A New Quantum-Behaved PSO: Based on Double δ-Potential Wells Model

QDDS: A Novel Quantum Swarm Algorithm Inspired by a Double Dirac Delta Potential

“…The convergence profiles in Figures 1 through 12 point out that QDDS is fairly consistent in its ability to converge to local optima of acceptable quality. It is obvious that the solutions to the problems discussed in the paper are in fact local optima, however the solution qualities corresponding to some of these local optima obtained using QDDS are evidently superior to some related reports in the literature [3,6,11,12]. One way to improve the performance of QDDS may be to not use gradient descent but a problem-independent optima seeking mechanism in the 𝛿 update step of the algorithm in Section III.…”

“…One line of thought contends that the attractive coupling offered by a multi-well attractor is stronger than that offered by a singular one therefore facilitating a stronger stable equilibrium criterion [7]. Xie et al [6] have recently proposed a quantum-behaved PSO based on a double delta model which assimilates the following three components: a) the global best (gbest) position, b) an agent's location with respect to the gbest position and c) an agent's location with respect to the mean of individual agents' best positions. The authors chose to model the personal and global best positions as centers of two singular delta potential wells, thereby arriving at a multi-scale representation of a double delta potential well.…”

“…The traditional types of QPSO are quite efficient and inexpensive candidates suitable for highly non-linear and nonconvex optimization leveraging the quantum nature of the particles and the corresponding wavefunctions that sample a larger region of the solution space as compared to their classical counterpart employing a binary strategy: a particle is either present at a unique location or not. However, the intuitively simple rendering of the binding force exerted by a single delta well on a particular particle has been the subject of scrutiny and further research as demonstrated by [6]. One line of thought contends that the attractive coupling offered by a multi-well attractor is stronger than that offered by a singular one therefore facilitating a stronger stable equilibrium criterion [7].…”

Chaotic Quantum Double Delta Swarm Algorithm Using Chebyshev Maps: Theoretical Foundations, Performance Analyses and Convergence Issues

“…The interim gbest position transitions are shown by dotted lines. The solutions to the 23 test problems outlined in the paper are local minima, however the quality of solutions that the C-QDDS and QDDS algorithm provide to some of these problems are markedly better than those reported in some studies in the literature [4,23,24,25]. A logical next-step to improve the optima seeking capability of the QDDS/C-QDDS approach is to introduce a problem-independent random walk in the recomputing step of the algorithm instead of using gradient descent.…”