Nonlinear Function Optimization Research Articles

An Efficient Parallel Infilling Strategy and Its Application in Sheet Metal Forming

Infilling strategies play an important role in kriging based optimization, especially when computationally expensive simulations are involved. In order to improve the efficiency of constructing a high-precision kriging model, an improved expected improvement criterion (IEI) and a parallel infilling strategy are proposed based on the maximum expected improvement (EI) criterion. In the proposed parallel infilling strategy, new sample points are generated by employing IEI criterion coupled with EI criterion. During the improved sampling process, redundant and pseudo sample are deleted in order to avoid failure of constructing a kriging model. An improved weighted particle swarm optimization (WPSO) algorithm is proposed to improve optimization efficiency. The proposed parallel infilling strategy is applied to nonlinear function optimization and variable blank holder force (VBHF) optimization in a double-c stamped part. Based on the LHD and software DYNAFORM, kriging models between the VBHF and forming quality are constructed. Compared with the initial kriging models, the meat relative error of kriging models with the proposed parallel infilling strategy for the wrinkling and average thinning rate are reduced by 95% and 55%, respectively. The optimal VBHF is obtained by the WPSO. The results show that, cracking has been completely eliminated and wrinkling has been decreased, greatly improving the forming quality of the double-c stamped part.

Adaptive Protection Strategy in a Microgrid Under Disparate Operating Modes

—Microgrids usually operate in grid-connected or islanded mode. Due to substantial variation in fault current, same protection coordination scheme cannot be applied in both modes. Moreover, network topology keeps on changing due to momentary events. In this paper, an adaptive protection strategy is proposed to avoid any miscoordination between numerical directional overcurrent relays under a fault instance. Through this scheme, the relay settings can be updated online as per the operating mode and prevailing topology. The proposed tactic employs a central protection center with data storage and programming capability, smart electronic devices and communication channels to acquire and transfer real-time data. The relay coordination problem is formulated as a non-linear optimization function, with coordination time interval constraints. The optimal relay settings under both operating modes are obtained through non-linear programming and hybrid genetic algorithm non-linear programming method. To handle contingencies of communication channel failure, a novel inclusive mode settings are also introduced to protect the system in both modes even with line or DG outages. The proposed adaptive approach is tested on a nine bus radial distribution system with DGs. It has been found that the proposed scheme provides reliable system protection under different operating scenario.

Use of Evolutionary Computation to Improve Rock Slope Back Analysis

Generally, in geotechnical engineering, back analyses are used to investigate uncertain parameters. Back analyses can be undertaken by considering known conditions, such as failure surfaces, displacements, and structural performances. Many geotechnical problems have irregular solution domains, with the objective function being non-convex, and may not be continuous functions. As such, a complex non-linear optimization function is typically required for most geotechnical problems to attain a better understanding of these uncertainties. Therefore, particle swarm optimization (PSO) and a genetic algorithm (GA) are utilized in this study to facilitate in back analyses mainly based on upper bound finite element limit analysis method. These approaches are part of evolutionary computation, which is appropriate for solving non-linear global optimization problems. By using these techniques with upper-bound finite element limit analysis (UB-FELA), two case studies showed that the results obtained are reasonable and reliable while maintaining a balance between computational time and accuracy.

The article

Normally the sum of ratios problems are reduced into a sequence of single-ratio problems and then solved by existing methods. Because of their combinatorial nature, the computational complexity grows exponentially. A sum of non-linear fractional function optimization problem with several fractions is proved to be a NP-complete problem indicating that an efficient algorithm may not exist. The non-linear sum of fractional functions are linearized by piecewise linearization technique and converted into a linear sum of fractional programming problem. Optimal solution is found at for the new problem. The number of iterations depends on the contribution of decision variables to objective function value

Multiobjective Imperialist Competitive Algorithm for Solving Nonlinear Constrained Optimization Problems

