E-SPLIT: A Hierarchical Genetic Algorithm for Energy-Efficient Distributed AI Services

E-SPLIT: A Hierarchical Genetic Algorithm for Energy-Efficient Distributed AI Services Lina Magoulaa, Nikolaos Koursioumpasa, Ioannis Stavrakakisa, Nancy Alonistiotia aDept. of Informatics and Telecommunications, National and Kapodistrian University of Athens, Greece Abstract As we progress toward a new era of Artificial Intelligence (AI)-enabled wireless networks, the focus shifts to deploying distributed intelligence to enhance network automation, scalability, and responsiveness. Despite its merits, it often leads to resource-intensive deployments, which raise energy concerns. These concerns are further amplified by the limited availability of resource orchestration strategies capable of addressing the multi-faceted nature of distributed AI. This work targets energy consumption minimization of distributed AI services by proposing a custom meta-heuristic, two-tier hierarchical genetic algorithm (HGA) that integrates a divide-and-conquer strategy to provide effective chained decision-making. The first tier of HGA determines the optimal placement of model partitions within an AI service on the underlying network, while the second tier focuses on strategic resource allocation for each partition, ensuring that service latency requirements are met. A safe strategy selection is proposed, applying a custom repair mechanism and a penalty function that discourages constraints violation. Evaluation results show the effectiveness and robustness of the proposed HGA, compared to two state-of-the-art baseline solutions, on different network environments and evaluation scenarios. HGA achieves up to 94.1% decrease in the total energy consumption per service compared to the baselines, while entirely eliminating infeasible strategies. Keywords: 6G, Energy Efficiency, Service Placement, Resource Allocation, Genetic Algorithm, Distributed AI Preprint submitted to Computer Communications December 11, 2025 1. Introduction As technology moves from 5G and Beyond 5G (B5G) to 6G networks, a clear transition from operatorto user-centric paradigms is observed [1]. This paradigm shift is triggered by the wide proliferation of smart devices (ranging from smartphones to industrial robots) [2, 3] and the need to support new and challenging use cases and applications [4]. In response to this paradigm shift, unprecedented and innovative concepts emerge, focusing on decentralized and distributed intelligence across the network, enabling collaborative operation of heterogeneous network systems (e.g., deep edge, edge, cloud) and dynamic service adaptation. This shift necessitates novel distributed approaches to Artificial Intelligence (AI), leveraging the capabilities of 6G networks, in order to enhance system automation and proactive adaptation, as well as effective resource management across the device–edge–cloud computing continuum. Such Distributed AI approaches typically rely on model splitting/partitioning, where AI models of reduced computational complexity are shared among (in general heterogeneous) devices, enhancing scalability and reducing network delays [5]. Since the publication of Rel. 18 and 19 of the 3rd Generation Partnership Project (3GPP), there has been an attempt to adopt distributed AI by introducing multiple distributed Network Data Analytics Functions (NWDAFs) and incorporating the Model Training Logical Function (MTLF) [6], while investigating AI model transfer mechanisms for flexible deployment and management [7, 8]. Despite its apparent advantages and the undertaken significant standardization efforts, distributed AI has not yet experienced the anticipated largescale adoption due to the energy concerns that are intensified as the number of the engaged connected devices increases exponentially. These concerns are exacerbated by a recent study [9] that estimates a global data center electricity use of about 415 TWh in 2024 (about 1.5% of global demand) and is projected to more than double, reaching about 945 TWh by 2030. AIaccelerated servers alone grow at about 30% annually and account for nearly half of the aforementioned electricity growth. In the USA, AI-associated data centers may be responsible for almost half of total electricity demand growth by 2030. Several critical challenges related to the application of distributed AI to wireless networks have already been identified, significantly affecting the overall energy consumption of the involved devices [10]. Firstly, distributed 2 AI models partitioned and shared across the network require frequent transmissions between computing devices. Such transmissions may include high dimensional intermediate model outputs of complex neural network architectures comprising millions or even billions of parameters (e.g. Transformers [11]), imposing a significant communication burden. On one hand, periodically transmitting large volumes of updates imposes notable energy demands on the computing devices. On the other hand, network delays are introduced since the required communication