Local Optimal Points Research Articles

Fibonacci multi-modal optimization algorithm in noisy environment

Noises are very common in practical optimization problems. It will cause interference on optimization algorithms and thus makes the algorithms difficult to find a true global extreme point and multiple local extreme points. For the problem, this paper proposes a Fibonacci multi-modal optimization (FMO) algorithm. Firstly, the proposed algorithm alternates between global search and local optimization in order not to fall into local optimum points and to retain multiple optimum points. And then, a Fibonacci regional scaling criterion is proposed in the FMO algorithm to alleviate the effects of noise, and the position of optimum point is determined according to its probability distribution under noise interference. In experiments, we evaluate the performance of the proposed FMO algorithm through 35 benchmark functions. The experimental results show that compared with Particle Swarm Optimization (PSO) algorithm, three improved versions of PSO, and Genetic algorithm (GA), the proposed FMO algorithm can gain more accurate location of optimum point and more global and local extreme points under noisy environment. Finally, an example of practical optimization in radio spectrum monitoring is used to show the performance of the FMO algorithm.

Energy and Exergy Evaluation of Multi-channel Photovoltaic/Thermal Hybrid System: Simulation and Experiment

In this research, a pilot study and analysis of an innovative multi-channel photovoltaic/thermal (MCPV/T) system in a geographic location (35° 44' 35'' N, 50° 57' 25'' E) has been carried out. This system consists of integrating a photovoltaic panel and two PV/T heat-sink converters. The total electrical, exergy and energy efficiencies of the system at air flow rate of 0.005 kg/s and radiation intensity of 926 w/m2 were 9.73%, 10.72%, and 47.24%, respectively. An air flow rate of 0.011 kg/s and the radiation intensity of 927 w/m2 were also achieved to be 9.35%, 10.40% and 65.10%, respectively. Based on simulation results considering experiments validations, as the air flow rate increases, the overall energy efficiency increases to the maximal amount of 80%. However, the maximum exergy efficiency value has a local optimal point of 13.46% at a fluid flow rate of 0.024 kg/s. Similarly, with increasing channel heights, the total energy efficiency decreased to 70%, and the maximum exergy efficiency has a local optimal point of 13.64% at channel height of 0.011 m. As an overall achievement, the system has higher energy quality (exergy efficiency) in laminar flow regime and has higher energy efficiency under turbulent flow conditions.

Convolutional neural networks with fractional order gradient method

This paper proposes a fractional order gradient method for the backward propagation of convolutional neural networks. To overcome the problem that fractional order gradient method cannot converge to real extreme point, a simplified fractional order gradient method is designed based on Caputo’s definition. The parameters within layers are updated by the designed gradient method, but the propagations between layers still use integer order gradients, and thus the complicated derivatives of composite functions are avoided and the chain rule will be kept. By connecting every layers in series and adding loss functions, the proposed convolutional neural networks can be trained smoothly according to various tasks. Some practical experiments are carried out in order to demonstrate fast convergence, high accuracy and ability to escape local optimal point at last.

Kinetic modeling of LPG catalytic cracking using Langmuir–Hinshelwood–Hougen–Watson theory

In this study, HZSM-5(1) and HZSM-5(2) zeolites were prepared with Al(NO3)3 and Al(OH)3 sources, respectively. Kinetic modeling of liquefied petroleum gas (LPG) cracking over synthesized HZSM-5 zeolites with different framework aluminum (Al) locations was investigated at 500–650 °C using Langmuir–Hinshelwood–Hougen–Watson theory. In a proposed LPG cracking mechanism, 26 elementary surface reaction steps including C–H and C–C protolytic cracking, hydrogen transfer, isomerization and absorption–desorption of olefins and also 2 lumped reactions for C5+ formation, were considered. Due to the existence of numerous local optimal points, genetic algorithm was employed. The estimation of kinetic parameters was performed by minimizing the mean of the sum of squares between theoretical and experimental data.

