Single-objective Optimization Algorithms Research Articles

Emulous mechanism based multi-objective moth–flame optimization algorithm

In recent years, there has been growing interest in using metaheuristic algorithms to solve various complex engineering optimization problems. Most of the real-world problems comprise of more than one objective. Due to the inherent difficulty of such problems and lack of proficiency, researchers in different domains often aggregate multiple objectives and use single-objective optimization algorithms to solve them. However, the aggregation-based methods fail to solve the multi-objective problems (MOPs) effectively. Several multi-objective evolutionary algorithms (MOEAs) have been proposed and are being used to solve such problems in the past few years. In this paper, we propose an Emulous Mechanism-based multi-objective Moth–Flame Optimization (EMMFO) algorithm, where the moth positions are updated based on the pairwise competitions between the moths in each generation. The proposed EMMFO is tested on a diverse set of multi-objective benchmark functions like ZDT, DTLZ, WFG, CEC09 special session test suites and four constrained engineering design problems. The results are compared with various state-of-the-art multi-objective algorithms like NSGAII, SPEA2, PESA2, MOEA/D, MOPSO, MOACO, NSMFO, IEMO, CLPSO-LS, MOEA/D-CRA, PAL-SAPSO, and MORBABC/D. Extensive experimental results demonstrate superior optimization performance of the proposed algorithm.

Range Free Localization for Three Dimensional Wireless Sensor Networks Using Multi Objective Particle Swarm Optimization

Accurate and fast localization of randomly deployed sensor nodes is needed for many applications in wireless sensor networks. Localization also benefits in recognizing the geographically area where an event took place. There is no meaning of any event information without the knowledge of its location coordinates. DV-Hop is one of the main range free localization technique, which estimates the position of nodes using distance vector. Particle swarm optimization is suitable for the localization issues because of its fast computing speed and high precision. To further reduce the positioning error, the traditional DV-Hop localization algorithm based on single objective optimization algorithm is converted into a multi objective optimization algorithm. In our proposed scheme, we have considered six different single objective functions and three different multi objective functions. In this paper, a multi objective particle swarm optimization based DV-Hop localization is proposed in 3-dimensional wireless sensor networks. The proposed functions has been evaluated on the basis of computation time, average localization error and localization error variance. The simulation results show that our proposed multi objective function performs better as compared to traditional single objective function.

Multiobjective Optimization of 316L Laser Cladding Powder Using Gray Relational Analysis

During laser cladding of repair parts, multiple objectives must be synthesized; however, the multiobjective optimization of laser cladding is difficult. In this paper, the gray correlation of microhardness, residual stress and wear rate is established to transform these three parameters into a single-objective optimization algorithm to perform a gray correlation. By also using response surface methodology to obtain a mathematical model of the gray correlation degree, the model was analyzed and verified by analysis of variance, and the model accuracy was 90%. The optimal process parameters were determined using the gray correlation model, and the maximum gray correlation was 0.9204832, the microhardness reached 203.65 HV, the residual stress was 45.72 MPa, and the wear rate was 1923.56 μm3/N m. The phases and microstructure of the laser-cladded coating were characterized by scanning electron microscopic analysis of a sample prepared under the optimal processing parameters. This study provides guidance for the multiobjective optimization of process parameters for 316L powder cladding.

Lightning Stroke Localization – A Time-Domain Approach Based on Evolutionary Optimization

In this article we analyze a localization problem based on evolutionary optimization algorithms and an analytical electromagnetic-field-to-line coupling model. A computationally efficient, analytical model for calculating time-domain lightning-induced voltages serves as the forward solver in the optimization process. The model takes into account electric permittivity and conductivity of a lossy ground. The inverse problem is solved with the aid of a single-objective global optimization algorithm. It is demonstrated that the covariant matrix adaptation - evolution strategy algorithm shows the best performance among considered state-of-the-art algorithms. The influence of other problem parameters, e.g., the size of the search space, the fluctuation of the return-stroke pulsewidth and amplitude, and the presence of noise, on the localization error is discussed. While the growing size of the search domain has a significant impact on the convergence properties of the optimization process, this is not the case for the signal distortion, whose influence can be virtually neglected.

