Replica Exchange using q-Gaussian Swarm Quantum Particle Intelligence
  Method
  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 G\=o coarse-graining potential energy function.
