A hybrid co-evolutionary cultural algorithm based on particle swarm optimization for solving global optimization problems
Introduction
In recent years, as a new class of optimization algorithms, evolutionary algorithms have been paid more and more attention. Compared with traditional mathematic methods, intelligent evolutionary algorithms have achieved great success on solving complex, nonlinear, discrete optimization problems [1].
Particle swarm optimization (PSO) [2], [3], which was proposed by Kennedy and Eberhart in 1995, is a kind of evolutionary algorithm based on swarm intelligence. It was inspired by the social behavior of birds foraging. Compared with genetic algorithm (GA), PSO uses a velocity-position model without complex genetic operations. Therefore, it has excellent efficiency. Because of its simplicity and easiness in implementation, PSO has attracted more and more attention, and has been applied in many areas, such as multi-dimensional optimization problem, neural network training, fuzzy control system designs [4], [5], [6], [7], [8], [9], [10], [11], [12], [13].
However, basic PSO still can be improved. Accelerating convergence speed and avoiding local optima are the two most important and appealing goals in PSO researches [14]. In recent years, a large number of approaches have been developed to improve the efficiency of the algorithm to achieve these two goals. In these developments, control of algorithm parameters, combination with auxiliary search operators and topological structure improvement are three most salient and promising approaches [15]. Liu et al. [16] proposed a hybrid PSO algorithm named CPSO which integrated chaotic local searching behavior into PSO. Compared with basic PSO, CPSO is superior in term of searching quality, efficiency and robustness. Xu and Gu [17] incorporated PSO and differential evolution (DE), and proposed a hybrid algorithm called PSOPDE. Simulation results suggest that PSOPDE behaves better and has higher efficiency. Liang et al. [18] proposed comprehensive-learning PSO (CLPSO) to improve PSO on avoiding local optima. However, it is seen to be difficult to achieve both of the two goals simultaneously. Many of the PSO improvements can help the algorithms get better optima, but meanwhile, make the convergence speed slower.
Cultural algorithm (CA) was firstly purposed by Reynolds [19] in 1994. It was inspired by human sociology and developed in order to model the evolution of the cultural component of an evolutionary computational system over time as it accumulates experience [20]. CA simulates the social and cultural changes. The individuals of cultural algorithm are divided into two parts: population space and belief space. The two spaces evolve respectively and communicate with each other through specific protocols. As a result, CA can provide an explicit mechanism for global knowledge and a useful algorithm framework which to model self-adaptation in an evolutionary or swarm intelligence system [21], [22], [23], such as genetic algorithm (GA) [24], particle swarm optimization (PSO) [25], ant colony optimization (ACO) [26], differential evolution (DE) [27]. The dual inheritance enhances the efficiency of the algorithm.
Many researchers devote to improve the evolutionary algorithms mentioned above and have proposed a lot of promising methods. However, the experiment results are still not satisfying for large-scale complex real-world problems. Each algorithm above has only one population, and the influence of other existing populations or outer environment is ignored. In order to overcome this obstacle, a concept called “co-evolution” is introduced into intelligent computation field. The original idea of co-evolution was first proposed by Darwin [28], and used to describe the mutual influences in evolving processes of different species. Co-evolutionary algorithm (CEA) is a kind of new evolution algorithm on the base of co-evolutionary theory. Generally, CEA can be divided into two kinds: Cooperative Co-evolutionary Algorithm (CoopCEA) and Competitive Co-evolutionary Algorithm (CompCEA). CoopCEA [29], [30] was firstly proposed by M.A. Potter and K.A.D. Jong in 1994. The universal model of CoopCEA was put forward in 2000 [31]. C.D. Rosin and R.K. Belew published the research of CompCEA in 1995 [32]. CEA overcomes many disadvantages of traditional evolution algorithm, hence more and more scholars devote to this field. But, currently, there has not been a unified framework of CEA. Researchers in different fields often set up their own models and algorithms under co-evolution framework according to their own ideas [33], [34], [35].