Abstract Nonlinear constrained optimization problem (NCOP) has been arisen in a diverse range of sciences such as portfolio, economic management, airspace engineering and intelligence system etc. In this paper, a new multiobjective imperialist competitive algorithm for solving NCOP is proposed. First, we review some existing excellent algorithms for solving NOCP; then, the nonlinear constrained optimization problem is transformed into a biobjective optimization problem. Second, in order to improve the diversity of evolution country swarm, and help the evolution country swarm to approach or land into the feasible region of the search space, three kinds of different methods of colony moving toward their relevant imperialist are given. Thirdly, the new operator for exchanging position of the imperialist and colony is given similar as a recombination operator in genetic algorithm to enrich the exploration and exploitation abilities of the proposed algorithm. Fourth, a local search method is also presented in order to accelerate the convergence speed. At last, the new approach is tested on thirteen well-known NP-hard nonlinear constrained optimization functions, and the experiment evidences suggest that the proposed method is robust, efficient, and generic when solving nonlinear constrained optimization problem. Compared with some other state-of-the-art algorithms, the proposed algorithm has remarkable advantages in terms of the best, mean, and worst objective function value and the standard deviations.

Mitigation Strategy for Duck Curve in High Photovoltaic Penetration Power System Using Concentrating Solar Power Station

Concentrating solar power (CSP) station is counted as a promising flexible power supply when the net load power curve is duck-shaped in high photovoltaic (PV) penetration power system, which may lead to the serious phenomenon of PV curtailment and a large-capacity power shortage. This paper presents a mitigation strategy that replaces thermal power station with CSP station to participate in the optimal operation of power system for solving the duck-shaped net load power curve problem. The proposed strategy utilizes the dispatchability of thermal storage system (TSS) and the fast output regulation of unit in the CSP station. Simultaneously, considering the operation constraints of CSP station and network security constraints of the system, an optimization model is developed to minimize the overall cost including operation and penalty. The results obtained by nonlinear optimization function demonstrate that the replacement of concentrating solar power (CSP) station contributes to reducing the PV curtailment and lost load, while increasing the available equivalent slope for power balance. Thus, the proposed mitigation strategy can promote the penetration of PV generation and improve the flexibility of power system.

An augmented animal migration optimization algorithm using worst solution elimination approach in the backdrop of differential evolution

A new algorithm has been formulated based on the basic animal migration optimization (AMO) algorithm. During the course of this proposed work it was revealed for the first time that AMO algorithm is a true replica of DEGL algorithm and when mathematical analysis was carried out the similarities were brought to notice which was till date not reported. Further during the investigation it was also witnessed that AMO algorithm in its virgin form is capable of delivering a competitive performance when applied to optimization of non-linear functions referring to CEC 2014 test suite. Such successful achievements using basic AMO algorithm inspired the present authors to take it as a challenge for exploring the possibility of improving the conventional AMO algorithm with an objective of providing it with a new shape and build an efficient framework for tackling the handicaps encountered in original AMO algorithm. In fact the incessant quest of modifying the basic algorithm gave birth to a new algorithm known as augmented animal migration optimization algorithm in the backdrop of differential evolution (AAMO-DE). The proposed algorithm even though incorporated the philosophy of Jaya algorithm,it created a memory hierarchy of worst solutions generated in each iteration. And unlike Jaya algorithm where the position update equation employ the current worst solution the proposed one picks up a random worst solution from the archive to achieve better diversity and also drops the global best term which often yields biased solutions. The proposed AAMO-DE algorithm could accomplish highly encouraging results when CEC 2014 test suite problems were subjected to validation check. The performance of the proposed algorithm was truly impressive in comparison with its counterparts comprising of state-of-the-art algorithms. In case of application to real world engineering problems the outcomes were very promising and really proves that the proposed AAMO-DE algorithm is not only a strong contender in the optimization community exhibiting excellent results but is also a potentially robust algorithm and has the ability to converge towards global optima without being trapped in local minima as evident from test examples.

