An Improved Bacteria Foraging Optimization Algorithm for High Dimensional Multi-objective Optimization Problems

2018 ◽  
pp. 540-549 ◽  
Author(s):  
Yueliang Lu ◽  
Qingjian Ni
Keyword(s):  
Optimization Algorithm ◽  
Optimization Problems ◽  
High Dimensional ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Bacteria Foraging Optimization Algorithm

A Hybrid Optimization Algorithm for Single and Multi-Objective Optimization Problems

2017 ◽  
pp. 491-521 ◽  
Author(s):  
Rizk M. Rizk-Allah ◽  
Aboul Ella Hassanien
Keyword(s):  
Optimization Algorithm ◽  
Firefly Algorithm ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Hybrid Optimization ◽  
Multi Objective Optimization ◽  
Local Optima ◽  
Fruit Fly Optimization ◽  
Multi Objective ◽  
Hybrid Optimization Algorithm

This chapter presents a hybrid optimization algorithm namely FOA-FA for solving single and multi-objective optimization problems. The proposed algorithm integrates the benefits of the fruit fly optimization algorithm (FOA) and the firefly algorithm (FA) to avoid the entrapment in the local optima and the premature convergence of the population. FOA operates in the direction of seeking the optimum solution while the firefly algorithm (FA) has been used to accelerate the optimum seeking process and speed up the convergence performance to the global solution. Further, the multi-objective optimization problem is scalarized to a single objective problem by weighting method, where the proposed algorithm is implemented to derive the non-inferior solutions that are in contrast to the optimal solution. Finally, the proposed FOA-FA algorithm is tested on different benchmark problems whether single or multi-objective aspects and two engineering applications. The numerical comparisons reveal the robustness and effectiveness of the proposed algorithm.

scholarly journals Bézier Simplex Fitting: Describing Pareto Fronts of´ Simplicial Problems with Small Samples in Multi-Objective Optimization

2019 ◽  
Vol 33 ◽  
pp. 2304-2313 ◽  
Author(s):  
Ken Kobayashi ◽  
Naoki Hamada ◽  
Akiyoshi Sannai ◽  
Akinori Tanaka ◽  
Kenichi Bannai ◽  
...  
Keyword(s):  
Sample Size ◽  
Optimization Problems ◽  
Solution Set ◽  
Small Samples ◽  
High Dimensional ◽  
Large Sample Size ◽  
Multi Objective Optimization ◽  
Dimensional Solution ◽  
Multi Objective ◽  
Simplex Model

Multi-objective optimization problems require simultaneously optimizing two or more objective functions. Many studies have reported that the solution set of an M-objective optimization problem often forms an (M − 1)-dimensional topological simplex (a curved line for M = 2, a curved triangle for M = 3, a curved tetrahedron for M = 4, etc.). Since the dimensionality of the solution set increases as the number of objectives grows, an exponentially large sample size is needed to cover the solution set. To reduce the required sample size, this paper proposes a Bézier simplex model and its fitting algorithm. These techniques can exploit the simplex structure of the solution set and decompose a high-dimensional surface fitting task into a sequence of low-dimensional ones. An approximation theorem of Bézier simplices is proven. Numerical experiments with synthetic and real-world optimization problems demonstrate that the proposed method achieves an accurate approximation of high-dimensional solution sets with small samples. In practice, such an approximation will be conducted in the postoptimization process and enable a better trade-off analysis.

Modified teaching-learning-based optimization algorithm for multi-objective optimization problems

2022 ◽  
pp. 1-10
Author(s):  
Zhi Wang ◽  
Shufang Song ◽  
Hongkui Wei
Keyword(s):  
Optimization Algorithm ◽  
Learning Strategy ◽  
Optimization Problems ◽  
Teaching Strategy ◽  
Multi Objective Optimization ◽  
Aerodynamic Optimization ◽  
Multi Objective ◽  
Teaching Learning Based Optimization ◽  
Benchmark Test Functions ◽  
Teaching Learning

When solving multi-objective optimization problems, an important issue is how to promote convergence and distribution simultaneously. To address the above issue, a novel optimization algorithm, named as multi-objective modified teaching-learning-based optimization (MOMTLBO), is proposed. Firstly, a grouping teaching strategy based on pareto dominance relationship is proposed to strengthen the convergence efficiency. Afterward, a diversified learning strategy is presented to enhance the distribution. Meanwhile, differential operations are incorporated to the proposed algorithm. By the above process, the search ability of the algorithm can be encouraged. Additionally, a set of well-known benchmark test functions including ten complex problems proposed for CEC2009 is used to verify the performance of the proposed algorithm. The results show that MOMTLBO exhibits competitive performance against other comparison algorithms. Finally, the proposed algorithm is applied to the aerodynamic optimization of airfoils.

scholarly journals Matrix Adaptation Evolution Strategy with Multi-Objective Optimization for Multimodal Optimization

Algorithms ◽  
2019 ◽  
Vol 12 (3) ◽  
pp. 56
Author(s):  
Wei Li
Keyword(s):  
Covariance Matrix ◽  
Optimization Algorithm ◽  
Optimization Problems ◽  
Population Diversity ◽  
Evolution Strategy ◽  
Multimodal Optimization ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Covariance Matrix Adaptation ◽  
Adaptation Evolution

The standard covariance matrix adaptation evolution strategy (CMA-ES) is highly effective at locating a single global optimum. However, it shows unsatisfactory performance for solving multimodal optimization problems (MMOPs). In this paper, an improved algorithm based on the MA-ES, which is called the matrix adaptation evolution strategy with multi-objective optimization algorithm, is proposed to solve multimodal optimization problems (MA-ESN-MO). Taking advantage of the multi-objective optimization in maintaining population diversity, MA-ESN-MO transforms an MMOP into a bi-objective optimization problem. The archive is employed to save better solutions for improving the convergence of the algorithm. Moreover, the peaks found by the algorithm can be maintained until the end of the run. Multiple subpopulations are used to explore and exploit in parallel to find multiple optimal solutions for the given problem. Experimental results on CEC2013 test problems show that the covariance matrix adaptation with Niching and the multi-objective optimization algorithm (CMA-NMO), CMA Niching with the Mahalanobis Metric and the multi-objective optimization algorithm (CMA-NMM-MO), and matrix adaptation evolution strategy Niching with the multi-objective optimization algorithm (MA-ESN-MO) have overall better performance compared with the covariance matrix adaptation evolution strategy (CMA-ES), matrix adaptation evolution strategy (MA-ES), CMA Niching (CMA-N), CMA-ES Niching with Mahalanobis Metric (CMA-NMM), and MA-ES-Niching (MA-ESN).

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