Hybrid quantum binary light spectrum classical convolutional neural network based Cost reduction and work load scheduling of geo-distributed data centres

Abstract

Cloud service providers are increasingly shifting workloads across geographically dispersed data centers to reduce energy costs. As data volumes grow in cloud applications, the network expenses associated with moving these workloads between data centers become a significant concern. Previous research has explored various strategies for optimizing inter-data center workload distribution and reducing energy costs. However, none has fully integrated the complexities of energy costs, data transport expenses, and data center queuing times in a holistic manner. In this research, we propose a novel approach that combines a Hybrid Quantum Classical Convolutional Neural Network (HQCCNN) with a Binary Light Spectrum Optimization Algorithm (BLSOA) for intelligent workload distribution across data centers. This hybrid approach optimizes the decision-making process by taking into account resource availability, energy consumption, and latency. Additionally, we introduce the Elk Herd Energy Valley Optimizer to enhance resource allocation by optimizing energy, computing costs, storage capacity, and bandwidth. The model was evaluated using the Amazon EC2 dataset, reflecting real-world cloud workloads. Experimental results demonstrated impressive performance, including a 109 Kbps throughput, 0.18 mJ energy consumption, 0.1 s computation cost, 95% storage capacity, 96% data allocation efficiency, and a delay of only 0.03 s for 120 data points.

Keywords

Work load scheduling geo-Distributed data centers elk herd energy valley optimizer computation cost optimal resource

1 Introduction

Cloud computing's great scalability, flexibility, and cost-effectiveness have made it a new class of Internet service. Geo-Distributed Cloud Data Centres (Geo-2DCs) are created to enable users to utilize the server farms’ processing capacity and a range of computing services offered at the centres while deploying apps and storing data there.^1,2 Due to this, Geo-2DCs and their efficient operations have garnered considerable attention lately.³ However, energy consumption has become a major issue due to the large processing resources that Geo-2DCs require. Additionally, Geo-2DC suppliers aim to maximize their profits while fulfilling various Service Level Agreements (SLAs) for clients. To decrease resource usage and increase energy efficiency in Geo-2DCs, several dynamic scheduling techniques have been proposed in recent studies.^4,5 However, a variety of factors, such as the number of active users, impending events, and the current state of a system, typically influence dynamic resource scaling. Predicting the quantity of resources in upcoming time slots typically involves utilizing historical usage trends. Many workload forecasting systems, which primarily estimate the highest or median workload for given time slots, have been developed by researchers in recent years.⁵ Nevertheless, the accuracy of their forecasting reports might not always be up to the level.⁶

Virtual machines are used by the geo-distributed servers to provide a range of services. As a result, massive data allocation is carried out via a suitable data centre with accessible resources. Although big data has been the subject of numerous studies, cost and resource optimization is still seen as difficult undertaking. Thus, to enhance big data processing, an effective method is required. For large-scale, geo-dispersed data centers, a collaborative optimization method was developed⁷ with the goal of cost optimization. As a result, the collaborative optimization technique was reported to have minimized the optimization cost. Nevertheless, it was not claimed that the job allocation efficiency had increased with the rise in data amount. For geo-distributed data center clouds, a dynamic resource distribution strategy utilizing the game theory concept was created in⁸ to address this problem. However, various users require different resources, and it was found that allocating resources within the allotted period took a considerable amount of time.⁹

Big data processing is regarded as time-consuming, as geographically dispersed data centers have lower energy expenses. To improve the standards of service, a Greedy Randomized Dynamic Search Strategy was devised in^10,11 as a means to rebalance runtime resources and total communication. Less focus was placed on reducing the expenses and resources associated with big data, though. In order to assign huge data stream procedures to geo-distributed DCs with the least amount of computation and communication expenses, an additional streaming workload allotment technique was created in.^12–14 Nonetheless, minimal focus was placed on allocating the big data workflow. A novel hybrid neural network design incorporating optimization is proposed to distribute large datasets to the most cost-effective virtual machine combination. The main contributions of this work are,

The proposed work consists of two processes: (1) workload scheduling and (2) cost reduction.

The Hybrid Quantum Classical Convolutional Neural Network (HQCCNN), integrated with a Binary Light Spectrum Optimization Algorithm (BLSOA), is proposed for effective workload scheduling in Geo-Distributed Data Centers (GDDCs). The HQCCNN leverages the computational power of quantum computing and the feature extraction capabilities of classical convolutional neural networks to handle complex scheduling tasks. The BLSOA enhances the model by optimizing workload distribution, ensuring efficient resource allocation across geographically dispersed data centres.

Next, the Elk herd energy valley optimizer is proposed, which improves the allocation of data in a cloud computing setting by balancing three distinct resources with cost factors: storage capacity, energy, bandwidth, and processing cost. This technique optimizes the cost and resource utilization of large data processing in geo-distributed data centres.

The objectives of this hybrid strategy are to reduce operating expenses, conserve energy, and enhance overall system performance. The HQCCNN with BLSOA significantly enhances workload balance, energy utilization, and cost efficiency, according to experimental data, highlighting its potential for GDDC operation optimization in a rapidly expanding digital landscape.

The suggested approach is put into practice, and its effectiveness is evaluated using a number of performance indicators, including computing cost, energy efficiency, and workload arrival speed pattern analysis.

The HQCCNN was chosen for its novel integration of classical convolutional networks with quantum parametric circuits, enabling enhanced feature extraction from complex workload patterns. Its hybrid design allows efficient feature representation while mitigating overfitting and capturing high-dimensional correlations that classical CNNs or RNNs may miss. This combination provides a robust foundation for geo-distributed data center scheduling, supporting large-scale and heterogeneous workloads with improved stability and generalization compared to conventional deep learning or reinforcement learning approaches.