Parameter estimation of Gumbel distribution using Quasi-Newton Broyden Fletcher Goldfarb Shanno (BFGS) method and its application on data of daily precipitation in Purworejo regency

Extreme data on an observation can occur due to rare events in the observation, and therefore they should be examined. One of methods to collect extreme data is block maxima. The distribution of extreme datasets collected using block maxima method is called extreme value distribution. Gumbel distribution is defined as extreme value distribution with two parameters. It is difficult to determine exact values in the parameter estimation of Gumbel distribution using maximum likelihood (ML) method. Therefore, the present research seeks to estimate the parameters using approximate solution of BFGS quasi-Newton method. The BFGS method is one of the most popular members of quasi Newton method. The purpose of this research was to determine the parameter estimation of Gumbel distribution with quasi Newton BFGS method. The quasi Newton BFGS method is a numerical method used for nonlinear function optimization without constraint so that the method can be used for parameter estimation from Gumbel distribution whose distribution function is in the form of exponential double function. The parameter estimation of the Gumbel distribution by numerical approach using the quasi Newton BFGS method is done by calculating the parameter values that make the distribution function maximum. This research is a theory research and application by studying several journals and textbooks. The results of this research we obtained the quasi Newton BFGS algorithm and estimation of Gumbel distribution parameters. Such method was applied to data of daily precipitation in Purworejo regency for the purpose of estimating the distribution parameters. The parameter estimation using ML and the quasi-Newton BFGS results in and the Gumbel distribution for period I, and and for period II, and . This indicates that high intensity and range of precipitation have decreased.

A new fusion of salp swarm with sine cosine for optimization of non-linear functions

The foremost objective of this article is to develop a novel hybrid powerful meta-heuristic that integrates the salp swarm algorithm with sine cosine algorithm (called HSSASCA) for improving the convergence performance with the exploration and exploitation being superior to other comparative standard algorithms. In this method, the position of salp swarm in the search space is updated using the position equations of sine cosine; hence the best and possible optimal solutions are obtained based on the sine or cosine function. During this process, each salp adopts the information sharing strategy of sine and cosine functions to improve their exploration and exploitation ability. The inspiration behind incorporating changes in salp swarm optimizer algorithm is to assist the basic approach to avoid premature convergence and to rapidly guide the search towards the probable search space. The algorithm is validated on 22 standard mathematical optimization functions and 3 applications namely the 3-bar truss, tension/compression spring and cantilever beam design problems. The aim is to examine and confirm the valuable behaviors of HSSASCA in searching the best solutions for optimization functions. The experimental results reveal that HSSASCA algorithm achieves the highest accuracies with least runtime in comparison with the others.

Consensus of One-Sided Lipschitz Multiagents Under Switching Topologies

This paper considers the leader-following consensus of multiagents with one-sided Lipschitz nonlinear dynamics by considering switching topologies. For the suitable selection of the consensus control gain matrix and coupling weight, a new condition for consensus is achieved for switching communication links with a directed spanning tree in the topology by constraining the dwell time. Employing a communication restoration mechanism allows a method to be obtained for the case in which a topology violates a permanent directed spanning tree. Computationally straightforward consensus controller design conditions that are necessary and sufficient for the former conditions are also developed for both cases. These simpler conditions can be used to obtain consensus protocol gains directly through convex routines. An algorithm is also provided to solve nonlinear constraints using the cone complementary linearization approach by considering a nonlinear objective function optimization problem. A numerical simulation is provided for multiagents that demonstrates the proposed control schemes’ efficiency.

Inverse Analysis of Rock Creep Model Parameters Based on Improved Simulated Annealing Differential Evolution Algorithm

