Quantum-Behaved Particle Swarm Optimization: Analysis of Individual Particle Behavior and Parameter Selection

Abstract

Quantum-behaved particle swarm optimization (QPSO), motivated by concepts from quantum mechanics and particle swarm optimization (PSO), is a probabilistic optimization algorithm belonging to the bare-bones PSO family. Although it has been shown to perform well in finding the optimal solutions for many optimization problems, there has so far been little analysis on how it works in detail. This paper presents a comprehensive analysis of the QPSO algorithm. In the theoretical analysis, we analyze the behavior of a single particle in QPSO in terms of probability measure. Since the particle's behavior is influenced by the contraction-expansion (CE) coefficient, which is the most important parameter of the algorithm, the goal of the theoretical analysis is to find out the upper bound of the CE coefficient, within which the value of the CE coefficient selected can guarantee the convergence or boundedness of the particle's position. In the experimental analysis, the theoretical results are first validated by stochastic simulations for the particle's behavior. Then, based on the derived upper bound of the CE coefficient, we perform empirical studies on a suite of well-known benchmark functions to show how to control and select the value of the CE coefficient, in order to obtain generally good algorithmic performance in real world applications. Finally, a further performance comparison between QPSO and other variants of PSO on the benchmarks is made to show the efficiency of the QPSO algorithm with the proposed parameter control and selection methods.

Design of Non-Uniformly Spaced Circular Arrays of Parasitic Dipoles for Lower Side Lobe Level with Maximum Directivity

“…QPSO detailed in [17][18] is developed by Sun et al in 2004 is founded on the primordial law of particle swarm and rules of quantum mechanics in which all particles have the features of quantum deportment. It is described only by the position vector there is no velocity vector in QPSO.…”

“…In our case the value of α is 0.75. Setting the value of α in the interval (0.5, 0.8), can generates good results, see literature report [17][18]. Details of the QPSO algorithm are available in the article [17][18].…”

“…First of all, the radiated electric field is computed using the current distribution and the array structure and after that directivity and other array parameters are calculated. Matlab based method of moments (MoM) [14][15][16] code is used for simulation and to evaluate the performance of the antenna designs using optimization process generated by quantum particle swarm optimization (QPSO) [17][18]. Here, we have used QPSO algorithm because it provides better results than other algorithms in many antenna design problems [19][20][21][22].…”

“…Here, we have used QPSO algorithm because it provides better results than other algorithms in many antenna design problems [19][20][21][22]. QPSO perform better than PSO and its different versions on well-known benchmark functions [17][18]. QPSO provides better results than backtracking search algorithm (BSA) in linear antenna array failure correction to obtain the fixed value of side lobe level and VSWR [19].…”

Quantum Particle Swarm Optimization for Synthesis of Non-uniformly Spaced Linear Arrays with Broadband Frequency Invariant Pattern

“…The reason for the choice of QPSO is because of its validity [14][15][16] over other algorithms. Moreover, in this paper, QPSO algorithm is compared with firefly algorithm (FA), a nature-inspired metaheuristic optimization algorithm which is described in [17][18][19].…”