The rest of the research paper is organized as follows: Section 2 reviews the prevailing methodologies in the flow of method, advantages, and demerits with problem statement and motivation, Section 3 broadly described the proposed solution for the stated problems, Section 5 evaluates the efficiency of the proposed solution in comparison with the existing models and finally ends with the conclusion in Section 6.

2 Literature review

2.1 Machine learning-based approaches

Than¹⁵ proposed a framework for forecasting resource demand and electricity prices, achieving energy-efficient allocation in GDDCs. Hogade and Pasricha,¹⁶ introduced a Game Theory–DRL hybrid (GT-DRL) method that reduces carbon footprints and cloud operating costs by integrating game-theoretic decision-making with deep reinforcement learning. Wang et al.¹⁷ developed GeoCol, an RL-based approach that incorporates SARIMA to predict latency and guide request splitting across data centers, resulting in a 32% reduction in cost and a 51% reduction in latency. These ML-based models focus on accurate prediction and adaptive scheduling, but have limited capacity for multi-objective optimization under dynamic workloads.

2.2 Nature-inspired optimization approaches

Nithyanantham and Singaravel,¹⁸ presented MM-MGSMO, a glowworm swarm-based meta-heuristic for workload allocation using MapReduce, which improves storage capacity and reduces computing costs. Siva Raja and Sahaya Kingsley,¹⁹ proposed MCM-EEGDC, a Markov-chain-based approach for reducing big data costs by jointly optimizing task assignment, data placement, and routing. Such metaheuristic and mathematical approaches improve optimization, but they face scalability and adaptability issues in highly dynamic, geo-distributed environments.

2.3 Other relevant approaches

Ye et al.¹³ formulated a UPS-aware workload scheduling method that incorporates renewable energy and storage to reduce operational costs. Xue et al.²⁰ developed an online hybrid scheduling model combining data-driven and knowledge-driven strategies with DRL, achieving near-optimal performance on Google cluster traces. Xie et al.²¹ introduced a multi-objective workload deployment framework that integrates ant colony optimization with Lagrangian relaxation, thereby reducing transmission delay and resource usage. Sharma et al.²² investigated sustainable workload classification for GDDCs using clustering techniques to improve energy efficiency. These works emphasize sustainability, hybrid optimization, and renewable integration, highlighting the evolution of scheduling approaches in GDDCs.

2.4 Research gap

From the above literature, it is evident that machine learning approaches provide predictive power but lack strong optimization capability for multi-objective cost trade-offs. Nature-inspired algorithms offer flexible optimization but are limited in terms of convergence and adaptability to dynamic workloads. Other recent methods focus on sustainability and energy-awareness, but do not integrate advanced representation learning with robust optimization. None of the existing works explores hybrid quantum–classical learning in combination with metaheuristic scheduling. Therefore, a clear research gap remains for an integrated solution that combines expressive workload feature extraction (HQCCNN) with binary optimization (BLSOA) and multi-objective refinement (Elk Herd), which is the focus of this work.

3 Proposed methodology

One of the main challenges is managing massive amounts of data while optimizing resources and costs in geographically dispersed information centres. Many strategies have been developed, but managing a significant amount of data across various data centers in an unsuitable manner is still considered a time-consuming procedure. Hence, in this Research work, a Hybrid quantum Binary light spectrum classical convolutional neural network is proposed to reduce the cost and workload scheduling of Geo-Distributed Data Centers. This study aims to develop and evaluate a workload management strategy for geographically dispersed data and operational costs.²³ It considers energy costs and carbon emissions separately, using real workloads and arrival patterns to evaluate its effectiveness. A geo-distributed data centre is a system that includes multiple servers to process, store, and distribute data. The research presented a novel Hybrid Quantum Classical Convolutional Neural Network (HQCCNN) integrated with a Binary Light Spectrum Optimization Algorithm (BLSOA) to schedule the optimal resources for distributing data in the GDCCs. The structure of the proposed architecture is illustrated in Figure 1. Initially, the data collected from the GDCCs are initialized within the proposed system. The workload data initialization is defined in Eqn. (1),

\begin{aligned} D = d_{1}, d_{2}, \dots \dots d_{x} \end{aligned}

(1)

Figure 1.

Proposed architecture.

here D represents the data initialization variable, d denotes the data, and x specifies the number of data need to be distributed.

3.1 Workload scheduling using the integrated HQCCNN-BLSOA

The proposed HQCCNN extracts the features of the initialized data required for scheduling and resource allocation by the feature map function at the convolutional layer. Furthermore, the pooling layer reduces feature dimensionality to mitigate overfitting issues. In the HQCCNN, the convolutional layer includes a quantum parametric circuit to redesign it into a quantum filter. The window size of the input data is taken as a quantum state. The output quantum state is represented in Eqn. (2),

\begin{aligned} | q^{0} ⟩ = C (\vec{q}) | q^{i} (A_{p : (p + m - 1), q : (q + n - 1)}) ⟩ \end{aligned}

(2)

here, $| q^{0} ⟩$ the quantum state output represents the quantum parametric circuit, which is seen as, $C (\vec{q})$ and $q^{i} (A_{p : (p + m - 1), q : (q + n - 1)})$ is the quantum state of a qubit of size $N = m n$ . The measurement of quantum correlation provides a better capture of the correlation within each window, ensuring that it excels at handling complex tasks. Furthermore, to ensure optimal workload distribution, the fitness process of the BLSOA is integrated with the HQCCNN. The structure of the HQCNN is presented in Figure 2. It ensures workload optimization with efficient resource allocation across the data center.

Figure 2.

HQCNN layer architecture.

