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.

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.

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.

scholarly journals An Improved SPEA2 Algorithm with Adaptive Selection of Evolutionary Operators Scheme for Multiobjective Optimization Problems

2016 ◽  
Vol 2016 ◽  
pp. 1-20 ◽  
Author(s):  
Fuqing Zhao ◽  
Wenchang Lei ◽  
Weimin Ma ◽  
Yang Liu ◽  
Chuck Zhang
Keyword(s):  
Evolutionary Algorithms ◽  
Optimization Problems ◽  
Evolutionary Process ◽  
Search Space ◽  
Multiobjective Evolutionary Algorithms ◽  
Local Optima ◽  
Adaptive Selection ◽  
Convergence Performance ◽  
Evolutionary Operators ◽  
Polynomial Mutation

A fixed evolutionary mechanism is usually adopted in the multiobjective evolutionary algorithms and their operators are static during the evolutionary process, which causes the algorithm not to fully exploit the search space and is easy to trap in local optima. In this paper, a SPEA2 algorithm which is based on adaptive selection evolution operators (AOSPEA) is proposed. The proposed algorithm can adaptively select simulated binary crossover, polynomial mutation, and differential evolution operator during the evolutionary process according to their contribution to the external archive. Meanwhile, the convergence performance of the proposed algorithm is analyzed with Markov chain. Simulation results on the standard benchmark functions reveal that the performance of the proposed algorithm outperforms the other classical multiobjective evolutionary algorithms.

scholarly journals A Multipopulation Coevolutionary Strategy for Multiobjective Immune Algorithm

2014 ◽  
Vol 2014 ◽  
pp. 1-23 ◽  
Author(s):  
Jiao Shi ◽  
Maoguo Gong ◽  
Wenping Ma ◽  
Licheng Jiao
Keyword(s):  
State Of The Art ◽  
Immune Algorithm ◽  
Population Diversity ◽  
Entire Population ◽  
Test Problems ◽  
Evolutionary Search ◽  
Multiobjective Evolutionary Algorithms ◽  
Search Range ◽  
Dynamic Information ◽  
Exchange Information

How to maintain the population diversity is an important issue in designing a multiobjective evolutionary algorithm. This paper presents an enhanced nondominated neighbor-based immune algorithm in which a multipopulation coevolutionary strategy is introduced for improving the population diversity. In the proposed algorithm, subpopulations evolve independently; thus the unique characteristics of each subpopulation can be effectively maintained, and the diversity of the entire population is effectively increased. Besides, the dynamic information of multiple subpopulations is obtained with the help of the designed cooperation operator which reflects a mutually beneficial relationship among subpopulations. Subpopulations gain the opportunity to exchange information, thereby expanding the search range of the entire population. Subpopulations make use of the reference experience from each other, thereby improving the efficiency of evolutionary search. Compared with several state-of-the-art multiobjective evolutionary algorithms on well-known and frequently used multiobjective and many-objective problems, the proposed algorithm achieves comparable results in terms of convergence, diversity metrics, and running time on most test problems.

scholarly journals Principled Design and Runtime Analysis of Abstract Convex Evolutionary Search

2017 ◽  
Vol 25 (2) ◽  
pp. 205-236 ◽  
Author(s):  
Alberto Moraglio ◽  
Dirk Sudholt
Keyword(s):  
Evolutionary Algorithms ◽  
Search Algorithm ◽  
Geometric Theory ◽  
Search Space ◽  
Fitness Landscapes ◽  
Runtime Analysis ◽  
Evolutionary Search ◽  
Search Spaces ◽  
Underlying Space ◽  
Geometric Crossover

Geometric crossover is a formal class of crossovers that includes many well-known recombination operators across representations. In previous work, it was shown that all evolutionary algorithms with geometric crossover (but no mutation) do the same form of convex search regardless of the underlying representation, the specific selection mechanism, offspring distribution, search space, and problem at hand. Furthermore, it was suggested that the generalised convex search could perform well on generalised forms of concave and approximately concave fitness landscapes regardless of the underlying space and representation. In this article, we deepen this line of enquiry and study the runtime of generalised convex search on concave fitness landscapes. This is a first step toward linking a geometric theory of representations and runtime analysis in the attempt to (1) set the basis for a more general, unified approach for the runtime analysis of evolutionary algorithms across representations, and (2) identify the essential matching features of evolutionary search behaviour and landscape topography that cause polynomial performance. We present a general runtime result that can be systematically instantiated to specific search spaces and representations and present its specifications to three search spaces. As a corollary, we obtain that the convex search algorithm optimises LeadingOnes in [Formula: see text] fitness evaluations, which is faster than all unbiased unary black box algorithms.

scholarly journals On the use of two reference points in decomposition based multiobjective evolutionary algorithms

