A Hybrid Model Of Particle Swarm Optimization And Continuous Ant Colony Optimization For Multimodal Functions Optimization

Each university has different regulations in making lecture schedule according to the conditions of respective institution. In this study, regulation on lecture scheduling used the maximum limit of credits of lecturer in a day, in which if exceeds the maximum limit, then the schedule of course will be moved on another day. This study attempts to optimize the schedule preparation in each semester by considering the maximum limit of credits of a lecturer in a day. Lecture scheduling is a combination of space, time, and resources. It is categorized into combinatorial optimization group. There are two methods for solving the combinatorial optimization problems, i.e. exact and approximation method. The approximation method consists of two types, heuristics and metaheuristics. The algorithm metaheuristics categories include genetic algorithm (GA), particle swarm optimization (PSO), ant colony optimization (ACO), bee colony optimization (BCO), simulated annealing, and so on. This paper employed metaheuristics approach. Research on the preparation of lecture scheduling using ACO algorithm has been conducted and proven to be able to prepare the lecture scheduling. The ACO algorithm has numbers of parameters that in solving issues, one must manually set a number of parameters by using the Design of Experiments (DoE) tool, which takes time to solve the optimization problem. Hence, to solve the issue, an automated parameter optimization is required. PSO algorithm has fewer parameters compared to the ACO. Therefore, the purpose of this paper is a hybrid between PSO and ACO in preparing lecture scheduling.

Particle swarm optimization (PSO) can be interpreted physically as a particular discretization of a stochastic damped mass-spring system. Knowledge of this analogy has been crucial to derive the PSO continuous model and to introduce different PSO family members including the generalized PSO (GPSO) algorithm, which is the generalization of PSO for any time discretization step. In this paper, we present the stochastic analysis of the linear continuous and generalized PSO models for the case of a stochastic center of attraction. Analysis of the GPSO second order trajectories is performed and clarifies the roles of the PSO parameters and that of the cost function through the algorithm execution: while the PSO parameters mainly control the eigenvalues of the dynamical systems involved, the mean trajectory of the center of attraction and its covariance functions with the trajectories and their derivatives (or the trajectories in the near past) act as forcing terms to update first and second order trajectories. The similarity between the oscillation center dynamics observed for different kinds of benchmark functions might explain the PSO success for a broad range of optimization problems. Finally, a comparison between real simulations and the linear continuous PSO and GPSO models is shown. As expected, the GPSO tends to the continuous PSO when time step approaches zero. Both models account fairly well for the dynamics (first and second order moments) observed in real runs. This analysis constitutes so far the most realistic attempt to better understand and approach the real PSO dynamics from a stochastic point of view.

Nowadays, clustering plays a critical role in most research areas such as engineering, medicine, biology, data mining, etc. Evolutionary algorithms, including continuous ant colony optimization, particle swarm optimization, and genetic algorithms, have been employed for data clustering. To improve searching skills, this paper examines four strategies, combining of continuous ant colony optimization and particle swarm optimization, and proposes a strategy which is a combination of these two algorithms with genetic algorithm. Available methods and the proposed method were implemented over several sets of benchmark data to assess the validity. Results were compared with the results of continuous ant colony optimization and particle swarm optimization. The high capacity and resistance of combined methods are obvious according to results.

This paper presents a solution to the problem of pattern formation on a grid map, for a homogeneous multi-robot system. In this paper we propose a natural swarm inspired algorithm based on the Particle Swarm Optimization (PSO) model and Virtual Pheromone mechanism. Basically, a virtual pheromone trail based method is proposed as the message passing mechanism among the robots, where robots make distributed movement decisions through local interactions. For one individual robot, there are two working modes, exploration and dispersion, with different indicators in the PSO model. By cooperating and communicating through the virtual pheromone, agents of the multi-robot system switch between the two phases. The PSO method helps to allocate reasonable robots to different parts of the predefined pattern. A series of experiments on simulator is carried out and proves the convergence and excellent scalability of our algorithm. By optimizing some parameter in the PSO model with the help of the simulator, the efficiency of pattern formation is further improved.

