A rank based particle swarm optimization algorithm with dynamic adaptation

The particle swarm optimization (PSO) technique is a powerful stochastic evolutionary algorithm that can be used to find the global optimum solution in a complex search space. This paper presents a variation on the standard PSO algorithm called the rank based particle swarm optimizer, or PSO_rank, employing cooperative behavior of the particles to significantly improve the performance of the original algorithm. In this method, in order to efficiently control the local search and convergence to global optimum solution, the γ best particles are taken to contribute to the updating of the position of a candidate particle. The contribution of each particle is proportional to its strength. The strength is a function of three parameters: strivness, immediacy and number of contributed particles. All particles are sorted according to their fitness values, and only the γ best particles will be selected. The value of γ decreases linearly as the iteration increases. A time-varying inertia weight decreasing non-linearly is introduced to improve the performance. PSO_rank is tested on a commonly used set of optimization problems and is compared to other variants of the PSO algorithm presented in the literature. As a real application, PSO_rank is used for neural network training. The PSO_rank strategy outperformed all the methods considered in this investigation for most of the functions. Experimental results show the suitability of the proposed algorithm in terms of effectiveness and robustness.     

A novel hybrid differential evolution and particle swarm optimization algorithm for unconstrained optimization

An algorithm called DE-PSO is proposed which incorporates concepts from DE and PSO, updating particles not only by DE operators but also by mechanisms of PSO. The proposed algorithm is tested on several benchmark functions. Numerical comparisons with different hybrid meta-heuristics demonstrate its effectiveness and efficiency.     

A novel particle swarm optimization algorithm based on particle migration

Inspired by the migratory behavior in the nature, a novel particle swarm optimization algorithm based on particle migration (MPSO) is proposed in this work. In this new algorithm, the population is randomly partitioned into several sub-swarms, each of which is made to evolve based on particle swarm optimization with time varying inertia weight and acceleration coefficients (LPSO-TVAC). At periodic stage in the evolution, some particles migrate from one complex to another to enhance the diversity of the population and avoid premature convergence. It further improves the ability of exploration and exploitation. Simulations for benchmark test functions illustrate that the proposed algorithm possesses better ability to find the global optima than other variants and is an effective global optimization tool.     

Improved particle swarm algorithm for hydrological parameter optimization

In this paper, a new method named MSSE-PSO (master-slave swarms shuffling evolution algorithm based on particle swarm optimization) is proposed. Firstly, a population of points is sampled randomly from the feasible space, and then partitioned into several sub-swarms (one master swarm and other slave swarms). Each slave swarm independently executes PSO or its variants, including the update of particles’ position and velocity. For the master swarm, the particles enhance themselves based on the social knowledge of master swarm and that of slave swarms. At periodic stage in the evolution, the master swarm and the whole slave swarms are forced to mix, and points are then reassigned to several sub-swarms to ensure the share of information. The process is repeated until a user-defined stopping criterion is reached. The tests of numerical simulation and the case study on hydrological model show that MSSE-PSO remarkably improves the accuracy of calibration, reduces the time of computation and enhances the performance of stability. Therefore, it is an effective and efficient global optimization method.     

A particle swarm optimization algorithm for makespan and total flowtime minimization in the permutation flowshop sequencing problem