The Road is Enough! Extrinsic Calibration of Non-overlapping Stereo Camera and LiDAR using Road Information

This paper presents a framework for the targetless extrinsic calibration of stereo cameras and Light Detection and Ranging (LiDAR) sensors with a non-overlapping Field of View (FOV). In order to solve the extrinsic calibrations problem under such challenging configuration, the proposed solution exploits road markings as static and robust features among the various dynamic objects that are present in urban environment. First, this study utilizes road markings that are commonly captured by the two sensor modalities to select informative images for estimating the extrinsic parameters. In order to accomplish stable optimization, multiple cost functions are defined, including Normalized Information Distance (NID), edge alignment and, plane fitting cost. Therefore a smooth cost curve is formed for global optimization to prevent convergence to the local optimal point. We further evaluate each cost function by examining parameter sensitivity near the optimal point. Another key characteristic of extrinsic calibration, repeatability, is analyzed by conducting the proposed method multiple times with varying randomly perturbed initial points.

Developing an improved approach to solving a new gas lift optimization problem

The increased speed and accuracy in solving optimization problems of gas allocation in the gas lift process are of high importance. Solving gas allocation optimization problems generally involves two steps: (1) The gas lift performance curve (GLPC) fitting (gas lift modeling) and (2) optimizing the allocation of gas between wells. Therefore, in order to increase the speed and accuracy of solving gas allocation optimization problems, both steps need to be improved. In order to increase the accuracy of the first step, a new correlation was proposed in which, in addition to increasing the accuracy of fit, the optimization speed was improved by decreasing the number of constants used in the correlation. Besides, in order to improve the performance of the second step, water cycle optimization algorithm was used and the results obtained from this algorithm were compared with the results obtained from previous studies on teaching–learning-based optimization (TLBO) algorithm, continuous ant colony (CACO) algorithm, genetic algorithm (GA) and particle swarm optimization algorithm (PSO) for solving the five-well Nishikiori index problem. The results suggested that the water cycle optimization algorithm has a very good performance in terms of convergence rate, non-capture at local optimum points and repeatability. Finally, as a new problem, the gas allocation between the wells of one of the heavy oil fields in the southwest of Iran was optimized with predetermined oil production rates. The goal of optimization was to obtain the minimum amount of gas required to produce the predetermined oil rates using the water cycle optimization algorithm. The results showed that optimization is of higher importance in lower oil production targets, resulting in higher additional oil production.

An Improved Electromagnetic Field Optimization for the Global Optimization Problems.

Electromagnetic field optimization (EFO) is a relatively new physics-inspired population-based metaheuristic algorithm, which simulates the behavior of electromagnets with different polarities and takes advantage of a nature-inspired ratio, known as the golden ratio. In EFO, the population consists of electromagnetic particles made of electromagnets corresponding to variables of an optimization problem and is divided into three fields: positive, negative, and neutral. In each iteration, a new electromagnetic particle is generated based on the attraction-repulsion forces among these electromagnetic fields, where the repulsion force helps particle to avoid the local optimal point, and the attraction force leads to find global optimal. This paper introduces an improved version of the EFO called improved electromagnetic field optimization (iEFO). Distinct from the EFO, the iEFO has two novel modifications: new solution generation function for the electromagnets and adaptive control of algorithmic parameters. In addition to these major improvements, the boundary control and randomization procedures for the newly generated electromagnets are modified. In the computational studies, the performance of the proposed iEFO is tested against original EFO, existing physics-inspired algorithms, and state-of-the-art meta-heuristic algorithms as artificial bee colony algorithm, particle swarm optimization, and differential evolution. Obtained results are verified with statistical testing, and results reveal that proposed iEFO outperforms the EFO and other considered competitor algorithms by providing better results.

