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.

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

Mathematics ◽

10.3390/math8091565 ◽

2020 ◽

Vol 8 (9) ◽

pp. 1565 ◽

Cited By ~ 1

Author(s):

Xingping Sun ◽

Linsheng Jiang ◽

Yong Shen ◽

Hongwei Kang ◽

Qingyi Chen

Keyword(s):

Differential Evolution ◽

Clustering Analysis ◽

Numerical Optimization ◽

Optimization Algorithms ◽

Search Space ◽

Population Diversity ◽

Convergence Of Algorithms ◽

Adaptive Differential Evolution ◽

Complex Methods ◽

Single Objective

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.

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Solving the Traveling Salesman’s Problem Using the African Buffalo Optimization

Computational Intelligence and Neuroscience ◽

10.1155/2016/1510256 ◽

2016 ◽

Vol 2016 ◽

pp. 1-12 ◽

Cited By ~ 23

Author(s):

Julius Beneoluchi Odili ◽

Mohd Nizam Mohmad Kahar

Keyword(s):

Mathematical Model ◽

Optimization Algorithm ◽

Search Space ◽

Metaheuristic Algorithm ◽

African Buffalo ◽

Exploration And Exploitation ◽

Organizational Skills ◽

Careful Observation ◽

Good Memory

This paper proposes the African Buffalo Optimization (ABO) which is a new metaheuristic algorithm that is derived from careful observation of the African buffalos, a species of wild cows, in the African forests and savannahs. This animal displays uncommon intelligence, strategic organizational skills, and exceptional navigational ingenuity in its traversal of the African landscape in search for food. The African Buffalo Optimization builds a mathematical model from the behavior of this animal and uses the model to solve 33 benchmark symmetric Traveling Salesman’s Problem and six difficult asymmetric instances from the TSPLIB. This study shows that buffalos are able to ensure excellent exploration and exploitation of the search space through regular communication, cooperation, and good memory of its previous personal exploits as well as tapping from the herd’s collective exploits. The results obtained by using the ABO to solve these TSP cases were benchmarked against the results obtained by using other popular algorithms. The results obtained using the African Buffalo Optimization algorithm are very competitive.

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Modified chemical reaction optimization and its application in engineering problems

Mathematical Biosciences and Engineering ◽

10.3934/mbe.2021354 ◽

2021 ◽

Vol 18 (6) ◽

pp. 7143-7160

Author(s):

Shijing Ma ◽

◽

Yunhe Wang ◽

Shouwei Zhang ◽

Keyword(s):

Chemical Reactions ◽

Chemical Reaction ◽

Optimization Algorithm ◽

Optimization Algorithms ◽

Differential Evolution Algorithm ◽

Search Space ◽

Evolutionary Optimization ◽

Chemical Reaction Optimization ◽

Reaction Optimization ◽

Proposed Model

<abstract><p>Chemical Reaction Optimization (CRO) is a simple and efficient evolutionary optimization algorithm by simulating chemical reactions. As far as the current research is concerned, the algorithm has been successfully used for solving a number of real-world optimization tasks. In our paper, a new real encoded chemical reaction optimization algorithm is proposed to boost the efficiency of the optimization operations in standard chemical reactions optimization algorithm. Inspired by the evolutionary operation of the differential evolution algorithm, an improved search operation mechanism is proposed based on the underlying operation. It is modeled to further explore the search space of the algorithm under the best individuals. Afterwards, to control the perturbation frequency of the search strategy, the modification rate is increased to balance between the exploration ability and mining ability of the algorithm. Meanwhile, we also propose a new population initialization method that incorporates several models to produce high-quality initialized populations. To validate the effectiveness of the algorithm, nine unconstrained optimization algorithms are used as benchmark functions. As observed from the experimental results, it is evident that the proposed algorithm is significantly better than the standard chemical reaction algorithm and other evolutionary optimization algorithms. Then, we also apply the proposed model to address the synthesis problem of two antenna array synthesis. The results also reveal that the proposed algorithm is superior to other approaches from different perspectives.</p></abstract>

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Framework for the optimization of online computable models

COMPEL The International Journal for Computation and Mathematics in Electrical and Electronic Engineering ◽

10.1108/compel-10-2012-0211 ◽

2014 ◽

Vol 33 (3) ◽

pp. 745-758 ◽

Cited By ~ 5

Author(s):

Benoit Delinchant ◽

Frédéric Wurtz ◽

João Vasconcelos ◽

Jean-Louis Coulomb

Keyword(s):

Simulation Model ◽

Web Service ◽

Optimization Algorithm ◽

Design Methodology ◽

Optimization Algorithms ◽

Software Component ◽

The Internet ◽

Content Type ◽

Optimization Framework

Purpose – The purpose of this paper is to make easily accessible models to test and compare the optimization algorithms we develop. Design/methodology/approach – For this, the paper proposes an optimization framework based on software component, web service, and plugin to exploit these models in different environments. Findings – The paper illustrates the discussion with optimizations in Matlab™ and R (www.r-project.org) of a transformer described and exploitable from the internet. Originality/value – The originality is to make easy implementation of simulation model and optimization algorithm coupling using software component, web service, and plugin.

