scholarly journals A Simplified Hypervolume-Based Evolutionary Algorithm for Many-Objective Optimization

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Hong Ji ◽  
Cai Dai
Keyword(s):  
Optimization Problems ◽  
State Of The Art ◽  
Main Idea ◽  
Nearest Neighbors ◽  
Computational Effort ◽  
Test Functions ◽  
Particular Solution ◽  
Selection Operator ◽  
Update Strategy ◽  
External Population

Evolutionary algorithms based on hypervolume have demonstrated good performance for solving many-objective optimization problems. However, hypervolume needs prohibitively expensive computational effort. This paper proposes a simplified hypervolume calculation method which can be used to roughly evaluate the convergence and diversity of solutions. The main idea is to use the nearest neighbors of a particular solution to calculate the volume as the solution’s hypervolume value. Moreover, this paper improves the selection operator and the update strategy of external population according to the simplified hypervolume. Then, the proposed algorithm (SHEA) is compared with some state-of-the-art algorithms on fifteen test functions of CEC2018 MaOP competition, and the experimental results prove the feasibility of the proposed algorithm.

scholarly journals A Hybrid Whale Optimization Algorithm for Global Optimization

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1477
Author(s):  
Chun-Yao Lee ◽  
Guang-Lin Zhuo
Keyword(s):  
Global Optimization ◽  
Optimization Algorithm ◽  
Optimization Problems ◽  
Whale Optimization Algorithm ◽  
Initial Population ◽  
Test Functions ◽  
Benchmark Test ◽  
Thermal Exchange ◽  
Whale Optimization ◽  
Benchmark Test Functions

This paper proposes a hybrid whale optimization algorithm (WOA) that is derived from the genetic and thermal exchange optimization-based whale optimization algorithm (GWOA-TEO) to enhance global optimization capability. First, the high-quality initial population is generated to improve the performance of GWOA-TEO. Then, thermal exchange optimization (TEO) is applied to improve exploitation performance. Next, a memory is considered that can store historical best-so-far solutions, achieving higher performance without adding additional computational costs. Finally, a crossover operator based on the memory and a position update mechanism of the leading solution based on the memory are proposed to improve the exploration performance. The GWOA-TEO algorithm is then compared with five state-of-the-art optimization algorithms on CEC 2017 benchmark test functions and 8 UCI repository datasets. The statistical results of the CEC 2017 benchmark test functions show that the GWOA-TEO algorithm has good accuracy for global optimization. The classification results of 8 UCI repository datasets also show that the GWOA-TEO algorithm has competitive results with regard to comparison algorithms in recognition rate. Thus, the proposed algorithm is proven to execute excellent performance in solving optimization problems.

scholarly journals GMBO: Group Mean-Based Optimizer for Solving Various Optimization Problems

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1190
Author(s):  
Mohammad Dehghani ◽  
Zeinab Montazeri ◽  
Štěpán Hubálovský
Keyword(s):  
Optimization Algorithm ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Random Search ◽  
Optimization Algorithms ◽  
Gravitational Search Algorithm ◽  
Main Idea ◽  
Population Based ◽  
Grey Wolf Optimizer ◽  
Whale Optimization

There are many optimization problems in the different disciplines of science that must be solved using the appropriate method. Population-based optimization algorithms are one of the most efficient ways to solve various optimization problems. Population-based optimization algorithms are able to provide appropriate solutions to optimization problems based on a random search of the problem-solving space without the need for gradient and derivative information. In this paper, a new optimization algorithm called the Group Mean-Based Optimizer (GMBO) is presented; it can be applied to solve optimization problems in various fields of science. The main idea in designing the GMBO is to use more effectively the information of different members of the algorithm population based on two selected groups, with the titles of the good group and the bad group. Two new composite members are obtained by averaging each of these groups, which are used to update the population members. The various stages of the GMBO are described and mathematically modeled with the aim of being used to solve optimization problems. The performance of the GMBO in providing a suitable quasi-optimal solution on a set of 23 standard objective functions of different types of unimodal, high-dimensional multimodal, and fixed-dimensional multimodal is evaluated. In addition, the optimization results obtained from the proposed GMBO were compared with eight other widely used optimization algorithms, including the Marine Predators Algorithm (MPA), the Tunicate Swarm Algorithm (TSA), the Whale Optimization Algorithm (WOA), the Grey Wolf Optimizer (GWO), Teaching–Learning-Based Optimization (TLBO), the Gravitational Search Algorithm (GSA), Particle Swarm Optimization (PSO), and the Genetic Algorithm (GA). The optimization results indicated the acceptable performance of the proposed GMBO, and, based on the analysis and comparison of the results, it was determined that the GMBO is superior and much more competitive than the other eight algorithms.