In this paper, a particle swarm optimization algorithm (PSO) is presented to solve the permutation flowshop sequencing problem (PFSP) with the objectives of minimizing makespan and the total flowtime of jobs. For this purpose, a heuristic rule called the smallest position value (SPV) borrowed from the random key representation of Bean [J.C. Bean, Genetic algorithm and random keys for sequencing and optimization, ORSA Journal of Computing 6(2) (1994) 154–160] was developed to enable the continuous particle swarm optimization algorithm to be applied to all classes of sequencing problems. In addition, a very efficient local search, called variable neighborhood search (VNS), was embedded in the PSO algorithm to solve the well known benchmark suites in the literature. The PSO algorithm was applied to both the 90 benchmark instances provided by Taillard [E. Taillard, Benchmarks for basic scheduling problems, European Journal of Operational Research, 64 (1993) 278–285], and the 14,000 random, narrow random and structured benchmark instances provided by Watson et al. [J.P. Watson, L. Barbulescu, L.D. Whitley, A.E. Howe, Contrasting structured and random permutation flowshop scheduling problems: Search space topology and algorithm performance, ORSA Journal of Computing 14(2) (2002) 98–123]. For makespan criterion, the solution quality was evaluated according to the best known solutions provided either by Taillard, or Watson et al. The total flowtime criterion was evaluated with the best known solutions provided by Liu and Reeves [J. Liu, C.R. Reeves, Constructive and composite heuristic solutions to the P∥∑C_i scheduling problem, European Journal of Operational Research 132 (2001) 439–452], and Rajendran and Ziegler [C. Rajendran, H. Ziegler, Ant-colony algorithms for permutation flowshop scheduling to minimize makespan/total flowtime of jobs, European Journal of Operational Research, 155(2) (2004) 426–438]. For the total flowtime criterion, 57 out of the 90 best known solutions reported by Liu and Reeves, and Rajendran and Ziegler were improved whereas for the makespan criterion, 195 out of the 800 best known solutions for the random and narrow random problems reported by Watson et al. were improved by the VNS version of the PSO algorithm.     

Modeling of EDM responses by support vector machine regression with parameters selected by particle swarm optimization

Electrical discharge machining (EDM) is inherently a stochastic process. Predicting the output of such a process with reasonable accuracy is rather difficult. Modern learning based methodologies, being capable of reading the underlying unseen effect of control factors on responses, appear to be effective in this regard. In the present work, support vector machine (SVM), one of the supervised learning methods, is applied for developing the model of EDM process. Gaussian radial basis function and ε-insensitive loss function are used as kernel function and loss function respectively. Separate models of material removal rate (MRR) and average surface roughness parameter (Ra) are developed by minimizing the mean absolute percentage error (MAPE) of training data obtained for different set of SVM parameter combinations. Particle swarm optimization (PSO) is employed for the purpose of optimizing SVM parameter combinations. Models thus developed are then tested with disjoint testing data sets. Optimum parameter settings for maximum MRR and minimum Ra are further investigated applying PSO on the developed models.     

A hybrid simplex search and particle swarm optimization for unconstrained optimization

This paper proposes the hybrid NM-PSO algorithm based on the Nelder–Mead (NM) simplex search method and particle swarm optimization (PSO) for unconstrained optimization. NM-PSO is very easy to implement in practice since it does not require gradient computation. The modification of both the Nelder–Mead simplex search method and particle swarm optimization intends to produce faster and more accurate convergence. The main purpose of the paper is to demonstrate how the standard particle swarm optimizers can be improved by incorporating a hybridization strategy. In a suite of 20 test function problems taken from the literature, computational results via a comprehensive experimental study, preceded by the investigation of parameter selection, show that the hybrid NM-PSO approach outperforms other three relevant search techniques (i.e., the original NM simplex search method, the original PSO and the guaranteed convergence particle swarm optimization (GCPSO)) in terms of solution quality and convergence rate. In a later part of the comparative experiment, the NM-PSO algorithm is compared to various most up-to-date cooperative PSO (CPSO) procedures appearing in the literature. The comparison report still largely favors the NM-PSO algorithm in the performance of accuracy, robustness and function evaluation. As evidenced by the overall assessment based on two kinds of computational experience, the new algorithm has demonstrated to be extremely effective and efficient at locating best-practice optimal solutions for unconstrained optimization.     

