A Vector Angle-Based Evolutionary Algorithm for Unconstrained Many-Objective Optimization

Xiang, Yi; Li, Miqing; Chen, Zefeng

doi:10.1109/tevc.2016.2587808

Cited by 364 publications

(164 citation statements)

References 54 publications

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“…The effectiveness of the proposed SDR is also verified on six MOEAs, namely, NSGA-II [2], SPEA2 [20], PESA-II [21], GrEA [9], KnEA [14], and VaEA [15]. In MOEA/DD, the size of neighborhood T is set to ⌈0.1N ⌉, the neighborhood selection probability δ is set to 0.9, and the maximum number of solutions replaced by each offspring n r is set to ⌈0.01N ⌉, with N denoting the population size.…”

Section: A Experimental Settings 1) Dominance Relationsmentioning

confidence: 99%

“…is a metric for measuring the convergence degree of x, which has been widely used in many MOEAs [15], [33]- [35], θ xy denotes the acute angle between the objective values of the two candidate solutions, namely,…”

Section: A the Proposed Dominance Relationmentioning

confidence: 99%

“…The proposed SDR is then embedded in NSGA-II [2], SPEA2 [20], PESA-II [21], GrEA [9], KnEA [14], and VaEA [15], and compared with the original versions of the six MOEAs. NSGA-II, SPEA2, and PESA-II are three classical MOEAs, which have been demonstrated to be effective in solving MOPs.…”

Section: Performance Of Sdr On Existing Moeasmentioning

confidence: 99%

“…These methods first eliminate a few worse candidate solutions based on Pareto dominance, then distinguish the incomparable candidate solutions by the secondary selection criterion. Existing methods belonging to this category mainly adopt three basic ideas: The first idea is to develop new criterion to bias those with good convergence and diversity in the incomparable candidate solutions, such as KnEA [14] and VaEA [15]; the second idea employs performance indicators to distinguish the quality of incomparable candidate solutions by selecting those with large contributions, such as HypE [16] and AR-MOEA [17]; and the third idea is to combine Pareto dominance with decomposition based algorithms, such as MOEA/DD [18] and BCE-MOEA/D [19].…”

mentioning

confidence: 99%

“…3) The performance of the proposed SDR is also assessed by embedding it in two existing MOEAs developed for solving MOPs, namely, SPEA2 [20] and PESA-II [21], and three existing MOEAs tailored for handling MaOPs, namely, GrEA [9], KnEA [14], and VaEA [15]. Experimental results demonstrate that the proposed SDR maintains a good balance between convergence and diversity, which can considerably improve the performance of the MOEAs.…”

mentioning

confidence: 99%

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A Strengthened Dominance Relation Considering Convergence and Diversity for Evolutionary Many-Objective Optimization

Tian

Cheng

Zhang

et al. 2019

IEEE Trans. Evol. Computat.

277

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Abstract-Both convergence and diversity are crucial to evolutionary many-objective optimization, whereas most existing dominance relations show poor performance in balancing them, thus easily leading to a set of solutions concentrating on a small region of the Pareto fronts. In this paper, a novel dominance relation is proposed to better balance convergence and diversity for evolutionary manyobjective optimization. In the proposed dominance relation, an adaptive niching technique is developed based on the angles between the candidate solutions, where only the best converged candidate solution is identified to be nondominated in each niche. Experimental results demonstrate that the proposed dominance relation outperforms existing dominance relations in balancing convergence and diversity. A modified NSGA-II is suggested based on the proposed dominance relation, which shows competitiveness against the state-of-the-art algorithms in solving many-objective optimization problems. The effectiveness of the proposed dominance relation is also verified on several other existing multi-and many-objective evolutionary algorithms.

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Section: A Experimental Settings 1) Dominance Relationsmentioning

confidence: 99%

Section: A the Proposed Dominance Relationmentioning

confidence: 99%

Section: Performance Of Sdr On Existing Moeasmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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A Strengthened Dominance Relation Considering Convergence and Diversity for Evolutionary Many-Objective Optimization

Tian

Cheng

Zhang

et al. 2019

IEEE Trans. Evol. Computat.