channel capacity increases proportionally to the number of computing devices and model partitions. Consequently, the smooth operation of a distributed AI process may be significantly impacted, particularly in dynamic network environments with time-varying conditions (e.g., in terms of channel quality and traffic loads), thereby necessitating effective resource management and model partition placement within the underlying network infrastructure. Secondly, AI model architectures require calculations whose complexity and intensity is tightly related to the size of the model and the selected model partitioning. Consequently, model size and partitioning strongly affect the energy demands. Finally, the stringent AI performance (e.g., low response times) required by critical services and applications [12], in conjunction with the computing heterogeneity across the engaged devices, call for high resource availability and energy consumption. As a result, resources should be allocated and orchestrated considering energy consumption issues, as well. Motivated by the open research challenges, this study proposes a novel, energy-efficient framework capable of joint multi-service placement and execution, considering AI model partitioning and ensuring compliance with AI service delay requirements. More specifically, we propose a custom metaheuristic two-tier hierarchical genetic algorithm (HGA) that adopts a divideand-conquer strategy, splitting the original complex problem into two sequentially interdependent sub-problems of reduced computational complexity. The placement sub-problem refers to selecting devices capable of executing AI model partitions, while the execution sub-problem refers to allocating resources to each model partition. The proposed solution considers dynamicity in the network environment and the involved devices (in terms of resource availability and AI service execution capabilities). It encompasses the ever increasing complexity of an AI model that can significantly affect the overall energy consumption of a system. In ever-changing network environments, feasible solutions may be sparse. As a result, our approach enforces feasibility by introducing custom repair operators and penalty functions contributing 3 to a safe strategy selection. Contribution: The key contributions of our two-tier HGA are summarized below: •We target energy-efficient distributed AI service deployment and execution, while respecting service latency requirements. •We focus on joint multi-service placement, considering AI model partitioning, while providing per-partition resource allocation decisions. •We provide dynamic strategies adapted to service availability, timevarying device computational and communication resources, and network conditions. •AI model complexity is integrated into both energy consumption and service end-to-end latency toward an AI focused system model and problem formulation. •Our approach includes topologyand delay-aware path selection between consecutive partitions to further decrease energy consumption and service latency. •We contribute to a safe strategy selection by enforcing solution feasibility with custom repair operators in conjunction with a custom penalty function that both prevent hardand minimize softconstraint violations. •We target per-service energy minimization to contribute toward fairness across AI service deployment. The rest of the paper is organized as follows. Section 2 presents relevant state-of-the-art works. Section 3 provides the system model. Section 4 provides the problem formulation. Section 5 describes key definitions along with the proposed solution that is evaluated in Section 7 using the simulation setup of Section 6. Finally, Section 8 concludes the paper. 2. Related Work The ever-increasing use of energy-hungry Artificial Intelligence (AI) in future wireless networks has led to the development of energy-efficient deployment strategies. Recent research has focused on optimizing the placement of AI services and the allocation of computational and communication resources toward energy-efficient AI service deployment, while maintaining 4 service performance. Key approaches include joint optimization of service placement and offloading, energy-efficient strategies for AI model partitioning and placement, and AI-driven solutions for dynamic resource management in cloud, edge and hybrid environments. Several research works have focused on AI service placement to enable efficient training and/or inference without explicit resource allocation. In [13] the authors model the problem of energy-efficient placement of services for AI applications as a multi-period optimization problem. They propose a heuristic approach to jointly place services and schedules requests targeting an overall energy consumption and latency minimization. The work [14] tackles the problem of efficiently allocating AI models by selectively offloading parts of inference tasks between devices and edge servers under given time and energy constraints. The authors in [15] propose Harmony, a deep reinforcement