Success History-Based Adaptive Differential Evolution Using Turning-Based Mutation

Single objective optimization algorithms are the foundation of establishing more complex methods, like constrained optimization, niching and multi-objective algorithms. Therefore, improvements to single objective optimization algorithms are important because they can impact other domains as well. This paper proposes a method using turning-based mutation that is aimed to solve the problem of premature convergence of algorithms based on SHADE (Success-History based Adaptive Differential Evolution) in high dimensional search space. The proposed method is tested on the Single Objective Bound Constrained Numerical Optimization (CEC2020) benchmark sets in 5, 10, 15, and 20 dimensions for all SHADE, L-SHADE, and jSO algorithms. The effectiveness of the method is verified by population diversity measure and population clustering analysis. In addition, the new versions (Tb-SHADE, TbL-SHADE and Tb-jSO) using the proposed turning-based mutation get apparently better optimization results than the original algorithms (SHADE, L-SHADE, and jSO) as well as the advanced DISH and the jDE100 algorithms in 10, 15, and 20 dimensional functions, but only have advantages compared with the advanced j2020 algorithm in 5 dimensional functions.

On the Extension of the DIRECT Algorithm to Multiple Objectives

Deterministic global optimization algorithms like Piyavskii–Shubert, direct, ego and many more, have a recognized standing, for problems with many local optima. Although many single objective optimization algorithms have been extended to multiple objectives, completely deterministic algorithms for nonlinear problems with guarantees of convergence to global Pareto optimality are still missing. For instance, deterministic algorithms usually make use of some form of scalarization, which may lead to incomplete representations of the Pareto optimal set. Thus, all global Pareto optima may not be obtained, especially in nonconvex cases. On the other hand, algorithms attempting to produce representations of the globally Pareto optimal set are usually based on heuristics. We analyze the concept of global convergence for multiobjective optimization algorithms and propose a convergence criterion based on the Hausdorff distance in the decision space. Under this light, we consider the well-known global optimization algorithm direct, analyze the available algorithms in the literature that extend direct to multiple objectives and discuss possible alternatives. In particular, we propose a novel definition for the notion of potential Pareto optimality extending the notion of potential optimality defined in direct. We also discuss its advantages and disadvantages when compared with algorithms existing in the literature.

Insights into Exploration and Exploitation Power of Optimization Algorithm Using DSCTool

When making statistical analysis of single-objective optimization algorithms’ performance, researchers usually estimate it according to the obtained optimization results in the form of minimal/maximal values. Though this is a good indicator about the performance of the algorithm, it does not provide any information about the reasons why it happens. One possibility to get additional information about the performance of the algorithms is to study their exploration and exploitation abilities. In this paper, we present an easy-to-use step by step pipeline that can be used for performing exploration and exploitation analysis of single-objective optimization algorithms. The pipeline is based on a web-service-based e-Learning tool called DSCTool, which can be used for making statistical analysis not only with regard to the obtained solution values but also with regard to the distribution of the solutions in the search space. Its usage does not require any special statistic knowledge from the user. The gained knowledge from such analysis can be used to better understand algorithm’s performance when compared to other algorithms or while performing hyperparameter tuning.

A user-friendly method for constructing realistic dental model based on two-dimensional/three-dimensional registration

PurposeThis paper aims to obtain a texture dental model with real images and improve the rendering effect of the dental model.Design/methodology/approachThe paper proposes a semiautomatic method to construct a realistic dental model with real images based on two-dimensional/three-dimensional (2D/3D) registration. First, a 3D digital dental model and three intraoral images are obtained by a 3D scanner and digital single-lens reflex camera. Second, the camera projection poses for every intraoral images are calculated by using the single-objective optimization algorithm. Third, with camera poses, the preliminary projection texture mapping is performed; besides, the seam between two textures is marked. Finally, the marked regions are fused based on the image pyramid to eliminate obvious seams.FindingsThe paper provides a method to construct a realistic dental model. The method can map three intraoral images to the dental model. The experimental results show that the textured dental model without obvious distortion, dislocation and seams is constructed with simple interactions.Originality/valueThe proposed method can be applied to the digital smile design system to improve the communication efficiency between doctors, patients and technicians.