On the basis of the analyses of Ant Colony Optimization (ACO) and Particle Swarm Optimization (PSO), Continuous Ant- Particle Swarm Optimization (CA-PSO) applied in continuous function optimization is proposed. After the space partition is properly employed, ACO is applied to search the sensitive areas through the whole solution space. And then PSO is initialized according to ACO search results and applied to search the optimal solution in every area. After every iteration, swarm renovation is processed following Ant-Colony topological structure and transfer rules. As a result, the ants gradually assemble in the areas where optimal solution is mostly likely to be. With the number growth of particles in the sensitive areas, local PSO can search more meticulously until find the optimal solution. In conclusion, the CA-PSO can not only ensure the distributing diversity of the solution, but also avoid suboptimal solution when it is applied in the Multimodal function optimization.

Particle Swarm Optimization (PSO) is an evolution-nary computation technique. Separate adjustment to inertia weight and learning factors in PSO undermines the integrity and intelligent characteristic in the evolutionary process of particle swarm to some extent, thus it is not suitable for solving most complicated optimization problems. On the basis of previous researches, the aim of this study was to improve the computational efficiency of PSO and avoid premature convergence for multimodal, higher dimensional complicated optimization problems by considering the mutual influences of inertia weight and learning factors on the updates of particle's veloci-ties. A great number of experiment data provided evidence that the nonlinear adjustment to inertia weight, cognitive learning factor and social learning factor within a certain interval is a good selection. Moreover, the simulation results on four typical functions show that the improved strategy of PSO proposed in the paper is available for solving multimodal and higher dimensional complicated optimization problems, and can accelerate convergence speed, improve optimization quality effectively in comparison to the algorithms of standard PSO and existing relevant improved PSO.

Particle swarm optimization (PSO) is a kind of population-based search methods, that is inspired by social behavior observed in nature, such as flocks of irds and schools of fish. PSO has been receiving attentions, since it has a powerful search ability in function optimization problems, and several improvement has been studied to apply PSO to the multimodal function optimization and optimization in the dynamic environments. The purpose of this paper is to improve PSO performance deteriorated by the degeneracy of particle velocities, in case of high-dimensional optimization problems. We propose a novel PSO model, called the Rotated Particle Swarm (RPS), by introducing the coordinate conversion. The numerical simulation results show that the proposed RPS is effective in optimizing high-dimensional functions.

This article proposes the hybrid Nelder–Mead (NM)–Particle Swarm Optimization (PSO) algorithm based on the NM simplex search method and PSO for the optimization of multimodal functions. The hybrid NM–PSO algorithm is very easy to implement, in practice, since it does not require gradient computation. This hybrid procedure performed the exploration with PSO and the exploitation with the NM simplex search method. In a suite of 17 multi-optima test functions taken from the literature, the computational results via various experimental studies showed that the hybrid NM–PSO approach is superior to the two original search techniques (i.e. NM and PSO) in terms of solution quality and convergence rate. In addition, the presented algorithm is also compared with eight other published methods, such as hybrid genetic algorithm (GA), continuous GA, simulated annealing (SA), and tabu search (TS) by means of a smaller set of test functions. On the whole, the new algorithm is demonstrated to be extremely effective and efficient at locating best-practice optimal solutions for multimodal functions.

