A Hybrid Butterfly Optimization Algorithm for Numerical Optimization Problems

The butterfly optimization algorithm (BOA) is a swarm-based metaheuristic algorithm inspired by the foraging behaviour and information sharing of butterflies. BOA has been applied to various fields of optimization problems due to its performance. However, BOA also suffers from drawbacks such as diminished population diversity and the tendency to get trapped in local optimum. In this paper, a hybrid butterfly optimization algorithm based on a Gaussian distribution estimation strategy, called GDEBOA, is proposed. A Gaussian distribution estimation strategy is used to sample dominant population information and thus modify the evolutionary direction of butterfly populations, improving the exploitation and exploration capabilities of the algorithm. To evaluate the superiority of the proposed algorithm, GDEBOA was compared with six state-of-the-art algorithms in CEC2017. In addition, GDEBOA was employed to solve the UAV path planning problem. The simulation results show that GDEBOA is highly competitive.

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Improved Particle Swarm Optimization Algorithm and its Application Based on the Aggregation Degree

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.427-429.1934 ◽

2013 ◽

Vol 427-429 ◽

pp. 1934-1938

Author(s):

Zhong Rong Zhang ◽

Jin Peng Liu ◽

Ke De Fei ◽

Zhao Shan Niu

Keyword(s):

Particle Swarm Optimization ◽

Optimization Algorithm ◽

Particle Swarm Optimization Algorithm ◽

Optimization Problems ◽

Particle Swarm ◽

Population Diversity ◽

Function Optimization ◽

Local Optimum ◽

Swarm Optimization ◽

Improved Particle Swarm Optimization

The aim is to improve the convergence of the algorithm, and increase the population diversity. Adaptively particles of groups fallen into local optimum is adjusted in order to realize global optimal. by judging groups spatial location of concentration and fitness variance. At the same time, the global factors are adjusted dynamically with the action of the current particle fitness. Four typical function optimization problems are drawn into simulation experiment. The results show that the improved particle swarm optimization algorithm is convergent, robust and accurate.

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An Improved Whale Optimization Algorithm for the Traveling Salesman Problem

Symmetry ◽

10.3390/sym13010048 ◽

2020 ◽

Vol 13 (1) ◽

pp. 48

Author(s):

Jin Zhang ◽

Li Hong ◽

Qing Liu

Keyword(s):

Traveling Salesman Problem ◽

Optimization Algorithm ◽

Optimization Problems ◽

Relevant Literature ◽

Population Diversity ◽

Traveling Salesman ◽

Whale Optimization Algorithm ◽

Neighborhood Search ◽

Whale Optimization ◽

The Traveling Salesman Problem

The whale optimization algorithm is a new type of swarm intelligence bionic optimization algorithm, which has achieved good optimization results in solving continuous optimization problems. However, it has less application in discrete optimization problems. A variable neighborhood discrete whale optimization algorithm for the traveling salesman problem (TSP) is studied in this paper. The discrete code is designed first, and then the adaptive weight, Gaussian disturbance, and variable neighborhood search strategy are introduced, so that the population diversity and the global search ability of the algorithm are improved. The proposed algorithm is tested by 12 classic problems of the Traveling Salesman Problem Library (TSPLIB). Experiment results show that the proposed algorithm has better optimization performance and higher efficiency compared with other popular algorithms and relevant literature.

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An improved arithmetic optimization algorithm with forced switching mechanism for global optimization problems

Mathematical Biosciences and Engineering ◽

10.3934/mbe.2022023 ◽

2022 ◽

Vol 19 (1) ◽

pp. 473-512

Author(s):

Rong Zheng ◽

◽

Heming Jia ◽

Laith Abualigah ◽

Qingxin Liu ◽

...

Keyword(s):