FS-MOEA: A Novel Feature Selection Algorithm for IDSs in Vehicular Networks

For Intrusion Detection Systems (IDSs) in Vehicular Ad Hoc Networks (VANETs), single-objective optimization algorithm has inherited limitations for the feature selection problem with the multiple objectives. Moreover, the imbalanced problem commonly exists in various datasets. Thus, in this paper, a feature selection algorithm based on a many-objective optimization algorithm (FS-MOEA) is proposed for IDSs in VANETs, in which Adaptive Non-dominant Sorting Genetic <xref ref-type="algorithm" rid="alg3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Algorithm-III</xref> (A-NSGA-III) serves as the many-objective optimization algorithm. Two improvements, called Bias and Weighted (B&W) niche-preservation and Information Gain (IG)-Analytic Hierarchy Process (AHP) prioritizing, are further designed in FS-MOEA. The former is used to counterbalance the imbalanced problem in datasets by assigning rare classes higher priorities, while the latter is employed to search the optimal feature subset for FS-MOEA. In IG-AHP prioritizing, a more distinct measurement, i.e. average IG, is used as the dominant factor to guide the decision analysis of AHP. Experimental results show that the proposed FS-MOEA can not only improve the performance of IDSs in VANETs but also alleviate the negative impact of the imbalanced problem.

A new combined model based on multi-objective salp swarm optimization for wind speed forecasting

Wind energy as the representative renewable energy sources attracted the global attention and wind power plays a significant role in power system. Thus, wind speed forecasting is highly critical in wind power grid management. The short-term wind speed prediction can effectively support power grid-management to reduce wind curtailments. In the past, lots of researches had often considered how to enhance the accuracy or stability in short wind speed forecasting. Nevertheless, just focus on one criterion is the inability to build an effective predictive system. In this paper, a novel combined forecasting system was proposed and effectively applied to address the issue of wind speed prediction while obtaining high precision and strong stability simultaneously at the same time. Four ANNs (artificial neural networks) were combined by the optimal weighting coefficients determined by MSSO (multi-objective salp swarm optimizer) in this system and data decomposition and denoising are included in the data preprocessing stage. The multi-objective optimization algorithm overcomes the weakness of the single-objective optimization algorithm that can only achieve one criterion. It can simultaneously optimize accuracy and stability. The 10-minute wind speed data of three data sets of Penglai, China were selected for multi-step forecasting to evaluate the effectiveness of the proposed combined model. And experimental results show that the proposed model not only achieves excellent precision and stability but also outperforms other proposed combined models.

A multi-objective perspective on performance assessment and automated selection of single-objective optimization algorithms

We build upon a recently proposed multi-objective view onto performance measurement of single-objective stochastic solvers. The trade-off between the fraction of failed runs and the mean runtime of successful runs – both to be minimized – is directly analyzed based on a study on algorithm selection of inexact state-of-the-art solvers for the famous Traveling Salesperson Problem (TSP). Moreover, we adopt the hypervolume indicator (HV) commonly used in multi-objective optimization for simultaneously assessing both conflicting objectives and investigate relations to commonly used performance indicators, both theoretically and empirically. Next to Penalized Average Runtime (PAR) and Penalized Quantile Runtime (PQR), the HV measure is used as a core concept within the construction of per-instance algorithm selection models offering interesting insights into complementary behavior of inexact TSP solvers.

Optimization algorithms for the conditions of complex catalytic reactions

A procedure was developed for the investigation of complex catalytic reactions using optimization algorithms. The first stage is a solution of the inverse problem of chemical kinetics involving the recovery of unknown parameters by single-objective optimization algorithms. In the second stage, based on the kinetic model, we solved the problem of determining the optimal conditions for the reaction resorting to multi-objective optimization algorithms. Parallelization models of computing for solving the multi-objective optimization problem are considered.

Identifying practical significance through statistical comparison of meta-heuristic stochastic optimization algorithms

In this paper, we propose an extension of a recently proposed Deep Statistical Comparison (DSC) approach, called practical Deep Statistical Comparison (pDSC), which takes into account practical significance when making a statistical comparison of meta-heuristic stochastic optimization algorithms for single-objective optimization. For achieving practical significance, two variants of the standard DSC ranking scheme are proposed. The first is called sequential pDSC, and takes into account practical significance by preprocessing of the independent optimization runs in a sequential order. The second is called Monte Carlo pDSC, and avoids any dependency of practical significance with regard to the ordering of optimization runs. The analysis of identifying practical significance on benchmark tests for single-objective problems, shows that for some cases, both variants of pDSC compared to the Chess Rating System for Evolutionary Algorithms (CRS4EAs) approach give different conclusions. Preprocessing for practical significance is carried out in a similar way, but there are cases when the conclusion for practical significance differ, which comes from the different statistical concepts used to identify practical significance.