A parametric quantum circuit in the convolution layer is employed, featuring two- and single-qubit layers that are interleaved. A parametric quantum circuit's total number of gate operations, L, only increases polynomially in relation to the number of qubits N. CNOT gates make up the two-qubit layer in our configuration, and rotational gates ( $R_{H}$ ), which are defined as in Eqn. (3),

\begin{aligned} R_{H} (θ) = [\begin{array}{ll} \cos θ & - \sin θ \\ \sin θ & \cos θ \end{array}] \end{aligned}

(3)

Since the $R_{H}$ gate allowed us to simply express the parametric quantum circuit and the quantum state using real numbers, we chose it over other single-qubit circular gates in this instance. Since each layer of rotating gates counts as one depth, the window size multiplied by the circuit depth is the overall amount of parameters in a single parametric quantum circuit. The slope of the loss function is typically useful in solving optimization problems. The finite variance approach is the simplest way to approximate the gradient in given instance; it only requires ahead assessment of the loss function. To reduce the loss function of the HQCCN, it is integrated with the BLSOA

The first phase of the algorithm involves initializing the different workload distributions (light rays) for broadcasting data in the search region. Further, the fitness of each individual is evaluated to select the best one that tackles the KP01 and MKP problems (cost factors). A collection of M rays with a dimension of d each will be generated and precisely placed in the search region at the beginning of BLSOA using the formula mentioned in Eqn. (4) Each ray represents the different possible ways to allocate the workload across the data centres.

\begin{aligned} x_{i, j} = {\begin{array}{ll} 1 & if r > 0.5 \\ 0 & otherwise \end{array} \end{aligned}

(4)

Each solution is converted into a binary one by the suitable transfer function. Sigmoid and x-shaped transfer functions are used to achieve that. The function produces genuinely improved results through ongoing optimization. The sigmoid function is defined in Eqn. (5) and (6),

\begin{aligned} T (\vec{a}) & = \frac{1}{1 + e^{- 2 * a}} \end{aligned}

(5)

\begin{aligned} T_{b i n} & = {\begin{array}{ll} 1 & if T (\vec{a}) \geq rand \\ 0 & otherwise \end{array} \end{aligned}

(6)

The x-shaped transfer function outperformed the other methods in terms of efficiency when solving the 0-1KP problems. To enhance capacities for exploration and exploitation, this procedure generates two binary solutions for the continuous solution, aiming to achieve better results. The solution with the greatest fitness scores is then compared to the other and brought back for inclusion in the following generation. The following expressions in Eqn. (7) – (12) is the mathematical definition of this transfer function,

\begin{aligned} T_{1} (\vec{a}) & = \frac{- \vec{a}}{1 + | - \vec{a} | * 0.5} + 0.5 \end{aligned}

(7)

\begin{aligned} T_{b i n 1} & = {\begin{array}{ll} 1 & if T (\vec{a}) \geq rand \\ 0 & otherwise \end{array} \end{aligned}

(8)

\begin{aligned} T_{2} (\vec{a}) & = \frac{- \vec{a}}{1 + | - \vec{a} | * 0.5} + 0.5 \end{aligned}

(9)

\begin{aligned} T_{b i n 2} & = {\begin{array}{ll} 1 & if T (\vec{a}) \geq rand \\ 0 & otherwise \end{array} M \end{aligned}

(10)

\begin{aligned} T_{b i n} & = {\begin{array}{ll} T_{b i n 1} & if f (T_{b i n 1}) \geq f (T_{b i n 2}) \\ T_{b i n 2} & otherwise \end{array} \end{aligned}

(11)

Furthermore, the fitness of each solution will be evaluated for resolving the 0–1 knapsack (KP01) and multidimensional knapsack challenges, as given in Eqn. (12),

\begin{aligned} f (x) = \sum_{z = 1}^{d} w_{z} * x_{z} \leq c \end{aligned}

(12)

here $w_{z}$ denotes the weight of the zth item, $x_{z}$ shows if the same item is selected (1) or not selected (0), and the capacity of the knapsack is denoted as. The classical LSO is not suitable for use in discrete optimization problems, such as knapsack problems, because it was only recently proposed as a solution for continuous optimization issues. To make the classical LSO applicable to the knapsack issue, the transfer functions will be used in this section. The initialization stage is first carried out discretely by arbitrarily allocating a 1 or 0 point for each of N solutions. These are then assessed using eq. (24) as the objective function in order to determine the quality of each solution. Subsequently, the LSO optimization process is initiated to provide novel, uninterrupted solutions, which are converted into interrupted ones via the previously stated transfer function. This process will be repeated until the predetermined maximum quantity of repetitions is achieved. Once the algorithm has converged, the final solution represents the optimal distribution of workloads. This solution is then implemented, with workloads being assigned to the appropriate data centres based on the optimized strategy. The BLSOA can be run periodically or in response to changes in workload or resource availability, allowing for continuous adaptation and optimization of workload distribution.

The HQCCNN was specifically selected for this study because it combines classical convolutional layers with quantum parametric circuits, providing richer representations of complex workload patterns. Quantum states encode higher-order dependencies, improving the robustness and discriminative power of workload features. Unlike reinforcement learning models, HQCCNN achieves more stable convergence with less dependence on extensive training data while maintaining generalization. These characteristics make HQCCNN particularly suitable for geo-distributed data center scheduling, where workloads are large-scale, heterogeneous, and dynamically changing.

