scholarly journals Chaos-based second-order bas for multimodal function optimization

Filomat ◽  
2020 ◽  
Vol 34 (15) ◽  
pp. 5159-5172
Author(s):  
Xiaoxiao Li ◽  
Xuefeng Zhou ◽  
Zhihao Xu ◽  
Guanrong Tang
Keyword(s):  
Fitness Function ◽  
Chaotic Map ◽  
Optimal Solution ◽  
Variable Region ◽  
Second Order ◽  
Function Optimization ◽  
Good Convergence ◽  
Multimodal Function Optimization ◽  
Multimodal Function ◽  
Swarm Intelligence Optimization

Aiming at solving a drawback of the second-order beetle antenna search (SOBAS), a variant of the beetle antenna search (BAS), that it is difficult to find the global optimal solution and the low convergence accuracy when applied to the multimodal optimization functions with high dimension or large variable region, a chaotic-based second-order BAS algorithm (CSOBAS) is proposed by introducing chaos theory into the SOBAS. The algorithm mainly has three innovations: 1) chaos initialization: choosing the one with the smallest fitness function value from twenty beetles with different positions for iterative search; 2) using chaotic map to tune the randomization parameter in the detection rule; 3) imposing a chaotic perturbation on the current beetle to hope to help the search to jump out the local optimal solution. Eight different chaotic maps are used to demonstrate their impact on the simulation results. With six typical multimodal functions, performance comparisons between the CSOBAS and the SOBAS are conducted, validating the effectiveness of the CSOBAS and its superiority compared to the SOBAS. What?s more, the CSOBAS with an appropriate chaotic map can achieve a very good convergence quality compared to other swarm intelligence optimization algorithms while maintaining an individual.

scholarly journals Hybrid PSO-SA Type Algorithms for Multimodal Function Optimization and Reducing Energy Consumption in Embedded Systems

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Lhassane Idoumghar ◽  
Mahmoud Melkemi ◽  
René Schott ◽  
Maha Idrissi Aouad
Keyword(s):  
Energy Consumption ◽  
Embedded Systems ◽  
Evolutionary Algorithm ◽  
Optimal Solution ◽  
Function Optimization ◽  
Time Saving ◽  
Local Optima ◽  
Hybrid Evolutionary Algorithm ◽  
Multimodal Function Optimization ◽  
Multimodal Function

The paper presents a novel hybrid evolutionary algorithm that combines Particle Swarm Optimization (PSO) and Simulated Annealing (SA) algorithms. When a local optimal solution is reached with PSO, all particles gather around it, and escaping from this local optima becomes difficult. To avoid premature convergence of PSO, we present a new hybrid evolutionary algorithm, called HPSO-SA, based on the idea that PSO ensures fast convergence, while SA brings the search out of local optima because of its strong local-search ability. The proposed HPSO-SA algorithm is validated on ten standard benchmark multimodal functions for which we obtained significant improvements. The results are compared with these obtained by existing hybrid PSO-SA algorithms. In this paper, we provide also two versions of HPSO-SA (sequential and distributed) for minimizing the energy consumption in embedded systems memories. The two versions, of HPSO-SA, reduce the energy consumption in memories from 76% up to 98% as compared to Tabu Search (TS). Moreover, the distributed version of HPSO-SA provides execution time saving of about 73% up to 84% on a cluster of 4 PCs.

scholarly journals Swine influenza inspired optimization algorithm and its application to multimodal function optimization and noise removal

2012 ◽  
Vol 1 (1) ◽  
pp. 18
Author(s):  
Shyam S. Pattnaik ◽  
Devidas G. Jadhav ◽  
Swapna Devi ◽  
Radha Kanto Ratho
Keyword(s):  
Optimization Algorithm ◽  
Search Algorithm ◽  
Swine Influenza ◽  
Optimal Solution ◽  
Noise Removal ◽  
Function Optimization ◽  
Swine Flu ◽  
Multimodal Function Optimization ◽  
Spread Model ◽  
Multimodal Function

Swine Influenza Inspired Optimization (SIIO) is a search algorithm proposed for optimal solution. The authors followed the SIR (susceptible - infectious-recovered) virus spread model of Swine Influenza to develop the new evolutionary algorithm named as SIIO. SIR model is used to frame optimization algorithm following the spread and control phenomenon of the swine flu virus in the human population. The fitness based classes viz. susceptible (S), infectious (I) and recovered (R) of the individuals are made and treatment is used for the affected individuals by imitating the health information from the best fitness individual. The proposed algorithm shows improved performance on multi-dimensional unimodal and multimodal standard numerical benchmark functions than the compared optimization algorithms. The performance of the SIIO algorithm is better in terms of speed of convergence and quality of solutions. The SIIO is also applied for the Gaussian noise removal with Blind Source Separation (BSS) based on Independent Component Analysis (ICA).

