Particle swarm optimization (PSO) is a population-based stochastic optimization algorithm motivated by intelligent collective behavior of some animals such as flocks of birds or schools of fish. Since presented in 1995, it has experienced a multitude of enhancements. As researchers have learned about the technique, they derived new versions aiming to different demands, developed new applications in a host of areas, published theoretical studies of the effects of the various parameters and proposed many variants of the algorithm. This paper introduces its origin and background and carries out the theory analysis of the PSO. Then, we analyze its present situation of research and application in algorithm structure, parameter selection, topology structure, discrete PSO algorithm and parallel PSO algorithm, multi-objective optimization PSO and its engineering applications. Finally, the existing problems are analyzed and future research directions are presented.

Particle swarm optimization algorithm: an overview

“Exploration and exploitation are the two cornerstones of problem solving by search.” For more than a decade, Eiben and Schippers' advocacy for balancing between these two antagonistic cornerstones still greatly influences the research directions of evolutionary algorithms (EAs) [1998]. This article revisits nearly 100 existing works and surveys how such works have answered the advocacy. The article introduces a fresh treatment that classifies and discusses existing work within three rational aspects: (1) what and how EA components contribute to exploration and exploitation; (2) when and how exploration and exploitation are controlled; and (3) how balance between exploration and exploitation is achieved. With a more comprehensive and systematic understanding of exploration and exploitation, more research in this direction may be motivated and refined.

Exploration and exploitation in evolutionary algorithms: A survey

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Digital control of dynamic systems

Particle swarm optimization (PSO) is a heuristic global optimization method, proposed originally by Kennedy and Eberhart in 1995. It is now one of the most commonly used optimization techniques. This survey presented a comprehensive investigation of PSO. On one hand, we provided advances with PSO, including its modifications (including quantum-behaved PSO, bare-bones PSO, chaotic PSO, and fuzzy PSO), population topology (as fully connected, von Neumann, ring, star, random, etc.), hybridization (with genetic algorithm, simulated annealing, Tabu search, artificial immune system, ant colony algorithm, artificial bee colony, differential evolution, harmonic search, and biogeography-based optimization), extensions (to multiobjective, constrained, discrete, and binary optimization), theoretical analysis (parameter selection and tuning, and convergence analysis), and parallel implementation (in multicore, multiprocessor, GPU, and cloud computing forms). On the other hand, we offered a survey on applications of PSO to the following eight fields: electrical and electronic engineering, automation control systems, communication theory, operations research, mechanical engineering, fuel and energy, medicine, chemistry, and biology. It is hoped that this survey would be beneficial for the researchers studying PSO algorithms.

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A Comprehensive Survey on Particle Swarm Optimization Algorithm and Its Applications

Molecular docking methodology explores the behavior of small molecules in the binding site of a target protein. As more protein structures are determined experimentally using X-ray crystallography or nuclear magnetic resonance (NMR) spectroscopy, molecular docking is increasingly used as a tool in drug discovery. Docking against homology-modeled targets also becomes possible for proteins whose structures are not known. With the docking strategies, the druggability of the compounds and their specificity against a particular target can be calculated for further lead optimization processes. Molecular docking programs perform a search algorithm in which the conformation of the ligand is evaluated recursively until the convergence to the minimum energy is reached. Finally, an affinity scoring function, ΔG [U total in kcal/mol], is employed to rank the candidate poses as the sum of the electrostatic and van der Waals energies. The driving forces for these specific interactions in biological systems aim toward complementarities between the shape and electrostatics of the binding site surfaces and the ligand or substrate.

Software for molecular docking: a review

In this paper, inspired by the analysis of convergence of PSO, we study the individual particle of a PSO system moving in a quantum multidimensional space and establish a quantum delta potential well model for PSO. After that, a trial method of parameter control and QDPSO is proposed. The experiment result shows much advantage of QDPSO to the traditional PSO.

Particle swarm optimization with particles having quantum behavior

Based on the quantum-behaved particle swarm optimization (QPSO) algorithm, we formulate the philosophy of QPSO and introduce a so-called mainstream thought of the population to evaluate the search scope of a particle and thus propose a novel parameter control method of QPSO. After that, we test the revised QPSO algorithm on several benchmark functions and the experiment results show its superiority.

A global search strategy of quantum-behaved particle swarm optimization

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.

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Quantum-behaved particle swarm optimization: Analysis of individual particle behavior and parameter selection

Particle swarm optimization (PSO) is a population-based evolutionary search technique, which has comparable performance with genetic algorithm. The existing PSOs, however, are not global-convergence-guaranteed algorithms. In the previous work, we proposed quantum-behaved particle swarm optimization (QPSO) algorithm that outperforms traditional PSOs in search ability as well as having less parameter to control. This paper focuses on discussing two adaptive parameter control methods for QPSO. After the ideology of QPSO is formulated, the experiment results of stochastic simulation are given to show how to select the parameter value to guarantee the convergence of the particle in QPSO. Finally, two adaptive parameter control methods are presented and experiment results on benchmark functions testify their efficiency.

Wenbo Xu

Papers

Particle swarm optimization with particles having quantum behavior

A global search strategy of quantum-behaved particle swarm optimization

Quantum-behaved particle swarm optimization: Analysis of individual particle behavior and parameter selection

Adaptive parameter control for quantum-behaved particle swarm optimization on individual level

An improved quantum-behaved particle swarm optimization algorithm with weighted mean best position