scholarly journals Investigation of Improved Cooperative Coevolution for Large-Scale Global Optimization Problems

Algorithms ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 146
Author(s):  
Aleksei Vakhnin ◽  
Evgenii Sopov
Keyword(s):  
Global Optimization ◽  
Evolutionary Algorithms ◽  
Numerical Experiments ◽  
Large Scale ◽  
Optimization Problems ◽  
State Of The Art ◽  
Fixed Number ◽  
High Dimensional ◽  
Cooperative Coevolution ◽  
Large Scale Problems

Modern real-valued optimization problems are complex and high-dimensional, and they are known as “large-scale global optimization (LSGO)” problems. Classic evolutionary algorithms (EAs) perform poorly on this class of problems because of the curse of dimensionality. Cooperative Coevolution (CC) is a high-performed framework for performing the decomposition of large-scale problems into smaller and easier subproblems by grouping objective variables. The efficiency of CC strongly depends on the size of groups and the grouping approach. In this study, an improved CC (iCC) approach for solving LSGO problems has been proposed and investigated. iCC changes the number of variables in subcomponents dynamically during the optimization process. The SHADE algorithm is used as a subcomponent optimizer. We have investigated the performance of iCC-SHADE and CC-SHADE on fifteen problems from the LSGO CEC’13 benchmark set provided by the IEEE Congress of Evolutionary Computation. The results of numerical experiments have shown that iCC-SHADE outperforms, on average, CC-SHADE with a fixed number of subcomponents. Also, we have compared iCC-SHADE with some state-of-the-art LSGO metaheuristics. The experimental results have shown that the proposed algorithm is competitive with other efficient metaheuristics.

scholarly journals Chi-Squared Distance Metric Learning for Histogram Data

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Wei Yang ◽  
Luhui Xu ◽  
Xiaopan Chen ◽  
Fengbin Zheng ◽  
Yang Liu
Keyword(s):  
Nearest Neighbor ◽  
State Of The Art ◽  
Metric Learning ◽  
Nearest Neighbors ◽  
Distance Metric Learning ◽  
Distance Metric ◽  
Projected Gradient Method ◽  
Proper Distance ◽  
Chi Squared ◽  
Real World Datasets

Learning a proper distance metric for histogram data plays a crucial role in many computer vision tasks. The chi-squared distance is a nonlinear metric and is widely used to compare histograms. In this paper, we show how to learn a general form of chi-squared distance based on the nearest neighbor model. In our method, the margin of sample is first defined with respect to the nearest hits (nearest neighbors from the same class) and the nearest misses (nearest neighbors from the different classes), and then the simplex-preserving linear transformation is trained by maximizing the margin while minimizing the distance between each sample and its nearest hits. With the iterative projected gradient method for optimization, we naturally introduce thel2,1norm regularization into the proposed method for sparse metric learning. Comparative studies with the state-of-the-art approaches on five real-world datasets verify the effectiveness of the proposed method.

A Novel Approach to Designing Surrogate-assisted Genetic Algorithms by Combining Efficient Learning of Walsh Coefficients and Dependencies

2021 ◽  
Vol 1 (2) ◽  
pp. 1-23
Author(s):  
Arkadiy Dushatskiy ◽  
Tanja Alderliesten ◽  
Peter A. N. Bosman
Keyword(s):  
Boolean Functions ◽  
Surrogate Model ◽  
Optimization Problems ◽  
State Of The Art ◽  
Fitness Function ◽  
Optimal Solution ◽  
Problem Structure ◽  
Novel Approach ◽  
Efficient Learning ◽  
Nk Landscapes