A Sequential Niche Technique for Multimodal Function Optimization

1993 ◽  
Vol 1 (2) ◽  
pp. 101-125 ◽  
Author(s):  
David Beasley ◽  
David R. Bull ◽  
Ralph R. Martin
Keyword(s):  
Fitness Function ◽  
Optimization Methods ◽  
Function Optimization ◽  
Convergence Time ◽  
Problem Space ◽  
Unimodal Function ◽  
Fitness Sharing ◽  
Multimodal Function Optimization ◽  
Multimodal Function ◽  
Multimodal Problems

A technique is described that allows unimodal function optimization methods to be extended to locate all optima of multimodal problems efficiently. We describe an algorithm based on a traditional genetic algorithm (GA). This technique involves iterating the GA but uses knowledge gained during one iteration to avoid re-searching, on subsequent iterations, regions of problem space where solutions have already been found. This gain is achieved by applying a fitness derating function to the raw fitness function, so that fitness values are depressed in the regions of the problem space where solutions have already been found. Consequently, the likelihood of discovering a new solution on each iteration is dramatically increased. The technique may be used with various styles of GAs or with other optimization methods, such as simulated annealing. The effectiveness of the algorithm is demonstrated on a number of multimodal test functions. The technique is at least as fast as fitness sharing methods. It provides an acceleration of between 1 and l0p on a problem with p optima, depending on the value of p and the convergence time complexity.

A Proposal of Memory and Prediction Based Genetic Algorithm Using Speciation in Dynamic Multimodal Function Optimization

2011 ◽  
Vol 15 (8) ◽  
pp. 1082-1094 ◽  
Author(s):  
Takumi Ichimura ◽  
◽  
Hiroshi Inoue ◽  
Akira Hara ◽  
Tetsuyuki Takahama ◽  
...  
Keyword(s):  
Genetic Algorithm ◽  
Dynamic Environment ◽  
Optimal Solution ◽  
Difficult Problem ◽  
Function Optimization ◽  
Multimodal Functions ◽  
Multimodal Function Optimization ◽  
Multimodal Function ◽  
Precise Prediction ◽  
Niching Method

It is a difficult problem for evolutionary algorithms to search an optimal solution in multimodal functions with dynamic environments, where individuals searchmore than one optimum and their fitness values change over time. In this paper, we propose a method of Memory and Prediction Based Genetic Algorithm Using Speciation. This method is extended with a case based memory and a meta learner for precise prediction of environmental change. Especially, the individuals in a memory consist of 4 kinds of predictors and they can adjust to the change of dynamic environment adaptively. Speciation has shown to be an effective technique for multimodal optimization. A niching method based on speciation can be used to classify a population into groups according to their similarity measured by a distance. In this paper, each group by speciation has a memory and the individuals stored in the memory can respond to the situation according to the dynamic environment. In order to verify the effectiveness, the method is examined to search for an optimal solutions in multimodal functions.

Niche Genetic Algorithm Based on Sexual Reproduction and Multimodal Function Optimization Problem

2013 ◽  
pp. 8-16
Author(s):  
Yulong Tian ◽  
Tao Gao ◽  
Weifang Zhai ◽  
Yaying Hu ◽  
Xinfeng Li
Keyword(s):  
Genetic Algorithm ◽  
Sexual Reproduction ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Evolutionary Optimization ◽  
Function Optimization ◽  
Premature Convergence ◽  
Multimodal Functions ◽  
Multimodal Function Optimization ◽  
Multimodal Function

In this paper, a genetic algorithm with sexual reproduction and niche selection technology is proposed. Simple genetic algorithm has been successfully applied to many evolutionary optimization problems. But there is a problem of premature convergence for complex multimodal functions. To solve it, the frame and realization of niche genetic algorithm based on sexual reproduction are presented. Age and sexual structures are given to the individuals referring the sexual reproduction and “niche” phenomena, importing the niche selection technology. During age and sexual operators, different evolutionary parameters are given to the individuals with different age and sexual structures. As a result, this genetic algorithm can combat premature convergence and keep the diversity of population. The testing for Rastrigin function and Shubert function proves that the niche genetic algorithm based on sexual reproduction is effective.

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