Development and correlation analysis of non-dominated sorting buffalo optimization NSBUF II using Taguchi’s design coupled gray relational analysis and ANN

African Buffalo Optimization (ABO) is a latest bio-inspired optimization technique in the domain of evolutionary optimization, which mimics the migratory behaviour of the buffalo foraging for food across the African plains and forests. The ABO is, by now, recognized as a single-objective optimization algorithm, comprising the ability to solve both, the continuous and discrete optimization problems. However, a multi-objective version of ABO could be more useful for industrial problems. An aim is made in this article to develop the multi-objective variant of ABO, namely NSBUF II, which incorporates Pareto search for non-dominated solutions in the state space and a local search module for faster convergence. Selection of parameters for the NSBUF II is extremely sensitive to the obtained Pareto fronts. Thus, a Grey Relational Analysis (GRA) coupled with Taguchi’s L16 orthogonal array is adopted, which efficiently obtains the best set of parameters for the NSBUF II. Initially the proposed NSBUF II is tested using utilization based bi-objective production cell design problem and compared with published Multi-Objective Particle Swarm Optimization (MOPSO), and Non-dominated Sorting Genetic Algorithm (NSGA II) successfully. To analyse the performance of the NSBUF II, Self-Organizing Map (SOM) is applied, which is a powerful tool for visualizing the high-dimensional data in low dimensional maps. Applied SOM visually reveals the hidden correlational structure among the design parameters and the objective space. The performance of the NSBUF II is validated statistically NSBUF II is further verified with a real-world case obtained based on the Abrasive Water Jet Machining (AWJM) process. Validation test proves the competence of the proposed NSBUF II for real-world problem solving. The contribution of this paper is threefold. First, a novel multi-objective NSBUF II algorithm is developed. Second, a SOM based visual analysis is proposed to visualize the correlation among design parameters and Pareto fronts. Third, the NSBUF II is employed to solve a combinatorial production cell design problem followed by a real-world industrial problem.

Multi-center variable-scale search algorithm for combinatorial optimization problems with the multimodal property

Combinatorial optimization problems (COPs) are discrete problems arising from aerospace, bioinformatics, manufacturing, and other fields. One of the classic COPs is the scheduling problem. Moreover, these problems are usually multimodal optimization problems with a quantity of global and local optima. As a result, many search algorithms can easily become trapped into local optima. In this article, we propose a multi-center variable-scale search algorithm for solving both single-objective and multi-objective COPs. The algorithm consists of two distinct points. First, the multi-center strategy chooses several individuals with better performance as the only parents of the next generation, which means that there are a number of separate searching areas around the searching center. Second, the next generation of the population is produced by a variable-scale strategy with an exponential equation based on the searching center. The equation is designed to control the neighborhood scale, and adaptively realize the large-scale and small-scale searches at different search stages to balance the maintenance of diversity and convergence speed. In addition, an approach of adjusting centers is proposed concerning the number and distribution of centers for solving multi-objective COPs. Finally, the proposed algorithm is applied to three COPs, including the well-known flexible job shop scheduling problem, the unrelated parallel machine scheduling problem, and the test task scheduling problem. Both the single-objective optimization algorithm and the multi-objective optimization algorithm demonstrate competitive performance compared with existing methods.

A Method for Reducing Cogging Torque of Integrated Propulsion Motor

How to reduce the cogging torque of the integrated propeller motor is an important means to improve its noise performance because cogging torque is one of the key factors causing torque ripple. We proposed a method to reduce the cogging torque by optimizing the size of the Halbach array’s auxiliary pole. First, an analytical model for the airgap magnetic field of Halbach array based on different dimensions (including the circumference ratio and the radial thickness) of the auxiliary pole is given. Then the finite element method is used to verify the analytical model. On the basis, we calculated the cogging torque of different size of auxiliary poles as sample data by combining different circumference ratio and radial thickness. Furthermore, using the two-variable single-objective neural network genetic optimization algorithm based on Backpropagation (BP), we obtain the optimal size of the auxiliary pole. Finally, comparing the motor cogging torque and torque ripple before and after optimization indicated that the cogging torque and torque ripple are effectively reduced after optimizing the size of the auxiliary pole.

Nonlinear biobjective optimization: improvements to interval branch &amp; bound algorithms

Interval based solvers are commonly used for solving single-objective nonlinear optimization problems. Their reliability and increasing performance make them useful when proofs of infeasibility and/or certification of solutions are a must. On the other hand, there exist only a few approaches dealing with nonlinear optimization problems, when they consider multiple objectives. In this paper, we propose a new interval branch & bound algorithm for solving nonlinear constrained biobjective optimization problems. Although the general strategy is based on other works, we propose some improvements related to the termination criteria, node selection, upperbounding and discarding boxes using the non-dominated set. Most of these techniques use and/or adapt components of IbexOpt, a state-of-the-art interval-based single-objective optimization algorithm. The code of our plugin can be found in our git repository ( https://github.com/INFPUCV/ibex-lib/tree/master/plugins/optim-mop ).