Surrogate-assisted evolutionary algorithms have the potential to be of high value for real-world optimization problems when fitness evaluations are expensive, limiting the number of evaluations that can be performed. In this article, we consider the domain of pseudo-Boolean functions in a black-box setting. Moreover, instead of using a surrogate model as an approximation of a fitness function, we propose to precisely learn the coefficients of the Walsh decomposition of a fitness function and use the Walsh decomposition as a surrogate. If the coefficients are learned correctly, then the Walsh decomposition values perfectly match with the fitness function, and, thus, the optimal solution to the problem can be found by optimizing the surrogate without any additional evaluations of the original fitness function. It is known that the Walsh coefficients can be efficiently learned for pseudo-Boolean functions with k -bounded epistasis and known problem structure. We propose to learn dependencies between variables first and, therefore, substantially reduce the number of Walsh coefficients to be calculated. After the accurate Walsh decomposition is obtained, the surrogate model is optimized using GOMEA, which is considered to be a state-of-the-art binary optimization algorithm. We compare the proposed approach with standard GOMEA and two other Walsh decomposition-based algorithms. The benchmark functions in the experiments are well-known trap functions, NK-landscapes, MaxCut, and MAX3SAT problems. The experimental results demonstrate that the proposed approach is scalable at the supposed complexity of O (ℓ log ℓ) function evaluations when the number of subfunctions is O (ℓ) and all subfunctions are k -bounded, outperforming all considered algorithms.

Solving Mono- and Multi-Objective Problems Using Hybrid Evolutionary Algorithms and Nelder-Mead Method

2021 ◽  
Vol 12 (4) ◽  
pp. 98-116
Author(s):  
Noureddine Boukhari ◽  
Fatima Debbat ◽  
Nicolas Monmarché ◽  
Mohamed Slimane
Keyword(s):  
Convergence Rate ◽  
Optimization Problem ◽  
Optimization Problems ◽  
State Of The Art ◽  
Hybrid Approach ◽  
Optimization Methods ◽  
Global Optimum ◽  
Stochastic Methods ◽  
Local Optima ◽  
Portfolio Optimization Problem

Evolution strategies (ES) are a family of strong stochastic methods for global optimization and have proved their capability in avoiding local optima more than other optimization methods. Many researchers have investigated different versions of the original evolution strategy with good results in a variety of optimization problems. However, the convergence rate of the algorithm to the global optimum stays asymptotic. In order to accelerate the convergence rate, a hybrid approach is proposed using the nonlinear simplex method (Nelder-Mead) and an adaptive scheme to control the local search application, and the authors demonstrate that such combination yields significantly better convergence. The new proposed method has been tested on 15 complex benchmark functions and applied to the bi-objective portfolio optimization problem and compared with other state-of-the-art techniques. Experimental results show that the performance is improved by this hybridization in terms of solution eminence and strong convergence.

scholarly journals Differential Evolution: A Survey and Analysis

2018 ◽  
Vol 8 (10) ◽  
pp. 1945 ◽  
Author(s):  
Tarik Eltaeib ◽  
Ausif Mahmood
Keyword(s):  
Global Optimization ◽  
Differential Evolution ◽  
Optimization Problems ◽  
State Of The Art ◽  
Population Based ◽  
Vital Role ◽  
Fine Tuning ◽  
Control Parameters ◽  
Hybrid Techniques ◽  
Global Optimizer

Differential evolution (DE) has been extensively used in optimization studies since its development in 1995 because of its reputation as an effective global optimizer. DE is a population-based metaheuristic technique that develops numerical vectors to solve optimization problems. DE strategies have a significant impact on DE performance and play a vital role in achieving stochastic global optimization. However, DE is highly dependent on the control parameters involved. In practice, the fine-tuning of these parameters is not always easy. Here, we discuss the improvements and developments that have been made to DE algorithms. In particular, we present a state-of-the-art survey of the literature on DE and its recent advances, such as the development of adaptive, self-adaptive and hybrid techniques.

scholarly journals Correlation Tracking via Self-Adaptive Fusion of Multiple Features

Information ◽  
2018 ◽  
Vol 9 (10) ◽  
pp. 241 ◽  
Author(s):  
Zhi Chen ◽  
Peizhong Liu ◽  
Yongzhao Du ◽  
Yanmin Luo ◽  
Wancheng Zhang
Keyword(s):  
State Of The Art ◽  
Correlation Filter ◽  
Multiple Features ◽  
Multi Scale ◽  
Tracking Algorithms ◽  
Model Update ◽  
Adaptive Fusion ◽  
Tracking Model ◽  
Update Strategy ◽  
Self Adaptive