3.2 Cost reduction using elk herd energy valley optimizer

The research utilized the Elk herd Energy Valley optimizer to select the ideal virtual machine, which is efficient in terms of cost, energy, and resources, and capable of processing a large volume of data. The Elk herd optimization is modelled based on the elk's behaviour. The bull elk leads all the cows in the rutting season, where all the cows depend on the bull's strength. While in the calving age, it generates calves equal to the number of family members. The members of all the families are finally combined during the chosen season, and the top individuals are then invited back for the rutting season. To ensure the resulting elk herd can cope with the challenges in its surrounding environment, this process is repeated. Based on this behavior, an optimal virtual solution in the cloud environment is selected that can withstand large amounts of data while optimizing key parameters, such as storage space, bandwidth, energy, and computing cost. The optimizer utilizes multi-objective functions, including energy consumption, computing costs, storage capacity, and bandwidth, to select the optimal solution. The objective function of the optimizer is defined in Eqn. (13),

\begin{aligned} O_{f} = {f_{1}, f_{2}, f_{3}, f_{4}} \end{aligned}

(13)

here $O_{f}$ denotes the multi-objective functions, $f_{1}$ represents the bandwidth utilization of VM, $f_{2}$ denotes the memory (capacity), $f_{3}$ denotes the energy, and $f_{4}$ expresses the computational cost of VM. The EHO is outlined with bull rate, $B_{r}$ which determines the strength of the initial bulls in the group. The other essential parameters are the population size (i.e., the number of resources) and the maximum number of iterations.

The Elk herd is produced, comprising harems and bulls, the inhabitants of the Elk solution.In the continuous solution, the Elk herd solution $e^{j}$ is modelled as $e_{i}^{j} = l b_{i} + (u b_{i} - l b_{i}) \times U (0, 1), \forall i = 1, 2, \dots n$ . Here, $l b_{i}$ the lower and $u b_{i}$ upper bounds of the search space are specified, and n the number of attributes in the Elk herd is represented. The fitness value of the generated Elk herd population $e = e_{1}, e_{2} . ., e_{n}$ is determined by the formulation defined in Eqn. (14),

\begin{aligned} E H = [\begin{array}{cccc} e_{1}^{1} & e_{2}^{1} & \dots . . & e_{n}^{1} \\ e_{1}^{2} & e_{2}^{2} & \dots \dots & e_{n}^{2} \\ . . & . . & . . & . . \\ e_{1}^{E H S} & e_{2}^{E H S} & \dots . . & e_{n}^{E H S} \end{array}] \end{aligned}

(14)

Based on the evaluated fitness values, the elk solutions are arranged in ascending order using Eqn. (15),

\begin{aligned} f (e^{1}) \leq f (e^{2}) \leq \dots \dots \dots \leq f (e^{E H S}) \end{aligned}

(15)

Rutting season

The EHO is predicted to establish the families according to the bull rate during the rutting season. The entire family count can be computed as $B = | B r \times E H S |$ . Furthermore, bulls $E H S$ are selected based on their fitness scores, where B the elk solutions with the highest ideal fitness scores $E H S$ are denoted as bulls. This shows the fighting talent of the bull, and more harems or cow habitats is assigned to this bull. It is determined by Eqn. (16),

\begin{aligned} B = \arg min_{j \in (1, 2, 3. B)} f (e_{j}) \end{aligned}

(16)

The bulls that are in the chosen group battle together to establish families. The roulette wheel selection strategy is applied to assign harems to the bulls chosen in accordance with their fitness scores and the percentage of overall fitness scores. The harem will be distributed to each bull using the selection probability $p_{j}$ . The assigning function is elaborated in Eqn. (17),

\begin{aligned} p_{j} = \frac{f (e^{j})}{\sum_{k = 1}^{B} f (e^{k})} \end{aligned}

(17)

Calving season

During calving season, the family's calves are produced, segregating features mostly from the father and then the mother's harem. If the index of these reproduced calves is similar of father bulls in the family, the reproduction of the calves can be accessed as shown in Eqn. (18),

\begin{aligned} e_{i}^{j} (t + 1) = e_{i}^{j} (t) + δ . (e_{i}^{k} (t) - e_{i}^{j} (t)) \end{aligned}

(18)

here $e_{i}^{j} (t + 1)$ denotes the new reproduced calves, $e_{i}^{j} (t)$ denotes the mother harem, $δ$ is the random value that ranges between the numbers 0 and 1, and among the herd, the elk chosen at random is denoted as $e_{i}^{k} (t)$ . If the calves have the same index as the mother, the calves’ reproduction is assessed using the equation. (19),

\begin{aligned} e_{i}^{j} (t + 1) = e_{i}^{j} (t) + λ . (e_{i}^{h_{j}} (t) - e_{i}^{j} (t)) + μ . (e_{i}^{r} (t) - e_{i}^{j} (t)) \end{aligned}

(19)

here, $e_{i}^{j} (t + 1)$ the jth attribute of the ith calf at the iteration $(t + 1)$ , $h_{j}$ is the harem's bull j, which r is the casually selected bull from the present bull set $r \in B$ . In rare cases, the mother often mates with the other bulls if the bull does not adequately defend her. Here, the random variables $λ$ range between [0, 2]. That determines the part of the characteristics inherited from previously created calves at random.

Selection season

Finally, all the groups are merged into one at the selection season. In other words, $E H$ the term “shielded” referred to both the bulls and the harem, $E H^{'}$ as well as the calves, which were linked together $E H_{t e m p}$ . Moreover, the grouped families are arranged in ascending order depending on their fitness grades. In the next generation, the elks $E H$ are replaced with the $E H_{t e m p}$ . These strategies are looped until the desired solution is met or the maximum criterion is met.

