Narrow Results

This paper investigates the affine sum-of-ratios problem (SRP) which has numerous applications in many fields of economy and engineering. For globally computing the affine SRP, based on equivalent transformation and new affine relaxation problem, a reduced outer space branch-and-bound algorithm is designed. The designed algorithm has been proven to converge to a global optimal solution of the problem (SRP) eventually. Meanwhile, the maximum iteration time for the algorithm in the worst case is estimated by analyzing its computational complexity. Finally, numerical experimental results indicate that the presented algorithm is robust and effective.

Autonomous intelligent systems have been widely implemented in a broad range of applications. These applications often involve data-dense tasks where an efficient feature selection process is required to eliminate redundant features and improve model performance. However, the feature selection tasks with high dimensionality still remain challenging to deal with. In order to address high-dimensional feature selection problems with greater effectiveness and efficiency, this paper proposes a particle swarm optimizer variant named PSO-BEE that allows the swarm to take full advantage of exploration and exploitation at due evolutionary stages. At the early stage, a large size of candidate exemplar group is formed for diversity enhancement, attempting to find as many new combinations of features as possible. At the later stage, a tiny size of candidate exemplar group is constructed, allowing updated particles to learn from the few best elite exemplars to continuously refine feature selection solutions with a lower classification error rate. Three PSO-BEE variants with distinct preferences for exploration and exploitation are proposed based on different parameter adjustment strategies. Experiments are executed on 500, 1000, and 2000-dimensional benchmark suites presented by CEC and real-world feature selection datasets from the Machine Learning Repository. Experimental results demonstrate the competitive performance of PSO-BEE in high-dimensional global optimization and feature selection when compared with several state-of-the-art approaches.

In this article, a novel technique for non-linear global optimization is presented. The main goal is to find the optimal global solution of non-linear problems avoiding sub-optimal local solutions or inflection points. The proposed technique is based on a two steps concept: properly keep decreasing the value of the objective function, and calculating the corresponding independent variables by approximating its inverse function. The decreasing process can continue even after reaching local minima and, in general, the algorithm stops when converging to solutions near the global minimum. The implementation of the proposed technique by conventional numerical methods may require a considerable computational effort on the approximation of the inverse function. Thus, here a novel Artificial Neural Network (ANN) approach is implemented to reduce the computational requirements of the proposed optimization technique. This approach is successfully tested on some highly non-linear functions possessing several local minima. The results obtained demonstrate that the proposed approach compares favorably over some current conventional numerical (Matlab functions) methods, and other non-conventional (Evolutionary Algorithms, Simulated Annealing) optimization methods.

In this paper the performance of the Cultural Algorithms-Iterated Local Search (CA-ILS), a new continuous optimization algorithm, is empirically studied on multimodal test functions proposed in the Special Session on Real-Parameter Optimization of the 2005 Congress on Evolutionary Computation. It is compared with state-of-the-art methods attending the Session to find out whether the algorithm is effective in solving difficult problems. The test results show that CA-ILS may be a competitive method, at least in the tested problems. The results also reveal the classes of problems where CA-ILS can work well and/or not well.

The structure and energetics of Pd_N (N = 5–80) clusters have been studied extensively by a Monte Carlo method based on Sutton–Chen many-body potential. The basin-hopping algorithm is used to find the low-energy minima on the potential energy surface for each nuclearity. A variety of structure types (icosahedral, decahedral and fcc closed-packed) are observed for Pd clusters. Some of the icosahedral global minima do not have a central atom. The resulting structures have been compared with the previous theoretical results.

The structure and energetic of Palladium-Cobalt clusters (N = 11–20) have been studied extensively by a Monte Carlo method based on Sutton–Chen many-body potential. The basin-hopping algorithm was used to determine the global minima of bimetallic clusters. The structural changes with cluster size were observed. Most of the structures had built on icosahedral packing. Second energy difference analyzes were performed to investigate the relative stability of a cluster with respect to its size and composition is discussed.