A competitive and cooperative co-evolutionary approach to multi-objective particle swarm optimization algorithm design

Multi-objective particle swarm optimization (MOPSO) is an optimization technique inspired by bird flocking, which has been steadily gaining attention from the research community because of its high convergence speed. On the other hand, in the face of increasing complexity and dimensionality of today’s application coupled with its tendency of premature convergence due to the high convergence speeds, there is a need to improve the efficiency and effectiveness of MOPSO. In this paper a competitive and cooperative co-evolutionary approach is adapted for multi-objective particle swarm optimization algorithm design, which appears to have considerable potential for solving complex optimization problems by explicitly modeling the co-evolution of competing and cooperating species. The competitive and cooperative co-evolution model helps to produce the reasonable problem decompositions by exploiting any correlation, interdependency between components of the problem. The proposed competitive and cooperative co-evolutionary multi-objective particle swarm optimization algorithm (CCPSO) is validated through comparisons with existing state-of-the-art multi-objective algorithms using established benchmarks and metrics. Simulation results demonstrated that CCPSO shows competitive, if not better, performance as compared to the other algorithms.     

Enhanced speciation in particle swarm optimization for multi-modal problems

In this paper, we present a novel multi-modal optimization algorithm for finding multiple local optima in objective function surfaces. We build from Species-based particle swarm optimization (SPSO) by using deterministic sampling to generate new particles during the optimization process, by implementing proximity-based speciation coupled with speciation of isolated particles, and by including “turbulence regions” around already found solutions to prevent unnecessary function evaluations. Instead of using error threshold values, the new algorithm uses the particle’s experience, geometric mean, and “exclusion factor” to detect local optima and stop the algorithm. The performance of each extension is assessed with leave-it-out tests, and the results are discussed. We use the new algorithm called Isolated-Speciation-based particle swarm optimization (ISPSO) and a benchmark algorithm called Niche particle swarm optimization (NichePSO) to solve a six-dimensional rainfall characterization problem for 192 rain gages across the United States. We show why it is important to find multiple local optima for solving this real-world complex problem by discussing its high multi-modality. Solutions found by both algorithms are compared, and we conclude that ISPSO is more reliable than NichePSO at finding optima with a significantly lower objective function value.     

An improved particle swarm optimization algorithm combined with piecewise linear chaotic map

Particle swarm optimization (PSO) has gained increasing attention in tackling complex optimization problems. Its further superiority when hybridized with other search techniques is also shown. Chaos, with the properties of ergodicity and stochasticity, is definitely a good candidate, but currently only the well-known logistic map is prevalently used. In this paper, the performance and deficiencies of schemes coupling chaotic search into PSO are analyzed. Then, the piecewise linear chaotic map (PWLCM) is introduced to perform the chaotic search. An improved PSO algorithm combined with PWLCM (PWLCPSO) is proposed subsequently, and experimental results verify its great superiority.     

Modified particle swarm optimization algorithm with simulated annealing behavior and its numerical verification

The hybrid algorithm that combined particle swarm optimization with simulated annealing behavior (SA-PSO) is proposed in this paper. The SA-PSO algorithm takes both of the advantages of good solution quality in simulated annealing and fast searching ability in particle swarm optimization. As stochastic optimization algorithms are sensitive to their parameters, proper procedure for parameters selection is introduced in this paper to improve solution quality. To verify the usability and effectiveness of the proposed algorithm, simulations are performed using 20 different mathematical optimization functions with different dimensions. The comparative works have also been conducted among different algorithms under the criteria of quality of the solution, the efficiency of searching for the solution and the convergence characteristics. According to the results, the SA-PSO could have higher efficiency, better quality and faster convergence speed than compared algorithms.     

An efficient co-swarm particle swarm optimization for non-linear constrained optimization

This paper proposes a new co-swarm PSO (CSHPSO) for constrained optimization problems, which is obtained by hybridizing the recently proposed shrinking hypersphere PSO (SHPSO) with the differential evolution (DE) approach. The total swarm is subdivided into two sub swarms in such a way that the first sub swarms uses SHPSO and second sub swarms uses DE. Experiments are performed on a state-of-the-art problems proposed in IEEE CEC 2006. The results of the CSHPSO is compared with SHPSO and DE in a variety of fashions. A statistical approach is applied to provide the significance of the numerical experiments. In order to further test the efficacy of the proposed CSHPSO, an economic dispatch (ED) problem with valve points effects for 40 generating units is solved. The results of the problem using CSHPSO is compared with SHPSO, DE and the existing solutions in the literature. It is concluded that CSHPSO is able to give the minimal cost for the ED problem in comparison with the other algorithms considered. Hence, CSHPSO is a promising new co-swarm PSO which can be used to solve any real constrained optimization problem.     

