Hiqmet Kamberaj

Hiqmet Kamberaj

We present a newly developed Replica Exchange algorithm using q -Gaussian Swarm Quantum Particle Optimization (REX@q-GSQPO) method for solving the problem of finding the global optimum. The basis of the algorithm is to run multiple copies of independent swarms at different values of q parameter. Based on an energy criterion, chosen to satisfy the detailed balance, we are swapping the particle coordinates of neighboring swarms at regular iteration intervals. The swarm replicas with high q values are characterized by high diversity of particles allowing escaping local minima faster, while the low q replicas, characterized by low diversity of particles, are used to sample more efficiently the local basins. We compare the new algorithm with the standard Gaussian Swarm Quantum Particle Optimization (GSQPO) and q-Gaussian Swarm Quantum Particle Optimization (q-GSQPO) algorithms, and we found that the new algorithm is more robust in terms of the number of fitness function calls, and more efficient in terms ability convergence to the global minimum. In additional, we also provide a method of optimally allocating the swarm replicas among different q values. Our algorithm is tested for three benchmark functions, which are known to be multimodal problems, at different dimensionalities. In addition, we considered a polyalanine peptide of 12 residues modeled using a Gō coarse-graining potential energy function.

Hiqmet Kamberaj

We present a newly developed -Gaussian Swarm Quantum-like Particle Optimization (q-GSQPO) algorithm to determine the global minimum of the potential energy function. Swarm Quantum-like Particle Optimization (SQPO) algorithms have been derived using different attractive potential fields to represent swarm particles moving in a quantum environment, where the one which uses a harmonic oscillator potential as attractive field is considered as an improved version. In this paper, we propose a new SQPO that uses -Gaussian probability density function for the attractive potential field (q-GSQPO) rather than Gaussian one (GSQPO) which corresponds to harmonic potential. The performance of the q-GSQPO is compared against the GSQPO. The new algorithm outperforms the GSQPO on most of the time in convergence to the global optimum by increasing the efficiency of sampling the phase space and avoiding the premature convergence to local minima. Moreover, the computational efforts were comparable for both algorithms. We tested the algorithm to determine the lowest energy configurations of a particle moving in a 2, 5, 10, and 50 dimensional spaces.