An enhanced time evolutionary optimization for solving engineering design problems

Time evolutionary optimization (TEO) is a novel population-based meta-heuristic optimization algorithm, inspired by natural selection and evolution of creatures over time. Time and the environment are two main factors of evolution at TEO. In this paper, enhanced time evolutionary optimization (ETEO) is presented. ETEO is the new version of TEO which modifies time evolutionary factor and applied population clustering. Population clustering amplified environmental factor to increase the efficiency of ETEO. For this purpose, a memory is used to save some best designs and ETEO can escape from local optimal points. The algorithm was validated by solving several constraint benchmarks and engineering design problems. The comparison results between the proposed algorithm and other metaheuristic methods contain TEO, indicate the ETEO is competitive with them, and in some cases superior to, other available heuristic methods in terms of the efficiency, faster convergence rate, robustness of finding final solution and requires a smaller number of function evaluations for solving constrained engineering problems.

Structure design of six-component strain-gauge-based transducer for minimum cross-interference via hybrid optimization methods

Cross-interference is an important performance index for multi-channel strain-gauge-based transducer. In this study, a comprehensive optimization model for minimum cross-interference while satisfying constraints of principal sensitivity and cross-sensitivity is presented for a six-component wheel force transducer (WFT) structure design. The WFT structure has a “T”-type elastic body other than the conventional Maltese cross-type. Based on structure finite element analysis and circuit analysis, the quantified principal sensitivity, cross-sensitivity, and cross-interference are discussed. Then, a mechanical-electrical multidisciplinary optimization model is constructed which has a complex objective function and many constraints. Trial computations show that this model has multiple local optimal points. Hybrid optimization methods including simulated annealing (SA) algorithm and sequence quadratic programming (SQP) algorithm are then adopted to obtain a better design. The optimization results reveal that, for the studied “T”-type transducer structure, relatively stronger lateral beam and weaker longitudinal beam are helpful to achieve low cross-interference. The performance of the optimized structure is verified by comparison with the benchmark structure and by stepwise loading. The presented comprehensive optimization model has good generality applicable to different-type multi-channel strain-gauge-based transducer structure design.

An adaptive hybrid approach: Combining genetic algorithm and ant colony optimization for integrated process planning and scheduling

Optimization algorithms can differ in performance for a specific problem. Hybrid approaches, using this difference, might give a higher performance in many cases. This paper presents a hybrid approach of Genetic Algorithm (GA) and Ant Colony Optimization (ACO) specifically for the Integrated Process Planning and Scheduling (IPPS) problems. GA and ACO have given different performances in different cases of IPPS problems. In some cases, GA has outperformed, and so do ACO in other cases. This hybrid method can be constructed as (I) GA to improve ACO results or (II) ACO to improve GA results. Based on the performances of the algorithm pairs on the given problem scale. This proposed hybrid GA-ACO approach (hAG) runs both GA and ACO simultaneously, and the better performing one is selected as the primary algorithm in the hybrid approach. hAG also avoids convergence by resetting parameters which cause algorithms to converge local optimum points. Moreover, the algorithm can obtain more accurate solutions with avoidance strategy. The new hybrid optimization technique (hAG) merges a GA with a local search strategy based on the interior point method. The efficiency of hAG is demonstrated by solving a constrained multi-objective mathematical test-case. The benchmarking results of the experimental studies with AIS (Artificial Immune System), GA, and ACO indicate that the proposed model has outperformed other non-hybrid algorithms in different scenarios.

A Mixed-Strategy-Based Whale Optimization Algorithm for Parameter Identification of Hydraulic Turbine Governing Systems with a Delayed Water Hammer Effect

