A Decomposition-based Evolutionary Algorithm with Correlative Selection Mechanism for Many-objective Optimization

2020 ◽  
pp. 1-36
Author(s):  
Ruochen Liu ◽  
Ruinan Wang ◽  
Renyu Bian ◽  
Jing Liu ◽  
Licheng Jiao
Keyword(s):  
Evolutionary Algorithms ◽  
Evolutionary Algorithm ◽  
Reference Point ◽  
Optimization Problems ◽  
State Of The Art ◽  
Reference Points ◽  
Test Problems ◽  
Selection Mechanism ◽  
Multi Objective Optimization ◽  
Decomposition Approach

Decomposition-based evolutionary algorithms have been quite successful in dealing with multi-objective optimization problems. Recently, more and more researchers attempt to apply the decomposition approach to solve many-objective optimization problems. A many-objective evolutionary algorithm based on decomposition with correlative selection mechanism (MOEA/D-CSM) is also proposed to solve many-objective optimization problems in this paper. Since MOEA/D-SCM is based on a decomposition approach which adopts penalty boundary intersection (PBI), a set of reference points must be generated in advance. Thus, a new concept related to the set of reference points is introduced first, namely, the correlation between an individual and a reference point. Thereafter, a new selection mechanism based on the correlation is designed and called correlative selection mechanism. The correlative selection mechanism finds their correlative individuals for each reference point as soon as possible so that the diversity among population members is maintained. However, when a reference point has two or more correlative individuals, those worse correlative individuals may be removed from a population so that the solutions can be ensured to move towards the Pareto-optimal front. In a comprehensive experimental study, we apply MOEA/D-CSM to a number of many-objective test problems with 3 to 15 objec-tives and make a comparison with three state-of-the-art many-objective evolutionary algorithms, namely, NSGA-III, MOEA/D and RVEA. Experimental results show that the proposed MOEA/D-CSM can produce competitive results on most of the problems considered in this study.

scholarly journals Improved Lebesgue Indicator-Based Evolutionary Algorithm: Reducing Hypervolume Computations

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 19
Author(s):  
Saúl Zapotecas-Martínez ◽  
Abel García-Nájera ◽  
Adriana Menchaca-Méndez
Keyword(s):  
Evolutionary Algorithms ◽  
Evolutionary Algorithm ◽  
Lebesgue Measure ◽  
Pareto Front ◽  
Optimization Problems ◽  
State Of The Art ◽  
Computational Cost ◽  
Computational Time ◽  
Multi Objective Optimization ◽  
Multi Objective

One of the major limitations of evolutionary algorithms based on the Lebesgue measure for multi-objective optimization is the computational cost required to approximate the Pareto front of a problem. Nonetheless, the Pareto compliance property of the Lebesgue measure makes it one of the most investigated indicators in the designing of indicator-based evolutionary algorithms (IBEAs). The main deficiency of IBEAs that use the Lebesgue measure is their computational cost which increases with the number of objectives of the problem. On this matter, the investigation presented in this paper introduces an evolutionary algorithm based on the Lebesgue measure to deal with box-constrained continuous multi-objective optimization problems. The proposed algorithm implicitly uses the regularity property of continuous multi-objective optimization problems that has suggested effectiveness when solving continuous problems with rough Pareto sets. On the other hand, the survival selection mechanism considers the local property of the Lebesgue measure, thus reducing the computational time in our algorithmic approach. The emerging indicator-based evolutionary algorithm is examined and compared versus three state-of-the-art multi-objective evolutionary algorithms based on the Lebesgue measure. In addition, we validate its performance on a set of artificial test problems with various characteristics, including multimodality, separability, and various Pareto front forms, incorporating concavity, convexity, and discontinuity. For a more exhaustive study, the proposed algorithm is evaluated in three real-world applications having four, five, and seven objective functions whose properties are unknown. We show the high competitiveness of our proposed approach, which, in many cases, improved the state-of-the-art indicator-based evolutionary algorithms on the multi-objective problems adopted in our investigation.

