Testing various numerical optimization methods on a series of artificial test functions

The laws of gravity and mass interactions inspire the gravitational search algorithm (GSA), which nds optimal regions of complex search spaces through the interaction of individuals in a population of particles. Although GSA has proven effective in both science and engineering, it is still easy to suffer from premature convergence especially facing complex problems. In this paper, we pro- posed a new hybrid algorithm by integrating genetic algorithm (GA) and GSA (GA-GSA) to avoid premature convergence and to improve the search ability of GSA. In GA-GSA, crossover and mutation operators are introduced from GA to GSA for jumping out of the local optima. To demonstrate the search ability of the proposed GA-GSA, 23 complex benchmark test functions were employed, including unimodal and multimodal high-dimensional test functions as well as multimodal test functions with xed dimensions. Wilcoxon signed-rank tests were also utilized to execute statistical analysis of the results obtained by PSO, GSA, and GA-GSA. Experimental results demonstrated that the proposed algorithm is both efficient and effective.

In this paper, we first establish some sufficient and some necessary global optimality conditions for quadratic integer programming problems. Then we present a new local optimization method for quadratic integer programming problems according to its necessary global optimality conditions. A new global optimization method is proposed by combining its sufficient global optimality conditions, local optimization method and an auxiliary function. The numerical examples are also presented to show that the proposed optimization methods for quadratic integer programming problems are very efficient and stable.

Description: The implementation of well testing models for dynamic characterization of Naturally Fractured Vuggy Reservoirs (NFVR) commonly involves inverse modeling. Thus, this work introduces new results about dynamic description of NFVR by using a triple porosity-dual permeability model. The values of the inter-porosity flow parameters, storativity ratios, permeability ratio between fractures and vugs, wellbore storage coefficient, skin and total permeability, are automatically identified in Laplace Space by using a gradient Newton-type global optimization method named The Tunneling. This method offers more reliable results in comparison to the local optimization methods commonly used in parameters estimations. Applications: The precision and computational efficiency of the Tunneling Method are demonstrated through the reliable results obtained from the automatic analysis of synthetic examples, where a very comprehensive and large set of synthetic noisy data was used. In all cases, the Tunneling Method obtained optimal solutions. Likewise, the analysis of several field well test data cases recorded in NFVR are shown to confirm the benefits above mentioned. Results, Observations, and Conclusions: The parameters determination in the problem here addressed is non-unique due to the ill-posedness problem forcing the local optimization methods to stop in non-optimal solutions. Likewise, local methods require many realizations until converge into an optimal solution. Thus, the superiority of the Tunneling Method for overcoming these challenges is demonstrated through the reliable analysis of several synthetic and field data cases. Performing the optimization in the Laplace space makes the procedure very efficient in computing time. To moderate or eliminate the non-uniqueness problem, information about storativity ratios obtained from core or well log analysis, can be used through the optimization process. Significance of Subject Matter: Currently, the well test data analysis is the only available procedure to estimate the dynamic parameters which characterize NFVRs. Likewise, the approach introduced in this work allows obtaining more reliable estimations of these parameters than local optimization methods.

Multivariate quartic polynomial optimization problems, as a special case of the general polynomial optimization, have a lot of practical applications in real world and are proved to be NP-hard. In this paper, some necessary local optimality conditions and some necessary global optimality conditions for quartic polynomial optimization problems with mixed variables are established. Then some local optimization methods, including weakly local optimization methods for general problems with mixed variables and strongly local optimization methods for quartic polynomial optimization problems with mixed variables, are proposed by exploiting these necessary local optimality conditions and necessary global optimality conditions. A global optimization method is proposed for quartic polynomial optimization problems by combining these local optimization methods together with some auxiliary functions. Some numerical examples are also given to illustrate that these approaches are very efficient.

ABSTRACTAn autonomous power generation system (APGS) contains units such as diesel energy generator, solar photovoltaic units, wind turbine generator and fuel cells along with energy-storing units such as the flywheel energy storage system and battery energy storage system. The components either run at lower/higher power output or may turn on/off at different instants of their operation. Due to this, the conventional controllers will not provide desired performance under varied load conditions. This paper proposes an adaptive fuzzy logic PID (AFPID) controller for load frequency control. In order to achieve an improved performance, a modified whale optimization algorithm (mWOA) was also proposed in this paper for tuning of the AFPID parameters. The proposed algorithm was first evaluated using standard test functions and compared with other recent algorithms to authenticate the competence of algorithm. The proposed mWOA algorithm outperforms PSO, GSA, DE and FEP algorithms in five out of seven unimodal test functions and four out of six multimodal test functions. The effectiveness of the AFPID compared with the conventional PID and the proposed AFPID provides better performance. Reduction of 39.13% in error criteria (objective function) compared with WOA-PID controller. The proposed approach was also compared with some recently proposed frequency control approaches in a widely used two-area test system.

Utilization of surface wave dispersive properties may be roughly divided into three steps: field data acquisition, dispersion-curve picking, and inversion of phase velocities (

Here, we present an extension of the classical steepest descent method for solving global continuous optimization problems. To this end, we apply the concept of Jackson's derivative to compute the negative of the q-gradient of the objective function, used as the search direction. The use of Jackson's derivative has shown to be an effective mechanism for escaping from local minima. The q-gradient algorithm is complemented with strategies for selecting the parameter q and to compute the step length. These strategies are implemented in a way such that the search process gradually shifts from global in the beginning to local as the algorithm converges. For testing this new approach, we considered a set of multimodal test functions and compared our results with those obtained by Evolutionary Algorithms (EAs) widely used in optimizing multidimensional and multimodal functions. Overall, the q-gradient method performs well against the EAs arriving in forth position in a direct comparison with them, for the dimensions 10 and 30.

