Evolutionary Many-Objective Optimization: A Comparative Study of the State-of-the-Art

Li, Kaiwen; Wang, Rui; Zhang, Tao; Ishibuchi, Hisao

doi:10.1109/access.2018.2832181

Cited by 148 publications

(69 citation statements)

References 98 publications

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“…SPEA2+SDE is a genetic algorithm designed for many-objective optimisation. Very recently, it has been found to perform in general best out of various state-of-the-art many-objective algorithms in several experimental studies [41,43]. PAES is the most popular evolution strategy which has a (1+1) evolution form.…”

Section: Overviewmentioning

confidence: 99%

Many-Objective Test Suite Generation for Software Product Lines

Hierons

Liu

et al. 2020

ACM Trans. Softw. Eng. Methodol.

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Where a licence is displayed above, please note the terms and conditions of the licence govern your use of this document. When citing, please reference the published version. Take down policy While the University of Birmingham exercises care and attention in making items available there are rare occasions when an item has been uploaded in error or has been deemed to be commercially or otherwise sensitive.

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Section: Overviewmentioning

confidence: 99%

Many-Objective Test Suite Generation for Software Product Lines

Hierons

Liu

et al. 2020

ACM Trans. Softw. Eng. Methodol.

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“…It is a very important and difficult task to evaluate the performance of MOEAs. At present, evaluation focuses mainly on the following three aspects: (a) the approximation degree between the solution set and the Pareto optimal surface (convergence), (b) the distribution uniformity of the solution set in the target space (distribution uniformity), and (c) the extensive degree of the solution set (widespread distribution) [14,31,35]. In this paper, the performance of the improved algorithm in different test problems is evaluated by HV, inverted generational distance (IGD), and the average Hausdorff distance (∆ 2 ).…”

Section: Evaluation Metricsmentioning

confidence: 99%

“…The decomposition-based multi-objective evolutionary algorithm (MOEA/D) and multiple single-objective Pareto sampling algorithms (MSOPS) are the most representative algorithms [9]. In the MOEA/D framework, there are several aggregation functions, such as weighted sum (WS), weighted Tchebycheff (WT), and penalty-based boundary intersection (PBI) [14]. After the objective function is decomposed, the solution of an objective is optimized mainly through its neighboring objectives, so that the neighborhood sizes (NS) naturally affect the quality of the whole optimal solution set.…”

mentioning

confidence: 99%

Using the Decomposition-Based Multi-Objective Evolutionary Algorithm with Adaptive Neighborhood Sizes and Dynamic Constraint Strategies to Retrieve Atmospheric Ducts

Mai

Shi

Liao

et al. 2020

Sensors

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The traditional method of retrieving atmospheric ducts is to use the special sensor of weather balloons or rocket soundings to obtain information intelligently, and it is very expensive. Today, with the development of technology, it is very convenient to retrieve the atmospheric ducts from Global Navigation Satellite System (GNSS) phase delay and propagation loss observation data, and then the GNSS receiver on the ground forms an automatic receiving sensor. This paper proposes a hybrid decomposition-based multi-objective evolutionary algorithm with adaptive neighborhood sizes (EN-MOEA/ACD-NS), which dynamically imposes some constraints on the objectives. The decomposition-based multi-objective evolutionary algorithm (MOEA/D) updates the solutions through neighboring objectives, the number of which affects the quality of the optimal solution. Properly constraining the optimization objectives can effectively balance the diversity and convergence of the population. The experimental results from the Congress on Evolutionary Computation (CEC) 2009 on test instances with hypervolume (HV), inverted generational distance (IGD), and average Hausdorff distance ∆ 2 metrics show that the new method performs similarly to the evolutionary algorithm MOEA/ACD-NS, which considers only the dynamic change of the neighborhood sizes. The improved algorithm is applied to the practical problem of jointly retrieving atmospheric ducts with GNSS signals, and its performance further demonstrates its feasibility and practicability. the multi-objective optimization can make full use of multi-source observation information and can improve the reliability of the solution. The traditional method can only obtain a Pareto optimal solution that is not necessarily satisfactory to the decision-maker; the rationality of prior knowledge also affects the selection of the optimal solution. This paper proposes a multi-objective evolutionary algorithm (MOEA) for MOP problems in order to obtain a set of Pareto optimal solutions [5,6]. According to the optimization framework, MOEAs can be roughly divided into three categories, namely: (a) Pareto-based approaches [7], (b) indicator-based approaches [8], and (c) decomposition-based approaches [9].Pareto-based methods sort the individuals according to the dominant relationship among them, and then the optimal solution is selected. The Pareto-based approach is the most popular method in the evolutionary multi-objective optimization community. NSGA-II and SPEA2 are the most representative algorithms, and they are very effective when dealing with two or three objective functions [7,10]. However, when the number of objective functions increases to more than three, most of the solutions in the NSGA-II and SPEA2 search spaces become non-dominated solutions, resulting in a rapid decline in search capabilities.Indicator-based MOEAs use the value of performance indicators to guide the search direction, which drives whole generated solutions to the Pareto solution sets. As the calculation of the Pareto dominance relatio...

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“…In this paper, in order to provide a comprehensive assessment on the performance of all the competitors, two widely used performance indicators, i.e., inverted generational distance (IGD) [71] and Hypervolume (HV) [71], were adopted to measure the convergence and the diversity of the final solution set. A lower value of IGD and a larger value of HV indicate a better performance to approach the true PF and to spread solutions uniformly along the true PF.…”

Section: Performance Measuresmentioning

confidence: 99%

“…When computing the IGD indicator, no less than 500 sampling points from the true PF were used. For the HV calculation, the reference points were set to 1.1 times the upper bound of the PF, i.e., (1.1, 1.1) for biobjective problems and to (1.1, 1.1, 1.1) for three-objective problems, as suggested in [71]. All the algorithms were run 30 times, and the mean results and standard deviations were collected for comparison.…”

Section: Performance Measuresmentioning

confidence: 99%

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

Lin

Wang

et al. 2019

Complexity

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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.

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Evolutionary Many-Objective Optimization: A Comparative Study of the State-of-the-Art

Cited by 148 publications

References 98 publications

Many-Objective Test Suite Generation for Software Product Lines

Many-Objective Test Suite Generation for Software Product Lines

Using the Decomposition-Based Multi-Objective Evolutionary Algorithm with Adaptive Neighborhood Sizes and Dynamic Constraint Strategies to Retrieve Atmospheric Ducts

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

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