Metal nanoalloys on oxide surface are a widely studied topic in surface science and technology. In this study, the structures of CoPd nanoalloys adsorbed on MgO(001) have been searched by basin-hopping global optimization method within an atomistic model. Two different sizes (34 and 38 atom) have been considered for all compositions of CoPd/MgO(001) nanoalloys. Co and Pd atoms, for all the compositions, have cube-on-cube (001) epitaxy with substrate at interface. For both sizes, we have found that Pd rich composition nanoalloys have three layers, Co rich composition nanoalloys have four layers in morphology. Excess energy and second difference in energy analyzes have been performed to investigate the relative stability of nanoalloys with respect to their size and composition.

Structural optimization of ternary Cu–Ag–Au nanoalloys with 38 and 55 atoms was performed using the basin-hopping algorithm and the Gupta many-body potential was adopted to model interatomic interactions. The optimization results show that, while the Ag atoms prefer to segregate to the surface, Cu atoms were located at the core of the nanoalloy due to the higher surface and cohesive energy, whereas Au atoms mainly are located on the surface of the nanoalloys. It is found that the size has little effect on the segregation phenomena of Cu, Ag and Au atoms in the Cu–Ag–Au ternary nanoalloy. We estimated the melting temperatures of Cu–Ag–Au ternary nanoalloys using caloric curves and Lindemann index data obtained from classical molecular dynamics (MD) simulations. The results showed that the melting temperature is closely associated with the size and composition of the nanoalloys and varying the composition gives rise to a fluctuation in melting temperatures. Also, structural evolutions and dynamical behaviors of nanoalloys in melting process are investigated with root mean square displacement (RMSD).

Social learning-integrated flower pollination algorithm (SLFPA) is a solution to issues that meta-heuristic algorithms face when solving the influence maximization problem. These issues include the high probability of entrapment in local optima, a decrease in population diversity during later iterations, and low accuracy of solution. In human society, people often learn from others behavior. This mechanism of social learning is incorporated into the flower pollination algorithm. A global pollination strategy is devised to increase population diversity and avoid being trapped in local optima, which utilizes both the global optimal individual and the most improved individual. To enhance the accuracy of the algorithm, we have developed a local pollination strategy that involves creating a learning object based on close friends. We tested the proposed algorithm on six real social networks and compared it to six other advanced heuristic algorithms, and the results demonstrate the effectiveness of algorithm and improved the accuracy of the solution.

In this paper, a global optimization meta-heuristic, the great deluge algorithm, is extended and applied to optimize the reliability of complex systems. Two different kinds of optimization problems (i) Reliability optimization of a complex system with constraints on cost and weight (ii) Optimal redundancy allocation in a multi-stage mixed system with constraints on cost and weight are solved to demonstrate the effectiveness of the algorithm. A software developed in ANSI C, implements the algorithm. In terms of both accuracy and speed, it is observed that the present algorithm, the modified great deluge algorithm (MGDA) yielded far superior results compared to those obtained by the simulated annealing, the improved non-equilibrium simulated annealing and other optimization algorithms. Further, when both accuracy and speed are considered simultaneously, both MGDA and another meta-heuristic, ant colony optimization (ACO) yielded comparable results. In conclusion, the MGDA, can be used as an efficient alternative to ACO and other existing optimization techniques.

A novel monotonization method is proposed for converting a non-monotone programming problem into a monotone programming problem. An equivalent monotone programming problem with only inequality constraints is obtained via this monotonization method. Then the existing convexification and concavification methods can be used to convert the monotone programming problem into an equivalent better-structured optimization problem.

This paper presents motivations and algorithmic details of some generalized controlled random search (CRS) algorithms for global optimization. It also carries out an extensive numerical study of the generalized CRS algorithms to demonstrate their superiorities over their original counterparts. The numerical study is carried out using a set of 50 test problems many of which are inspired by practical applications. Numerical experiments indicate that the generalized algorithms are considerably better than the previous versions. The algorithms are also compared with the DIRECT algorithm (Jones et al., 1993). The comparison shows that the generalized CRS algorithms are better than the DIRECT algorithm in high dimensional problems. Thus, they offer a reasonable alternative to many currently available stochastic algorithms, especially for problems requiring "direct search type" methods.