Global optimization seeks a minimum or maximum of a multimodal function over a discrete or continuous domain. In this paper, we propose a hybrid heuristic--based on the CGRASP and GENCAN methods--for finding approximate solutions for continuous global optimization problems subject to box constraints. Experimental results illustrate the relative effectiveness of CGRASP---GENCAN on a set of benchmark multimodal test functions.

Cross-Hill: A heuristic method for global optimization

In recent years shallow gas blowouts have occurred several times in Balikpapan residential areas due to drilling activities for groundwater exploration and geological structures that play as a gas trap. It is necessary to identify structures containing shallow gas by implementing geophysical methods namely Vertical Electrical Sounding (VES). VES is an electrical resistivity method which involves the rapid measurement of variations of the ground resistivity with increasing electrode spaces. The output of this method is a 1-D resistivity model used to identify shallow gas. The 1-D resistivity model can be obtained by the inversion technique. In general, the inversion of VES data is conducted using local optimization method. However, this method has several limitations hence we need to implement a global optimization method in VES data inversion. In this work, the RRPSO algorithm was implemented, which is a global optimization method, in VES data inversion to obtain 1-D resistivity model. First, the RR-PSO algorithm is built and tested to invert synthetic data to evaluate the algorithm's performance. In this stage, the similarity index and several statistical parameters of the inversion results were calculated. After the synthetic test, the algorithm is implemented on field data inversion. The result shows that the RR-PSO algorithm has successfully inverted both the synthetic and field data. In the synthetic test, the similarity index obtained is more than 95%. The 1-D resistivity model from field data inversion indicates at the depth of 20 – 55 m a high resistivity anomaly that is identified as shallow gas. For further study, the RR-PSO algorithm could be implemented for other VES data to construct 2-D resistivity model in the study area (Palm Hills Resident area, south Balikpapan) for imaging the shallow gas presence as a mitigation measure.

Improving the runtime of MRF based method for MRI brain segmentation

Most mathematical optimization models of the applied problems are multimodal. Many methods and algorithms have been developed and are being developed for their solution. To verify the effectiveness of such methods, many test functions and problems have been developed. But most of such test functions are simple. They are symmetric, of low dimension, and have known solutions. This complicates the verification of the effectiveness of existing and new methods of global optimization. The paper proposes modifications of known test functions that satisfy the efficiency conditions. The minima of these functions are found by the method of exact quadratic regularization. The results obtained are significantly better than the solutions obtained by other methods.

This paper aims the design of efficient and effective optimization algorithms for function optimization. For that purpose we present a new framework of the derandomized evolution strategy with covariance matrix adaptation, which combines the hybrid step size adaptation that is proposed in this paper as a robust alternate to the cumulative step size adaptation and normalization mechanism of covariance matrix. Experiment is conducted on 8 classical unimodal and multimodal test functions and the performance of the proposed strategy is compared with that of the standard strategy. Results show that the proposed strategy beats the standard strategy when the population size becomes larger than the default one, while the performance of proposed strategy is as well or better than that of the standard strategy under the default population size.

Optimal sensor network deployment in built environments for tracking, surveillance, and monitoring of dynamic phenomena is one of the most challenging issues in sensor network design and applications (e.g., people movement). Most of the current methods for sensor network deployment and optimization are empirical and they often result in important coverage gaps in the monitored areas. To overcome these limitations, several optimization methods have been proposed in the recent years. However, most of these methods oversimplify the environment and do not consider the complexity of 3D architectural nature of the built environments specially for indoor applications (e.g., indoor navigation, evacuation, etc.). In this paper, we propose a novel local optimization algorithm based on a 3D Voronoi diagram, which allows a clear definition of the proximity relations between sensors in 3D indoor environments. This proposed structure is integrated with an IndoorGML model to efficiently manage indoor environment components and their relations as well as the sensors in the network. To evaluate the proposed method, we compared our results with the Genetic Algorithm (GA) and the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) algorithms. The results show that the proposed method achieved 98.86% coverage which is comparable to GA and CMA-ES algorithms, while also being about six times more efficient.

*† ‡ § An efficient and high-fidelity design approach is proposed by combining global and local optimization methods for wing planform and surface design. For enhanced design results, aerodynamic shape optimization process is carried out via 2-stage with different optimization strategy. In the first stage, global optimization techniques are applied to planform design with a few geometric design variables. In the second stage, local optimization techniques are used for wing surface design with a lot of design variables to maintain a sufficient design space with high DOF (Degree of Freedom) geometric change. For global optimization, meta-modeling techniques such as RS (Response Surface) and Kriging methods are used in conjunction with Genetic Algorithm (GA). For local optimization, a discrete adjoint variable method is used. By the successive combination of global and local optimization techniques, drag minimization is performed for a multi-body aircraft configuration while maintaining the baseline lift and the wing weight at the same time. Through the design process, performances of the test models are remarkably improved in comparison with the single stage design approach. The capability of proposed design framework including wing planform design variables can be evaluated by the drag decomposition method which can provide improvement of induced drag and wave drag, respectively.