For solving the parameter optimization problem of a hydraulic turbine governing system (HTGS) with a delayed water hammer (DWH) effect, a Mixed-Strategy-based Whale Optimization Algorithm (MSWOA) is proposed in this paper, in which three improved strategies are designed and integrated to promote the optimization ability. Firstly, the movement strategies of WOA have been improved to balance the exploration and exploitation. In the improved movement strategies, a dynamic ratio based on improved JAYA algorithm is applied on the strategy of searching for prey and a chaotic dynamic weight is designed for improving the strategies of bubble-net attacking and encircling prey. Secondly, a guidance of the elite’s memory inspired by Particle swarm optimization (PSO) is proposed to lead the movement of the population to accelerate the convergence speed. Thirdly, the mutation strategy based on the sinusoidal chaotic map is employed to avoid prematurity and local optimum points. The proposed MSWOA are compared with six popular meta-heuristic optimization algorithms on 23 benchmark functions in numerical experiments and the results show that the MSWOA has achieved significantly better performance than others. Finally, the MSWOA is applied on parameter identification problem of HTGS with a DWH effect, and the comparative results confirm the effectiveness and identification accuracy of the proposed method.

Global optimal constrained ICA and its application in extraction of movement related cortical potentials from single-trial EEG signals

Background and objectiveThe constrained ICA (cICA) is a recent approach which can extract the desired source signal by using prior information. cICA employs gradient-based algorithms to optimize non convex objective functions and therefore global optimum solution is not guaranteed. In this study, we propose the Global optimal constrained ICA (GocICA) algorithm for solving the conventional cICA problems. Due to the importance of movement related cortical potentials (MRCPs) for neurorehabilitation and developing a suitable mechanism for detection of movement intention, single-trial MRCP extraction is presented as an application of GocICA. MethodsIn order to evaluate the performance of the proposed technique, two kinds of datasets including simulated and real EEG data have been utilized in this paper. The GocICA method has been implemented based on the most popular meta-heuristic optimization algorithms such as Genetic Algorithm (GA), Particle Swarm Optimization (PSO) and Charged System Search (CSS) where the results have been compared with those of conventional cICA and two ICA-based methods (JADE and Infomax). ResultsIt was found that GocICA enhanced the extracted MRCP from multi-channel EEG better than both conventional cICA and ICA-based methods and also outperformed them in single-trial MRCP detection with higher true positive rates (TPRs) and lower false positive rates (FPRs). Moreover, CSS-cICA resulted in the greatest TPR (91.2232 ± 3.4708) and the lowest FPR (8.7465 ± 3.7705) for single-trial MRCP detection from real EEG data and the greatest signal-to-noise ratio (SNR) (39.2818) and the lowest mean square error (MSE) and individual performance index (IPI) (41.8230 and 0.0012, respectively) for single-trial MRCP extraction from simulated EEG data. ConclusionsThese results confirm the superiority of GocICA with respect to conventional cICA that is due to the ability of meta-heuristic optimization algorithms to escape from local optimal point. As such, GocICA is a promising new algorithm for single-trial MRCP detection which can be used for detecting other types of event related cortical potentials (ERPs) such as P300 and also for EEG artifact removal.

Trasfugen: Traffic assignment of urban network by an approximation fuzzy genetic algorithm

This paper proposes the Trasfugen method for traffic assignment aimed at solving the user equilibrium problem. To this end, the method makes use of a genetic algorithm. A fuzzy system is proposed for controlling the mutation and crossover rates of the genetic algorithm, and the corrective strategy is exploited for handling the equilibrium problem constraints. In the model, an approximation algorithm is proposed for obtaining the paths between the origin–destination pairs in the demand matrix. Unlike the traditional deterministic algorithm that has exponential time complexity, this approximation algorithm has polynomial time complexity and is executed much faster. Afterward, the Trasfugen method is applied to the urban network of Tehran metropolitan and the efficiency is investigated. Upon comparing the results obtained from the proposed model with those obtained from the conventional traffic assignment method, namely, the Frank–Wolfe method; it is shown that the proposed algorithm, while acting worse during the initial iterations, achieves better results in the subsequent iterations. Moreover, it prevents the occurrence of local optimal points as well as early/premature convergence, thus producing better results than the Frank–Wolfe algorithm.