In the numerical simulation of geotechnical engineering, correctly determining rock parameters is one of the keys to ensure the accuracy of calculation. However, in order to obtain high-precision rock parameters under complex conditions, the inverse analysis method is required to characterize the high nonlinearity and global searching optimization. In this paper, considering that the differential evolution (DE) algorithm has strong robustness in solving the non-convex, multi-peak and nonlinear function optimization problems, it is applied to inversion of rock parameters. At the same time, considering that single DE algorithm may fall into the local optimal problem, a simulated annealing (SA) algorithm which can accept the worsening solution with certain probability is introduced in the search process, so that the hybrid algorithm (SADE) can jump out of the local optimum and find the global optimal solution. By selecting two typical basic test functions to compare the performance of a single difference evolutionary algorithm (DE) and a differential evolution-simulated annealing algorithm (SADE), it is proved that the SADE has the capacity of jumping out of the local optimum, which makes up for the deficiency that the DE may fall into the local optimum. The numerical simulation on triaxial creep experimental models validates that the proposed SADE has faster convergence rate, better global convergence and the strong robustness for nonlinear function optimization. Application of the SADE for inversing of rock creep model parameters illustrates high accuracy and efficiency, which demonstrates the promising of the improved SADE for recognizing creep parameters of rocks under complex stress state.

Minimization of polymerization shrinkage effects on composite resins by the control of irradiance during the photoactivation process.

High levels of shrinkage stress caused by volumetric variations during the activation process are one of the main problems in the practical application of composite resins. Objective The aim of this study is to reduce the shrinkage stress and minimize the effects caused by composite resin volumetric variation due to the photopolymerization. In this way, this work proposes a systematic study to determine the optimal dimming function to be applied to light curing processes.Material and Methods The study was performed by applying mathematical techniques to the optimization of nonlinear objective functions. The effectiveness of the dimming function was evaluated by monitoring the polymerization shrinkage stress during the curing process of five brands/models of composites. This monitoring was performed on a universal testing machine using two steel bases coupled in the arms of the machine where the resin was inserted and polymerized. The quality of the composites cured by the proposed method was analyzed and compared with the conventional photoactivation method by experiments to determine their degree of conversion (DC). Absorbance measurements were performed using Fourier-transform infrared spectroscopy (FT-IR). A T-test was performed on DC results to compare the photoactivation techniques. We also used scanning electron microscopy (SEM) to analyze in-vitro the adhesion interface of the resin in human teeth.Results Our results showed that the use of the optimal dimming function, named as exponential, resulted in the significant reduction of the shrinkage stress (~36.88% ±6.56 when compared with the conventional method) without affecting the DC (t=0.86, p-value=0.44). The SEM analyses show that the proposed process can minimize or even eliminate adhesion failures between the tooth and the resin in dental restorations.Conclusion The results from this study can promote the improvement of the composite resin light curing process by the minimization of polymerization shrinkage effects, given an operational standardization of the photoactivation process.

New Method to Optimize the Production Functions in the System of Safety in Operation Management

Abstract The Safety in Operation system represents the framework within which every technological process operates. Any technological parameter - production, quality, must be analyzed in terms of this system. Mathematical and/or empirical modeling, as the first stage in the determination of the technological processes optimum operation regimes, represents a “must” both in the phase of conception, but mainly in the operation analysis phase. From this standpoint, the introduction of the active optimization method based on scheduled experiment represents an efficient tool to relieve the extreme conditions and to get information for technological processes optimum management. The work is focused on the mathematical modeling of the production function for an assembly of 13 drawing frames from two Romanian units, in terms of maintainability and reliability parameters. After determining the polynomial that characterizes the model, the work investigates the optimization of non-linear multi-variable polynomial function, and explains the context of getting the extreme values within the multi-factorial space. The work defines in its structure the notions of the safety in operation system used in research, applies quantitative study on a system from textile spinning mill field (one notices reliable operation times, break-down times, number of failures and the production of the technical systems on a pre-established time horizon); it statistically validates and mathematically optimizes the results. The theoretical approach consists in an algorithm in a unitary software application that can be used as a tool in the decision problems appeared during the technological process.

