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13th International Conference on evolutionary multi-Criterion optimization, EMO 2025

作者： Nan, Yang Ishibuchi, Hisao Pang, Lie Meng Department of Computer Science and Engineering Southern University of Science and Technology Shenzhen518055 China

ISBN: (纸本)9789819635375

In the evolutionary multi-objective optimization (EMO) field, evolutionary algorithms have a population to store a well-converged and well-distributed solution set. In the literature, the population size is usually specified in the range of 100–300 to approximate the entire Pareto front. Recently, a new framework with an external archive has been actively studied where a solution set selected from the archive is used to approximate the Pareto front. In this framework, a small population size can be better than a standard population size since a smaller population size means a larger number of generations under the termination condition specified by the same number of evaluated solutions. In this paper, we numerically examine whether better results are obtained from a smaller population size specification than a standard specification when the algorithm performance is evaluated using a solution set selected from an external archive. In our experiments, we examine the performance of four representative EMO algorithms (NSGA-II, NSGA-III, MOEA/D, and SMS-EMOA) with four specifications of the population size (36, 66, 120, and 210) on two frequently-used artificial test suites (DTLZ and WFG) and three real-world test suites (RWA, DDMOP, and RE). Our experimental results show that better results are obtained from a smaller population size specification in many cases when we cannot evaluate many solutions (i.e., when solution evaluation is expensive). © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2025.

关键词： evolutionary multi-objective optimization Performance comparison Small population size

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Achieving comprehensive water productivity improvement: A multi-objective simulation-optimization model for water productivity-oriented irrigation water management

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AGRICULTURAL WATER MANAGEMENT 2025年 309卷

作者： Li, Gang Zhang, Chenglong Huo, Zailin Liu, Yanqi China Agr Univ State Key Lab Efficient Utilizat Agr Water Resourc Beijing 100083 Peoples R China China Agr Univ Ctr Agr Water Res China Beijing 100083 Peoples R China Katholieke Univ Leuven Dept Earth & Environm Sci Div Soil & Water Management B-3000 Leuven Belgium

Improving water productivity (WP) from multiple perspectives is crucial for irrigated agriculture in arid areas, particularly due to challenges such as low crop WP, limited economic returns, and secondary soil salinization. In this study, a multi-objective simulation-optimization model is established for maximizing irrigation water productivity (IWP), economic water productivity (EWP), and nutritional water productivity (NWP) concurrently. Moreover, the Environmental Policy Integrated Climate (EPIC) crop growth model and water-salt balance equations are incorporated to readily simulate daily physical processes of crop growth and dynamic water and salt movement. The crop parameters required for simulating these physical processes are parameterized and calibrated based on existing studies. Subsequently, it's implemented in a case study within the Jiefangzha Irrigation Subarea, which is divided into 44 irrigation subsystems (basic irrigation decision-making units) to reflect the spatial distribution of input data. The Non-dominated Sorting Genetic Algorithm-III (NSGA-III) and Elite Opposition-Based Learning (EOBL) strategy are used to solve the problem and enhance the diversity of the randomly generated initial population accordingly, thus optimal solutions can be generated for supporting high- efficiency irrigation water use. Results indicate that (1) Optimal objectives (mean of the 44 irrigation subsystems) for IWP, EWP, and NWP are 6.72 Yuan/m3, 2.36 Kg/m3, 20041.7 Kcal/m3, with IWP increasing by 32.58 % over the status-quo. (2) Irrigation subsystems 41, 42, and 44 suffer severe salt accumulation, where salt- tolerant sunflowers should be prioritized for planting. (3) Crop root growth processes, sowing time, and growing periods have a strong influence on the salt concentration of actual root zone. Moreover, the proposed model emphasizes the influence of dynamic water-salt movement processes on crop growth and WP. Therefore, the study expands the research on multifac

关键词： Water productivity evolutionary multi-objective optimization Salinity control EPIC NSGA-III

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An adaptive decomposition-based evolutionary algorithm for many-objective optimization

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INFORMATION SCIENCES 2019年 491卷 204-222页

