Dataset for the paper "Quantum-Assisted Joint Multi-Objective Routing and Load Balancing for Socially-Aware Networks", Dimitrios Alanis, Jie Hu, Panagiotis Botsinis, Zunaira Babar, Soon Xin Ng, and Lajos Hanzo, IEEE Access (accepted). Results may reproduced using the Graphics Layout Engine (GLE). Abstract: The widespread use of mobile networking devices, such as smart phones and tablets, has substantially increased the number of nodes in the the operational networks. These devices often suffer from the lack of power and bandwidth. Hence, we have to optimize their message-routing for the sake of maximizing their capabilities. However, the optimal routing typically relies on a delicate balance of diverse and often conflicting objectives, such as the route's delay and power consumption. The network design also has to consider the nodes' user-centric social behavior. Hence, the employment of socially-aware load balancing becomes imperative for avoiding the potential formation of bottlenecks in the network's packet-flow. In this treatise, we propose a novel algorithm, referred to as the \emph{Multi-Objective Decomposition Quantum Optimization} (MODQO) algorithm, which exploits the Quantum Parallelism to its full potential by reducing the database correlations for performing multi-objective routing optimization, while at the same time balancing the tele-traffic load among the nodes without imposing a substantial degradation on the network's delay and power consumption. Furthermore, we introduce a novel socially aware load balancing metric, namely the normalized entropy of the normalized composite betweenness of the associated socially-aware network, for striking a better trade-off between the network's delay and power consumption. We analytically prove that the MODQO algorithm achieves the full-search based accuracy at a significantly reduced complexity, which is several orders of magnitude lower than that of the full-search. Finally, we compare the MODQO algorithm to the classic NSGA-II evolutionary algorithm and demonstrate that the MODQO succeeds in halving the network's average delay, whilst simultaneously reducing the network's average power consumption by 6 dB without increasing the computational complexity. Acknowledgement: The financial support of the EPSRC under the grant EP/L018659/1, that of the European Research Council, Advanced Fellow Grant and that of the Royal Society's Wolfson Research Merit Award is gratefully acknowledged. Additionally, the authors acknowledge the use of the IRIDIS High Performance Computing Facility, and associated support services at the University of Southampton, in the completion of this work. Finally, Jie Hu gratefully acknowledges the financial support of University of Electronic Science and Technology of China, No. A03013023601053, and that of National Natural Science Foundation of China (NSFC), Grant No. 61601097. Figure 7: Exemplified twin-layer network topology with $N_{\text{MC}}=5$ MCs and $N_{\text{MR}}=7$ MRs for a coverage area of $(100\times 100)$ m$^2$ square block. The association of a specific MC with a specific MR is annotated using the dashed lines. The presence of a central inteligence cluster head node is assumed, albeit not portrayed in this figure. The dataset of the MCs' and the MRs' locations can be found in "./Fig7/MC_loc.dat" and in "./Fig7/MC_loc.dat", respectively. Figure 8: Solution space of the route-combinations of the socially-aware network of Fig. 7 in terms of their average power consumtpion $\bar{P}$,quantified in dBm per route, and their average delay $\bar{D}$, quantified in number of hops per route. For the sake of simplicity, we have opted for only portraying the 100 lowest-rank PFs. The dataset of the solution space can be be found in "./Fig8/Datasets/solution_space.dat", while that of the Pareto-optimal solutions and that of the maximum normalized entropy solution can be found in "./Fig8/Datasets/opf_space.dat" and "./Fig8/Datasets/opf_space_max_entropy.dat", respectively. Figure 