Multiobjective Imperialist Competitive Algorithm for Solving Nonlinear Constrained Optimization Problems

Nonlinear Constrained Optimization Problem (NCOP) has been arisen in a diverse range of sciences such as portfolio, economic management, airspace engineering and intelligence system etc. In this paper, a new multiobjective imperialist competitive algorithm for solving NCOP is proposed. First, we review some existing excellent algorithms for solving NOCP; then, the nonlinear constrained optimization problem is transformed into a bi objective optimization problem. Second, in order to improve the diversity of evolution country swarm and help the evolution country swarm to approach or land into the feasible region of the search space, three kinds of different methods of colony moving toward their relevant imperialist are given. Thirdly, the new operator for exchanging position of the imperialist and colony is given similar as a recombination operator in genetic algorithm to enrich the exploration and exploitation abilities of the proposed algorithm. Fourth, a local search method is also presented in order to accelerate the convergence speed. At last, the new approach is tested on thirteen well-known NP-hard nonlinear constrained optimization functions, and the experiment evidences suggest that the proposed method is robust, efficient, and generic when solving nonlinear constrained optimization problem. Compared with some other state of the art algorithms, the proposed algorithm has remarkable advantages in terms of the best, mean, and worst objective function value and the standard deviations.

RGB-D foreground extraction from a moving camera using nonlinear pixel classification

We propose a foreground extraction method from a freely moving RGB-D video camera that uses a nonlinear optimization function to classify pixels in every frame as either foreground or background. The method starts with extracting sparse features in every frame. These features are then matched to create a nonlinear optimization function that is used to label each pixel in the depth image as either foreground or background. Finally, the inverse mapping from depth to RGB data is used to extract the foreground from the RGB image. Our results show that even in the presence of high camera motion, it is possible to reliably extract the foreground from the RGB-D video data captured from a freely moving camera.

New chaotic flower pollination algorithm for unconstrained non-linear optimization functions

Flower pollination algorithm (FPA) is susceptible to local optimum and substandard precision of calculations. Chaotic operator (CO), which is used in local algorithms to optimize the best individuals in the population, can successfully enhance the properties of the flower pollination algorithm. A new chaotic flower pollination algorithm (CFPA) has been proposed in this work. Further FPA and its four proposed variants by using different chaotic maps are tested on nine mathematical benchmark functions of high dimensions. Proposed variants of CFPA are CFPA1, CFPA2, CFPA3 and CFPA4. The result of the experiment indicates that the proposed chaotic flower pollination variant CFPA2 could increase the precision of minimization of function value and CPU time to run an algorithm.

Methane OSR over Pt-Ni/δ-Al2O3: Performance and power law type kinetics

Methane oxidative steam reforming (OSR) performance of two bimetallic Pt-Ni/δ-Al2O3 catalysts, having Pt:Ni loadings, 0.2:10 and 0.3:10, were tested first. In the tests, residence time (W/F), carbon-to-oxygen (C/O2) feed ratio, and temperature were used as the experimental parameters. Increase in temperature resulted in direct and indirect - through enhanced TOX yielding higher energy - increase in SR rate. As Pt:Ni metal loading ratio did not lead to significant changes in activity, the preliminary kinetic tests to determine merely kinetically controlled region were conducted over 0.2Pt-10Ni catalyst. Considering the outcomes of the preliminary tests, the kinetic experiments were performed for practical reaction conditions extending up to 20% methane conversion with feed ratio intervals of 4.0 < C/O2 < 7.34 and 2.03 < S/C < 3.08 at two different residence time (W/F) values to obtain a power-law type rate equation. Reaction orders were estimated as 0.81, 1.60 and 0.44 for methane, oxygen and steam, respectively, by using multivariable non-linear optimization function of MATLAB™. The apparent activation energy of methane OSR was calculated as 24.61 kJ mol−1 and pre-exponential factor as 0.110 μmol mgcat−1 s−1 kPa−2.85 for the 375–450 °C temperature interval. The same analysis performed for a narrower temperature range, 375–425 °C, gave k0 and EA values as 0.251 μmol mgcat−1 s−1 kPa−2.85 and 29.17 kJ mol−1, respectively, confirming the high sensitivity of OSR pathway to temperature.