Genetic Diversity as an Objective in Multi-Objective Evolutionary Algorithms

2003 ◽  
Vol 11 (2) ◽  
pp. 151-167 ◽  
Author(s):  
Andrea Toffolo ◽  
Ernesto Benini
Keyword(s):  
Genetic Diversity ◽  
Evolutionary Algorithms ◽  
Evolutionary Algorithm ◽  
Selection Pressure ◽  
Evaluation Method ◽  
State Of The Art ◽  
Search Space ◽  
Test Problems ◽  
Multi Objective ◽  
Diversity Evaluation

A key feature of an efficient and reliable multi-objective evolutionary algorithm is the ability to maintain genetic diversity within a population of solutions. In this paper, we present a new diversity-preserving mechanism, the Genetic Diversity Evaluation Method (GeDEM), which considers a distance-based measure of genetic diversity as a real objective in fitness assignment. This provides a dual selection pressure towards the exploitation of current non-dominated solutions and the exploration of the search space. We also introduce a new multi-objective evolutionary algorithm, the Genetic Diversity Evolutionary Algorithm (GDEA), strictly designed around GeDEM and then we compare it with other state-of-the-art algorithms on a well-established suite of test problems. Experimental results clearly indicate that the performance of GDEA is top-level.

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 Evolutionary Search with Multiple Utopian Reference Points in Decomposition-Based Multiobjective Optimization

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-22 ◽  
Author(s):  
Wu Lin ◽  
Qiuzhen Lin ◽  
Zexuan Zhu ◽  
Jianqiang Li ◽  
Jianyong Chen ◽  
...  
Keyword(s):  
Evolutionary Algorithms ◽  
Reference Point ◽  
Ideal Point ◽  
Search Space ◽  
Weight Vector ◽  
Reference Points ◽  
Test Problems ◽  
Evolutionary Search ◽  
Multiobjective Evolutionary Algorithms ◽  
Nadir Point

Decomposition-based multiobjective evolutionary algorithms (MOEA/Ds) have become increasingly popular in recent years. In these MOEA/Ds, evolutionary search is guided by the used weight vectors in decomposition function to approximate the Pareto front (PF). Generally, the decomposition function will be constructed by the weight vectors and the reference point, which play an important role to balance convergence and diversity during the evolutionary search. However, in most existing MOEA/Ds, only one ideal point is used as the reference point for all the evolutionary search, which is harmful to search the entire PF when tackling the problems with difficult-to-approximate PF boundaries. To address the above problem, this paper proposes an evolutionary search method with multiple utopian reference points in MOEA/Ds. Similar to the existing MOEA/Ds, each solution is associated with one weight vector, which provides an evolutionary search direction, while the novelty of our approach is to use multiple utopian reference points, which can provide evolutionary search directions for different weight vectors. Corner solutions are used to approximate the nadir point and then multiple utopian reference points for evolutionary search can be constructed based on the ideal point and the nadir point, which are uniformly distributed on the coordinate axis or planes. The use of these utopian points can prevent solutions to gather in the same region of PF and helps to strike a good balance of exploration and exploitation in the search space. The performance of our proposed algorithm is validated on tackling 16 recently proposed test problems with difficult-to-approximate PF boundaries and empirically compared to eight state-of-the-art multiobjective evolutionary algorithms. The experimental results demonstrate the superiority of the proposed algorithm on solving most of the test problems adopted.

scholarly journals An Ensemble Framework of Evolutionary Algorithm for Constrained Multi-Objective Optimization

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 116
Author(s):  
Junhua Ku ◽  
Fei Ming ◽  
Wenyin Gong
Keyword(s):  
Evolutionary Algorithms ◽  
Real World ◽  
Optimization Problems ◽  
State Of The Art ◽  
Multi Objective Optimization ◽  
The Real ◽  
Multi Objective ◽  
The Past ◽  
Hypervolume Indicator ◽  
Real World Problems