作者： Han, Dong Du, Wenli Du, Wei Jin, Yaochu Wu, Chunping East China Univ Sci & Technol Key Lab Adv Control & Optimizat Chem Proc Minist Educ Shanghai 200237 Peoples R China Univ Surrey Dept Comp Sci Guildford GU2 7XH Surrey England Shanghai Jiao Tong Univ Sch Mech Engn Shanghai 200237 Peoples R China

Penalty boundary intersection (PBI) is one popular method in decomposition based evolutionary multi-objective algorithms, where the penalty factor is crucial for striking a balance between convergence and diversity in a high-dimensional objective space. Meanwhile, the distribution of the obtained solutions highly depends on the setting of the weight vectors. This paper proposes an adaptive decomposition-based evolutionary algorithm for many-objective optimization, which introduces one adaptation mechanism for PBI-based decomposition and the other for adjusting the weight vector. The former assigns a specific penalty factor for each subproblem by using the distribution information of both population and the weight vectors, while the latter adjusts the weight vectors based on the objective ranges to handle problems with different scales on the objectives. We have compared the proposed algorithm with seven state-of-the-art many-objective evolutionary algorithms on a number of benchmark problems. The empirical results demonstrate the superiority of the proposed algorithm. (C) 2019 Elsevier Inc. All rights reserved.

关键词： evolutionary multi-objective optimization Many-objective optimization Decomposition Convergence Diversity Penalty boundary intersection Adaptation

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A Meta-objective Approach for Many-objective evolutionary optimization

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evolutionary COMPUTATION 2020年第1期28卷 1-25页

作者： Gong, Dunwei Liu, Yiping Yen, Gary G. China Univ Min & Technol Sch Informat & Control Engn Xuzhou 221116 Jiangsu Peoples R China Osaka Prefecture Univ Grad Sch Engn Dept Comp Sci & Intelligent Syst Sakai Osaka 5998531 Japan Oklahoma State Univ Sch Elect & Comp Engn Stillwater OK 74078 USA

Pareto-based multi-objective evolutionary algorithms experience grand challenges in solving many-objective optimization problems due to their inability to maintain both convergence and diversity in a high-dimensional objective space. Exiting approaches usually modify the selection criteria to overcome this issue. Different from them, we propose a novel meta-objective (MeO) approach that transforms the many-objective optimization problems in which the new optimization problems become easier to solve by the Pareto-based algorithms. MeO converts a given many-objective optimization problem into a new one, which has the same Pareto optimal solutions and the number of objectives with the original one. Each meta-objective in the new problem consists of two components which measure the convergence and diversity performances of a solution, respectively. Since MeO only converts the problem formulation, it can be readily incorporated within any multi-objective evolutionary algorithms, including those non-Pareto-based ones. Particularly, it can boost the Pareto-based algorithms' ability to solve many-objective optimization problems. Due to separately evaluating the convergence and diversity performances of a solution, the traditional density-based selection criteria, for example, crowding distance, will no longer mistake a solution with poor convergence performance for a solution with low density value. By penalizing a solution in term of its convergence performance in the meta-objective space, the Pareto dominance becomes much more effective for a many-objective optimization problem. Comparative study validates the competitive performance of the proposed meta-objective approach in solving many-objective optimization problems.

关键词： Many-objective optimization evolutionary multi-objective optimization meta-objective convergence diversity

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KnRVEA: A hybrid evolutionary algorithm based on knee points and reference vector adaptation strategies for many-objective optimization

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APPLIED INTELLIGENCE 2019年第7期49卷 2434-2460页

作者： Dhiman, Gaurav Kumar, Vijay Thapar Inst Engn & Technol Comp Sci & Engn Dept Patiala 147004 Punjab India

In this paper, a many-objective evolutionary algorithm, named as a hybrid evolutionary algorithm based on knee points and reference vector adaptation strategies (KnRVEA) is proposed. Knee point strategy is used to improve the convergence of solution vectors. In the proposed algorithm, a novel knee adaptation strategy is introduced to adjust the distribution of knee points. KnRVEA is compared with five well-known evolutionary algorithms over thirteen benchmark test functions. The results reveal that the proposed algorithm provides better results than the others in terms of Inverted Generational Distance and Hypervolume. The computational complexity of the proposed algorithm is also analyzed. The statistical testing is performed to show the statistical significance of proposed algorithm. The proposed algorithm is also applied on three real-life constrained many-objective optimization problems to demonstrate its efficiency. The experimental results show that the proposed algorithm is able to solve many-objective real-life problems.