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A Multiobjective Mesh Optimization Algorithm for Improving the Solution Accuracy of PDE Computations

International Journal of Computational Methods ◽

10.1142/s021987621650002x ◽

2016 ◽

Vol 13 (01) ◽

pp. 1650002 ◽

Cited By ~ 2

Author(s):

Jibum Kim

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Optimization Algorithm ◽

Numerical Experiments ◽

Optimization Algorithms ◽

Mesh Optimization ◽

Partial Differential ◽

Solution Accuracy ◽

Single Objective

Mesh qualities affect both the efficiency and accuracy for solving partial differential equations (PDEs). In this paper, we present a multiobjective mesh optimization algorithm, which improves the accuracy for solving PDEs. Our algorithm is designed to simultaneously improve more than two aspects of the mesh, while being able to successfully decrease errors for solving various PDEs. Numerical experiments show that our algorithm is able to significantly decrease errors compared with existing single objective mesh optimization algorithms.

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Mexican Axolotl Optimization: A Novel Bioinspired Heuristic

Mathematics ◽

10.3390/math9070781 ◽

2021 ◽

Vol 9 (7) ◽

pp. 781

Author(s):

Yenny Villuendas-Rey ◽

José L. Velázquez-Rodríguez ◽

Mariana Dayanara Alanis-Tamez ◽

Marco-Antonio Moreno-Ibarra ◽

Cornelio Yáñez-Márquez

Keyword(s):

Computational Complexity ◽

Optimization Algorithm ◽

Optimization Algorithms ◽

Cuckoo Search ◽

Search Space ◽

Monarch Butterfly ◽

Mexican Axolotl ◽

Dragonfly Algorithm ◽

Whale Optimization ◽

Exact Optimization

When facing certain problems in science, engineering or technology, it is not enough to find a solution, but it is essential to seek and find the best possible solution through optimization. In many cases the exact optimization procedures are not applicable due to the great computational complexity of the problems. As an alternative to exact optimization, there are approximate optimization algorithms, whose purpose is to reduce computational complexity by pruning some areas of the problem search space. To achieve this, researchers have been inspired by nature, because animals and plants tend to optimize many of their life processes. The purpose of this research is to design a novel bioinspired algorithm for numeric optimization: the Mexican Axolotl Optimization algorithm. The effectiveness of our proposal was compared against nine optimization algorithms (artificial bee colony, cuckoo search, dragonfly algorithm, differential evolution, firefly algorithm, fitness dependent optimizer, whale optimization algorithm, monarch butterfly optimization, and slime mould algorithm) when applied over four sets of benchmark functions (unimodal, multimodal, composite and competition functions). The statistical analysis shows the ability of Mexican Axolotl Optimization algorithm of obtained very good optimization results in all experiments, except for composite functions, where the Mexican Axolotl Optimization algorithm exhibits an average performance.

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Improved grey wolf algorithm for optimization problems

Indonesian Journal of Electrical Engineering and Computer Science ◽

10.11591/ijeecs.v22.i3.pp1573-1579 ◽

2021 ◽

Vol 22 (3) ◽

pp. 1573

Author(s):

Hafiz Maaz Asgher ◽

Yana Mazwin Mohmad Hassim ◽

Rozaida Ghazali ◽

Muhammad Aamir

Keyword(s):

Optimization Algorithm ◽

Optimization Problem ◽

Optimization Problems ◽

Research Work ◽

Search Space ◽

Whale Optimization Algorithm ◽

Grey Wolf ◽

Exploration And Exploitation ◽

Grey Wolf Optimization ◽

Whale Optimization

The grey wolf optimization (GWO) is a nature inspired and meta-heuristic algorithm, it has successfully solved many optimization problems and give better solution as compare to other algorithms. However, due to its poor exploration capability, it has imbalance relation between exploration and exploitation. Therefore, in this research work, the poor exploration part of GWO was improved through hybrid with whale optimization algorithm (WOA) exploration. The proposed grey wolf whale optimization algorithm (GWWOA) was evaluated on five unimodal and five multimodal benchmark functions. The results shows that GWWOA offered better exploration ability and able to solve the optimization problem and give better solution in search space. Additionally, GWWOA results were well balanced and gave the most optimal in search space as compare to the standard GWO and WOA algorithms.

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Reverse guidance butterfly optimization algorithm integrated with information cross-sharing

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-210815 ◽

2021 ◽

pp. 1-22

Author(s):

Jun Luo ◽

Qin Tian ◽

Meng Xu

Keyword(s):

Local Search ◽

Optimization Algorithm ◽

Search Space ◽

Experimental Results ◽

Neighborhood Search ◽

Weight Factor ◽

Exploration And Exploitation ◽

Local Optima ◽

Slow Convergence ◽

Engineering Problems

Aiming at the disadvantages of slow convergence and the premature phenomenon of the butterfly optimization algorithm (BOA), this paper proposes a modified BOA (MBOA) called reverse guidance butterfly optimization algorithm integrated with information cross-sharing. First, the quasi-opposition concept is employed in the global search phase that lacks local exploitation capabilities to broaden the search space. Second, the neighborhood search weight factor is added in the local search stage to balance exploration and exploitation. Finally, the information cross-sharing mechanism is introduced to enhance the ability of the algorithm to jump out of the local optima. The proposed MBOA is tested in fourteen benchmark functions and three constrained engineering problems. The series of experimental results indicate that MBOA shows better performance in terms of convergence speed, convergence accuracy, stability as well as robustness.

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