Fuzzy systems (FSs) have been extensively applied to automatic control, pattern recognition, and decision analysis. However, a common bottleneck is encountered in the derivation of fuzzy rules, which is often difficult, time consuming, and relies on expert knowledge. To automate the design of FSs, many metaheuristic learning algorithms have been proposed. One major optimization category uses Swarm Intelligence (SI) model (Kennedy et al., 2001). The SI technique studies collective behavior in decentralized systems. Its development was based on mimicking the social behavior of animals or insects in an effort to find the optima in the problem space. SI models are initialized with a population of random solutions. One well-known SI model is particle swarm optimization (PSO) (Kennedy & Eberhart, 1995). Many modified PSO models have been proposed and successfully applied to different optimization problems (Clerc & Kennedy, 2002; Bergh & Engelbrecht, 2004; Ratnaweera et al., 2004; Juang, 2004; Kennedy & Mendes, 2006; Parrott & Li, 2006; Chen & Li, 2007). FS design using PSO has also been proposed in several studies (Juang, 2004; Chatterjee et al., 2005; Juang et al., 2007; Araujo & Coelho, 2008; Sharma et al., 2009). Another well-known SI is ant colony optimization (ACO) (Dorigo & Stutzle, 2004). The ACO technique is inspired by real ant colony observations. It is a multi-agent approach that was originally proposed to solve difficult discrete combinatorial optimization problems, such as the traveling salesman problem (TSP) (Dorigo et al., 1996; Dorigo & Gambardella, 1997). In the original ACO meta-heuristic, artificial ant colonies cooperate to find good solutions for difficult discrete optimization problems. Different ACO models have been applied to FS design problems (Cassillas et al., 2000; Cassillas et al., 2005; Mucientes & Casillas; 2007; Juang & Lo, 2007; Juang et al., 2008; Juang & Lu; 2009). In (Cassillas et al.,2000; Mucientes & Casillas; 2007; Juang et al., 2008; Juang & Lu; 2009), the FS input space was partitioned in grid type with antecedent part parameters of an FS manually assigned in advance. In (Juang & Lo, 2007), the FS input space was flexibly partitioned using a fuzzy clustering-like algorithm in order to reduce the total number of rules. For all of these studies, the consequent part parameters were optimized in discrete space using ACO. Since only the consequent part parameters are optimized, and the optimization space is restricted to be discrete, the designed FSs are unsuitable for problems where high accuracy is a major concern. Source: Fuzzy Systems, Book edited by: Ahmad Taher Azar, ISBN 978-953-7619-92-3, pp. 216, February 2010, INTECH, Croatia, downloaded from SCIYO.COM

Particle Swarm Optimization (PSO) has become a popular method of feature selection in classification problems, due to its powerful search capability and computational simplicity. Classification problems, such as facial emotion recognition, often involve data sets containing high volumes of features, not all of which are useful for classification. Redundant and irrelevant features have the potential to negatively impact the performance and accuracy of facial emotion recognition systems. The feature selection process identifies the most relevant features to achieve improved classification performance. While the use of PSO as a feature selection method in facial emotion recognition systems has seen some successes, it is still susceptible to the issue of premature convergence. This work presents seven PSO variants which mitigate against the premature convergence problem through the incorporation of three random probability distributions (Cauchy, Gaussian and Levy). At each iteration of the proposed PSO models, probability distributions are used to increase search diversity and reduce the number of redundant features used for classification. The seven PSO variants presented in this study have demonstrated positive results when tested on real world data sets, outperforming the standard PSO model and other related work within the field.

As demonstrated in Chap. 3, different evolutionary algorithms, including genetic algorithm (GA), simulated annealing (SA) algorithm, hybrid GASA algorithm, particle swarm optimization (PSO) algorithm, continuous ant colony optimization (CACO) algorithm, artificial bee colony (ABC) algorithm, and immune algorithm (IA), are employed to determine suitable for parameter combination of an SVR-based electric load forecasting model. These forecasting results indicate that almost all SVR-based models with different evolutionary algorithms are superior to other competitive forecasting models (including ARIMA, HW, GRNN, and BPNN models); however, these algorithms almost lack knowledge memory or storage mechanisms which would be neither time-consuming nor inefficient in searching the suitable parameters, that is, premature convergence (being trapped in local optimum). For example, for SVRGA model, in GA processing, new individuals are generated by the following operators, selection, crossover, and mutation. For all types of objective functions, the generation begins with a binary coding for the parameter set. Based on this special binary coding process, GA is able to solve some specified problems which are not easily to be solved by traditional algorithms. GA can empirically provide a few best fitted offsprings from the whole population; however, after some generations, due to low diversity of the population, it might lead to a premature convergence [1]. For SVRSA model, SA algorithm is a generic probabilistic search technique that simulates the material physical process of heating and controlled cooling. Each step of SA attempts to replace the current state by a random move. The new state may then be accepted with a probability that depends both on the difference between the corresponding function values and also on a global parameter, temperature. Thus, SA has some institution to reach more ideal solutions. However, SA algorithm requires the subtle and skillful adjustment in the annealing schedule; therefore, the settings of the size of the temperature steps during annealing, the temperature range, the number of restarts, and the redirection of the search will be taken into account carefully [1]; in addition, its Monte Carlo scheme and lack of knowledge memory mechanism will also lead to time-consuming and inefficient searching in annealing process.