Integrating particle swarm optimization with genetic algorithms for solving nonlinear optimization problems

Heuristic optimization provides a robust and efficient approach for solving complex real-world problems. The aim of this paper is to introduce a hybrid approach combining two heuristic optimization techniques, particle swarm optimization (PSO) and genetic algorithms (GA). Our approach integrates the merits of both GA and PSO and it has two characteristic features. Firstly, the algorithm is initialized by a set of random particles which travel through the search space. During this travel an evolution of these particles is performed by integrating PSO and GA. Secondly, to restrict velocity of the particles and control it, we introduce a modified constriction factor. Finally, the results of various experimental studies using a suite of multimodal test functions taken from the literature have demonstrated the superiority of the proposed approach to finding the global optimal solution.     

Self-adaptive velocity particle swarm optimization for solving constrained optimization problems

Particle swarm optimization (PSO) is originally developed as an unconstrained optimization technique, therefore lacks an explicit mechanism for handling constraints. When solving constrained optimization problems (COPs) with PSO, the existing research mainly focuses on how to handle constraints, and the impact of constraints on the inherent search mechanism of PSO has been scarcely explored. Motivated by this fact, in this paper we mainly investigate how to utilize the impact of constraints (or the knowledge about the feasible region) to improve the optimization ability of the particles. Based on these investigations, we present a modified PSO, called self-adaptive velocity particle swarm optimization (SAVPSO), for solving COPs. To handle constraints, in SAVPSO we adopt our recently proposed dynamic-objective constraint-handling method (DOCHM), which is essentially a constituent part of the inherent search mechanism of the integrated SAVPSO, i.e., DOCHM + SAVPSO. The performance of the integrated SAVPSO is tested on a well-known benchmark suite and the experimental results show that appropriately utilizing the knowledge about the feasible region can substantially improve the performance of the underlying algorithm in solving COPs.     

The fitness evaluation strategy in particle swarm optimization

The particle swarm optimization (PSO) computational method has recently become popular. However, it has limitations. It may trap into local optima and cause the premature convergence phenomenon, especially for multimodal and high-dimensional problems. In this paper, we focus on investigating the fitness evaluation in terms of a particle’s position. Particularly, we find that the fitness evaluation strategy in the standard PSO has two drawbacks, i.e., “two steps forward and one step back” and “two steps back and one step forward”. In addition, we propose a general fitness evaluation strategy (GFES), by which a particle is evaluated in multiple subspaces and different contexts in order to take diverse paces towards the destination position. As demonstrations of GFES, a series of PSOs with GFES are presented. Experiments are conducted on several benchmark optimization problems. The results show that GFES is effective at handling multimodal and high-dimensional problems.     

A discrete particle swarm optimization for lot-streaming flowshop scheduling problem

We consider an n-job, m-machine lot-streaming problem in a flowshop with equal-size sublots where the objective is to minimize the total weighted earliness and tardiness. To solve this problem, we first propose a so-called net benefit of movement (NBM) algorithm, which is much more efficient than the existing linear programming model for obtaining the optimal starting and completion times of sublots for a given job sequence. A new discrete particle swarm optimization (DPSO) algorithm incorporating the NBM algorithm is then developed to search for the best sequence. The new DPSO improves the existing DPSO by introducing an inheritance scheme, inspired by a genetic algorithm, into particles construction. To verify the proposed DPSO algorithm, comparisons with the existing DPSO algorithm and a hybrid genetic algorithm (HGA) are made. Computational results show that the proposed DPSO algorithm with a two-point inheritance scheme is very competitive for the lot-streaming flowshop scheduling problem.     