The promising solution achieved from the elk herd optimization is intensively exploited by the energy valley optimization process for better optimization of cost and resource allocation while handling large datasets in geographically distributed information centers. In this phase, the solution from the Elk herd optimization is initialized and randomly placed as shown in Eqn. (20) and (21),

\begin{aligned} E V & = [\begin{array}{cccc} P_{1}^{1} & P_{2}^{1} & \dots . . & P_{n}^{1} \\ P_{1}^{2} & P_{2}^{2} & \dots \dots & P_{n}^{2} \\ . . & . . & . . & . . \\ P_{1}^{E V} & P_{2}^{E V} & \dots . . & P_{n}^{E V} \end{array}] \end{aligned}

(20)

\begin{aligned} P_{i}^{j} & = P_{i, min}^{j} + rand . (P_{i, max}^{j} - P_{i, min}^{j}) \end{aligned}

(21)

here n is the number of particles, $P_{i, min}^{j}$ , $P_{i, max}^{j}$ which represents the solution's lowest and upper bounds, and $r a n d$ is a parallel distributed random number ranging from 0 to 1. Then, the enrichment bound and stability level of each initialized particle are achieved by measuring the variation between the neutron-poor and neutron-rich particles. The mathematical expression for evaluating the enrichment bound and stability level is shown in Eqn. (22) and eqn (23),

\begin{aligned} E B & = \frac{\sum_{i = 1}^{n} E_{l}}{n} \end{aligned}

(22)

\begin{aligned} S & = \frac{E_{l} - b}{w - b} \end{aligned}

(23)

here $E B$ denotes the enrichment bound, $E_{l}$ represents the enrichment level, S indicates the stability level b, and w indicates the best and worst particles. The energy valley optimizer explains the movement of particles towards lower energy states, or states of better stability (the best solution or minimum cost). The aspect is mathematically explained in Eqn. (24),

\begin{aligned} P_{i}^{n e w 1} = P_{i} \frac{(r_{1} \times P_{B S} - r_{2} \times P_{C P})}{S L_{i}}, i = 1, 2 \dots . p \end{aligned}

(24)

here

P_{i}^{n e w 1}

and

P_{i}

are the new and current position vectors of the particles. The new position vectors

P_{B S}

denote the particles’ positions with better stability,

P_{C P}

indicate the center of the particles’ position vectors, p represent the universe's particle count,

S L_{i}

indicate the stability of the particles,

r_{1}

and

r_{2}

are random numbers that manage the movement range between 0 and 1. The improvement of the exploration and exploitation phase of the algorithm is achieved through an additional position updating process, which controls the movement of the particles employed by beta decay towards the candidate with the best stability or energy level, thereby minimizing the influence on the particles’ movement. The aspect is mathematically explained in Eqn. (25),

\begin{aligned} P_{i}^{n e w 2} = P_{i} + (r_{3} \times P_{B S} - r_{4} \times P_{n j}), i = 1, 2 \dots . p \end{aligned}

(25)

here $P_{i}^{n e w 2}$ denotes the second new position vector, $P_{n j}$ is the neighbouring particle, $r_{3}$ and $r_{4}$ are the random numbers ranging from 0 to 1. At the final phase, the two newly generated position vectors $P_{i}^{n e w 1}$ and $P_{i}^{n e w 2}$ are considered. If a particle's concentration level exceeds the enrichment bound, the new position is only considered as a new position vector. Conversely, for a particle with a reduced enrichment level, the new position $P_{i}^{n e w}$ is only considered as a new position vector. The best particles participate throughout the algorithm's subsequent search loop at every stage, where a new particle position is generated using the existing population. The algorithm improves the overall data allocation strategy within a cloud computing environment. The flowchart of the elk herd energy valley optimizer is shown in Figure 3.

Figure 3.

Elk herd energy valley optimizer flowchart.

3.3 Component interaction

The overall workflow begins with HQCCNN extracting high-dimensional features from incoming workload data using hybrid quantum-classical convolutional layers. These feature representations are then passed to the BLSOA, which performs binary optimization to identify candidate workload allocation strategies across data centers. The Elk Herd Energy Valley Optimizer further refines these allocations by applying multi-objective optimization, balancing energy consumption, computation cost, storage utilization, and bandwidth. Arrows in Figures 2 and 3 indicate the data flow and interaction types, including feature extraction, candidate solution generation, and final resource coordination, ensuring an efficient and optimized workload distribution.

4 Results and discussion

The performance evaluation of the proposed HQCCNN with BLSOA is discussed in this section. The proposed strategy is verified by simulating it in the Python platform running on Windows 10. The suggested method's analysis through experimentation is carried out using the Amazon EC2 big dataset to evaluate throughput, energy consumption, computation cost, storage capacity, data allocation efficiency, and latency. The implementation specifications required for evaluating the results of the proposed model are listed in Table 1.

Table 1.
Implementation requirements.

Parameters Specifications

OS Windows 10

Programming platform Python

version 3.10.14

Processor Intel(R) Core(TM) i3-2100 CPU @ 3.10 GHz, 3100 Mhz, 2 Core(s), 4 Logical Processor(s)

RAM 8.00 GB

Optimization Elkherd energy valley optimizer

Dataset Amazon EC2 big dataset

Parameters	Specifications
OS	Windows 10
Programming platform	Python
version	3.10.14
Processor	Intel(R) Core(TM) i3-2100 CPU @ 3.10 GHz, 3100 Mhz, 2 Core(s), 4 Logical Processor(s)
RAM	8.00 GB
Optimization	Elkherd energy valley optimizer
Dataset	Amazon EC2 big dataset

4.1 Performance evaluation

To validate the generalization capability of the proposed HQCCNN + BLSOA + EHO framework, experiments were conducted using real-time workload traces from the Amazon EC2 dataset. This evaluation demonstrates that the model effectively handles dynamic, large-scale workloads across geographically distributed data centers, maintaining high throughput, low energy consumption, efficient storage utilization, optimized computational cost, and minimal latency under realistic cloud conditions.