Optimization Algorithm ◽

Optimization Problems ◽

Heuristic Method ◽

Population Diversity ◽

Test Functions ◽

Design Problems ◽

Local Optima ◽

Switching Mechanism ◽

Engineering Design Problems

<abstract> <p>Arithmetic optimization algorithm (AOA) is a newly proposed meta-heuristic method which is inspired by the arithmetic operators in mathematics. However, the AOA has the weaknesses of insufficient exploration capability and is likely to fall into local optima. To improve the searching quality of original AOA, this paper presents an improved AOA (IAOA) integrated with proposed forced switching mechanism (FSM). The enhanced algorithm uses the random math optimizer probability (<italic>RMOP</italic>) to increase the population diversity for better global search. And then the forced switching mechanism is introduced into the AOA to help the search agents jump out of the local optima. When the search agents cannot find better positions within a certain number of iterations, the proposed FSM will make them conduct the exploratory behavior. Thus the cases of being trapped into local optima can be avoided effectively. The proposed IAOA is extensively tested by twenty-three classical benchmark functions and ten CEC2020 test functions and compared with the AOA and other well-known optimization algorithms. The experimental results show that the proposed algorithm is superior to other comparative algorithms on most of the test functions. Furthermore, the test results of two training problems of multi-layer perceptron (MLP) and three classical engineering design problems also indicate that the proposed IAOA is highly effective when dealing with real-world problems.</p> </abstract>

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Hybrid Algorithm Based on Ant Colony Optimization and Simulated Annealing Applied to the Dynamic Traveling Salesman Problem

Entropy ◽

10.3390/e22080884 ◽

2020 ◽

Vol 22 (8) ◽

pp. 884

Author(s):

Petr Stodola ◽

Karel Michenka ◽

Jan Nohel ◽

Marian Rybanský

Keyword(s):

Simulated Annealing ◽

Ant Colony Optimization ◽

Traveling Salesman Problem ◽

Optimization Problems ◽

Dynamic Environment ◽

Population Diversity ◽

Traveling Salesman ◽

Ant Colony ◽

Local Optimum ◽

Use Of Knowledge

The dynamic traveling salesman problem (DTSP) falls under the category of combinatorial dynamic optimization problems. The DTSP is composed of a primary TSP sub-problem and a series of TSP iterations; each iteration is created by changing the previous iteration. In this article, a novel hybrid metaheuristic algorithm is proposed for the DTSP. This algorithm combines two metaheuristic principles, specifically ant colony optimization (ACO) and simulated annealing (SA). Moreover, the algorithm exploits knowledge about the dynamic changes by transferring the information gathered in previous iterations in the form of a pheromone matrix. The significance of the hybridization, as well as the use of knowledge about the dynamic environment, is examined and validated on benchmark instances including small, medium, and large DTSP problems. The results are compared to the four other state-of-the-art metaheuristic approaches with the conclusion that they are significantly outperformed by the proposed algorithm. Furthermore, the behavior of the algorithm is analyzed from various points of view (including, for example, convergence speed to local optimum, progress of population diversity during optimization, and time dependence and computational complexity).

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GIS-Based Niche Hybrid Bat Algorithm for Solving Optimal Spatial Search

Mathematical Problems in Engineering ◽

10.1155/2020/2843436 ◽

2020 ◽

Vol 2020 ◽

pp. 1-11

Author(s):

Guoming Du ◽

Yangbo Chen ◽

Wei Sun

Keyword(s):

Optimization Problems ◽

Bat Algorithm ◽

Population Diversity ◽

Premature Convergence ◽

Local Optimum ◽

Guangzhou City ◽

Location Allocation ◽

Geographic Space ◽

Spatial Search ◽

Gis Technique

Complex nonlinear optimization problems are involved in optimal spatial search, such as location allocation problems that occur in multidimensional geographic space. Such search problems are generally difficult to solve by using traditional methods. The bat algorithm (BA) is an effective method for solving optimization problems. However, the solution of the standard BA is easily trapped at one of its local optimum values. The main cause of premature convergence is the loss of diversity in the population. The niche technique is an effective method to maintain the population diversity, to enhance the exploration of the new search domains, and to avoid premature convergence. In this paper, a geographic information system- (GIS-) based niche hybrid bat algorithm (NHBA) is proposed for solving the optimal spatial search. The NHBA is able to avoid the premature convergence and obtain the global optimal values. The GIS technique provides robust support for processing a substantial amount of geographical data. A case in Fangcun District, Guangzhou City, China, is used to test the NHBA. The comparative experiments illustrate that the BA, GA, FA, PSO, and NHBA algorithms outperform the brute-force algorithm in terms of computational efficiency, and the optimal solutions are more easily obtained with NHBA than with BA, GA, FA, and PSO. Moreover, the precision of NHBA is higher and the convergence of NHBA is faster than those of the other algorithms under the same conditions.