关键词： evolutionary multi-objective optimization Many-objective optimization Convergence Diversity

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Approximate non-dominated sorting for evolutionary many-objective optimization

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INFORMATION SCIENCES 2016年第0期369卷 14-33页

作者： Zhang, Xingyi Tian, Ye Jin, Yaochu Anhui Univ Sch Comp Sci & Technol Inst Bioinspired Intelligence & Min Knowledge Hefei 230039 Peoples R China Univ Surrey Dept Comp Sci Guildford GU2 7XH Surrey England Donghua Univ Coll Informat Sci & Technol Shanghai 201620 Peoples R China

Non-dominated sorting has widely been adopted and shown to be very effective in dominance based evolutionary multi-objective optimization where the number of objectives is two or three. In. dealing with many-objective optimization problems, where the number of objectives is more than three, however, the effectiveness of dominance based evolutionary algorithms will seriously degrade and the computational complexity of non dominated sorting will considerably increase. In this paper, we propose an approximate non-dominated sorting algorithm for many-objective optimization, where the dominance relationship between two solutions is determined by a maximum of three objective comparisons on top of a sorted population according to one of the objectives. The time complexity of the proposed approximate sorting is independent of the number of objectives, which significantly enhances the time efficiency, in particular when the number of objectives is large. To examine the influence of inaccurate sorting on the search performance, the proposed approximate sorting method is embedded in three popular dominance based evolutionary many-objective optimization algorithms. Our experimental results on 16 widely used many-objective optimization benchmark problems suggest that the approximate non-dominated sorting method is not only computationally much more efficient than the state-of-the-art accurate non-dominated sorting methods, but also leads to better search performance on most test problems used in this study. (C) 2016 Elsevier Inc. All rights reserved.

关键词： evolutionary multi-objective optimization Computational complexity Non-dominated sorting Approximation Many-objective optimization

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Efficient Direct Aperture optimization via evolutionary Computation With Customized Variation Operators

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IEEE TRANSACTIONS ON EMERGING TOPICS IN COMPUTATIONAL INTELLIGENCE 2024年第2期8卷 1388-1401页

作者： Tian, Ye Guang, Yaopei Si, Langchun Cao, Ruifen Pei, Xi Zhang, Xingyi Anhui Univ Sch Comp Sci & Technol Hefei 230601 Peoples R China Univ Sci & Technol China Sch Nucl Sci & Technol Hefei 230026 Peoples R China

As a popular technique for intensity-modulated radiotherapy, direct aperture optimization (DAO) aims at generating treatment plans for cancer cases without the relaxation of optimization models. Conventional DAO methods are mainly based on mathematical programming, which can quickly generate a single plan but is inefficient in offering multiple candidate plans for clinical doctors. Recently, metaheuristics have been employed by DAO to offer many plans at a time;however, they are criticized for showing low efficiency in the evaluation and repair of iteratively generated offspring solutions. To provide an efficient DAO method, this work proposes a multi-objective evolutionary algorithm with customized variation operators. These operators can not only generate promising plans but also ensure their validity, and thus the search efficiency is improved by the acceleration of convergence and the elimination of repair operations. The experimental results demonstrate that the proposed DAO method is superior over existing heuristics and metaheuristics in terms of both effectiveness and efficiency.