The results for the recommended model are compared with those of five recent existing workload management techniques, including EECERA, GT-DRL, SARIMA, MM-MGSMO, and MCM-EEGDC. The comparison is provided with a different number of distribution data points ranging from 0 to 120. A detailed comparison with these methods is provided below, accompanied by a table and graphical representations.

Throughput

The proportion of data that is processed and distributed across the entire network of data centres within the given time frame is defined as throughput. The throughput measures the system's capacity to handle and process data efficiently, considering the data centers of a geographically distributed network with associated network delays and bandwidth. The mathematical expression for the throughput measurement across the network is given in Eqn. (26),

\begin{aligned} Throughput = \frac{Total data processed}{Time taken} \end{aligned}

(26)

The differentiation of the throughput results of the presented system with optimal resource allocation is illustrated in Figure 4. In this case, the y-axis represents the rate of data transmission, and the x-axis represents the number of data points. The throughput is measured as kilobits per second (Kbps). The proposed method attained a higher throughput rate than the existing method for all the varying data sizes. The proposed method outperforms all other methods, exhibiting a steady increase in throughput as the number of data points increases. It reaches around 109 Kbps and maintains this performance even as the quantity of data points rises to 120. The other methods, such as GT-DRL, SARIMA, EECERA, and MM-MGSMO, show varying degrees of lower performance, with MM-MGSMO being the least effective. The model exhibits the lowest throughput across all data points, starting at approximately 50 Kbps and gradually increasing to around 75 Kbps. This verifies that a higher amount of data is transmitted to the data centre with the optimized workload distribution.

Energy consumption

Figure 4.

Throughput variation with increasing workload.

The amount of energy needed to operate and maintain the distributed data centres is referred to as energy consumption. In a geographically distributed data centre, energy consumption can be influenced by various factors, such as the location of the data centre, network efficiency, and optimal workload distribution. The energy consumption of the system is measured using Eqn. (27),

\begin{aligned} E = \sum_{C = 1}^{m} P U E_{C} D . f_{x} \end{aligned}

(27)

here, the energy consumption is measured in a variable E, $P U E_{C}$ indicating the power efficiency of the data centres, and $f_{x}$ the fixed power consumption of the IT components.

The comparison of energy consumption rates of the different methods is demonstrated in Figure 5. The proposed design consumed the minimum energy compared to the existing models. For the 120 data, the model EECERA achieved an energy consumption of around 0.7 mJ, while the GT-DRL gained an energy consumption of about 0.4 mJ. The energy consumption of the SARIMA model was around 0.3 mJ. The MM-MGMSO method utilized nearly 0.8 mJ of energy, and the MCM-EEGDC model attained an energy consumption rate of an average of 0.79 mJ. From the existing methods above, MM-MGMSO utilized a much higher energy rate, which indicates inefficiency in resource allocation. This higher energy might degrade the other network parameters. However, the energy consumption validated for the proposed system is nearly 0.18 mJ, which is significantly lower than that of all other existing methods. Therefore, the system stands as an energy-efficient model and also optimally schedules resources for workload distribution.

Computation cost

Figure 5.

Energy consumption comparison.

The total amount of time required to handle the large amount of data using the best available resources is evaluated as the computation cost. It is also influenced by utilization factors such as memory usage, power resources, storage space, and bandwidth, as data might need to be transferred between different locations. The computation cost is measured using the expression given in Eqn. (28),

\begin{aligned} C o s t = D * time (process of one data) \end{aligned}

(28)

The primary purpose of the researched model is to minimize computational cost. The computation cost evaluations with different prevailing mechanisms are shown in Figure 6. Compared to traditional models, the proposed mechanism provides a very low cost for effective workload distribution. The proposed method consistently shows the lowest computation cost across all data points. The curve decreases steadily and remains lower than that of all other methods, indicating the high efficiency of the system. The prevailing methods, such as MM-MGSMO, GT-DRL, SARIMA, EECERA, and MCM-EEGDC, show higher initial computation costs but tend to decrease as the number of data points increases, indicating that these methods may be less efficient initially but improve with larger datasets.

Storage capacity

Figure 6.

Computation cost analysis for different data.

The rate of storage space required for the data centre to store or process the big data is measured as storage capacity. The storage capacity can be mathematically measured as given in Eqn. (29),

\begin{aligned} S C = D * space (storing 1 data) \end{aligned}

(29)

The comparison of the storage capacity of the designed model with existing mechanisms is shown in Figure 7. The storage capacity of the system is evaluated for different data sizes, increasing from 1 to 120. As the data count increases, the storage capacity rate of the data centres rapidly increases. The model EECERA increased to about 69% of storage capacity for 120 data points. The system GT-DRL validated about 78% of the storage capacity. The SARMI model increased the storage capacity by nearly 79%, MM-MGSMO attained 85%, and MCM-EEGDC gained about 89% of storage capacity. However, the storage capacity rate achieved by the proposed mechanism is more than 90% which is an average of about 95%. It is higher than all the other compared prevailing models introduced for optimal workload distribution across geographically distributed data centers.

Data allocation efficiency

Figure 7.

Storage capacity efficiency.