learning-driven Machine Learning (ML) cluster scheduler that places heterogeneous training jobs in a manner that minimizes average job completion time while respecting server capacities. Placement is decided per scheduling interval and then kept fixed until training job completion. Work [16] proposes a framework to place devices for distributed ML so as to reduce energy while maintaining performance. It evaluates placements by jointly considering energy costs, computational load, and data transfer, using both simulations and analytical studies. Another group of research works study the problem of joint AI service placement and efficient resource allocation focusing on energy and latency as performance indicators. Work in [17] focuses on minimizing the total computing time and energy consumption of all task nodes and maximize the inference accuracy of AI tasks by jointly optimizing the resource allocation and computing offloading decision of each node by solving a mixed-integer non-linear programming (MINLP) problem. They propose an ADMM (alternating direction multiplier method)-based approach, decomposing the initial complex problem into smaller subproblems, enabling scalable optimization for large networks. The authors in [18] focus on joint optimization of task offloading, resource allocation, and placement AI models as a whole (no model partitioning is considered) in 6G networks, to enable efficient AI-as-a-Service (AIaaS), aiming to minimize a weighted system cost that combines latency, energy consumption, and service utility. A Lyapunov-based optimization is proposed toward solution scalability. Work [19] tackles the joint AI service placement and resource allocation in a multi-user MEC system to minimize each user’s computation time and energy. The authors propose an ADMM method that 5 decomposes the problem into per-user parallel subproblems and use metaheuristics for placement strategies. [20] introduces an Edge AI-as-a-Service framework that enables configurable deployment of AI models across edge servers to optimize delay, energy consumption, and AI result quality (e.g., accuracy or confidence). Authors of [21] propose a reinforcement-learningbased solution that captures task offloading, resource allocation, and model placement decisions to minimize system energy consumption under latency and resource constraints. Work [22] targets long term average device energy minimization for multi-partition Deep Neural Networks inference, while respecting resource limits. In addition, [23] proposes a reinforcement-learning approach that learns generalizable device-placement policies for distributed training, targeting the end-to-end execution time of a training step. A set of works considers model partitioning to their placement and/or resource allocation decisions. Work [24] proposes an operator-fusion–aware device-placement method for distributed inference on heterogeneous devices to minimize end-to-end latency. In [25], the SplitPlace framework is proposed that uses a Multi-Armed Bandit selection for layeror semanticbased model splitting and places the resulting partitions on edge workers using decisionaware reinforcement learning. The goal is to jointly improve accuracy while reducing response time. The study [26] focuses on minimizing energy consumption of vision transformers (models of high complexity), while maintaining acceptable model accuracy and latency, using dynamic complexity adjustment, task redistribution, and resource-aware partitioning. Last but not least, works [27, 28, 29] focus on efficient resource management for a specific distributed AI framework, named Federated Learning, focusing on energy minimization, while considering targeted computation and communication requirements introduced in the training process. Despite the extensive past work, there are still major challenges to be addressed. Most prior works handle AI service as a non-divisible block, without considering model partitioning and/or per-partition resource allocation and ignoring inter-service dependencies. Even works that tackle model partitioning mostly focus on a single AI service, excluding joint multi-service optimization. In addition, works that focus on joint service placement and efficient resource allocation fail to consider service, device and network dynamicity, assuming static AI models and non time-varying conditions. Service activation/de-activation, time-varying resource availability and communication channel conditions can significantly affect the decision-making and should be part of the research scope. To the best of our knowledge this is the 6 first work that proposes an energy-efficient framework for joint multi-service placement and execution, considering AI model partitioning and imposed service delay thresholds. Our approach explicitly accounts for network and device dynamicity, as well as the impact that the growing complexity of AI models has on system energy consumption. To ensure solutions’ feasibility, we introduce custom repair operators and penalty functions, yielding a safe strategy selection mechanism. 