scholarly journals ETEA: A Euclidean Minimum Spanning Tree-Based Evolutionary Algorithm for Multi-Objective Optimization

2014 ◽  
Vol 22 (2) ◽  
pp. 189-230 ◽  
Author(s):  
Miqing Li ◽  
Shengxiang Yang ◽  
Jinhua Zheng ◽  
Xiaohui Liu
Keyword(s):  
Evolutionary Algorithm ◽  
Spanning Tree ◽  
Euclidean Distance ◽  
Minimum Spanning Tree ◽  
Optimization Problems ◽  
Multi Objective Optimization ◽  
Position Information ◽  
Multi Objective ◽  
Environmental Selection ◽  
Fitness Value

The Euclidean minimum spanning tree (EMST), widely used in a variety of domains, is a minimum spanning tree of a set of points in space where the edge weight between each pair of points is their Euclidean distance. Since the generation of an EMST is entirely determined by the Euclidean distance between solutions (points), the properties of EMSTs have a close relation with the distribution and position information of solutions. This paper explores the properties of EMSTs and proposes an EMST-based evolutionary algorithm (ETEA) to solve multi-objective optimization problems (MOPs). Unlike most EMO algorithms that focus on the Pareto dominance relation, the proposed algorithm mainly considers distance-based measures to evaluate and compare individuals during the evolutionary search. Specifically, in ETEA, four strategies are introduced: (1) An EMST-based crowding distance (ETCD) is presented to estimate the density of individuals in the population; (2) A distance comparison approach incorporating ETCD is used to assign the fitness value for individuals; (3) A fitness adjustment technique is designed to avoid the partial overcrowding in environmental selection; (4) Three diversity indicators—the minimum edge, degree, and ETCD—with regard to EMSTs are applied to determine the survival of individuals in archive truncation. From a series of extensive experiments on 32 test instances with different characteristics, ETEA is found to be competitive against five state-of-the-art algorithms and its predecessor in providing a good balance among convergence, uniformity, and spread.

A multi-objective evolutionary algorithm based on niche selection in solving irregular Pareto fronts

2021 ◽  
pp. 1-21
Author(s):  
Xin Li ◽  
Xiaoli Li ◽  
Kang Wang
Keyword(s):  
Evolutionary Algorithm ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Benchmark Problems ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Environmental Selection ◽  
Optimal Solution Set ◽  
Pareto Fronts

The key characteristic of multi-objective evolutionary algorithm is that it can find a good approximate multi-objective optimal solution set when solving multi-objective optimization problems(MOPs). However, most multi-objective evolutionary algorithms perform well on regular multi-objective optimization problems, but their performance on irregular fronts deteriorates. In order to remedy this issue, this paper studies the existing algorithms and proposes a multi-objective evolutionary based on niche selection to deal with irregular Pareto fronts. In this paper, the crowding degree is calculated by the niche method in the process of selecting parents when the non-dominated solutions converge to the first front, which improves the the quality of offspring solutions and which is beneficial to local search. In addition, niche selection is adopted into the process of environmental selection through considering the number and the location of the individuals in its niche radius, which improve the diversity of population. Finally, experimental results on 23 benchmark problems including MaF and IMOP show that the proposed algorithm exhibits better performance than the compared MOEAs.

A many-objective evolutionary algorithm based on vector angle distance scaling

2021 ◽  
Vol 40 (5) ◽  
pp. 10285-10306
Author(s):  
Xin Li ◽  
Xiaoli Li ◽  
Kang Wang
Keyword(s):  
Evolutionary Algorithms ◽  
Evolutionary Algorithm ◽  
Pareto Front ◽  
Optimization Problems ◽  
Adaptive Strategy ◽  
Great Success ◽  
Multi Objective ◽  
Environmental Selection ◽  
Fitness Value ◽  
Vector Angle

In the past two decades, multi-objective evolutionary algorithms (MOEAs) have achieved great success in solving two or three multi-objective optimization problems. As pointed out in some recent studies, however, MOEAs face many difficulties when dealing with many-objective optimization problems(MaOPs) on account of the loss of the selection pressure of the non-dominant candidate solutions toward the Pareto front and the ineffective design of the diversity maintenance mechanism. This paper proposes a many-objective evolutionary algorithm based on vector guidance. In this algorithm, the value of vector angle distance scaling(VADS) is applied to balance convergence and diversity in environmental selection. In addition, tournament selection based on the aggregate fitness value of VADS is applied to generate a high quality offspring population. Besides, we adopt an adaptive strategy to adjust the reference vector dynamically according to the scales of the objective functions. Finally, the performance of the proposed algorithm is compared with five state-of-the-art many-objective evolutionary algorithms on 52 instances of 13 MaOPs with diverse characteristics. Experimental results show that the proposed algorithm performs competitively when dealing many-objective with different types of Pareto front.