Interrogation of a spectral profile division multiplexed FBG sensor network using a modified particle swarm optimization method

This paper applies the concept of spectral profile division multiplexing to track each Bragg wavelength shift in a serially multiplexed fiber Bragg grating (FBG) network. Each sensor in the network is uniquely characterized by its own reflected spectrum shape, thus spectral overlapping is allowed in the wavelength domain. In contrast to the previous literature, spectral distortion caused by multiple reflections and spectral shadowing between FBG sensors, that occur in serial topology sensor networks, are considered in the identification algorithm. To detect the Bragg wavelength shift of each FBG, a nonlinear optimization function based on the output spectrum is constructed and a modified dynamic multi-swarm particle swarm optimizer is employed. The multiplexing approach is experimentally demonstrated on data from multiplexed sensor networks with up to four sensors. The wavelength prediction results show that the method can efficiently interrogate the multiplexed network in these overlapped situations. Specifically, the maximum error in a fully overlapped situation in the specific four sensor network demonstrated here was only 110 pm. A more general analysis of the prediction error and guidelines to optimize the sensor network are the subject of future work.

Frequency conversion sinusoidal chaotic neural network and its application

The optimization performance of transiently chaotic neural network (TCNN) is affected by various factors such as chaotic characteristic, model parameters, and annealing function, and its capacity of global optimization is limited. It is demonstrated that the non-monotonic activation function can generate richer chaotic characteristic than the monotonic activation function in the TCNN model. Besides, the activation function involving neurobiological mechanism can not only reflect the rich brain activity in brain waves, but also enhance the non-linear dynamic characteristic, which may further improve the global optimization ability. Hence, a novel chaotic neuron model is proposed with the non-monotonic activation function based on the neurobiological mechanisms from the electroencephalogram. The electroencephalogram consists of five brain waves (i.e., , , , , and waves) which are defined by the quality and intensity of brain waves with different frequency bands ranging from 0.5 Hz to 100 Hz. The brain wave with a higher frequency and a lower amplitude represents a more active brain. Researches demonstrate that the five brain waves can be simplified into sinusoidal waves with different frequencies. Hence, a frequency conversion sinusoidal (FCS) function which has the consistent frequency range and features with brain waves is designed based on the above neurobiological mechanisms. Then a novel chaotic neuron model with non-monotonic activation function which is composed of the FCS function and sigmoid function, is proposed for richer chaotic dynamic characteristic. The reversed bifurcation and the Lyapunov exponent of the chaotic neuron are given and the dynamic system is analyzed, indicating that the proposed FCS neuron model owns richer chaotic dynamic characteristic than transiently chaotic neuron model due to its special non-monotonic activation function. Based on the neuron model, a novel transiently-chaotic neural networkfrequency conversion sinusoidal chaotic neural network (FCSCNN) is constructed and the basis of model parameter selection is provided as well. To validate the effectiveness of the proposed model, the FCSCNN is applied to nonlinear function optimization and 10-city, 30-city, 75-city traveling salesman problem. The experimental results show that 1) the FCSCNN has a good performance under the condition of moderate a, smaller cA(0) and 2(0); 2) on the basis of the appropriate model parameters, the FCSCNN has better global optimization ability and optimization accuracy than Hopfield neural network, TCNN, improved-TCNN due to its richer chaotic characteristic in complicated combinational optimization problem, especially in middle and large scale problem.

Quantum-behaved particle swarm optimization with collaborative attractors for nonlinear numerical problems

In this paper, an improved quantum-behaved particle swarm optimization (CL-QPSO), which adopts a new collaborative learning strategy to generate local attractors for particles, is proposed to solve nonlinear numerical problems. Local attractors, which directly determine the convergence behavior of particles, play an important role in quantum-behaved particle swarm optimization (QPSO). In order to get a promising and efficient local attractor for each particle, a collaborative learning strategy is introduced to generate local attractors in the proposed algorithm. Collaborative learning strategy consists of two operators, namely orthogonal operator and comparison operator. For each particle, orthogonal operator is used to discover the useful information that lies in its personal and global best positions, while comparison operator is used to enhance the particle’s ability of jumping out of local optima. By using a probability parameter, the two operators cooperate with each other to generate local attractors for particles. A comprehensive comparison of CL-QPSO with some state-of-the-art evolutionary algorithms on nonlinear numeric optimization functions demonstrates the effectiveness of the proposed algorithm.