[Paper Review] Convergence Analysis and Parallel Computing Implementation for the Multiagent Coordination Optimization Algorithm

Qing Hui, Haopeng Zhang|arXiv (Cornell University)|Jun 2, 2013

Distributed Control Multi-Agent Systems37 references7 citations

TL;DR

This paper proposes a parallel implementation of the Multiagent Coordination Optimization (MCO) algorithm using MATLAB's parfor to accelerate convergence, while rigorously proving global convergence via semistability theory. The parallel MCO achieves 40–70% faster computation than serial MCO and outperforms PSO in both accuracy and speed on benchmark nonlinear, nonconvex functions.

ABSTRACT

In this report, a novel variation of Particle Swarm Optimization (PSO) algorithm, called Multiagent Coordination Optimization (MCO), is implemented in a parallel computing way for practical use by introducing MATLAB built-in function "parfor" into MCO. Then we rigorously analyze the global convergence of MCO by means of semistability theory. Besides sharing global optimal solutions with the PSO algorithm, the MCO algorithm integrates cooperative swarm behavior of multiple agents into the update formula by sharing velocity and position information between neighbors to improve its performance. Numerical evaluation of the parallel MCO algorithm is provided in the report by running the proposed algorithm on supercomputers in the High Performance Computing Center at Texas Tech University. In particular, the optimal value and consuming time are compared with PSO and serial MCO by solving several benchmark functions in the literature, respectively. Based on the simulation results, the performance of the parallel MCO is not only superb compared with PSO for solving many nonlinear, noncovex optimization problems, but also is of high efficiency by saving the computational time.

Motivation & Objective

• Address the need for faster, robust, and convergent multiagent optimization algorithms in real-time and distributed networked systems.
• Improve upon standard PSO by integrating cooperative control and neighbor-based information sharing to enhance convergence and solution quality.
• Enable practical deployment of MCO through efficient parallel computing implementation using MATLAB's parfor.
• Provide a rigorous global convergence analysis for MCO using semistability theory, ensuring theoretical robustness.
• Demonstrate scalability and performance gains of the parallel MCO on high-performance computing systems for large-scale optimization problems.

Proposed method

• Integrate MATLAB’s parfor function into the inner loop of the MCO algorithm to enable parallel execution across multiple workers.
• Modify the standard PSO update rule by incorporating neighbor-to-neighbor velocity and position sharing via a consensus-based control term.
• Apply semistability theory to rigorously analyze the global convergence of the MCO algorithm under distributed communication constraints.
• Use gradient-based adaptation and a distributed control term to accelerate convergence and improve solution accuracy.
• Implement the algorithm on Texas Tech University’s High Performance Computing Center to evaluate performance on supercomputers.
• Compare computational time and solution quality across serial MCO, parallel MCO, and PSO using standard benchmark functions (e.g., Sphere, Rosenbrock, Rastrigin).

Experimental results

Research questions

• RQ1 Can the MCO algorithm achieve global convergence under distributed communication and network constraints, and can this be formally proven?
• RQ2 How does the parallel implementation of MCO via MATLAB’s parfor affect computational efficiency and scalability?
• RQ3 Does the MCO algorithm outperform standard PSO in terms of solution accuracy and convergence speed on nonlinear, nonconvex optimization problems?
• RQ4 What is the actual speedup and time reduction achieved by parallel MCO compared to serial MCO across different benchmark functions?
• RQ5 How does the performance of parallel MCO compare to parallel PSO in terms of both computational time and solution quality?

Key findings

• The parallel MCO algorithm achieves a 40–70% reduction in computational time compared to the serial MCO implementation across all benchmark functions.
• The parallel MCO algorithm maintains solution accuracy comparable to the serial MCO, with best objective values consistently lower than those of PSO across all test functions.
• For the Sphere function, the parallel MCO achieved a best value of 4.1855×10⁻⁷, outperforming PSO’s best value of 3.3×10⁻³.
• The speedup metric for parallel MCO reached up to 2.5x on larger problem instances, with scalability confirmed across varying numbers of workers in the MATLABpool.
• The MCO algorithm demonstrated superior convergence performance on complex functions like Rastrigin and Griewank, achieving median values below 10⁻⁶ compared to PSO’s values above 10⁻³.
• Despite higher computational load, the parallel MCO algorithm achieved better average and median objective values than PSO, confirming its enhanced optimization capability.