In this paper, in order to fully use the advantages of PSO, CA and CEA, a hybrid Co-Evolutionary Cultural algorithm Based on Particle Swarm Optimization (CECBPSO) is proposed. In CECBPSO, a co-evolutionary mechanism between two cultural algorithms is built and PSO is introduced into the framework of CA. In the hybrid algorithm, a special set of individuals called shared global belief space (SGBS) is designed to coordinate knowledge and experience of the populations. And some new strategies are proposed to increase the diversity of individuals. Besides, a number of tests on parameter selection are done through an orthogonal experiment. Based on the results, a guideline on how to tune the parameters in CECBPSO to achieve good performance is given.
The remainder of this paper is organized as follows. In Section 2, we provide a brief survey of researches on PSO, CA and CEA. The proposed algorithm CECBPSO is introduced in Section 3. The tests on parameter selection are presented and discussed in Section 4. Experimental results demonstrating the performance of CECBPSO in comparison with several other algorithms over a suite of optimization problems are presented in Section 5. Finally, conclusions are drawn in Section 6.
Section snippets
Particle swarm optimization (PSO)
In basic PSO, proposed by Kennedy and Eberhart, a group of “birds” (i.e. particles) are represented as potential solutions. Each particle updates in the solution space according to some rules just like a bird searching for food, and ultimately stays in the best position. Initially, particles are initialized by a group of random velocities and positions within the corresponding ranges. Then particles update their velocities and positions as follows:
The proposed CECBPSO algorithm
In order to fully use the advantages of PSO, CA and CEA, a hybrid Co-Evolutionary Cultural algorithm Based on Particle Swarm Optimization (CECBPSO) is proposed. In this algorithm, a co-evolutionary mechanism between two cultural algorithms is established to take full advantage of CA and CEA.
Fig. 2 shows the framework of CECBPSO. In CECBPSO, there are two cultural-algorithm-populations and a shared global belief space (SGBS). PSOs are used in all the sub spaces (Belief space 1 and 2, and
Parameter discussion
Tuning parameters properly is very important for an evolutionary algorithm to achieve good performance. In basic PSO, there are three main parameters: inertia weight w, acceleration coefficients c1 and c2. There have been many researches on how to tune these parameters [37], [38], [39], [44], [45]. Strategy of varying the value of inertia weight (w) from 0.9 at the beginning of the search to 0.4 at the end of the search can greatly improve the performance of PSO for most optimization problems
Performance test
To evaluate the performance of CECBPSO, the algorithm is compared with other four algorithms: basic PSO, CPSO [16], PSOPDE [17] and CBPSO [25], using a suite of benchmark functions and real-life problems.
Conclusions
Considering the features of basic PSO, CA and CEA, a hybrid co-evolutionary cultural algorithm based on particle swarm optimization (CECBPSO) is proposed in this paper. In CECBPSO, a new co-evolutionary cultural framework is built through introducing a novel space called shared global belief space (SGBS) into the co-evolutionary mechanism. In the mechanism, operations of sharing knowledge and experience can help the algorithm improving the performance. And randomly reinitialized particles make
Acknowledgments
We are very grateful to the editors and anonymous reviewers for their valuable comments and suggestions to help us improve our paper. This work is supported by National High Technology Research and Development Program of China (863 Program) (No. 2009AA04Z141), National Natural Science Foundation of China (Grant No. 61174040, 61104178), Fundamental Research Funds for the Central Universities, and Shanghai Commission of Science and Technology (Grant No. 11ZR1409800).
Yang Sun received his B.S. degree in Department of Automation, School of Information Science and Engineering, East China University of Science and Technology (ECUST). He is currently a Ph.D. candidate in Research Institute of Automation, ECUST. His research interests include complex chemical process modeling, advanced control method, intelligent optimization algorithms, etc.
References (50)
- et al.
Improved particle swarm optimization combined with chaos
J. Chaos Soliton. Fract.
(2005) - et al.
Large scale evolutionary optimization using cooperative coevolution
J. Inform. Sci.
(2008) - et al.
A novel competitive co-evolutionary quantum genetic algorithm for stochastic job shop scheduling problem
J. Comput. Oper. Res.
(2010) - et al.