Multi-Objective Evolutionary Algorithm Based on Two Reference Points Decomposition and Historical Information Prediction

2021 ◽  
Vol 01 ◽  
Author(s):  
Er-chao Li ◽  
Kang-wei Li
Keyword(s):  
Evolutionary Algorithm ◽  
Optimization Problems ◽  
Reference Points ◽  
Multi Objective Optimization ◽  
Test Function ◽  
Historical Information ◽  
Multi Objective ◽  
Nadir Point ◽  
Overall Performance ◽  
Better Than

Aims: The main purpose of this paper is to solve the issues that the poor quality of offspring solutions generated by traditional evolutionary operators, and that the inability of the evolutionary algorithm based on decomposition to better solve the multi-objective optimization problems (MOPs) with complicated Pareto fronts (PFs). Background: For some complicated multi-objective optimization problems, the effect of the multi-objective evolutionary algorithm based on decomposition (MOEA/D) is poor. For specific complicated problems, there is less research on improving the algorithm's performance by setting and adjusting the direction vector in the decomposition-based evolutionary algorithm. And considering that in the existing algorithms, the optimal solutions are selected according to the selection strategy in the selection stage, without considering if it could produce the better solutions in the stage of individual generation to achieve the optimization effect faster. As a result of these, a multi-objective evolutionary algorithm that is based on two reference points decomposition and historical information prediction is proposed. Objective: In order to verify the feasibility of the proposed strategy, the F-series test function with complicated PFs is used as the test function to simulate the proposed strategy. Method: Firstly, the evolutionary operator based on Historical Information Prediction (EHIP) is used to generate better offspring solutions to improve the convergence of the algorithm; secondly, the decomposition strategy based on ideal point and nadir point is used to select solutions to solve the MOPs with complicated PFs, and the decomposition method with augmentation term is used to improve the population diversity when selecting solutions according to the nadir point. Finally, the proposed algorithm is compared to several popular algorithms by the F-series test function, and the comparison is made according to the corresponding performance metrics. Result: The performance of the algorithm is improved obviously compared with the popular algorithms after using the EHIP. When the decomposition method with augmentation term is added, the performance of the proposed algorithm is better than the algorithm with only the EHIP on the whole. However, the overall performance is better than the popular algorithms. Conclusion and Prospect: The experimental results show that the overall performance of the proposed algorithm is superior to the popular algorithms. The EHIP can produce better quality offspring solutions, and the decomposition strategy based on two reference points can well solve the MOPs with complicated PFs. This paper mainly demonstrates the theory without testing the practical problems. The following research mainly focuses on the application of the proposed algorithm to the practical problems such as robot path planning.

scholarly journals Comparison of synchronous and asynchronous parallelization of extreme surrogate-assisted multi-objective evolutionary algorithm

2020 ◽  
Author(s):  
Tomohiro Harada ◽  
Misaki Kaidan ◽  
Ruck Thawonmas
Keyword(s):  
Machine Learning ◽  
Evolutionary Algorithm ◽  
Optimization Problems ◽  
Computing Time ◽  
The Other ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Evaluation Time ◽  
Surrogate Function

Abstract This paper investigates the integration of a surrogate-assisted multi-objective evolutionary algorithm (MOEA) and a parallel computation scheme to reduce the computing time until obtaining the optimal solutions in evolutionary algorithms (EAs). A surrogate-assisted MOEA solves multi-objective optimization problems while estimating the evaluation of solutions with a surrogate function. A surrogate function is produced by a machine learning model. This paper uses an extreme learning surrogate-assisted MOEA/D (ELMOEA/D), which utilizes one of the well-known MOEA algorithms, MOEA/D, and a machine learning technique, extreme learning machine (ELM). A parallelization of MOEA, on the other hand, evaluates solutions in parallel on multiple computing nodes to accelerate the optimization process. We consider a synchronous and an asynchronous parallel MOEA as a master-slave parallelization scheme for ELMOEA/D. We carry out an experiment with multi-objective optimization problems to compare the synchronous parallel ELMOEA/D with the asynchronous parallel ELMOEA/D. In the experiment, we simulate two settings of the evaluation time of solutions. One determines the evaluation time of solutions by the normal distribution with different variances. On the other hand, another evaluation time correlates to the objective function value. We compare the quality of solutions obtained by the parallel ELMOEA/D variants within a particular computing time. The experimental results show that the parallelization of ELMOEA/D significantly reduces the computational time. In addition, the integration of ELMOEA/D with the asynchronous parallelization scheme obtains higher quality of solutions quicker than the synchronous parallel ELMOEA/D.

An Improved Adaptive Evolutionary Algorithm for Multi-Objective Optimization

2013 ◽  
Vol 303-306 ◽  
pp. 1494-1500
Author(s):  
Jian Wei Wang ◽  
Jian Ming Zhang
Keyword(s):  
Evolutionary Algorithm ◽  
Optimal Solution ◽  
Optimization Methods ◽  
Relative Fitness ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Fitness Value ◽  
Crossover Probability ◽  
Optimal Solution Set ◽  
Adaptive Evolutionary Algorithms

Aiming at effectively overcoming the disadvantages of traditional evolutionary algorithm which converge slowly and easily run into local extremism, an improved adaptive evolutionary algorithms is proposed. Firstly, in order to choose the optimal objective fitness value from the population in every generation, the absolute and relative fitness are defined. Secondly, fuzzy technique is adopted to adjust the weights of objective functions, crossover probability, mutation probability, crossover positions and mutation positions during the iterative process. Finally, three classical test functions are given to illustrate the validity of improved adaptive evolutionary algorithm, simulation results show that the diversity and practicability of the optimal solution set are better by using the proposed method than other multi-objective optimization methods.

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