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Survey of Distributed Algorithms for Resource Allocation over Multi-Agent Systems

Mohammadreza Doostmohammadian, Alireza Aghasi, Mohammad Pirani, Ehsan Nekouei, Houman Zarrabi, Reza Keypour, Apostolos I. Rikos, Karl H. Johansson

TL;DR

This survey develops a formal, coupling‑constrained view of distributed resource allocation over multi‑agent systems and systematically compares primal Laplacian‑gradient, dual gradient tracking, and ADMM approaches. It analyzes convergence, feasibility (including all‑time feasibility for certain methods), and network‑reliability considerations under connectivity, delays, and packet drops. The work surveys a broad set of applications—from smart grids and data centers to PEV charging and NUM—highlighting problem‑specific extensions and nonlinearities. It also points to future directions, including asynchronous, robust, and data‑driven adaptive DRA methods, with attention to energy efficiency and privacy.

Abstract

Resource allocation and scheduling in multi-agent systems present challenges due to complex interactions and decentralization. This survey paper provides a comprehensive analysis of distributed algorithms for addressing the distributed resource allocation (DRA) problem over multi-agent systems. It covers a significant area of research at the intersection of optimization, multi-agent systems, and distributed consensus-based computing. The paper begins by presenting a mathematical formulation of the DRA problem, establishing a solid foundation for further exploration. Real-world applications of DRA in various domains are examined to underscore the importance of efficient resource allocation, and relevant distributed optimization formulations are presented. The survey then delves into existing solutions for DRA, encompassing linear, nonlinear, primal-based, and dual-formulation-based approaches. Furthermore, this paper evaluates the features and properties of DRA algorithms, addressing key aspects such as feasibility, convergence rate, and network reliability. The analysis of mathematical foundations, diverse applications, existing solutions, and algorithmic properties contributes to a broader comprehension of the challenges and potential solutions for this domain.

Survey of Distributed Algorithms for Resource Allocation over Multi-Agent Systems

TL;DR

This survey develops a formal, coupling‑constrained view of distributed resource allocation over multi‑agent systems and systematically compares primal Laplacian‑gradient, dual gradient tracking, and ADMM approaches. It analyzes convergence, feasibility (including all‑time feasibility for certain methods), and network‑reliability considerations under connectivity, delays, and packet drops. The work surveys a broad set of applications—from smart grids and data centers to PEV charging and NUM—highlighting problem‑specific extensions and nonlinearities. It also points to future directions, including asynchronous, robust, and data‑driven adaptive DRA methods, with attention to energy efficiency and privacy.

Abstract

Resource allocation and scheduling in multi-agent systems present challenges due to complex interactions and decentralization. This survey paper provides a comprehensive analysis of distributed algorithms for addressing the distributed resource allocation (DRA) problem over multi-agent systems. It covers a significant area of research at the intersection of optimization, multi-agent systems, and distributed consensus-based computing. The paper begins by presenting a mathematical formulation of the DRA problem, establishing a solid foundation for further exploration. Real-world applications of DRA in various domains are examined to underscore the importance of efficient resource allocation, and relevant distributed optimization formulations are presented. The survey then delves into existing solutions for DRA, encompassing linear, nonlinear, primal-based, and dual-formulation-based approaches. Furthermore, this paper evaluates the features and properties of DRA algorithms, addressing key aspects such as feasibility, convergence rate, and network reliability. The analysis of mathematical foundations, diverse applications, existing solutions, and algorithmic properties contributes to a broader comprehension of the challenges and potential solutions for this domain.
Paper Structure (32 sections, 37 equations, 1 figure, 1 table)

This paper contains 32 sections, 37 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. The DRA Problem
  3. Motivational Example
  4. Mathematical Formulation
  5. Preliminaries
  6. Lipschitz Continuity, Smoothness, and Convexity for Distributed Optimization
  7. Algebraic Graph Theory
  8. Consensus and Coordination Algorithms
  9. Distributed Resource Allocation Algorithms
  10. General Algorithms
  11. Laplacian Gradient Solutions to the Primal-Formulation
  12. Dual-Problem-based Gradient Tracking Solutions
  13. ADMM-based Solutions
  14. Problem-Specific Solutions
  15. Convergence Rate
  16. ...and 17 more sections

Figures (1)

  • Figure 1: A group of generators producing electricity to meet the load demand: in case there is a power mismatch between the generated power and the demand, the generators readjust their produced power to meet this mismatch while optimizing the sum of local generation cost functions.