3. System Model This section provides the system model of a distributed AI-enabled wireless network topology using AI model partitioning. AI model partitioning is a distributed technique that allows the division of a complex AI architecture into multiple, less complex partitions. This process enables the distribution of operations across numerous network devices, thereby enabling collaborative AI model execution while mitigating computational and communication overloads. 3.1. Network Topology The network topology is modeled as an undirected graph G(N, E), where Nis a set of network devices and Eis a set of bidirectional wireless links connecting them. Each device and link is characterized by computational and communication resources that vary over time. The time is divided into discrete time units, named time steps, and denoted by t. Device Computational Capability: Let u(t) n∈N,f(t) n∈R+,m(t) n∈N, and d(t) n∈Ndenote the available number of CPU cores, the CPU speed (in Hz), the memory and disk size (in bits) of device nat time step t. As a result, each device at each time step tis represented as a resource quadruple R(t) n={u(t) n, f(t) n, m(t) n, d(t) n}. The CPU of each device nhas also an effective switched capacitance, denoted by ςn∈R+, which depends on the hardware architecture. Based on f(t) n, device ncan complete a certain number of FLOPs per cycle, denoted by a(t) n. Device Communication Capability: Each wireless link e(k,l)∈Eat timestep t, connects a pair of devices k, l ∈N, and is modeled as a flat-fading channel with a constant Gaussian noise power spectral density N0e∈R+ (in Watts/Hz), an achievable data rate r(t) e(k,l)∈R+(in bps) and a channel gain g(t) ek,l ∈R(linear). In addition, each source device kof a link e(k,l) 7 has time-varying communication characteristics. These include the available bandwidth b(t) e(k,l)∈R+(in Hz), the antenna frequency f(t) e(k,l)∈R+(in Hz) and transmission power tx(t) e(k,l)∈R+(in Watts) at time step t. 3.2. Distributed AI Services At each time step t, a set of K(t)AI services must be deployed over the underlying network topology with appropriate resource allocation to ensure efficient operation. Let S(t)={s(t) 1, s(t) 2, ..., s(t) K(t)}denote the set of AI services to be deployed at time step t. We consider that each AI service s(t) i∈S(t)is divided into a sequence of Lisequentially connected model partitions denoted by P(t) si={p(t) 1,si, ..., p(t) Li,si}. Each AI service imposes an end-to-end delay threshold Tthr(t) sito avoid undesirable service responsiveness. The jth model partition p(t) j,si∈P(t) siof service siis characterized by a set of resource and data requirements denoted by R(t) j,si, where R(t) j,si= {m(t) j,si,i(t) j,si,o(t) j,si,d(t) j,si,c(t) j,si}. This set of requirements includes the model partition size m(t) j,si∈N(i.e. the trainable parameters) (in bits), the data input shape i(t) j,si∈N, the output shape o(t) j,si∈N, the sample size precision d(t) j,si∈N (e.g. 16, 32) (in bits), and the model partition complexity c(t) j,si∈R+(in FLOPs). Partition Computational Cost: The processing of a partition p(t) j,siat device nintroduces a computational cost to the network. This cost is based on the computation time Tcomp j,si,n (t)∈R+(in seconds) and energy Ecomp j,si,n (t)∈R+ (in Joules) required by device nto process the partition. Both the computation time and energy depend on the available resources R(t) nof device nat time step t(see Section 4 for more details). Partition Communication Cost: Following the execution of a partition p(t) j,si, its output o(t) j,simust be transmitted to the device hosting the subsequent partition p(t) j+1,si. Let nsand nddenote the source and destination devices hosting partitions p(t) j,siand p(t) j+1,si, respectively. A communication cost is introduced to the network when transmitting across each wireless link e∈Ethat belongs to the path connecting the host devices of the two subsequent partitions at time step t. This cost is shaped by the transmission time Ttran (j,j+1; ns,nd),si (t)∈R+(in seconds) and energy Etran (j,j+1; ns,nd),si (t)∈R+ (in Joules) required (see Section 4 for more details). Table 1 summarizes the system model notations. 8 Parameter Description GUndirected graph of network topology NSet of network devices in network topology G ESet of wireless links in network topology G tTimestep, a discrete time unit R(t) nSet of available computational resources of network device nat time step t u(t) nAvailable CPU cores of network device nat time step t f(t) nAvailable CPU speed of network device nat time step t m(t) nAvailable memory size of network device nat time step t d(t) nAvailable disk size of network device nat time step t ςnEffective switched capacitance of network device n a(t) nTotal number of FLOPs per cycle that network device ncan complete at time step t N0eGaussian noise power spectral density of wireless link e r(t) e(k,l)Achievable data rate of source node of wireless link e(k,l)at time step t g(t) e(k,l)Channel gain of wireless link e(k,l)at time step t b(t) e(k,l)Available