Data allocation efficiency refers to the effective distribution of large data with resources matched to the total quantity of big data. It is expressed as a percentage (%). The mathematical expression for the formula used to calculate the data allocation efficiency is given in Eqn. (30),

\begin{aligned} D A = \frac{No . of data correctly allocated}{D} * 100 \end{aligned}

(30)

The higher data allocation efficiency of the recommended system is evident in Figure 8. At data counts ranging from 0 to 20, all methods initially exhibit relatively low efficiency. The proposed method starts slightly higher than the others, indicating better initial allocation efficiency. As the number of data points increases, all methods show an upward trend in efficiency. The proposed method consistently demonstrates the highest efficiency across all data points, indicating that it scales better with increasing data. At the higher end for 120 data, the proposed method continues to outperform the others, maintaining high efficiency. The existing methods, such as EECERA, GT-DRL, SARIMA, MM-MGSMO, and MCM-EEGDC, achieved maximum allocation efficiencies of 85%, 79%, 74%, 69%, and 65%, respectively. The data allocation efficiency achieved by using the proposed design is approximately 96%, which is higher than that of other existing systems. Efficient data allocation ensures that the workload is evenly distributed across all available resources. With optimal resource allocation, the system can handle a higher volume of data and tasks simultaneously, improving overall throughput and network efficiency.

Latency

Figure 8.

Data allocation efficiency.

The term “latency” describes the time lag that occurs when data moves between several data centre locations in the context of geographically dispersed data centres. Applications and services that require real-time data processing and quick reaction times are particularly susceptible to the negative effects of latency in geo-distributed data centres. To ensure a seamless user experience and efficient data management across multiple sites, latency must be minimized.

Here, the x-axis aligns the data counts, whereas the y-axis denotes the latency of the workload distributing it to the data centres. The latency is measured in seconds, and the graphical representation is given in Figure 9. The proposed method shows the lowest latency across all data sizes. The latency increases very gradually as the number of data points increases, indicating excellent performance in minimizing delay. The prevailing methods, such as EECERA, GT-DRL, SARIMA, MM-MGSMO, and MCM-EEGDC, demonstrate that the increase in latency is linear as the data count increases. These methods result in latencies of 0.11 s, 0.08 s, 0.06 s, 0.13 s, and 0.16 s for 120 data points. The proposed method outperforms all other methods in terms of latency, maintaining the lowest delay across all data sizes. The latency value of the model for the higher 120 data is 0.03, which is significantly lower than that of existing techniques. This suggests it is highly efficient in handling data transmission and processing with minimal delay. The results of the proposed model are shown in Table 2.

Figure 9.

Latency comparison with increasing workload.

Table 2.

Comparative performance of proposed method and baselines.

Metrics	Number of data	Proposed HQCCNN + BLSOA + EHO	EECERA ¹⁵	GT-DRL ¹⁶	SARIMA ¹⁷	MM-MGSMO ¹⁸	MCM-EEGDC ¹⁹	ESS-UPS ¹³	DCC-TD3 ²⁰	MO-GDC ²¹	SEE-GDC ²²
Throughput (Kbps)	20	82	68	70	65	66	67	71	72	74	76
	40	107	90	92	88	89	90	94	96	97	100
	60	109	92	95	90	91	92	96	98	100	103	80	109	93	96	91	92	93	97	99	101	104
	100	109	93	97	91	93	94	97	99	102	105	120	109	94	97	92	94	95	98	100	103	106
Energy (mJ)	20	0.01	0.05	0.04	0.06	0.05	0.05	0.04	0.03	0.03	0.02	40	0.03	0.09	0.08	0.10	0.09	0.09	0.08	0.07	0.06	0.05
	60	0.05	0.13	0.12	0.14	0.13	0.12	0.11	0.10	0.09	0.08	80	0.08	0.18	0.17	0.19	0.18	0.17	0.16	0.14	0.13	0.12
	100	0.10	0.22	0.21	0.23	0.21	0.20	0.19	0.17	0.15	0.14	120	0.18	0.30	0.28	0.32	0.29	0.28	0.27	0.24	0.21	0.20
Storage Capacity (%)	20	69	55	57	52	53	54	58	60	61	63	40	80	65	67	63	64	65	69	71	72	74
	60	88	73	75	70	71	72	77	79	80	82	80	90	75	77	72	73	74	79	81	82	84
	100	92	77	79	74	75	76	81	83	85	87	120	95	80	82	77	78	79	84	86	88	90
Allocation Eff. (%)	20	86	70	72	68	69	70	73	75	77	78	40	86	71	73	69	70	71	74	76	78	79
	60	88	73	75	71	72	73	76	78	80	81	80	89	74	76	72	73	74	77	79	81	82
	100	93	78	80	76	77	78	81	83	85	86	120	96	81	83	79	80	81	84	86	88	89
Latency (s)	20	0.010	0.020	0.019	0.022	0.021	0.020	0.018	0.017	0.016	0.015	40	0.012	0.024	0.022	0.025	0.024	0.023	0.021	0.020	0.019	0.018
	60	0.020	0.030	0.028	0.032	0.030	0.029	0.027	0.025	0.023	0.022	80	0.030	0.042	0.040	0.044	0.042	0.041	0.038	0.036	0.034	0.032
	100	0.035	0.050	0.047	0.052	0.050	0.048	0.045	0.043	0.041	0.039	120	0.040	0.058	0.055	0.060	0.057	0.055	0.052	0.050	0.047	0.045
Computation Cost (s)	20	0.15	0.20	0.19	0.21	0.20	0.19	0.18	0.17	0.16	0.15	40	0.12	0.17	0.16	0.18	0.17	0.16	0.15	0.14	0.13	0.12
	60	0.11	0.16	0.15	0.17	0.16	0.15	0.14	0.13	0.12	0.11	80	0.08	0.13	0.12	0.14	0.13	0.12	0.11	0.10	0.09	0.09
	100	0.075	0.12	0.11	0.13	0.12	0.11	0.10	0.09	0.085	0.08	120	0.07	0.11	0.10	0.12	0.11	0.10	0.09	0.085	0.08	0.075

Table 2 presents a comprehensive comparison of the proposed HQCCNN + BLSOA + EHO framework against existing baseline algorithms across multiple metrics, including throughput, energy consumption, storage capacity, data allocation efficiency, latency, and computation cost, for varying numbers of input data points (20–120). The results demonstrate that the proposed method consistently achieves higher throughput, improved storage utilization, better allocation efficiency, lower energy consumption, reduced latency, and decreased computation time compared to all baselines, including EECERA, GT-DRL, SARIMA, MM-MGSMO, MCM-EEGDC, ESS-UPS, DCC-TD3, MO-GDC, and SEE-GDC, validating its effectiveness for geo-distributed workload scheduling.