Many real-world optimization problems can be solved very efficiently by evolutionary algorithms. There exist many solutions in this field to solve multi-dimensional optimization problems, which is an important issue in today’s world. Swarm-based algorithms are very popular to solve these types of problems because of its effectiveness and quality of solutions. All swarm-based algorithms have different advantages and disadvantages. This paper has discussed two such mostly used algorithms, i.e., particle swarm optimization (PSO) and artificial bee colony (ABC). A fair comparison has been done between these two algorithms by implementing those to minimize five different standard benchmark functions. Results have been recorded and the performance of both the algorithms is analyzed with corresponding to the quality of solutions. It has been observed from the simulation results that ABC outperforms PSO in most of the cases corresponding to solution quality but it requires more time to converge than PSO.

The identification of nonlinear systems with artificial neural networks models has been successfully used in many applications. Most processes in industry are characterized by nonlinear and time-varying behavior. In this context, the identification of mathematical models for nonlinear systems is vital in many fields of engineering. The Radial Basis Function Neural Network (RBF-NN) is a powerful approach for nonlinear identification and can be improved using Particle Swarm Optimization (PSO) approaches. This paper presents a multivariable nonlinear system identification using RBF-NN combined with standard PSO and Constriction Factor PSO (CFPSO) approaches in order to determine the RBF-NN parameters. RBF-NN is considered to be a good choice for black-box modeling problems due to its rapid learning capacity and, therefore, has been applied successfully to nonlinear time series modeling and nonlinear identification. On the other hand, PSO was inspired by the choreography of bird flocks and fish schools and can be seen as a distributed behavior algorithm that performs multidimensional search. Furthermore, promising simulation results from performance analysis of the proposed RBF-NN with PSO training approaches are presented and discussed in this paper showing promising results.

Water quality planning relies on Biochemical Oxygen Demand BOD. BOD testing takes five days. The Particle Swarm Optimization (PSO) is increasingly used for water resource forecasting. This work designed a PSO technique for estimating everyday BOD at Al-Rustumiya wastewater treatment facility inlet. Al-Rustumiya wastewater treatment plant provided 702 plant-scale data sets during 2012-2022. The PSO model uses the daily data of the water quality parameters, including chemical oxygen demand (COD), chloride (Cl-), suspended solid (SS), total dissolved solids (TDS), and pH, to determine how each variable affects the daily incoming BOD. PSO and multiple linear regression (MLR) findings are compared, and their performance is evaluated using mean square error, relative absolute mistake, and coefficient of determination. PSO utilised COD, TDS, SS, pH, and Cl- as inputs, generating a mean square error of 1029.10, an average absolute relative error of 9.41%, and a coefficient of determination of 0.89. Comparisons demonstrated that the PSO model could accurately calculate the daily BOD at Al-Rustumiya wastewater treatment plant's inlet.

In the last decades, many efforts have been made to solve multimodal optimization problems using Particle Swarm Optimization (PSO). To produce good results, these PSO algorithms need to specify some niching parameters to define the local neighborhood. In this paper, our motivation is to propose the novel neighborhood structures that remove undesirable niching parameters without sacrificing performance. Hence, this paper has two main contributions. First, two novel parameter-free neighborhood structures named Topological Nearest-Better (TNB) neighborhood and Distance-based Nearest-Better (DNB) neighborhood are proposed in the topological space and decision space, respectively. Second, two proposed neighborhoods are combined with Fuzzy PSO (FPSO) and two novel niching algorithms, called TNB-FPSO and DNB-FPSO, are proposed for solving multimodal optimization problems. It should be noted that we use a zero-order fuzzy system to balance between exploration and exploitation in the proposed algorithms. To evaluate the performance of proposed algorithms, we performed a detailed empirical evaluation on the several standard multimodal benchmark functions. Our results show that DNB-FPSO statistically outperforms the other compared multimodal optimization algorithms.