bandwidth of source node of wireless link e(k,l)at time step t f(t) e(k,l)Antenna frequency of source node of wireless link e(k,l)at time step t tx(t) e(k,l)Transmission power of source node of wireless link e(k,l)at time step t K(t)Number of AI services at time step t S(t)Set of AI services at time step t LiNumber of model partitions of service si P(t) siSet of model partitions of service si p(t) j,siPartition jof service siat time step t Tthr(t) siEnd-to-end delay threshold of service siat time step t R(t) j,siSet of resource requirements of model partition pj,siat time step t m(t) j,siSize of model partition pj,siat time step t i(t) j,siData input shape of model partition pj,siat time step t o(t) j,siData output shape of model partition pj,siat time step t d(t) j,siData sample size of model partition pj,siat time step t c(t) j,siComplexity of model partition pj,siat time step t Tcomp j,si,n (t)Computation time to execute partition p(t) j,siat network device nat time step t Ecomp j,si,n (t)Computation energy to execute partition p(t) j,siat network device nat time step t Ttran (j,j+1; ns,nd),si (t)Time to transmit the output of partition p(t) j,sito the subsequent partition p(t) j+1,siat time step t Etran (j,j+1; ns,nd),si (t)Energy to transmit the output of partition p(t) j,sito the subsequent partition p(t) j+1,si at time step t Table 1: Notation Table 9 First/Second Tier Elites: The number of best-scored chromosomes in a generation that are included unaltered in the next generation. First/Second Tier Population: A fixed-size set of first/second tier chromosomes. Fitness Function2:A function that serves as a score for both first and second tier chromosomes and is formulated based on the objective function (11), in conjunction with the list of constraints presented in the previous section. Specifically: FF (t)=−[wff,1·Etotal avg (t)+wff,2·P(t)](20) As wff,1and wff,2we denote the weights assigned to each part of the equation. The first part of Eq. (20) is the objective function of our problem formulation. The second part P(t)is a penalty term defined to guarantee a safe HGA process [32]. Consequently, the firstand second-tier chromosomes that violate the constraints and result in infeasible solutions will be penalized. We define this penalty as follows: P(t)=(w1·v(t)+w2·(D(t) time)2+w3·D(t) res +w4·D(t) link +w5·O(t)) |S(t)|,(21) where: v(t)denotes the total number of constraint violations resulting from the combined firstand second-tier decisions at time step t, D(t) time =X si∈S(t) (T(t) si−Tthr(t) si)+,(22) 2Each term of the fitness function is normalized according to its own scale, ensuring balanced contributions and preventing bias toward any particular constraint. 16 D(t) res =X n∈N" X si∈S(t)X j∈P(t) si u(t) j,si,n ·f(t) j,si,n ·Ω(t) j,si,n −umax n (t)·fmax n (t)!+ + X si∈S(t)X j∈P(t) si u(t) j,si,n ·Ω(t) j,si,n −umax n (t)!+ + X si∈S(t)X j∈P(t) sim(t) j,si+ (i(t) j,si+o(t) j,si)·d(t) j,si·Ω(t) j,si,n −mmax n (t)!+ + X si∈S(t)X j∈P(t) sim(t) j,si+ (i(t) j,si+o(t) j,si)·dj,si·Ω(t) j,si,n −dmax n (t)!+#, (23) D(t) link =X e(k,l)∈E"X si∈S(t)X j∈P(t) siX ns∈NX nd∈N Λ(t) j,si,ns,nd,e(k,l)·b(t) j,si,ns−bmax e(k,l) (t)+ +X si∈S(t)X j∈P(t) siX ns∈NX nd∈N Λ(t) j,si,ns,nd,e(k,l)·tx(t) j,si,ns−txmax e(k,l) (t)+#. (24) For reminder purposes Λ(t) j,si,ns,nd,e(k,l)= Ω(t) j,si,nsΩ(t) j+1,si,ndΩ1(e(k,l);ns,nd)(t). The (·)+operator is used to penalize only when a condition exceeds the predetermined threshold. Eq. (22), based on constraint (12), defines the D(t) time as the distance between the total time T(t) si(computational and communication) required to execute service siand the time threshold imposed to the service at time step t. Similarly, following constraints (13)-(18), Eqs. (23) and (24) quantify the excess demand in computational (CPU cycles, CPU cores, memory and disk storage) and communication (bandwidth and transmission power) resources, respectively, relative to the maximum available capacity of each device or link. Finally, O(t)denotes the aggregate percentage-wise ratio of over-utilization across all devices and links, encompassing both computational and communication resources at time step t. 17 Figure 2: Illustration of HGA’s Methodology It captures, the extent to which the computational and communication resources exceed their maximum available capacities. In other words, for every resource type of a device or link that operates beyond 100% of its capacity, the amount by which it exceeds this threshold is expressed as a percentage, and O(t)is defined as the sum of these percentages across the entire system. 