In the real-world, symmetry or asymmetry widely exists in various problems. Some of them can be formulated as constrained multi-objective optimization problems (CMOPs). During the past few years, handling CMOPs by evolutionary algorithms has become more popular. Lots of constrained multi-objective optimization evolutionary algorithms (CMOEAs) have been proposed. Whereas different CMOEAs may be more suitable for different CMOPs, it is difficult to choose the best one for a CMOP at hand. In this paper, we propose an ensemble framework of CMOEAs that aims to achieve better versatility on handling diverse CMOPs. In the proposed framework, the hypervolume indicator is used to evaluate the performance of CMOEAs, and a decreasing mechanism is devised to delete the poorly performed CMOEAs and to gradually determine the most suitable CMOEA. A new CMOEA, namely ECMOEA, is developed based on the framework and three state-of-the-art CMOEAs. Experimental results on five benchmarks with totally 52 instances demonstrate the effectiveness of our approach. In addition, the superiority of ECMOEA is verified through comparisons to seven state-of-the-art CMOEAs. Moreover, the effectiveness of ECMOEA on the real-world problems is also evaluated for eight instances.

scholarly journals D2MOPSO: MOPSO Based on Decomposition and Dominance with Archiving Using Crowding Distance in Objective and Solution Spaces

2014 ◽  
Vol 22 (1) ◽  
pp. 47-77 ◽  
Author(s):  
N. Al Moubayed ◽  
A. Petrovski ◽  
J. McCall
Keyword(s):  
Optimization Problems ◽  
State Of The Art ◽  
Statistical Tests ◽  
Test Problems ◽  
Multi Objective Optimization ◽  
Improved Method ◽  
Particle Swarm Optimizer ◽  
Multi Objective ◽  
Wide Range ◽  
Comparison And Analysis

This paper improves a recently developed multi-objective particle swarm optimizer ([Formula: see text]) that incorporates dominance with decomposition used in the context of multi-objective optimization. Decomposition simplifies a multi-objective problem (MOP) by transforming it to a set of aggregation problems, whereas dominance plays a major role in building the leaders’ archive. [Formula: see text] introduces a new archiving technique that facilitates attaining better diversity and coverage in both objective and solution spaces. The improved method is evaluated on standard benchmarks including both constrained and unconstrained test problems, by comparing it with three state of the art multi-objective evolutionary algorithms: MOEA/D, OMOPSO, and dMOPSO. The comparison and analysis of the experimental results, supported by statistical tests, indicate that the proposed algorithm is highly competitive, efficient, and applicable to a wide range of multi-objective optimization problems.

scholarly journals An Opposition-Based Evolutionary Algorithm for Many-Objective Optimization with Adaptive Clustering Mechanism

2019 ◽  
Vol 2019 ◽  
pp. 1-27
Author(s):  
Wan Liang Wang ◽  
Weikun Li ◽  
Yu Le Wang
Keyword(s):  
Evolutionary Algorithms ◽  
Evolutionary Algorithm ◽  
Optimization Problems ◽  
Test Problems ◽  
Adaptive Clustering ◽  
Opposition Based Learning ◽  
Environmental Selection ◽  
Large Numbers ◽  
Complex Optimization ◽  
Nondominated Sorting

Balancing convergence and diversity has become a key point especially in many-objective optimization where the large numbers of objectives pose many challenges to the evolutionary algorithms. In this paper, an opposition-based evolutionary algorithm with the adaptive clustering mechanism is proposed for solving the complex optimization problem. In particular, opposition-based learning is integrated in the proposed algorithm to initialize the solution, and the nondominated sorting scheme with a new adaptive clustering mechanism is adopted in the environmental selection phase to ensure both convergence and diversity. The proposed method is compared with other nine evolutionary algorithms on a number of test problems with up to fifteen objectives, which verify the best performance of the proposed algorithm. Also, the algorithm is applied to a variety of multiobjective engineering optimization problems. The experimental results have shown the competitiveness and effectiveness of our proposed algorithm in solving challenging real-world problems.

scholarly journals An Entropy-Based Multiobjective Evolutionary Algorithm with an Enhanced Elite Mechanism

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Yufang Qin ◽  
Junzhong Ji ◽  
Chunnian Liu
Keyword(s):  
Evolutionary Algorithm ◽  
Pareto Front ◽  
Optimization Problem ◽  
State Of The Art ◽  
Early Stage ◽  
Test Problems ◽  
Multiobjective Optimization Problem ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Multi Objective