A particle swarm pattern search method for bound constrained global optimization

In this paper we develop, analyze, and test a new algorithm for the global minimization of a function subject to simple bounds without the use of derivatives. The underlying algorithm is a pattern search method, more specifically a coordinate search method, which guarantees convergence to stationary points from arbitrary starting points. In the optional search phase of pattern search we apply a particle swarm scheme to globally explore the possible nonconvexity of the objective function. Our extensive numerical experiments showed that the resulting algorithm is highly competitive with other global optimization methods also based on function values. Support for Luís N. Vicente was provided by Centro de Matemática da Universidade de Coimbra and by FCT under grant POCI/MAT/59442/2004.     

Chaotic catfish particle swarm optimization for solving global numerical optimization problems

Chaotic catfish particle swarm optimization (C-CatfishPSO) is a novel optimization algorithm proposed in this paper. C-CatfishPSO introduces chaotic maps into catfish particle swarm optimization (CatfishPSO), which increase the search capability of CatfishPSO via the chaos approach. Simple CatfishPSO relies on the incorporation of catfish particles into particle swarm optimization (PSO). The introduced catfish particles improve the performance of PSO considerably. Unlike other ordinary particles, the catfish particles initialize a new search from extreme points of the search space when the gbest fitness value (global optimum at each iteration) has not changed for a certain number of consecutive iterations. This results in further opportunities of finding better solutions for the swarm by guiding the entire swarm to promising new regions of the search space and accelerating the search. The introduced chaotic maps strengthen the solution quality of PSO and CatfishPSO significantly. The resulting improved PSO and CatfishPSO are called chaotic PSO (C-PSO) and chaotic CatfishPSO (C-CatfishPSO), respectively. PSO, C-PSO, CatfishPSO, C-CatfishPSO, as well as other advanced PSO procedures from the literature were extensively compared on several benchmark test functions. Statistical analysis of the experimental results indicate that the performance of C-CatfishPSO is better than the performance of PSO, C-PSO, CatfishPSO and that C-CatfishPSO is also superior to advanced PSO methods from the literature.     

An improved particle swarm optimizer for parametric optimization of flexible satellite controller

Parametric optimization of flexible satellite controller is an essential for almost all modern satellites. Particle swarm algorithm is a global optimization algorithm but it suffers from two major shortcomings, that of, premature convergence and low searching accuracy. To solve these problems, this paper proposes an improved particle swarm optimization (IPSO) which substitute “poorly-fitted-particles” with a cross operation. Based on decision possibility, the cross operation can interchange local optima between three particles. Thereafter the swarm is split in two halves, and random number (s) get generated by crossing the dimension of particle from both halves. This produces a new swarm. Now the new swarm and old swarm are mixed, and based on relative fitness a half of the particles are selected for the next generation. As a result of the cross operation, IPSO can easily jump out of local optima, has improved searching accuracy and accelerates the convergence speed. Some test functions with different dimensions are used to analyze the performance of IPSO algorithm. Simulation results show that the IPSO has more advantages than standard PSO and Genetic Algorithm PSO (GAPSO). In that it has a more stable performance and lower level of complexity. Thus the IPSO is applied for parametric optimization of flexible satellite control, for a satellite having solar wings and antennae. Simulation results shows that the IPSO can effectively get the best controller parameters vis-a-vis the other optimization methods.     

Reservoir flood control operation based on chaotic particle swarm optimization algorithm

Reservoir flood control operation is a complex engineering optimization problem with a large number of constraints. In order to solve this problem, a chaotic particle swarm optimization (CPSO) algorithm based on the improved logistic map is presented, which uses the discharge flow process as the decision variables combined with the death penalty function. According to the principle of maximum eliminating flood peak, a novel flood control operation model has been established with the goal of minimum standard deviation of the discharge flow process. At the same time, a piecewise linear interpolation function (PLIF) is applied to deal with the constraints for solving objective function. The performance of the proposed model and method is evaluated on two typical floods of Three Gorges reservoir. In comparison with existing models and other algorithms, the proposed model and algorithm can generate better solutions with the minimal flood peak discharge and the maximal peak-clipping rate for reservoir flood control operation.