Correlation filter (CF) based tracking algorithms have shown excellent performance in comparison to most state-of-the-art algorithms on the object tracking benchmark (OTB). Nonetheless, most CF based tracking algorithms only consider limited single channel feature, and the tracking model always updated from frame-by-frame. It will generate some erroneous information when the target objects undergo sophisticated scenario changes, such as background clutter, occlusion, out-of-view, and so forth. Long-term accumulation of erroneous model updating will cause tracking drift. In order to address problems that are mentioned above, in this paper, we propose a robust multi-scale correlation filter tracking algorithm via self-adaptive fusion of multiple features. First, we fuse powerful multiple features including histogram of oriented gradients (HOG), color name (CN), and histogram of local intensities (HI) in the response layer. The weights assigned according to the proportion of response scores that are generated by each feature, which achieve self-adaptive fusion of multiple features for preferable feature representation. In the meantime the efficient model update strategy is proposed, which is performed by exploiting a pre-defined response threshold as discriminative condition for updating tracking model. In addition, we introduce an accurate multi-scale estimation method integrate with the model update strategy, which further improves the scale variation adaptability. Both qualitative and quantitative evaluations on challenging video sequences demonstrate that the proposed tracker performs superiorly against the state-of-the-art CF based methods.

scholarly journals Multi-Agent Systems Applications in Energy Optimization Problems: A State-of-the-Art Review

Energies ◽  
2018 ◽  
Vol 11 (8) ◽  
pp. 1928 ◽  
Author(s):  
Alfonso González-Briones ◽  
Fernando De La Prieta ◽  
Mohd Mohamad ◽  
Sigeru Omatu ◽  
Juan Corchado
Keyword(s):  
Optimization Problems ◽  
State Of The Art ◽  
Smart Cities ◽  
Energy Optimization ◽  
Sensor Data ◽  
Multi Agent Systems ◽  
Agent Systems ◽  
Research Perspectives ◽  
Wide Range ◽  
Multi Agent

This article reviews the state-of-the-art developments in Multi-Agent Systems (MASs) and their application to energy optimization problems. This methodology and related tools have contributed to changes in various paradigms used in energy optimization. Behavior and interactions between agents are key elements that must be understood in order to model energy optimization solutions that are robust, scalable and context-aware. The concept of MAS is introduced in this paper and it is compared with traditional approaches in the development of energy optimization solutions. The different types of agent-based architectures are described, the role played by the environment is analysed and we look at how MAS recognizes the characteristics of the environment to adapt to it. Moreover, it is discussed how MAS can be used as tools that simulate the results of different actions aimed at reducing energy consumption. Then, we look at MAS as a tool that makes it easy to model and simulate certain behaviors. This modeling and simulation is easily extrapolated to the energy field, and can even evolve further within this field by using the Internet of Things (IoT) paradigm. Therefore, we can argue that MAS is a widespread approach in the field of energy optimization and that it is commonly used due to its capacity for the communication, coordination, cooperation of agents and the robustness that this methodology gives in assigning different tasks to agents. Finally, this article considers how MASs can be used for various purposes, from capturing sensor data to decision-making. We propose some research perspectives on the development of electrical optimization solutions through their development using MASs. In conclusion, we argue that researchers in the field of energy optimization should use multi-agent systems at those junctures where it is necessary to model energy efficiency solutions that involve a wide range of factors, as well as context independence that they can achieve through the addition of new agents or agent organizations, enabling the development of energy-efficient solutions for smart cities and intelligent buildings.

scholarly journals Generalized F(R, T) cosmological models with fermionic fields

2021 ◽  
Vol 2090 (1) ◽  
pp. 012063
Author(s):  
Koblandy Yerzhanov ◽  
Gulnur Bauyrzhan ◽  
Ratbay Myrzakulov
Keyword(s):  
Mathematical Model ◽  
Cosmological Model ◽  
Main Idea ◽  
Scale Factor ◽  
Specific Form ◽  
Fermion Field ◽  
Fermionic Fields ◽  
Particular Solution ◽  
The Universe ◽  
Symmetry Method

Abstract We investigated the gravity model F (R, T), which interacts with a fermion field in a uniform and isotropic at spacetime FLRW. The main idea and purpose of the work donewas to create a mathematical model and find a particular solution for the scale factor a, since it describes the dynamics of the evolution of the Universe. The solutions for this universe are obtained using the Noether symmetry method. With its help, a specific form of the Lagrangian is obtained. And the possible types of the scale factor were found. The evolution of the resulting cosmological model has been investigated.

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