A Holistic Optimization Framework for Mobile Cloud Task Scheduling

Mobile cloud computing (MCC) is extensively ubiquitous in the mobile Internet era and embraces complex environments because of the heterogeneity of devices and complexity of communications. Balancing the costs of different influencing objectives (e.g., energy consumption, system reliability, and quality of experience (QoE)) in MCC faces great challenges. This paper focuses on reasonably allocating computational tasks to suitable cores of mobile devices or cloud in MCC to minimize the total energy consumption, and maximize the system reliability and QoE. Concretely, this paper 1 proposes a holistic mobile cloud optimization model including energy consumption, system reliability, and QoE; 2 presents a DVFS-enabled and thermal-aware global energy consumption model which simultaneously considers the synergy of multiple factors concerning mobile devices, cloud, and networks; 3 constructs a tensor-based representation model to comprehensively reflect the complex relationship of multiple influencing factors and cope with their heterogeneity; and 4 proposes a customized optimization framework and two heuristic single-objective optimization (SOO) and triple-objective optimization (TOO) algorithms based on simulated annealing. Experimental results demonstrate that the proposed scheme outperforms the state-of-the-art scheduling schemes in SOO and the Pareto front in TOO can provide appropriate solutions to satisfy different application requirements.

A two-dimensional discrete fractional Fourier transform-based pansharpening scheme

ABSTRACTIn this paper, a new approach for fusion of multi-spectral (MS) and panchromatic (Pan) images based on 2D-discrete fractional Fourier transform (2D-DFRFT) is proposed. The proposed technique is closer in approach to the other filtering-based pansharpening schemes existing in the literature. In the proposed method histogram equalized Pan image is transformed using the 2D-DFRFT and further used to generate the pansharpened image using appropriate pansharpening rule. The angle parameters associated with the 2D-DFRFT provide additional degrees of freedom which are optimized by single-objective particle swarm optimization (PSO) algorithm for finding better pansharpening results. Simulation results of the proposed technique carried out in MATLAB are presented for IKONOS and GeoEye-1 satellite images and compared with existing fusion methods in terms of both visual perception and objective metrics such as Q-index (Q4), Spectral Angle Mapper (SAM), relative dimensionless global error (ERGAS) and quality with-no reference (QNR). It is observed that the proposed pansharpening scheme provides improved spectral and spatial quality as compared with the existing schemes. The effects of aliasing and mis-registration errors on the proposed method are also investigated and compared with existing pansharpening methods. It is seen that the proposed method is robust against aliasing and mis-registration errors.

A novel non-isolated positive output voltage buck-boost converter

Purpose A two switches non-isolated DC-DC novel buck-boost converter for charging the battery of electric vehicle is projected in this paper. The performance of the converter is compared with conventional buck-boost and transformer-less P/O buck-boost converter by Shan and Faqiang. The detail operation and performance analysis of the proposed converter is described both in continuous conduction mode and discontinuous conduction mode. A state space model and simulation model is designed in MATLAB. The PID controller parameters are tuned using Single-objective Salp swarm optimization algorithm using MATLAB. The controller is implemented using DSP board. The hardware and simulation results are projected in the paper to validate the effectiveness of the proposed buck-boost converter. A comparison analysis is projected among conventional converter and Shan &amp; Faqiang converter. Design/methodology/approach The converter state space model is designed and simulation model is also developed in MATALAB. The controller is implemented using DSP board. The parameters are obtained using optimization technique using SSA algorithm. The hardware design is also implemented, and the result is compared with the Shan and Faqiang converter. The efficiency of the converter is also tested. Findings The converter is providing a higher efficiency. The inductor current is also positive in both buck and boost mode. The robustness of the controller is better for a wide range of variation of input voltage because the output voltage remains almost constant. Therefore, this is very suitable for battery charging and PV module application. Practical implications For battery charging from PV module where voltage fluctuation is frequent. Social implications The authors can use household applications to charge the battery using PV module. Originality/value The converter design concept is new. Optimization is used to find the parameters of the controllers and is implemented in hardware design. The parameters obtained provide robustness in the converter performance.