 km |

Simulation time | 2500 sec |

Vehicle speed | 0–15 m/s |

Velocity threshold | 7 m/s |

MAC/PHY | IEEE 802.11p |

Vehicle density | 300–2100 Vehicle |

Route generator | SUMO |

Parameters | Values |
---|---|

T off-line | 500 °C |

α off-line | 0.998 |

T on-line | 25 °C |

α on-line | 0.992 |

**Table 3.**The average results obtained by the Dijkstra algorithm (DA), simulated annealing weighted sum (SAWS), the simulated annealing technique for order preference by similarity to the ideal solution (SATOPSIS) and the improved simulated annealing technique for order preference by similarity to the ideal solution (ISATOPSIS) in the tested scenarios. MTT, mean travel time; MTD, mean travel distance; FC, fuel consumption.

Method | MTT (s) | MTD (m) | FC (mL) | CO_{2} (g) |
---|---|---|---|---|

DA | 544.45 | 3396.84 | 496.603 | 873.206 |

SAWS | 432.55 | 3868.76 | 473.194 | 809.957 |

SATOPSIS | 439.29 | 3551.15 | 445.629 | 635.079 |

ISATOPSIS | 365.153 | 3656.367 | 428.904 | 560.668 |

**Table 4.**The overall average variance (Var) results obtained by all algorithms in the tested scenarios.

Method | Var MTT (s) | Var MTD (m) | Var FC (mL) | Var CO_{2} (g) |
---|---|---|---|---|

DA | 88.202 | 248.59 | 96.83 | 85.47 |

SAWS | 65.65 | 185.819 | 73.61 | 61.77 |

SATOPSIS | 44.157 | 136.46 | 67.408 | 39.0625 |

ISATOPSIS | 26.86 | 88.25 | 60.79 | 32.49 |

Simulation Parameters | Value |
---|---|

map dimension | 2 km × 1.5 km |

Simulation time | 1000 sec |

Vehicle speed | 0–15 m/s |

Velocity threshold | 7 m/s |

MAC/PHY | IEEE 802.11p |

Vehicle density | 100–500 |

Route generator | SUMO |

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Amer, H.; Salman, N.; Hawes, M.; Chaqfeh, M.; Mihaylova, L.; Mayfield, M.
An Improved Simulated Annealing Technique for Enhanced Mobility in Smart Cities. *Sensors* **2016**, *16*, 1013.
https://doi.org/10.3390/s16071013

**AMA Style**

Amer H, Salman N, Hawes M, Chaqfeh M, Mihaylova L, Mayfield M.
An Improved Simulated Annealing Technique for Enhanced Mobility in Smart Cities. *Sensors*. 2016; 16(7):1013.
https://doi.org/10.3390/s16071013

**Chicago/Turabian Style**

Amer, Hayder, Naveed Salman, Matthew Hawes, Moumena Chaqfeh, Lyudmila Mihaylova, and Martin Mayfield.
2016. "An Improved Simulated Annealing Technique for Enhanced Mobility in Smart Cities" *Sensors* 16, no. 7: 1013.
https://doi.org/10.3390/s16071013