Founded on the idea of subdividing the $(p-1)$-dimensional output space, a branch-and-bound algorithm for solving the sum-of-linear-ratios(SLR) problem is proposed. First, a two-stage equivalent transformation method is adopted to obtain an equivalent problem(EP) for the problem SLR. Second, by dealing with all nonlinear constraints and bilinear terms in EP and its sub-problems, a corresponding convex relaxation subproblem is obtained. Third, all redundant constraints in each convex relaxation subproblem are eliminated, which leads to a linear programming problem with smaller scale and fewer constraints. Finally, the theoretical convergence and computational complexity of the algorithm are demonstrated, and a series of numerical experiments illustrate the effectiveness and feasibility of the proposed algorithm.

Some works have recently shown the usefulness of simple models of nucleon separation energies in terms of neutron and proton numbers. However, the customary use of least squares in the process of parameter estimation turns out to be extremely sensible to the accuracy of the model and the extent and quality of data (e.g. highly vulnerable to the sample size or the possible existence of undesired errors in the experimental values). We will show how robust estimation by global optimization instead of least squares estimation improves on both the stability of the estimated parameters and the extrapolation to unknown energies. Comparison against recently determined experimental data will show a level of agreement comparable to the predictions made by the best and much more complex models.

High brightness electron beams play an important role in accelerator-based applications such as driving X-ray free electron laser (FEL) radiation. In this paper, we report on advances in global beam dynamics optimization of an accelerator design using start-to-end simulations and a new parallel multi-objective differential evolution optimization method. The global optimization results in significant improvement of the final electron beam brightness.

In the field of computer vision, camera calibration is a hot issue. For the existing coupled problem of calculating distortion center and the distortion factor in the process of camera calibration, this paper presents an iterative-decreasing calibration method based on regional circle, uses the local area of the circle plate to calculate the distortion center coordinates by iterative declining, and then uses the distortion center to calculate the local area calibration factors. Finally, makes distortion center and the distortion factor for the global optimization. The calibration results show that the proposed method has high calibration accuracy.

A new polygonal approximation algorithm, employing the concept of genetic evolution, is presented. In the proposed method, a chromosome is used to represent a polygon by a binary string. Each bit, called a gene, represents a point on the given curve. Three genetic operators, including selection, crossover, and mutation, are designed to obtain the approximated polygon whose error is bounded by a given norm. Many experiments show that the convergence is guaranteed and the optimal or near-optimal solutions can be obtained. Compared with the Zhu–Seneviratne algorithm,²⁴ the proposed algorithm successfully reduced the number of segments under the same error condition in the polygonal approximation.

With regards to the low search accuracy of the basic invasive weed optimization algorithm which is easy to get into local extremum, this paper proposes an adaptive invasive weed optimization (AIWO) algorithm. The algorithm sets the initial step size and the final step size as the adaptive step size to guide the global search of the algorithm, and it is applied to 20 famous benchmark functions for a test, the results of which show that the AIWO algorithm owns better global optimization search capacity, faster convergence speed and higher computation accuracy compared with other advanced algorithms.

A chaos particle swarm optimization (CPSO) algorithm based on the chaos operator (CS) is proposed for global optimization problems and parameter inversion of the nonlinear sun shadow model in our study. The CPSO algorithm combines the local search ability of CS and the global search ability of PSO algorithm. The CPSO algorithm can not only solve the global optimization problems effectively, but also address the parameter inversion problems of the date of sun shadow model location successfully. The results of numerical experiment and simulation experiment show that the CPSO algorithm has higher accuracy and faster convergence than the-state-of-the-art techniques. It can effectively improve the computing accuracy and computing efficiency of the global optimization problems, and also provide a novel method to solve the problems of integer parameter inversion in real life.

To overcome the shortcomings of the basic glowworm swarm optimization (GSO) algorithm, such as low accuracy, slow convergence speed and easy to fall into local minima, chaos algorithm and cloud model algorithm are introduced to optimize the evolution mechanism of GSO, and a chaos GSO algorithm based on cloud model (CMCGSO) is proposed in the paper. The simulation results of benchmark function of global optimization show that the CMCGSO algorithm performs better than the cuckoo search (CS), invasive weed optimization (IWO), hybrid particle swarm optimization (HPSO), and chaos glowworm swarm optimization (CGSO) algorithm, and CMCGSO has the advantages of high accuracy, fast convergence speed and strong robustness to find the global optimum. Finally, the CMCGSO algorithm is used to solve the problem of face recognition, and the results are better than the methods from literatures.