Liquid-Drop-Like Multi-Orbit Topology Versus Ring Topology in PSO for Lennard-Jones Problem

Abstract

The Lennard-Jones (L-J) Potential Problem is a challenging global optimization problem, due to the presence of a large number of local optima that increases exponentially with problem size. The problem is ‘NP-hard’, i.e., it is not possible to design an algorithm which can solve it on a time scale growing linearly with the problem size. For this challenging complexity, a lot of research has been done, to design algorithms to solve it. In this paper, an attempt is made to solve it by incorporating a recently designed multi-orbit (MO) dynamic neighborhood topology in Particle Swarm Optimization (PSO) which is one of the most popular natural computing paradigms. The MO topology is inspired from the cohesive interconnection network of molecules in a drop of liquid. In this topology, the swarm has heterogeneous connectivity with some subsets of the swarm strongly connected while with the others relatively isolated. This heterogeneity of connections balances the exploration–exploitation trade-off in the swarm. Further, it uses dynamic neighborhoods, in order to avoid entrapment in local optima. Simulations are performed with this new PSO on 14 instances of the L-J Problem, and the results are compared with those obtained by commonly used ring topology in conjunction with two adaptive inertia weight variants of PSO, namely Globally adaptive inertia weight and Locally adaptive inertia weight PSO. The results indicate that the L-J problem can be solved more efficiently, by the use of MO topology than the ring topology, with PSO.