5.2. Methodology This section provides the step-by-step methodology of the proposed HGA. Figure 2 illustrates the complete process in a circular flow, highlighting the iterative solutions’ refinement across generations. The complete list of steps along with their description are provided below. Step 1 [Initialization]: This step initiates HGA process, as it initializes the population of both firstand secondtier GAs. In this phase, a set of random chromosomes, referred to as the initial population, is generated for each tier. These chromosomes serve as the starting point (first generation) for subsequent evaluation and evolution. Step 2 [First Evaluation]: This step acts as a first evaluation point for each generation. A mutual fitness score is assigned to each combination of firstand secondtier chromosomes using Eq. (20). This score guides the evolutionary process toward better quality chromosomes that satisfy the objective (Eq. (11)) and comply to constraints (12)-(19). Step 3 [Repairing Phase]: This step introduces a custom repair mecha18 nism that facilitates the evolutionary process by contributing to constraint violations reduction. For each combination of firstand secondtier chromosomes that violates the constraints, the following actions are performed: •Detect over-utilized devices where the assigned model partitions exceed the available computational and/or communication resources. •Identify the violated resource types (e.g. cpu, bandwidth) of the overutilized devices. •Detect services that include partitions assigned to over-utilized devices and violate the time related constraint (Constraint (12)). Then, for each service locate the most time consuming partition both in terms of computation and communication. •Attempt to repair over-utilization by applying a percentage-wise reduction to the resources allocated to the partitions of an over-utilized device, for all identified violated resource types. The located most time consuming model partitions are excluded from this process as this will introduce further delays to the related services. Step 4 [Random Chromosome Injection]: This step contributes to avoiding premature convergence by introducing randomness to each population. At each generation, one random chromosome is injected into both the firstand second-tier populations, expanding the search space and increasing the diversity of the evolutionary process. Step 5 [Hypermutation]: This step is triggered when the distance of the fitness score from the best-scoring chromosomes (firstand second-tier) of two consecutive generations is higher than a pre-selected percentage threshold Hthr. The hypermutation enhances evolutionary diversity by increasing percentage-wise the rate of gene alteration that is known as the mutation rate (See Step 8). Step 6 [Fixed Memory]: This step initiates a fixed memory (FM) mechanism that stores the Bbest chromosomes found so far. With a predefined probability pfm, these stored chromosomes replace the Bworst chromosomes of the current generation, thereby ensuring that high-quality solutions are preserved across generations. Step 7 [Second Evaluation]: Following Step 6, the resulted firstand second-tier populations, are re-evaluated using Eq. (20). After this fitness 19 score assignment, both populations are sorted so that the best-scoring chromosomes are placed at the top. The top el chromosomes, known as elites, are transferred unaltered to the next generation to ensure the preservation of high-quality solutions. Step 8 [GA Operations]: In this step, the standard GA operations [33] are applied to both the firstand second-tier populations, enabling their evolution prior to transferring into the next generation. The following operations are performed: •Parent Selection: In each generation, first-tier chromosomes are selected as parents (following a Roulette Wheel approach ([34])) for crossover in order to create offspring for the next generation. Following this, second-tier parent selection must be aligned with the first-tier, as second-tier resource allocation inherently depends on the first-tier device selection. The parent selection is crucial to HGA’s convergence since fit parents tend to produce better and fitter solutions. •Crossover: Following parent selection, a crossover operation is applied in order to combine genetic information of the two selected parents of each tier to generate new offspring. A uniform crossover method is employed to each tier, where each gene of an offspring is inherited from one of the parents selected based on a probability pc, referred to as the crossover rate. •Mutation: Subsequent to offspring generation, a mutation operation is applied. Mutation enables the exploration of the search space as it randomly tweaks genes of firstand second-tier chromosomes with a probability pm, called mutation rate. This results to new candidates solutions, known as mutated chromosomes, introducing diversity in the population. Step 9 [New Generation Preparation]: This step concludes a generation cycle and prepares the next evolution. The firstand second-tier chromosomes produced by Step 8 along with the elites of Step 7 form the next generation population. Steps 2-9 are repeated until a termination criterion is met. An early stopping mechanism interrupts the search procedure when the best-scoring combination of firstand second-tier chromosomes does not improve for a certain number of generations. This reduces unnecessary computations and contributes to faster convergence. 