Erwie Zahara

A hybrid genetic algorithm and particle swarm optimization for multimodal functions

Heuristic optimization provides a robust and efficient approach for solving complex real-world problems. The focus of this research is on a hybrid method combining two heuristic optimization techniques, genetic algorithms (GA) and particle swarm optimization (PSO), for the global optimization of multimodal functions. Denoted as GA-PSO, this hybrid technique incorporates concepts from GA and PSO and creates individuals in a new generation not only by crossover and mutation operations as found in GA but also by mechanisms of PSO. The results of various experimental studies using a suite of 17 multimodal test functions taken from the literature have demonstrated the superiority of the hybrid GA-PSO approach over the other four search techniques in terms of solution quality and convergence rates.

A hybridized approach to data clustering

Data clustering helps one discern the structure of and simplify the complexity of massive quantities of data. It is a common technique for statistical data analysis and is used in many fields, including machine learning, data mining, pattern recognition, image analysis, and bioinformatics, in which the distribution of information can be of any size and shape. The well-known K-means algorithm, which has been successfully applied to many practical clustering problems, suffers from several drawbacks due to its choice of initializations. A hybrid technique based on combining the K-means algorithm, Nelder-Mead simplex search, and particle swarm optimization, called K-NM-PSO, is proposed in this research. The K-NM-PSO searches for cluster centers of an arbitrary data set as does the K-means algorithm, but it can effectively and efficiently find the global optima. The new K-NM-PSO algorithm is tested on nine data sets, and its performance is compared with those of PSO, NM-PSO, K-PSO and K-means clustering. Results show that K-NM-PSO is both robust and suitable for handling data clustering.

Hybrid Nelder-Mead simplex search and particle swarm optimization for constrained engineering design problems

Constrained optimization problems are very important in that they frequently appear in the real world. A constrained optimization problem consists of the optimization of a function subject to constraints, in which both the function and constraints may be nonlinear. Constraint handling is one of the major concerns when solving constrained optimization problems by hybrid Nelder-Mead simplex search method and particle swarm optimization, denoted as NM-PSO. This paper proposes embedding constraint handling methods, which include the gradient repair method and constraint fitness priority-based ranking method, in NM-PSO as a special operator to deal with satisfying constraints. Experiments using three benchmark function and three engineering design problems are presented and compared with the best known solutions reported in the literature. The comparison results with other evolutionary optimization methods demonstrate that NM-PSO with the embedded constraint operator proves to be extremely effective and efficient at locating optimal solutions.

Optimal multi-thresholding using a hybrid optimization approach

The Otsus method has been proven as an efficient method in image segmentation for bi-level thresholding. However, this method is computationally intensive when extended to multi-level thresholding. In this paper, we present a hybrid optimization scheme for multiple thresholding by the criteria of (1) Otsus minimum within-group variance and (2) Gaussian function fitting. Four example images are used to test and illustrate the three different methods: the Otsus method; the NM-PSO-Otsu method, which is the Otsus method with Nelder-Mead simplex search and particle swarm optimization; the NM-PSO-curve method, which is Gaussian curve fitting by Nelder-Mead simplex search and particle swarm optimization. The experimental results show that the NM-PSO-Otsu could expedite the Otsus method efficiently to a great extent in the case of multi-level thresholding, and that the NM-PSO-curve method could provide better effectiveness than the Otsus method in the context of visualization, object size and image contrast.

Hybrid simplex search and particle swarm optimization for the global optimization of multimodal 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.

