Study of Mixed-Integer Optimization Based on Graph-Based Decomposition for Cell-Free Networks

Jul 16, 2026

This letter develops a radio access network (RAN) framework for mixed discrete–continuous optimization arising in user-centric cell-free massive multiple-antenna networks. It decomposes clustering decisions and continuous resource allocation by representing feasible serving states as a graph with Hamming-topology neighborhoods. A serving-state graph abstraction enables topology-aware search-and-evaluate procedures, and a graph-based search-and-evaluate (GBSE) algorithm is proposed with complexity analysis. Energy-efficiency maximization at the RAN level is used to demonstrate applicability, with results showing Hamming neighborhoods improving the scalability–exploration trade-off and GBSE outperforming existing techniques.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages6

Reading Time15 min

I. INTRODUCTION

II. SYSTEM MODEL

A. RAN As A Graph

Study of Mixed-Integer Optimization Based on Graph-Based Decomposition for Cell-Free Networks Julio Cesar Cardoso Tesolin and Rodrigo C. de Lamare arXiv :2607 .090 17v 1 [ cs .IT] 10 Jul 2026 Abstract—This letter develops a radio access network (RAN) framework for mixed discrete–continuous optimization problems that arise in user-centric cell-free massive multiple-antenna networks. The novel framework exploits the structural decomposition between discrete clustering decisions and continuous resource allocation variables by modeling the space of feasible serving states as a graph with Hamming-topology neighborhoods. A serving-state graph abstraction is introduced to enable topologyaware search-and-evaluate optimization procedures and a graphbased search-and-evaluate (GBSE) algorithm is devised along with their complexity analysis. Energy efficiency maximization at the RAN level is presented as an application of considered alongside the proposed framework and GBSE algorithm. Numerical results show that minimal Hamming neighborhoods offer an attractive trade-off between scalability and exploration capability in graph-based optimization and GBSE outperforms existing techniques. Index Terms—Mixed-integer optimization, graph representations, cell-free networks, resource allocation. I. INTRODUCTION FUTURE mobile networks are expected to rely on clus tered cell-free (CF) massive multiple-input multipleoutput (mMIMO) architectures [1], [2], [3] to enable distributed cooperation among access points (AP) while mitigating fronthaul constraints by assigning each user equipment (UE) to a subset of geographically relevant APs. In both usercentric and AP-centric formulations, the clustering problem plays a central role in balancing performance, scalability, and signaling overhead. To address this challenge, a wide range of optimization-based approaches have been proposed, adopting diverse network performance indicators as objective functions while jointly considering discrete clustering decisions and resource allocation variables. Regardless of the assumptions on objective functions or constraints, many of these formulations naturally fall within the class of mixed discrete–continuous optimization problems. Several works have investigated clustering strategies using the channel norm or aimed at improving specific key performance indicators such as information rates. User-centric (UC) clustering approaches have been proposed to reduce signaling overhead and computational complexity [4], [5], [6], while other studies have focused on enhancing energy efficiency under UC formulations [7], [8], [9],[10] . Despite these advances, the cluster selection problem remains inherently combinatorial, and existing solutions often rely on solver-specific techniques or heuristic rules without explicitly exploiting the structure of the discrete serving-state space. As a result, scalability remains a key limitation, particularly in large-scale CF deployments. This letter proposes a solver-agnostic framework for UC clustering in CF-mMIMO networks. It is built upon: (i) modeling the discrete space of radio access network (RAN) serving states as a structured Hamming-topology graph; (ii) decomposing the resulting problem into a discrete outer-layer search and a inner-layer evaluation and (iii) enabling a family of graph-based search algorithms that navigate the serving-state graph using local neighborhood information. Then, a graph-based search-and-evaluate (GBSE) algorithm is devised to solve problems using the proposed framework [11] . An energy-efficiency optimization at the RAN level is presented as to demonstrate the applicability of the framework and the GBSE algorithm. Notation: Scalars are denoted by a, A ; column vectors by a ∈ Cn ; and matrices by A ∈ Cm ×n. A denotes a set and A denotes a graph. (·)T is the transpose, E{·} is the statistical expectation, and \#(·) is the set cardinality. O (·) represents the worst-case asymptotic comp

FAQs

What optimization problem does the document address in cell-free networks?

It addresses mixed discrete–continuous optimization problems that jointly involve discrete user-centric clustering decisions and continuous resource allocation variables in cell-free massive multiple-antenna systems.

How does the proposed method separate clustering from resource allocation?

It exploits structural decomposition by modeling discrete serving states as a graph and treating continuous resource allocation through an inner-layer evaluation linked to the discrete outer-layer search.

What is the serving-state graph abstraction used for?

It abstracts feasible serving states using a graph with Hamming-topology neighborhoods, enabling topology-aware search-and-evaluate optimization procedures.

What application and performance outcome are presented?

Energy-efficiency maximization at the RAN level demonstrates applicability, and numerical results indicate that minimal Hamming neighborhoods provide a favorable scalability–exploration trade-off, with GBSE outperforming existing techniques.

Jul 16, 2026

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