20 Offline and Online Phase: HGA consists of two phases: The offline and the online phase. During the offline phase, HGA explores different candidate solutions in each generation to converge on an optimal deployment of distributed AI services and an optimal resource allocation for each model partition within the underlying network topology. In the online phase, HGA is evaluated based on its performance in various evaluation scenarios involving semi-static and dynamic network topologies and device resource capabilities, where its strategies are applied in near real-time. 5.3. Computational Complexity The computational cost of HGA depends on the population size P, number of generations Gn, total model partitions L, network devices Nand network links E. Each generation involves fitness evaluation and GA operations for both tiers. The first-tier GA additionally performs Dijkstra’s shortest-path search for all partition pairs, resulting in a total complexity of O(L·E·log N)[35] per generation. Accordingly, the overall time complexity of HGA is estimated as: O(2 ·P·Gn ·(L·E·log N)) . HGA remains tractable since P,Gn, and L(algorithmic parameters) are bounded. It should be noted that the offline phase absorbs most of the computational cost, while the online phase (with small Pand Gn) achieves near real-time performance. 6. Simulation Setup The simulation setup is comprised of 30 heterogeneous (in terms of computational and communication capabilities) devices. These devices are uniformly distributed in an area of 500 x 500 meters, where each device is at least 5 meters away from the others. AI Services and Partitions Setup: Our evaluation setup considers up to 40 AI services, each resembling a complex Convolutional Neural Network (CNN) architecture. These CNN models differ in the number of their layers, ranging from 40 to 80. They also differ in their data input shape i(t) j,si, which is either [1, 3, 128, 128] or [1, 3, 224, 224] with a 32 bits precision. The output channels are within {16, 32, 64, 128, 256, 512}. Each CNN model comprises 80% convolutional layers (Conv2D) and 20% pooling layers (MaxPool2D), 21 as well as up to two Fully Connected (FC ) layers, each with 64, 128, or 256 neurons. The kernel size is either (3x3) or (5x5). As a result, each CNN model has a varying complexity ranging from 300 Mega Floating Operations (MFLOPs) to 1.4 Tera FLOPs (TFLOPs). Each CNN varies in the number of model partitions, ranging from 4 to 8. Overall in our setup, we consider the total number of model partitions ranging from 40 to 320. Finally, the end-to-end delay threshold considered for each AI service is in the range of [4, 15] seconds. Device Setup: The same minimum CPU speed fmin n (t)is assumed for all devices equal to 0.1 GHz, while the maximum one fmax n (t)at each time step is within [3, 5.5] GHz. The number of CPU cores range from 64 (umin n (t)) to 128 (umax n(t)) for each device. The maximum memory mmax n(t)and disk storage dmax n (t)are within {64, 128, 256}GB and {100, 500, 1000}GB, respectively. The number of FLOPs per cycle is the same for all devices, constant across time steps t, and equal to an= 32. The effective switched capacitance applied to all devices is equal to ςn= 10−28 Watt/Hz3. Regarding the communication capabilities of each device, the antenna frequency f(t) e(k,l)is within [1.8, 3.7] GHz and the transmission power tx(t) e(k,l)is within [10, 33] dBm. Network Environment Setup: We consider a non-free space (i.e., with obstacles) environment, where a mesh network topology of devices is deployed. Although focusing on a wireless mesh topology, this setup is used only as a representative distributed environment to validate the algorithm’s behavior under heterogeneous computational and communication conditions. The proposed framework and HGA formulation are topology-independent and can be readily applied to alternative infrastructures such as O-RAN edge networks or data center fabrics with programmable hardware. We set the reference distance d0= 1 meter, a constant path loss exponent e= 1.5 and the same constant Gaussian noise power spectral density N0e=−158 dBm/Hz applied to each link eof the topology. The spectral efficiency assumed for each link e is equal to 4 bits/Hz. The maximum available bandwidth at time step tb(t) e(k,l) allocated to each link e(k,l)is in the range of [80, 100] MHz. Two different network environments are considered in all performed experiments, in order to showcase the robustness of our HGA, namely a semi-static and a dynamic network environment. Four total evaluation scenarios are considered for both environments, differing in the maximum number of AI services, which is 10, 20, 30 and 40, respectively. Semi-Static Environment Setup: In the semi-static environment, ev22 AI Services Scenario 10 20 30 40 Population Size 250 Elites (el)80 Crossover Rate (pc)0.1 Mutation Rate (pm)0.1 Mutation Decay Rate 0.995 Hypermutation Threshold (Hthr)0.1 FM Replacement Rate (pfm)0.8 FM Size (B)10 Table 2: HGA Configuration Setup ery 10 time steps, each AI service considered in each scenario has a 5% probability of being deactivated/activated, altering the system load. However, the device and network network environment setups are initialized within the afore-described ranges and remain constant across time steps. Dynamic Environment Setup: In the dynamic environment, every 10 time steps the number of active AI services and the network conditions change. More specifically, each AI service considered in each scenario has a 10% probability of being deactivated/activated. Each device and wireless link in the network has a 30% probability of changing its resource availability within the previously described ranges. 