277

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A hybrid indicator many‐objective optimization algorithm for the selection and delivery of disaster relief materials problem

Zhu¹

2020

Concurrency and Computation

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Traditional methods fail to comprehensively consider the selection and delivery of disaster relief materials (SDDM) problem. To solve the problem, the SDDM will be comprehensively considered in this article, which will be built into a many-objective disaster relief materials selection and delivery model with four objectives to be optimized in the last kilometer of the disaster relief organization. Meanwhile, a many-objective optimization algorithm is designed to solve the proposed disaster relief materials model by employing the different excellent indicators. Two extensive simulation experiments are carried out. On the one hand, the performance of the designed many-objective is tested on DTLZ and WFG benchmark functions. On the other hand, the proposed many-objective model is solved by employing the designed algorithm. In addition, the simulation result shows that the designed algorithm is effective in solving the SDDMs problem. K E Y W O R D S benchmark function, indicators, many-objective optimization algorithm, selection and delivery of disaster relief materials 1 INTRODUCTION With the frequent occurrence of geological disasters in recent years, it has caused huge economic losses and human casualties such as floods, earthquakes, volcanic eruptions, forest fires. According to the laws of nature, the disasters are often irresistible and unavoidable. The planning of post-disaster relief operations will be crucial to reduce the positive damage and casualties. 1,2 Disaster relief materials often play an important role in ensuring the smooth overcoming of disasters. In other words, the timely delivery of the right relief materials to the disaster site has become extremely urgent. Therefore, there are usually two key points need to be solved for this problem from a macro perspective. On the one hand, materials with urgent rescue value should be selected for the disaster relief site. On the other hand, the selected materials should be delivered to the disaster relief site with minimum time cost. With the development of researching on this kind of problem, many excellent methods have been developed to solve the practical problem. 3,4 Wang et al 5 proposed a heuristic method based on nested partitions to solve the computational complexity problem. The basic idea of the method is to divide the solution area by fixing some variables, and determine the most promising sub-region according to the corresponding value of the linear programming relaxation problem. The simulation experiments show that the effective of this algorithm. Saeidian et al 6 compared the performance of genetic algorithm (GA) and bee algorithm (BA) in finding the optimum location of relief centers and allocating of the parcels to the distance between the center and the plot. For simulated data and real data, GA is faster than BA. Lourenco et al 7 designed an algorithm that can be executed by the software defined network (SDN) controller to generate an evacuation plan through the satellite network. The evacuation plan is the transmission plan that maximi...

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Many‐objective evolutionary computation based on adaptive hypersphere dynamic angle vector dominance

Zhang

2021

Concurrency and Computation

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Summary In real‐world, more and more MaOP (MaOPs) have emerged, which pose great challenge for traditional multi‐objective evolutionary algorithms (MOEAs). In this paper, a many‐objective evolutionary computation based on adaptive hypersphere dynamic angle vector dominance (AHDAVD‐MOEA) is proposed. The AHDAVD‐MOEA has three remarkable characteristics: (1) Based on the angle domination, a dynamic angle vector dominance relationship is proposed. In the evolution process, DAVD can dynamically adjust the population target space coordinate system according to the distribution of each generation of population in the target space, and at the same time calculate the angle vector of individuals to compare the dominance relations. Therefore, DAVD can dynamically describe the convergence and diversity of population, so as to achieve the goal of balancing the convergence and diversity of many target population. (2) Based on DAVD, an adaptive hypersphere dynamic angle vector dominance (AHDAVD) is proposed. After the DAVD process, AHDAVD adds an adaptive radius R to all dimensions of each non‐dominated solution to form a hypersphere to expand the dominance range of individuals. The dominance relationship among individuals is judged by the dominance range of the extended solution individuals, which further enhances the convergence of the population. (3) Based on the simplified harmonic normalized distance method, a simplified harmonic normalized distance method (SHNDM‐Lp) based on Lp‐norm (Where p is set to 1/M, and M is the target number) is proposed. SHNDM‐Lp uses Euclidean distance to measure the distance between individuals in many space, and uses fractional normal form to evaluate the proximity distance of solution individuals in many target space more effectively. The validity of the adaptive hypersphere dynamic angle vector dominance and the AHDAVD‐MOEA are tested by DTLZ and WFG series of 5‐, 8‐ and 10‐targets. The experimental results show that: (1) Compared with AD and other representative improved dominance relations, the adaptive hypersphere dynamic angle vector dominance relationship has significantly better performance; (2) Compared with other five classical many‐objective evolutionary algorithms, AHDAVD‐MOEA has obvious advantages in population convergence and diversity. Overall, the proposed AHDAVD‐MOEA is a promising optimizer in many‐objective optimization.

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A Vector Angle-Based Evolutionary Algorithm for Unconstrained Many-Objective Optimization

Cited by 364 publications

References 54 publications

A Strengthened Dominance Relation Considering Convergence and Diversity for Evolutionary Many-Objective Optimization

A Strengthened Dominance Relation Considering Convergence and Diversity for Evolutionary Many-Objective Optimization

A hybrid indicator many‐objective optimization algorithm for the selection and delivery of disaster relief materials problem

Many‐objective evolutionary computation based on adaptive hypersphere dynamic angle vector dominance

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