Many-Objective Test Problems to Visually Examine the Behavior of Multiobjective Evolution in a Decision Space

Ishibuchi, Hisao; Hitotsuyanagi, Yasuhiro; Tsukamoto, Noritaka; Nojima, Yusuke

doi:10.1007/978-3-642-15871-1_10

Cited by 88 publications

(67 citation statements)

References 29 publications

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“…In the calculation of HV, a crucial issue is the choice of the reference point. Choosing a reference point that is slightly larger than the worst value of each objective on the Pareto front has been found to be suitable since the effects of convergence and diversity of the set can be well balanced [3], [42]. Since the range of the Pareto front is unknown in TSP, we regard the point with 22 for each objective (i.e., r = 22 M ) as the reference point, given that it is slightly larger than the worst value of the mixed nondominated solution set constructed by all the obtained solution sets.…”

Section: Performance Verification Of Sdementioning

confidence: 99%

“…Following the practice in [42], the population size was set to 200 for the tested algorithms, and the archive was also maintained with the same size if required. A crossover probability p c = 1.0 and a mutation probability p m = 1/N (where N denotes the number of decision variables) were used.…”

Section: Performance Verification Of Sdementioning

confidence: 99%

“…In addition, in MOEA/D the population size cannot be arbitrarily specified since it is equal to the number of weight vectors. As suggested in [42], we used the closest number to 200 among the possible values as the population size (i.e., 220, 252, and 220 for 4-, 6-, and 10-objective problems, respectively).…”

Section: Comparison With State-of-the-art Algorithmsmentioning

confidence: 99%

“…This means that when testing an algorithm on this problem, not only do we clearly view the distribution of solutions in the decision space but also we can infer the ability of the algorithm to maintain diversity in the objective space [50]. Recently, Ishibuchi et al extended the Pareto-Box problem, making it to be easily used in the performance comparison of EMO algorithms for many-objective optimization [42].…”

Section: Comparison On the Pareto-box Test Problemmentioning

confidence: 99%

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Shift-Based Density Estimation for Pareto-Based Algorithms in Many-Objective Optimization

Yang

Liu

2014

IEEE Trans. Evol. Computat.

560

248

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Abstract-It is commonly accepted that Pareto-based evolutionary multiobjective optimization (EMO) algorithms encounter difficulties in dealing with many-objective problems. In these algorithms, the ineffectiveness of the Pareto dominance relation for a high-dimensional space leads diversity maintenance mechanisms to play the leading role during the evolutionary process, while the preference of diversity maintenance mechanisms for individuals in sparse regions results in the final solutions distributed widely over the objective space but distant from the desired Pareto front. Intuitively, there are two ways to address this problem: 1) modifying the Pareto dominance relation and 2) modifying the diversity maintenance mechanism in the algorithm. In this paper, we focus on the latter and propose a shift-based density estimation (SDE) strategy. The aim of our study is to develop a general modification of density estimation in order to make Pareto-based algorithms suitable for many-objective optimization. In contrast to traditional density estimation which only involves the distribution of individuals in the population, SDE covers both the distribution and convergence information of individuals. The application of SDE in three popular Paretobased algorithms demonstrates its usefulness in handling manyobjective problems. Moreover, an extensive comparison with five state-of-the-art EMO algorithms reveals its competitiveness in balancing convergence and diversity of solutions. These findings not only show that SDE is a good alternative to tackle manyobjective problems, but also present a general extension of Paretobased algorithms in many-objective optimization.

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Section: Performance Verification Of Sdementioning

confidence: 99%

Section: Performance Verification Of Sdementioning

confidence: 99%

Section: Comparison With State-of-the-art Algorithmsmentioning

confidence: 99%

Section: Comparison On the Pareto-box Test Problemmentioning

confidence: 99%

See 2 more Smart Citations

Shift-Based Density Estimation for Pareto-Based Algorithms in Many-Objective Optimization

Yang

Liu

2014

IEEE Trans. Evol. Computat.

560

248

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show abstract

“…In many-objective optimization, several scalable continuous benchmark function suites, such as DTLZ [9] and WFG [10], have been commonly used. Recently, researchers have also designed/presented some problem suites specially for many-objective optimization [11][12][13][14][15][16]. However, all of these problem suites only represent one or several aspects of real-world scenarios.…”

Section: Introductionmentioning

confidence: 99%

A benchmark test suite for evolutionary many-objective optimization

Cheng

Tian

et al. 2017

Complex Intell. Syst.

381

118

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In the real world, it is not uncommon to face an optimization problem with more than three objectives. Such problems, called many-objective optimization problems (MaOPs), pose great challenges to the area of evolutionary computation. received little attention. Several test problem suites which were designed for multi-objective optimization have still been dominantly used in many-objective optimization. In this paper, we carefully select (or modify) 15 test problems with diverse properties to construct a benchmark test suite, aiming to promote the research of evolutionary many-objective optimization (EMaO) via suggesting a set of test problems with a good representation of various real-world scenarios.Also, an open-source software platform with a user-friendly GUI is provided to facilitate the experimental execution and data observation.

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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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Many-Objective Test Problems to Visually Examine the Behavior of Multiobjective Evolution in a Decision Space

Cited by 88 publications

References 29 publications

Shift-Based Density Estimation for Pareto-Based Algorithms in Many-Objective Optimization

Shift-Based Density Estimation for Pareto-Based Algorithms in Many-Objective Optimization

A benchmark test suite for evolutionary many-objective optimization

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

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