6.1. HGA Setup The proposed HGA was realized through a fully custom Python implementation. Table 2 includes the configuration setup applied to both tiers of HGA and was used for all scenarios and in all evaluation experiments. The maximum number of generations is set to 1500, with early stopping triggered after 200 consecutive non-improving generations. The mutation rate, linearly decays at each generation. When the hyper-mutation is triggered, the mutation rate is increased by 50%. The weights defined in equations (20) and (21) are experimentally tuned and configured as wff,1= 0.6, wff,2= 0.4, w1= 0.26, w2= 0.26, w3= 0.16, w4= 0.16, and w5= 0.16. 7. Evaluation Results This section provides numerical results to assess the performance and robustness of the proposed HGA, as well as its comparative performance against two state-of-the-art baselines, under the network environments and evaluation scenarios presented in Section 6. Three main performance metrics 23 are considered: 1) the per AI service energy consumption, 2) the per AI service end-to-end (E2E) latency, 3) the total number of constraint violations (including hard and soft constraints). 7.1. Offline Phase (a) Fitness Score (b) Energy per AI Service (c) Total Violations (Soft & Hard) Figure 3: Offline phase of the proposed HGA for different number of AI services. The first set of the evaluation results concerns the offline phase of HGA. This offline phase was conducted within the dynamic network environment and across different evaluation scenarios. The introduced diversity enables robust tuning and enhances the generalization capabilities of the chained GA decision-making. Fig. 3 illustrates the performance of HGA, considering different number of AI services (|S| ={10,20,30,40}), as the generations evolve. Fig. 3a depicts the evolution of the fitness score across generations. The results indicate that HGA achieves high performance (observed after roughly 125 generations, indicated by the fitness score approaching zero) under network dynamicity and for the different number of AI services considered, demonstrating robustness and stability, as well as effective cooperation between the two GA tiers. Fig. 3b depicts the per AI service energy consumption, i.e. the average of the total computation and transmission energy across all services. As it can be inferred from the figure, the amount of consumed energy, for the different number of AI services, significantly decreases with the number of generations. In addition, the figure illustrates the capability of HGA to achieve similar energy per AI service, regardless of the number of AI services. Fluctuations 24 in the average energy consumption are observed. These can be attributed to the variations in the number of active AI services and the constantly changing network conditions. However, the amplitude of these fluctuations is highly constrained, showcasing the ability of HGA to find suitable strategies regardless of the environment dynamicity. These results indicate both an effective deployment strategy (first-tier GA) and efficient per model partition resource allocation (second-tier GA). In particular, the overall energy reductions (between the first and the last generation) are up to 86.5%, 87.9%, 93.5%, and 96.8% for 10, 20, 30, and 40 AI services, respectively. As already stated, the current work introduced a penalty function toward a safe HGA process. Accordingly, Fig. 3c depicts the total number of constraint violations, including both soft and hard ones, across generations. The results show an effective and efficient chained decision-making between the two GA tiers, as the total number of violations is (eventually, after a number of generations) eliminated in all evaluation scenarios. Despite the dynamicity in network conditions and AI services, HGA consistently converges to safe decision-making, enabling an efficient distributed AI service execution, while respecting the hardware-related constraints and the imposed end-to-end latency threshold. To summarize, during the offline phase, HGA showcases scalable performance (yielding similar results upon convergence) despite variations in the network conditions and number of active AI services. The divide-andconquer strategy introduced by our two-tier HGA, enables effective cooperation, leading to a per service energy consumption and violations-free chained decision-making that is comparable across all evaluation scenarios. 7.2. 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