12: Average MODQO inner step complexity quantified as a function of the number of CFEs for twin-layer networks consisting of $N_{\text{MR}}=\{5,6,\dots,10\}$ MRs and $N_{\text{MR}}=\{2,4,8,16\}$ MCs. The MODQO inner step complexity is compared to that of the exhaustive search and to its respective upper and lower bounds. The results have been averaged over $10^8$ runs. The dataset of the complexity of the MODQO inner step and of the Exhaustive Search when considering X MCs can be found in "./Fig12/Datasets/complexity_inner_X_MCs.dat", that of the MODQO upper and lower bounds can be found in "./Fig12/Datasets/modqo-inner-bounds.dat". Figure 13: Order of the surviving route-combinations' growth factor $\rho$ with respect to the average number $\bar{N}_{\text{NOPF}}$ of Pareto-optimal routes in the MC routing table for twin-layer networks comprised by $N_{\text{MC}}=\{4,8,16\}$ MCs and $N_{\text{MR}}=\{5,\dots,10\}$ MRs. The results have been averaged over $10^8$ runs. The figure has been generated using the dataset of "./Fig13/Datasets/rho_order.dat". Figure 14: Average MODQO outer step complexity quantified as a function of the number of CFEs for twin-layer networks consisting of $N_{\text{MR}}=\{5,6,\dots,10\}$ MRs and $N_{\text{MR}}=\{2,4,8,16\}$ MCs. The MODQO outer step complexity is compared to that of the exhaustive search, that of the CM method and to the lower bound of the NDQIO algorithm invoked jointly for all the available stages. The portrayed results have been averaged over $10^8$ runs. The dataset of the complexity of the MODQO outer step using both the CM and the QM methods when considering X MCs can be found in "./Fig14/Datasets/complexity_outer_X_MCs.dat", that of the Exhaustive Search is found in "./Fig14/Datasets/modqo-outer-es.dat", while that of the NDQIO algorithm lower bound can be found in "./Fig14/Datasets/outer_NDQIO_lb.dat". Figure 15: Average MODQO outer step complexity quantified as a function of the number of CFEs for twin-layer networks consisting of $N_{\text{MR}}=\{5,6,\dots,10\}$ MRs and $N_{\text{MR}}=\{2,4,8,16\}$ MCs. The MODQO average complexity is compared to that of the exhaustive search and that of the MODQO using the CM method. The portrayed results have been averaged over $10^8$ runs. The dataset of all three methods when considering X MCs can be found in "./Fig14/Datasets/complexity_total_X_MCs.dat". Figure 16: Average network delay performance $\bar{D}$ per route in terms of the number of established hops (a) and average network power consumption $\bar{P}$ per route in dBm (b) for both the MODQO algorithm and the NSGA-II for networks having from 5 to 10 MRs and 16 MCs. The NSGA-II initialization parameters are presented in Table VII. The results have been averaged over $10^8$ runs. Figure 16a has been generated using the datasets "/Fig16/Fig16a/Datasets/modqo_delay_16_MCs.dat" and "/Fig16/Fig16a/Datasets/ga_delay_16_MCs.dat" for the MODQO algorithm and the NSGA-II, respectively. Figure 16b has been generated using the datasets "/Fig16/Fig16b/Datasets/modqo_power_16_MCs.dat" and "/Fig16/Fig16b/Datasets/ga_power_16_MCs.dat" for the MODQO algorithm and the NSGA-II, respectively. Figure 17: Average normalized entropy of the normalized composite betweenness $\bar{H}[\bar{B}_{com}(S)]$ (a) and standard deviation of the normalized composite betweenness $\sigma_{\bar{B}_{com}}$(b) for both the MODQO algorithm and the NSGA-II for networks having from 5 to 10 MRs and 16 MCs. The NSGA-II initialization parameters are presented in Table VII. The results have been averaged over $10^8$ runs. Figure 17a has been generated using the datasets "/Fig17/Fig17a/Datasets/modqo_entropy_16_MCs.dat" and "/Fig17/Fig17a/Datasets/ga_entropy_16_MCs.dat" for the MODQO algorithm and the NSGA-II, respectively. Figure 17b has been generated using the datasets "/Fig17/Fig17b/Datasets/modqo_std_16_MCs.dat" and "/Fig16/Fig16b/Datasets/ga_std_16_MCs.dat" for the MODQO algorithm and the NSGA-II, respectively.