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An Improved Moth-Flame Optimization Algorithm with Adaptation Mechanism to Solve Numerical and Mechanical Engineering Problems

Entropy ◽

10.3390/e23121637 ◽

2021 ◽

Vol 23 (12) ◽

pp. 1637

Author(s):

Mohammad H. Nadimi-Shahraki ◽

Ali Fatahi ◽

Hoda Zamani ◽

Seyedali Mirjalili ◽

Laith Abualigah

Keyword(s):

Mechanical Engineering ◽

Optimization Problems ◽

Population Diversity ◽

Local Optimum ◽

Friedman Test ◽

Exploration And Exploitation ◽

Adaptation Mechanism ◽

Local Optima ◽

Engineering Problems ◽

Moth Flame Optimization Algorithm

Moth-flame optimization (MFO) algorithm inspired by the transverse orientation of moths toward the light source is an effective approach to solve global optimization problems. However, the MFO algorithm suffers from issues such as premature convergence, low population diversity, local optima entrapment, and imbalance between exploration and exploitation. In this study, therefore, an improved moth-flame optimization (I-MFO) algorithm is proposed to cope with canonical MFO’s issues by locating trapped moths in local optimum via defining memory for each moth. The trapped moths tend to escape from the local optima by taking advantage of the adapted wandering around search (AWAS) strategy. The efficiency of the proposed I-MFO is evaluated by CEC 2018 benchmark functions and compared against other well-known metaheuristic algorithms. Moreover, the obtained results are statistically analyzed by the Friedman test on 30, 50, and 100 dimensions. Finally, the ability of the I-MFO algorithm to find the best optimal solutions for mechanical engineering problems is evaluated with three problems from the latest test-suite CEC 2020. The experimental and statistical results demonstrate that the proposed I-MFO is significantly superior to the contender algorithms and it successfully upgrades the shortcomings of the canonical MFO.

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A Tent Marine Predators Algorithm with Estimation Distribution Algorithm and Gaussian Random Walk for Continuous Optimization Problems

Computational Intelligence and Neuroscience ◽

10.1155/2021/7695596 ◽

2021 ◽

Vol 2021 ◽

pp. 1-17

Author(s):

Chang-Jian Sun ◽

Fang Gao

Keyword(s):

Random Walk ◽

Population Distribution ◽

Optimization Problems ◽

Continuous Optimization ◽

Population Diversity ◽

Initial Population ◽

Local Optimum ◽

Marine Predators ◽

Gaussian Random Walk ◽

Estimation Distribution Algorithm

The marine predators algorithm (MPA) is a novel population-based optimization method that has been widely used in real-world optimization applications. However, MPA can easily fall into a local optimum because of the lack of population diversity in the late stage of optimization. To overcome this shortcoming, this paper proposes an MPA variant with a hybrid estimation distribution algorithm (EDA) and a Gaussian random walk strategy, namely, HEGMPA. The initial population is constructed using cubic mapping to enhance the diversity of individuals in the population. Then, EDA is adapted into MPA to modify the evolutionary direction using the population distribution information, thus improving the convergence performance of the algorithm. In addition, a Gaussian random walk strategy with medium solution is used to help the algorithm get rid of stagnation. The proposed algorithm is verified by simulation using the CEC2014 test suite. Simulation results show that the performance of HEGMPA is more competitive than other comparative algorithms, with significant improvements in terms of convergence accuracy and convergence speed.

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Simultaneous Feature Selection and Support Vector Machine Optimization Using an Enhanced Chimp Optimization Algorithm

Algorithms ◽

10.3390/a14100282 ◽

2021 ◽

Vol 14 (10) ◽

pp. 282

Author(s):

Di Wu ◽

Wanying Zhang ◽

Heming Jia ◽

Xin Leng

Keyword(s):