2017 ◽  
Vol 34 ◽  
pp. 89-102 ◽  
Author(s):  
Zhenkun Wang ◽  
Qingfu Zhang ◽  
Hui Li ◽  
Hisao Ishibuchi ◽  
Licheng Jiao
Keyword(s):  
Evolutionary Algorithms ◽  
Reference Points ◽  
Multiobjective Evolutionary Algorithms

scholarly journals A Constrained Solution Update Strategy for Multiobjective Evolutionary Algorithm Based on Decomposition

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Yuchao Su ◽  
Qiuzhen Lin ◽  
Jia Wang ◽  
Jianqiang Li ◽  
Jianyong Chen ◽  
...  
Keyword(s):  
Evolutionary Algorithms ◽  
Evolutionary Algorithm ◽  
Population Size ◽  
Test Problems ◽  
Multiobjective Evolutionary Algorithms ◽  
Number Of Solutions ◽  
Multiobjective Evolutionary Algorithm ◽  
Population Selection ◽  
Update Strategy

This paper proposes a constrained solution update strategy for multiobjective evolutionary algorithm based on decomposition, in which each agent aims to optimize one decomposed subproblem. Different from the existing approaches that assign one solution to each agent, our approach allocates the closest solutions to each agent and thus the number of solutions in an agent may be zero and no less than one. Regarding the agent with no solution, it will be assigned one solution in priority, once offspring are generated closest to its subproblem. To keep the same population size, the agent with the largest number of solutions will remove one solution showing the worst convergence. This improves diversity for one agent, while the convergence of other agents is not lowered. On the agent with no less than one solution, offspring assigned to this agent are only allowed to update its original solutions. Thus, the convergence of this agent is enhanced, while the diversity of other agents will not be affected. After a period of evolution, our approach may gradually reach a stable status for solution assignment; i.e., each agent is only assigned with one solution. When compared to six competitive multiobjective evolutionary algorithms with different population selection or update strategies, the experiments validated the advantages of our approach on tackling two sets of test problems.

How to Specify a Reference Point in Hypervolume Calculation for Fair Performance Comparison

2018 ◽  
Vol 26 (3) ◽  
pp. 411-440 ◽  
Author(s):  
Hisao Ishibuchi ◽  
Ryo Imada ◽  
Yu Setoguchi ◽  
Yusuke Nojima
Keyword(s):  
Reference Point ◽  
Pareto Front ◽  
Performance Comparison ◽  
Test Problems ◽  
Optimal Distribution ◽  
Multi Objective ◽  
Specification Method ◽  
All Solutions ◽  
Nadir Point ◽  
Distributed Solutions

The hypervolume indicator has frequently been used for comparing evolutionary multi-objective optimization (EMO) algorithms. A reference point is needed for hypervolume calculation. However, its specification has not been discussed in detail from a viewpoint of fair performance comparison. A slightly worse point than the nadir point is usually used for hypervolume calculation in the EMO community. In this paper, we propose a reference point specification method for fair performance comparison of EMO algorithms. First, we discuss the relation between the reference point specification and the optimal distribution of solutions for hypervolume maximization. It is demonstrated that the optimal distribution of solutions strongly depends on the location of the reference point when a multi-objective problem has an inverted triangular Pareto front. Next, we propose a reference point specification method based on theoretical discussions on the optimal distribution of solutions. The basic idea is to specify the reference point so that a set of well-distributed solutions over the entire linear Pareto front has a large hypervolume and all solutions in such a solution set have similar hypervolume contributions. Then, we examine whether the proposed method can appropriately specify the reference point through computational experiments on various test problems. Finally, we examine the usefulness of the proposed method in a hypervolume-based EMO algorithm. Our discussions and experimental results clearly show that a slightly worse point than the nadir point is not always appropriate for performance comparison of EMO algorithms.

Cognitive Reflection Effects on Time Discounting

2018 ◽  
Vol 39 (2) ◽  
pp. 99-106 ◽  
Author(s):  
Michał Białek ◽  
Przemysław Sawicki
Keyword(s):  
Individual Differences ◽  
Individual Difference ◽  
Delay Discounting ◽  
Reference Point ◽  
Reference Points ◽  
Cognitive Reflection Test ◽  
Process Information ◽  
Time Discounting ◽  
Cognitive Reflection ◽  
The Way

Abstract. In this work, we investigated individual differences in cognitive reflection effects on delay discounting – a preference for smaller sooner over larger later payoff. People are claimed to prefer more these alternatives they considered first – so-called reference point – over the alternatives they considered later. Cognitive reflection affects the way individuals process information, with less reflective individuals relying predominantly on the first information they consider, thus, being more susceptible to reference points as compared to more reflective individuals. In Experiment 1, we confirmed that individuals who scored high on the Cognitive Reflection Test discount less strongly than less reflective individuals, but we also show that such individuals are less susceptible to imposed reference points. Experiment 2 replicated these findings additionally providing evidence that cognitive reflection predicts discounting strength and (in)dependency to reference points over and above individual difference in numeracy.

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