关键词： Apertures Shape Metaheuristics Maintenance engineering evolutionary computation Convergence Search problems Direct aperture optimization evolutionary multi-objective optimization radiotherapy search efficiency variation operators

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evolutionary robust optimization in production planning - interactions between number of objectives, sample size and choice of robustness measure

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COMPUTERS & OPERATIONS RESEARCH 2017年第Mar.期79卷 266-278页

作者： Diaz, Juan Esteban Handl, Julia Xu, Dong-Ling Univ Manchester Alliance Manchester Business Sch Manchester M13 9PL Lancs England

We aim to find robust solutions in optimization settings where there is uncertainty associated with the operating/environmental conditions, and the fitness of a solution is hence best described by a distribution of outcomes. In such settings, the nature of the fitness distribution (reflecting the performance of a particular solution across a set of operating scenarios) is of potential interest in deciding solution quality, and previous work has suggested the inclusion of robustness as an additional optimization objective. However, there has been limited investigation of different robustness criteria, and the impact this choice may have on the sample size needed to obtain reliable fitness estimates. Here, we investigate different single and multi-objective formulations for robust optimization, in the context of a real-world problem addressed via simulation-based optimization. For the (limited evaluation) setting considered, our results highlight the value of an explicit robustness criterion in steering an optimizer towards solutions that are not only robust (as may be expected), but also associated with a profit that is, on average, higher than that identified by standard single-objective approaches. We also observe significant interactions between the choice of robustness measure and the sample size employed during fitness evaluation, an effect that is more pronounced for our multi-objective models. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： evolutionary multi-objective optimization Production planning Robust optimization Simulation-based optimization Uncertainty modelling

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Efficient dynamic resampling for dominance-based multiobjective evolutionary optimization

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ENGINEERING optimization 2017年第2期49卷 311-327页

作者： Cervantes, Alejandro Quintana, David Recio, Gustavo Univ Carlos III Madrid Dept Comp Sci Madrid Spain

multi-objective optimization problems are often subject to the presence of objectives that require expensive resampling for their computation. This is the case for many robustness metrics, which are frequently used as an additional objective that accounts for the reliability of specific sections of the solution space. Typical robustness measurements use resampling, but the number of samples that constitute a precise dispersion measure has a potentially large impact on the computational cost of an algorithm. This article proposes the integration of dominance based statistical testing methods as part of the selection mechanism of evolutionary multi-objective genetic algorithms with the aim of reducing the number of fitness evaluations. The performance of the approach is tested on five classical benchmark functions integrating it into two well-known algorithms, NSGA-II and SPEA2. The experimental results show a significant reduction in the number of fitness evaluations while, at the same time, maintaining the quality of the solutions.

关键词： evolutionary multi-objective optimization uncertainty resampling

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Archive of Useful Solutions for Directed Mating in evolutionary Constrained multiobjective optimization

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JOURNAL OF ADVANCED COMPUTATIONAL INTELLIGENCE AND INTELLIGENT INFORMATICS 2014年第2期18卷 221-231页

作者： Miyakawa, Minami Takadama, Keiki Sato, Hiroyuki Univ Electrocommun 1-5-1 Chofugaoka Chofu Tokyo 1828585 Japan

As an evolutionary approach to solve multi-objective optimization problems involving several constraints, recently a multi-objective evolutionary algorithm (MOEA) using two-stage non-dominated sorting and directed mating (TNSDM) has been proposed. In TNSDM, directed mating utilizes infeasible solutions dominating feasible solutions in the objective space to generate offspring. In our previous studies, significant contribution of directed mating to the improvement of the search performance was verified on several benchmark problems. However, in the conventional TNSDM, infeasible solutions utilized in directed mating are discarded in the selection process of parents (elites) population and cannot be utilized in the next generation. TNSDM has potential to further improve the search performance by archiving useful solutions for directed mating to the next generation and repeatedly utilizing them in directed mating. To further improve effects of directed mating in TNSDM, in this work, we propose an archiving strategy of useful solutions for directed mating. We verify the search performance of TNSDM using the proposed archive by varying the size of archive, and compare its search performance with the conventional CNSGA-II and RTS on m objectives k knapsacks problems. As results, we show that the search performance of TNSDM is improved by introducing the proposed archive in aspects of diversity of the obtained solutions in the objective space and convergence of solutions toward the optimal Pareto front.

关键词： evolutionary multi-objective optimization constraint-handling archive of solutions directed mating

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