Optimization of single and multi-areas economic dispatch problems based on evolutionary particle swarm optimization algorithm

Economic dispatch (ED) is a non-convex, non-linear, and non-smooth optimization problem that determines the optimal output power of generation units to meet the forecasted demand from an economic point of view. The objective of this study is to develop and examine the applicability of a newly developed evolutionary particle swarm optimization (E-PSO) algorithm for optimization of the ED problem, where practical constraints, namely, valve-point effects, prohibited operating zones, multiple fuel usage, dynamic ramp rate limits, transmission losses, tie-line capacity, and spinning reserve are considered. In the developed E-PSO algorithm, three operators including mutation, crossover, and selection are applied to enable the search process to skip local optimal points and enhance computational efficiency. To further enhance the performance of the algorithm, an approach is proposed to dynamically adjust the inertia, cognitive, and social weight coefficients to improve exploration and exploitation for smooth convergence. Upon validation of the E-PSO algorithm by means of standard benchmark functions, four case studies including isolated and interconnected power systems are examined and the results are compared with those from other algorithms. The findings show that the proposed features enable the E-PSO algorithm to successfully optimize the ED problem in lower simulation time, while all constraints are met.

Border-search and jump reduction method for size optimization of spatial truss structures

This paper proposes a sensitivity-based border-search and jump reduction method for optimum design of spatial trusses. It is considered as a two-phase optimization approach, where at the first phase, the first local optimum is found by few analyses, after the whole searching space is limited employing an efficient random strategy, and the second phase involves finding a sequence of local optimum points using the variables sensitivity with respect to corresponding values of constraints violation. To reach the global solution at phase two, a sequence of two sensitivity-based operators of border-search operator and jump operator are introduced until convergence is occurred. Sensitivity analysis is performed using numerical finite difference method. To do structural analysis, a link between open source software of OpenSees and MATLAB was developed. Spatial truss problems were attempted for optimization in order to show the fastness and efficiency of proposed technique. Results were compared with those reported in the literature. It shows that the proposed method is competitive with the other optimization methods with a significant reduction in number of analyses carried.

Iterative timing-induced interference suppression in a two-tier OFDMA uplink network

Consider a scenario in a two-tier cellular network wherein all subscribers adjust their transmission-times to be synchronously received at the macro base-station (MBS). This transmission timing arrangement causes asynchronous reception of signals and inter-carrier interference (ICI) at the femto base-station (FBS). In this paper, an iterative interference suppression scheme for reducing the ICI at the FBS is presented. By assuming a number of macro-users (MUs) and a single femto-user (FU), the mean square error (MSE) cost-function is first defined, based on which, the closed-forms for 3 underlying parameters, i.e., precoder, equalizer and the automatic gain controller are then derived by proposing a partial derivative-based sub-optimization scheme. To counteract the interrelation of the aforementioned parameters, an iterative algorithm is further proposed which results in finding a local-optimum point of the cost-function. To demonstrate the successful interference suppression performance of the proposed scheme, a per-subcarrier interference power analysis is also derived. The simulation results demonstrate a reasonable convergence after 6 iterations. Moreover, for the proposed scheme, a close bit error rate (BER) performance to that of a system without any timing-induced interference at low and medium SNRs (i.e., <20 dB) and a comparable performance at higher SNRs (i.e., 20 dB & <30 dB) are observed.

Optimal retrofit and debottlenecking using novel multi-effect dividing wall column

This paper proposes several novel multi-effect dividing wall column (MEDWC) configurations to retrofit and debottleneck side-stream columns or two-column sequences for multiple objectives such as increasing the column throughput, maximizing energy efficiency, and reducing carbon dioxide (CO2) emissions. This paper also proposes a new practical method that employs a coordinate descent methodology, which is assisted by a random search to avoid local optimal points and box search to overlook more promising solutions for optimal retrofitting. One industrial case was studied and analyzed to demonstrate the proposed configuration. The results show that the proposed modified coordinate descent methodology not only effectively avoided the local optimal points but also overlooked more promising solutions. The proposed method is competitive with the coordinate descent methodology and response surface methodology, which are popular optimization methods used in the chemical process industry. Both the structural and operating variables are effectively and simultaneously optimized. The proposed MEDWC sequence removes the bottleneck problem effectively and achieves substantial energy savings and CO2 emissions reduction. Notably, a 73.2% and 73.6% reduction in operating costs and CO2 emissions, respectively, can be achieved in the ethylene dichloride separation processes. The proposed configuration can be applied to both close-boiling and wide-boiling mixtures.

