Dynamic Heuristic Neuromorphic Solver for the Edge User Allocation Problem with Bayesian Confidence Propagation Neural Network

TL;DR

This work addresses the NP-hard Edge User Allocation problem in edge computing by introducing a neuromorphic solver based on Bayesian Confidence Propagation Neural Network (BCPNN) with Winner-Takes-All motifs. A dynamic heuristic generator biases WTA dynamics in real time, and explicit no-allocation units enable feasible solutions under tight resources, promoting scalable performance. On a 30-case synthetic EUA dataset, the approach achieves an average performance gap of about 12.8% relative to the optimal Gurobi solution, with high correlation and robust behavior across runs, and converges within roughly 150 time steps per configuration. The framework is designed for neuromorphic hardware compatibility (e.g., Loihi2) and supports energy-efficient deployment, with extensions toward incremental, real-time adaptation in dynamic EUA scenarios.

Abstract

We propose a neuromorphic solver for the NP-hard Edge User Allocation problem using an attractor network with Winner-Takes-All (WTA) mechanism implemented with the Bayesian Confidence Propagation Neural Network (BCPNN) framework. Unlike previous energy-based attractor networks, our solver uses dynamic heuristic biasing to guide allocations in real time and introduces a "no allocation" state to each WTA motif, achieving near-optimal performance with an empirically upper-bounded number of time steps. The approach is compatible with neuromorphic architectures and may offer improvements in energy efficiency.

Figures (7)

• Figure 1: A geographical visualization of the Edge User Allocation Problem. The figure shows multiple Edge Servers (ESs), and a set of User Devices (UEs) distributed across a geographical area. Each base station has a limited coverage range (dotted ellipses), within which it can potentially serve users. Different colors represent separate edge servers and their assigned users. The core challenge is to determine which users should be assigned to which servers, under capacity and coverage constraints.
• Figure 2: Overview of the proposed BCPNN--EUA model. Each row in the left panel represents a user and forms a WTA hypercolumn whose units correspond to the possible allocation states: being assigned to one of the servers (s1--s4) or left unallocated ("n/a"). Blue circles denote allocation units, the pink "n/a" units implement the explicit no-allocation option. yellow circle indicates that the user is outside the coverage of the server. The right panel shows the dynamic heuristic generator, which computes external input $I$ for all units based on relative demand, relative capacity, and server fill degrees $(D, C, f)$.
• Figure 3: The loadbias curve
• Figure 4: Performance comparison between BCPNN-EUA and the optimal Gurobi solutions across all 30 test cases. (a) PG between BCPNN-EUA and Gurobi, with error bars indicating the standard deviation across five runs. The red dashed line marks the 20% KPI threshold. (b) Raw scores of BCPNN-EUA and the corresponding Gurobi scores. The x-axis denotes the case index, and the y-axis the score for each case (lower is better, but scores are not comparable across different cases). Error bars on the BCPNN-EUA bars show the standard deviation across runs.
• Figure 5: Score evolution over timesteps for two representative runs of the BCPNN–EUA model.