Optimization Algorithm ◽

Classification Accuracy ◽

Search Algorithm ◽

Rank Correlation ◽

Population Diversity ◽

The Other ◽

Support Vector ◽

Local Optimum ◽

Original Algorithm ◽

Spearman’S Rank Correlation

Chimp Optimization Algorithm (ChOA), a novel meta-heuristic algorithm, has been proposed in recent years. It divides the population into four different levels for the purpose of hunting. However, there are still some defects that lead to the algorithm falling into the local optimum. To overcome these defects, an Enhanced Chimp Optimization Algorithm (EChOA) is developed in this paper. Highly Disruptive Polynomial Mutation (HDPM) is introduced to further explore the population space and increase the population diversity. Then, the Spearman’s rank correlation coefficient between the chimps with the highest fitness and the lowest fitness is calculated. In order to avoid the local optimization, the chimps with low fitness values are introduced with Beetle Antenna Search Algorithm (BAS) to obtain visual ability. Through the introduction of the above three strategies, the ability of population exploration and exploitation is enhanced. On this basis, this paper proposes an EChOA-SVM model, which can optimize parameters while selecting the features. Thus, the maximum classification accuracy can be achieved with as few features as possible. To verify the effectiveness of the proposed method, the proposed method is compared with seven common methods, including the original algorithm. Seventeen benchmark datasets from the UCI machine learning library are used to evaluate the accuracy, number of features, and fitness of these methods. Experimental results show that the classification accuracy of the proposed method is better than the other methods on most data sets, and the number of features required by the proposed method is also less than the other algorithms.

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Mobile Robot Path Planning with a Non-Dominated Sorting Genetic Algorithm

Applied Sciences ◽

10.3390/app8112253 ◽

2018 ◽

Vol 8 (11) ◽

pp. 2253 ◽

Cited By ~ 10

Author(s):

Yang Xue

Keyword(s):

Genetic Algorithm ◽

Evolutionary Algorithms ◽

Path Planning ◽

Optimization Problems ◽

Planning Problem ◽

Nsga Ii ◽

Multi Objective ◽

Mutation Operators ◽

Comparison Results ◽

Path Planning Problem

In many areas, such as mobile robots, video games and driverless vehicles, path planning has always attracted researchers’ attention. In the field of mobile robotics, the path planning problem is to plan one or more viable paths to the target location from the starting position within a given obstacle space. Evolutionary algorithms can effectively solve this problem. The non-dominated sorting genetic algorithm (NSGA-II) is currently recognized as one of the evolutionary algorithms with robust optimization capabilities and has solved various optimization problems. In this paper, NSGA-II is adopted to solve multi-objective path planning problems. Three objectives are introduced. Besides the usual selection, crossover and mutation operators, some practical operators are applied. Moreover, the parameters involved in the algorithm are studied. Additionally, another evolutionary algorithm and quality metrics are employed for examination. Comparison results demonstrate that non-dominated solutions obtained by the algorithm have good characteristics. Subsequently, the path corresponding to the knee point of non-dominated solutions is shown. The path is shorter, safer and smoother. This path can be adopted in the later decision-making process. Finally, the above research shows that the revised algorithm can effectively solve the multi-objective path planning problem in static environments.

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Robotic Path Planning Using Flower Pollination Algorithm

Recent Advances in Computer Science and Communications ◽

10.2174/2213275911666190320160837 ◽

2020 ◽

Vol 13 (2) ◽

pp. 191-199

Author(s):

Ishita Mehta ◽

Geetika Singh ◽

Yogita Gigras ◽

Anuradha Dhull ◽

Priyanka Rastogi

Keyword(s):

Particle Swarm Optimization ◽

Path Planning ◽

Ant Colony Optimization ◽

Optimization Algorithm ◽

Flower Pollination Algorithm ◽

Planning Problem ◽

Swarm Optimization ◽

Flower Pollination ◽

Cpu Time ◽

Path Planning Problem

Background: Robotic path planning is an important facet of robotics. Its purpose is to make robots move independently in their work environment from a source to a destination whilst satisfying certain constraints. Constraint conditions are as follows: avoiding collision with obstacles, staying as far as possible from the obstacles, traversing the shortest path, taking minimum time, consuming minimum energy and so on. Hence, the robotic path planning problem is a conditional constraint optimization problem. Methods: To overcome this problem, the Flower Pollination Algorithm, which is a metaheuristic approach is employed. The effectiveness of Flower Pollination Algorithm is showcased by using diverse maps. These maps are composed of several fixed obstacles in different positions, a source and a target position. Initially, the pollinators carrying pollen (candidate solutions) are at the source location. Subsequently, the pollinators must pave a way towards the target location while simultaneously averting any obstacles that are encountered enroute. The pollinators should also do so with the minimum cost possible in terms of distance. The performance of the algorithm in terms of CPU time is evaluated. Flower Pollination Algorithm was also compared to the Particle Swarm Optimization algorithm and Ant Colony Optimization algorithm. Results: It was observed that Flower Pollination Algorithm is faster than Particle Swarm Optimization and Ant Colony Optimization in terms of CPU time for the same number of iterations to find an optimized solution for robotic path planning. Conclusion: The Flower Pollination Algorithm can be effectively applied for solving robotic path planning problem with static obstacles.

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