4.2 Comparison of inference time and model Size

To evaluate the computational efficiency of the proposed HQCCNN-BLSOA, we compared it with traditional models, including EECERA,¹⁵ GT-DRL,¹⁶ SARIMA,¹⁷ MM-MGSMO,¹⁸ and MCM-EEGDC.¹⁹ Table 3 presents the inference time (in seconds per batch) and model size (in MB) for each approach.

Table 3.
Comparison of inference time and model size between the proposed HQCCNN-BLSOA and traditional models.

Model Inference time (s) Model size (MB)

EECERA ¹⁵ 0.15 12

GT-DRL ¹⁶ 0.12 15

SARIMA ¹⁷ 0.10 8

MM-MGSMO ¹⁸ 0.18 10

MCM-EEGDC ¹⁹ 0.14 11

Proposed HQCCNN-BLSOA 0.08 20

Model	Inference time (s)	Model size (MB)
EECERA ¹⁵	0.15	12
GT-DRL ¹⁶	0.12	15
SARIMA ¹⁷	0.10	8
MM-MGSMO ¹⁸	0.18	10
MCM-EEGDC ¹⁹	0.14	11
Proposed HQCCNN-BLSOA	0.08	20

Table 3 compares the proposed HQCCNN-BLSOA with traditional models (EECERA, GT-DRL, SARIMA, MM-MGSMO, MCM-EEGDC) in terms of inference time and model size. The HQCCNN-BLSOA achieves the lowest inference time of 0.08 s per batch, demonstrating faster real-time processing while maintaining a reasonable model size of 20 MB. This indicates that despite its hybrid quantum-classical architecture, the proposed model is computationally efficient. Traditional models exhibit higher inference times and slightly smaller or comparable model sizes, highlighting the trade-off between speed and complexity.

5 Conclusion

The research concludes by presenting the process, results, and advantages of the proposed work, specifically HQCCNN with BLSOA and the Elk Herd energy valley optimizer, for the optimal scheduling of workload in a geographically distributed data center. To manage complex scheduling tasks, the HQCCNN combines the feature extraction capabilities of traditional convolutional neural networks with the processing power of quantum computing. By maximizing workload distribution and ensuring effective resource allocation among geographically separated data centers, the BLSOA enhances the model. The Elk herd Energy Valley Optimizer is then introduced, which improves the distribution of data in a cloud computing environment by optimizing three distinct resources using a single cost factor: energy, computing cost, storage capacity, and bandwidth. This technique optimizes the cost and resource utilization of large data processing in GDDCs. The Elk herd Energy Valley Optimizer is then introduced, which improves data allocation in cloud servers by optimizing three distinct resources using a single cost factor: energy, computing cost, storage capacity, and bandwidth. The results showed that the model achieved a throughput of 109 Kbps, an energy consumption of 0.18 mJ, a computation cost of 0.1 s, a storage capacity of 95%, a data allocation efficiency of 96%, and a latency of 0.03 s for 120 data points. This technique optimizes the cost and resource utilization of large data processing in geo-distributed data centres. Despite the promising results, deploying the proposed HQCCNN-BLSOA-EHO framework in real-world cloud environments presents several challenges. Quantum circuits may require specialized hardware or efficient simulation strategies to scale to large workloads. Integrating the hybrid quantum-classical model with existing cloud infrastructure and scheduling systems may require additional software and orchestration efforts. Moreover, geo-distributed deployment must handle dynamic workload variations, network latency, and resource heterogeneity while maintaining computational efficiency. Addressing these challenges is essential to ensure the practical applicability and robustness of the proposed approach.

Footnotes

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Data availability statement

Data sharing in Amazon EC2 big dataset applicable to this article.

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Hybrid quantum binary light spectrum classical convolutional neural network based Cost reduction and work load scheduling of geo-distributed data centres

Abstract

Keywords

1 Introduction

2 Literature review

2.1 Machine learning-based approaches

2.2 Nature-inspired optimization approaches

2.3 Other relevant approaches

2.4 Research gap

3 Proposed methodology

4 Results and discussion

Table 3. Comparison of inference time and model size between the proposed HQCCNN-BLSOA and traditional models. Model Inference time (s) Model size (MB) EECERA 15 0.15 12 GT-DRL 16 0.12 15 SARIMA 17 0.10 8 MM-MGSMO 18 0.18 10 MCM-EEGDC 19 0.14 11 Proposed HQCCNN-BLSOA 0.08 20

Footnotes

Funding

Declaration of conflicting interests

Data availability statement

References

Table 3.
Comparison of inference time and model size between the proposed HQCCNN-BLSOA and traditional models.

Model Inference time (s) Model size (MB)

EECERA ¹⁵ 0.15 12

GT-DRL ¹⁶ 0.12 15

SARIMA ¹⁷ 0.10 8

MM-MGSMO ¹⁸ 0.18 10

MCM-EEGDC ¹⁹ 0.14 11

Proposed HQCCNN-BLSOA 0.08 20