Chaos embedded particle swarm optimization algorithms
J. Chaos Soliton. Fract.
(2009) The particle swarm optimization algorithm: convergence analysis and parameter selection
J. Inform. Process Lett.
(2003)- et al.
Optimal thermohydraulic performance of artificially roughened solar air heaters
J. Sol Energ.
(1991) - et al.
Evolutionary Optimization
(2002) - R.C. Eberhart, J. Kennedy, A new optimizer using particle swarm theory, in: Proceedings of the sixth International...
- J. Kennedy, R.C. Eberhart, Particle swarm optimization, in: Proceedings of the IEEE International Conference on Neural...
- Y. Shi, R.C. Eberhart, Fuzzy adaptive particle swarm optimization, in: Proceedings of the 2001 Congress on Evolutionary...
A hybrid of genetic algorithm and particle swarm optimization for recurrent network design
J. IEEE Trans. Syst. Man Cybern. B Cybern.
Coevolutionary particle swarm optimization using gaussian distribution for solving constrained optimization problems
J. IEEE Trans. Syst. Man Cybern. B Cybern.
Particle swarm optimization approaches to coevolve strategies for the iterated prisoner's dilemma
J. IEEE Trans. Evol. Comput.
OPSO: orthogonal particle swarm optimization and its application to task assignment problems
J. IEEE Trans. Syst. Man Cybern. Syst. Humans
An effective pso-based memetic algorithm for flow shop scheduling
J. IEEE Trans. Syst. Man Cybern. B Cybern.
Use of intelligent-particle swarm optimization in electromagnetic
J. IEEE Trans. Magn.
Adaptive particle swarm optimization
J. IEEE Trans. Syst. Man Cybern. B Cybern.
Guest editorial special issue on particle swarm optimization
J. IEEE Trans. Evol. Comput.
Comprehensive learning particle swarm optimizer for global optimization of multimodal functions
J. IEEE Trans. Evol. Comput.
Improved differential evolution approach based on cultural algorithm and diversity measure applied to solve economic load dispatch problems
J. Math. Comput. Simulat.
Cited by (74)
Particle Swarm Optimization or Differential Evolution—A comparison
2023, Engineering Applications of Artificial IntelligenceA survey of artificial immune algorithms for multi-objective optimization
2022, NeurocomputingA comprehensive survey on cultural algorithms
2021, Swarm and Evolutionary ComputationRemoval of hydrochlorothiazide from molecular liquids using carbon nanotubes: Radial basis function neural network modeling and culture algorithm optimization
2021, Journal of Molecular LiquidsCitation Excerpt :Radial basis function networks have various features, namely function approximation, time series prediction, classification and system control [13]. Compared with the conventional mathematic techniques, the computational models have obtained great success in solving complex and nonlinear optimization problems [14]. Cultural algorithm (CA) is an optimization method derived from the cultural evolution processes and was firstly introduced by Reynolds [15].
Yang Sun received his B.S. degree in Department of Automation, School of Information Science and Engineering, East China University of Science and Technology (ECUST). He is currently a Ph.D. candidate in Research Institute of Automation, ECUST. His research interests include complex chemical process modeling, advanced control method, intelligent optimization algorithms, etc.
Lingbo Zhang received his B.S. degree in Mathematics from Hunan Normal University, Changsha, China in 1997, M.S. and Ph.D. degree in Control Theory and Control Engineering from Central South University, Changsha, China respectively in 2000 and 2003. Since 2003, he has been with the Department of Automation, East China University, Shanghai, China, where he is currently an Associate Professor at School of Information Science and Engineering. His research interests include process control, robust control, etc. He is the author of about 20 papers in the above area.
Xingsheng Gu received the B.S. degree from Nanjing Institute of Chemical Technology in 1982, M. S. and Ph. D. degree from East China University of Chemical Technology in 1988 and 1993, respectively. He is currently a professor at School of Information Science and Engineering, East China University of Science and Technology. His research interests include planning and scheduling for process industry, modeling, control and optimization for industry processes, intelligent optimization, faults detection and diagnosis, etc.