Application of SiO2–water nanofluid to enhance oil recovery

The present study aims to investigate effects of nanofluid flooding on EOR and also compares its performance with water flooding in field scale using the published experimental data provided from core-scale studies. The nanofluid is based on water including silica nanoparticles. The relative permeability curves of water, nanofluid and oil for a light crude oil core sample obtained in an experimental study are used in this numerical investigation. A 2D heterogeneous reservoir model is constructed using the permeability and porosity of the last layer of SPE-10 model. It has been shown that nanofluid flooding can substantially improve the oil recovery in comparison with the water flooding case. Afterward, the operational parameters of the 13 injection and production wells have been optimized in order to meet the maximum cumulative oil production. First, pattern search (PS) algorithm was implemented which has a good convergence speed, but with a high probability of trapping in local optimum points. Particle swarm optimization (PSO) approach has also been employed, which requires a large number of population (to approach the global optimum) with so many simulations. Accordingly, a hybrid PSO–PS algorithm with confined domain is proposed. The hybrid algorithm starts with PSO and depending on the distribution density of the values of each parameter, confines the searching domain and provides a proper initial guess to be used by PS. It is concluded that the hybrid PSO–PS method could obtain the optimal solution with a high convergence speed and reduced possibility of trapping in local optimums.

Identification of realistic distillation column using hybrid particle swarm optimization and NARX based artificial neural network

Nonlinear identification of a distillation column is a challenging problem in the process industry. The performance of the controller of nonlinear and dynamic columns can be viewed or analyzed using this type of identification. In this work, a novel method is proposed for the identification of a distillation column using hybrid PSO (particle swarm optimization) and ANN (artificial neural network). Since the real distillation column is dynamic in nature, this hybrid system is used as a nonlinear function in NARX (nonlinear autoregressive with exogenous input) structure. This hybrid NARX model is called PSO-NARX-ANN. In PSO-NARX-ANN, NARX-ANN is trained by using the PSO algorithm. The PSO training process has the advantage of training neural network without getting trapped at local optimal points. Reflux rate and reboiler temperature were used as variable inputs while the top and the bottom compositions (mole fractions) were used as variable outputs. The column was realistically simulated in HYSYS process simulation software and data was generated. To ensure robustness and accuracy, 750 of the 1000 samples of data collected from HYSYS were used for training, and the remaining 250 samples of data were used for validation of the proposed model. The performance of proposed model compared with (back propagation) BP-ANN, NARX-BP-ANN, and PSO-ANN. The results showed that PSO-NARX-ANN outperformed all others.

Electricity scheduling strategy for home energy management system with renewable energy and battery storage: a case study

With the development of smart grid, energy consumption on residence will play an important role in the electricity market, while the Home Energy Management System (HEMS) has huge potential to help energy conservation. In this study, a practical HEMS model with renewable energy, storage devices and plug-in electric vehicles, considering the battery sustainability and the full utilisation of the renewable energy, is first established. Then, according to the combinations of the genetic algorithm (GA) and the multi-constrained integer programming method, an improved GA is proposed, which goal is to minimise the electricity purchase and maximise the renewable energy utilisation. Finally, it is demonstrated by an example that the proposed method is significant in cost saving and reducing energy wastes. To verify the performances of the proposed algorithm, the numerical results indicate that the proposed algorithm has high computational efficiency and good robustness. In addition, it can avoid the disadvantages easy to trap at a local optimal point, and are insensitive to initial solutions. The effect of the storage device on system property and the sensitivity of cost savings versus demand response, size of the battery, and the electricity price sell to the grid are also analysed.