Physics-Inspired Hamiltonian Particle Swarm Optimisation for Multi-Agent Movement

Abstract This study puts forward a Hamiltonian-inspired modification of Particle Swarm Optimisation (PSO) algorithm. Since the standard PSO procedure does not take into account physical properties like particle masses, geometrical sizes, and energy consumption, it is not fully applicable as a navigational and coordination tool in real-world environments. In particular, generic PSO mechanism cannot stop the particles from collisions. To address these issues, we propose a new PSO formulation based on a Hamiltonian interpretation. This approach allows bringing together the kinetic and potential energy terms with the forces acting on the agents, as well as the derivation of agent’s velocities and positions. The potential energy represents attraction toward both personal and global best positions in a spring-like manner. As a component of conservative forces derived from the potential energy term, we introduce a special repulsive potential function to prevent collisions among agents. The kinetic energy, which is derived via agent mass and momentum, determines the movement dynamics. To model the energy loss, we incorporate Rayleigh dissipation term that accounts for non-conservative forces. According to the proposed model, agent displacements are computed using the obtained velocity and momentum vectors. Additionally, we introduce individual and swarm energy efficiency metrics to study the agents’ motion in a 2D testing environment. The presented approach enables stable, coordinated, and collision-free multi-agent motion within a physics-inspired optimisation framework.