Multiobjective optimization problem (MOP) is an important and challenging topic in the fields of industrial design and scientific research. Multi-objective evolutionary algorithm (MOEA) has proved to be one of the most efficient algorithms solving the multi-objective optimization. In this paper, we propose an entropy-based multi-objective evolutionary algorithm with an enhanced elite mechanism (E-MOEA), which improves the convergence and diversity of solution set in MOPs effectively. In this algorithm, an enhanced elite mechanism is applied to guide the direction of the evolution of the population. Specifically, it accelerates the population to approach the true Pareto front at the early stage of the evolution process. A strategy based on entropy is used to maintain the diversity of population when the population is near to the Pareto front. The proposed algorithm is executed on widely used test problems, and the simulated results show that the algorithm has better or comparative performances in convergence and diversity of solutions compared with two state-of-the-art evolutionary algorithms: NSGA-II, SPEA2 and the MOSADE.

An Orthogonal Multi-objective Evolutionary Algorithm for Multi-objective Optimization Problems with Constraints

2004 ◽  
Vol 12 (1) ◽  
pp. 77-98 ◽  
Author(s):  
Sanyou Y. Zeng ◽  
Lishan S. Kang ◽  
Lixin X. Ding
Keyword(s):  
Evolutionary Algorithm ◽  
Optimization Problems ◽  
Engineering Problem ◽  
Test Problems ◽  
Pareto Optimal ◽  
Large Set ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Pareto Optimal Set ◽  
Optimal Set

In this paper, an orthogonal multi-objective evolutionary algorithm (OMOEA) is proposed for multi-objective optimization problems (MOPs) with constraints. Firstly, these constraints are taken into account when determining Pareto dominance. As a result, a strict partial-ordered relation is obtained, and feasibility is not considered later in the selection process. Then, the orthogonal design and the statistical optimal method are generalized to MOPs, and a new type of multi-objective evolutionary algorithm (MOEA) is constructed. In this framework, an original niche evolves first, and splits into a group of sub-niches. Then every sub-niche repeats the above process. Due to the uniformity of the search, the optimality of the statistics, and the exponential increase of the splitting frequency of the niches, OMOEA uses a deterministic search without blindness or stochasticity. It can soon yield a large set of solutions which converges to the Pareto-optimal set with high precision and uniform distribution. We take six test problems designed by Deb, Zitzler et al., and an engineering problem (W) with constraints provided by Ray et al. to test the new technique. The numerical experiments show that our algorithm is superior to other MOGAS and MOEAs, such as FFGA, NSGAII, SPEA2, and so on, in terms of the precision, quantity and distribution of solutions. Notably, for the engineering problem W, it finds the Pareto-optimal set, which was previously unknown.

scholarly journals Memory-Enhanced Dynamic Multi-Objective Evolutionary Algorithm Based on Lp Decomposition

2018 ◽  
Vol 8 (9) ◽  
pp. 1673 ◽  
Author(s):  
Xinxin Xu ◽  
Yanyan Tan ◽  
Wei Zheng ◽  
Shengtao Li
Keyword(s):  
Evolutionary Algorithms ◽  
Evolutionary Algorithm ◽  
Dynamic Optimization ◽  
Decomposition Method ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Multi Objective Optimization ◽  
Scalar Optimization ◽  
Multi Objective ◽  
Memory Scheme

Decomposition-based multi-objective evolutionary algorithms provide a good framework for static multi-objective optimization. Nevertheless, there are few studies on their use in dynamic optimization. To solve dynamic multi-objective optimization problems, this paper integrates the framework into dynamic multi-objective optimization and proposes a memory-enhanced dynamic multi-objective evolutionary algorithm based on L p decomposition (denoted by dMOEA/D- L p ). Specifically, dMOEA/D- L p decomposes a dynamic multi-objective optimization problem into a number of dynamic scalar optimization subproblems and coevolves them simultaneously, where the L p decomposition method is adopted for decomposition. Meanwhile, a subproblem-based bunchy memory scheme that stores good solutions from old environments and reuses them as necessary is designed to respond to environmental change. Experimental results verify the effectiveness of the L p decomposition method in dynamic multi-objective optimization. Moreover, the proposed dMOEA/D- L p achieves better performance than other popular memory-enhanced dynamic multi-objective optimization algorithms.

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