A genetic algorithm and a particle swarm optimizer hybridized with Nelder-Mead simplex search

This paper integrates Nelder-Mead simplex search method (NM) with genetic algorithm (GA) and particle swarm optimization (PSO), respectively, in an attempt to locate the global optimal solutions for the nonlinear continuous variable functions mainly focusing on response surface methodology (RSM). Both the hybrid NM-GA and NM-PSO algorithms incorporate concepts from the NM, GA or PSO, which are readily to implement in practice and the computation of functional derivatives is not necessary. The hybrid methods were first illustrated through four test functions from the RSM literature and were compared with original NM, GA and PSO algorithms. In each test scheme, the effectiveness, efficiency and robustness of these methods were evaluated via associated performance statistics, and the proposed hybrid approaches prove to be very suitable for solving the optimization problems of RSM-type. The hybrid methods were then tested by ten difficult nonlinear continuous functions and were compared with the best known heuristics in the literature. The results show that both hybrid algorithms were able to reach the global optimum in all runs within a comparably computational expense.

Solving constrained optimization problems with hybrid particle swarm optimization

Constrained optimization problems (COPs) are very important in that they frequently appear in the real world. A COP, in which both the function and constraints may be nonlinear, consists of the optimization of a function subject to constraints. Constraint handling is one of the major concerns when solving COPs with particle swarm optimization (PSO) combined with the Nelder–Mead simplex search method (NM-PSO). This article proposes embedded constraint handling methods, which include the gradient repair method and constraint fitness priority-based ranking method, as a special operator in NM-PSO for dealing with constraints. Experiments using 13 benchmark problems are explained and the NM-PSO results are compared with the best known solutions reported in the literature. Comparison with three different meta-heuristics demonstrates that NM-PSO with the embedded constraint operator is extremely effective and efficient at locating optimal solutions.

A Modified NM-PSO Method for Parameter Estimation Problems of Models

Ordinary differential equations usefully describe the behavior of a wide range of dynamic physical systems. The particle swarm optimization (PSO) method has been considered an effective tool for solving the engineering optimization problems for ordinary differential equations. This paper proposes a modified hybrid Nelder-Mead simplex search and particle swarm optimization (M-NM-PSO) method for solving parameter estimation problems. The M-NM-PSO method improves the efficiency of the PSO method and the conventional NM-PSO method by rapid convergence and better objective function value. Studies are made for three well-known cases, and the solutions of the M-NM-PSO method are compared with those by other methods published in the literature. The results demonstrate that the proposed M-NM-PSO method yields better estimation results than those obtained by the genetic algorithm, the modified genetic algorithm (real-coded GA (RCGA)), the conventional particle swarm optimization (PSO) method, and the conventional NM-PSO method.

Stochastic response surface optimization via an enhanced Nelder-Mead simplex search procedure

There is abundant literature on response surface methodology about how the Nelder–Mead simplex search (NMSS) procedure can be applied to the determination of optimum operating conditions for deterministic response surface functions. However, searching for the optima of stochastic functions seems a more realistic task for many practical situations. This is particularly true when the response surface functions have not been fitted or the physical models may not even exist, so gradient information is not available. In such cases, it might be interesting to employ simplex-search-type methods ‘on-line’ to sequentially optimize the actual response of interest. Toward that end, an enhanced NMSS is proposed in this article to explore the terrains of empirical (or experimental) optimization adaptively where the known response surface function incorporates additional white-noise errors. Internal modifications to basic operations in NMSS are made primarily according to some statistical process control statistics in estimating response variation and confidence bands for mean responses. A series of graphical illustrations are presented to give an insight into the way the new simplex-search-type approach accurately anchors the true optimum point in noisy environments. As evidenced by a wide variety of simulation studies on the published response functions, the new method proves to perform much better than two recent modifications of NMSS in solution quality achieved while applied to the stochastic response surface optimization problems.

Parameter Identification Problem Using Particle Swarm Optimization

Ordinary differential equations have been a useful tool for describing the behavior of wide variety of dynamic physical systems. In this study, a method for solving parameter identification problem for ordinary second order differential equations using particle swarm optimization approach is presented.Experiments using two case problems are presented and compared with the best known solutions reported in the literature. The comparison results demonstrate that PSO produced better estimated results with respect to previous findings from genetic algorithm.