A Comprehensive Survey on Particle Swarm Optimization Algorithm and Its Applications. School of Computer Science and Technology, Nanjing Normal University, Nanjing, Jiangsu 2.
China. 2School of Electronic Science and Engineering, Nanjing University, Nanjing, Jiangsu 2. China. Copyright . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Particle swarm optimization (PSO) is a heuristic global optimization method, proposed originally by Kennedy and Eberhart in 1. 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. Introduction. Artificial intelligence (AI) is the intelligence exhibited by machines. AI research is highly technical and specialized and is deeply divided into subfields that often fail to communicate with each other. Currently popular approaches of AI include traditional statistical methods .
CI is a fairly new research area. It is a set of nature- inspired computational methodologies and approaches to address complex real- world problems to which traditional approaches are ineffective or infeasible. CI includes artificial neural network (ANN), fuzzy logic, and evolutionary computation (EC).
Swarm intelligence (SI) is a part of EC. It researches the collective behavior of decentralized, self- organized systems, natural or artificial. Typical SI systems consist of a population of simple agents or boids interacting locally with one another and with their environment. The inspiration often comes from nature, especially biological systems . There is no centralized control structure dictating how individual agents should behave.
Well- known examples of SI include ant colonies, bird flocking, animal herding, bacterial growth, and fish schooling. Dorigo . Kennedy and Eberhart . Those are two most famous SI- based optimization algorithms. In addition to them, scholars have shown great interest in proposing new intelligent approaches. Karaboga and Basturk .
All papers are listed with the original titles and list of authors at the time of submission.
Krishnanand and Ghose . SI- based algorithms is presented in Figures 1 and 2, respectively. As seen from the figures, the number of total publications related to PSO is even higher than the sum of six other algorithms, and the number of publication per year related to PSO is the highest among all seven SI- based algorithms. This suggests PSO is the most prevalent SI- based optimization algorithms. Therefore, we center this review on PSO. Figure 1: Number of all publications w. SI- based algorithms.
Figure 2: Publication per year (2. SI- based algorithms.
Several public websites related to PSO (Table 1) were set up . There are several types of source codes, written in different programming languages, in those websites.
In addition, many publications about PSO and its applications were presented. Table 1: Public websites of PSO. This work first checked the coherency of PSO with principles required by SI. Second, we reviewed the studies on advances of PSO. Third, various applications of PSO is given.
Finally, we conclude the paper by summarizing the improvements and analyzing potential research directions. This survey was carried out mainly by examining the . In addition, IEEE Explorer and Google Scholar were also used. Particle Swarm Optimization: PSO Approach. Features of Self- Organization.
Self- organization is a key feature of SI system. It is a process where global order or coordination arises out of the local interactions between the components of an initially disordered system. This process is spontaneous; that is, it is not controlled by any agent inside or outside of the system. Features of SIIn addition, Millonas . They are proximity principle, quality principle, diverse response principle, stability principle, and adaptability principle.
Their meanings are listed in Table 2. Table 2: Five basic principles of SI. Algorithmic Structure of Standard PSOPSO performs searching via a swarm of particles that updates from iteration to iteration. To seek the optimal solution, each particle moves in the direction to its previously best (pbest) position and the global best (gbest) position in the swarm .
One haswhere denotes the particle index, the total number of particles, the current iteration number, the fitness function, and the position. The velocity and position of particles are updated by the following equations: where denotes the velocity, is the inertia weight used to balance the global exploration and local exploitation, and are uniformly distributed random variables within range , and and are positive constant parameters called . Another method is the . The second part, known as the .
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It encourages the particles to move toward their own best positions found so far. Pseudocode of PSOLet be the cost function to be minimized. The function takes a candidate solution of a vector of real numbers and produces a real number as output that indicates the cost function value. The gradient of is either unknown or hard to calculate. The goal is to find the global minimal (Pseudocode 1). Pseudocode 1: A standard PSO. Studies on PSOIn this review, we center in reporting the advances on PSO in the form of formal publications.
Publish with Scientific Data. Scientific Data is a peer-reviewed, open-access journal for descriptions of scientifically valuable datasets. Optimization methods applied to renewable and sustainable energy. Energy resources are very important form an economic and political perspective for all countries, which is why technological change in energy systems is a.
We divide advances into following six aspects: (i)modifications of PSO, including quantum- behaved PSO, bare- bones PSO, chaotic PSO, fuzzy PSO, PSOTVAC, opposition- based PSO, topology, and other slight modifications,(ii)hybridization of PSO with other metaheuristic methods, including genetic algorithm (GA), artificial immune system (AIS), Tabu search (TS), ACO, simulated annealing (SA), ABC, DE, biogeography- based optimization (BBO), and harmonic search (HS),(iii)extensions of PSO to other optimization fields, including multiobjective, constrained, discrete, and binary optimization,(iv)theoretical analysis of PSO, parameter selection and convergence analysis.(v)parallel implementation of PSO, including multicore, GPU computing, and cloud computing. QPSOSome researchers proposed quantum- behaved PSO (QPSO), which was motivated by concepts from quantum mechanics.
For example, Jau et al. Besides, elitist crossover of GA and adaptive decay of SA are used for conquering premature and controlling search policy. The results showed that QPSO- DM performs better than the others. The memetic algorithm was used to make all particles gain some experience through a local search before being involved in the evolutionary process, and the memory mechanism was used to introduce a . QPSO was the main optimizer of algorithm, which can give a good direction to the optimal global region. Nelder- Mead simplex method was used as a local search to fine- tune the obtained solution from QPSO.
Each particle contained three groups of Bloch coordinates of qubits, and all three groups of coordinates were regarded as approximate solutions describing the optimization result. Particles were updated using the rotation of qubits about an axis on the Bloch sphere. Gholizadeh and Moghadas .
Two numerical examples were presented to illustrate the efficiency of the presented method. BBPSOThe bare- bones PSO (BBPSO) . The performance of the resulting algorithm was tested on 1. The proposed algorithms were unified BBPSO (UBBPSO), integrated DE (IDE), and IDE without Tabu list and radius (IDE. The algorithm had three distinctive features: a particle updating strategy that did not require tuning up control parameters, a mutation operator with action range varying over time to expand the search capability, and an approach based on particle diversity to update the global particle leaders.
General relations were derived for search focus, search spread, and swarm stability at stagnation. The relations were applied to three particular PSO implementations: the standard PSO, a PSO with discrete recombination, and the BBPSO. A new strategy based on - means clustering was proposed to combine the powerful global search capability of MBBPSO and the high accurate local search capability of SM. This made the proposed algorithm achieve a nice balance between exploitation and exploration capability.
Meanwhile, an adaptive reinitialization strategy on inactive particles was proposed to help the swarm get away from local optimal positions. Based on CC framework, the original partitional clustering problem was first decomposed to several subproblems, each of which was then evolved by an optimizer independently. BBPSO was employed as the optimizer to solve each subproblem cooperatively.
In addition, a new centroid- based encoding schema was designed for each particle, and the Chernoff bounds were applied to decide a proper population size. They researched the distribution and diversity on the proposed disruption operator and illustrated the position relationship between the original and disrupted position.