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2010 IEEE World Congress on Computational Intelligence

作者： Dandois, Celine Divina, Federico Vanhoof, Wim Univ Namur Fac Comp Sci Rue Grandgagnage 21 B-5000 Namur Belgium Pablo Olavide Univ BIGS E-41013 Seville Spain

ISBN: (纸本)9781424481262

Learning concept descriptions from data is a challenging, and inherently multi-objective, optimization problem. The model induced by the learner has to be complete, consistent and easily interpretable, and producing it should take few computational resources. These objectives are often conflicting and require thus some heuristics to be balanced. The classical approach is to combine all the objectives into a single scoring function that is used for guiding the search in the hypothesis space. However, we believe that a multi-objective approach is more appropriate for this problem. Evolutionary Algorithms (EAs) are particularly suited for solving multi-objective optimization problems. In this paper, we propose an improved version of the Evolutionary Concept Learner (ECL) system, called Multi-Objective ECL (MOECL). While the search performed by ECL is based on a single-objective EA, MOECL adopts a multi-objective search strategy. It uses two objectives independent of class distribution, the true positive rate and the true negative rate, and is inspired by the simple and effective Pareto-based optimization algorithm SPEA2 for fitness assignement. Experiments show that the results of the MOECL system are globally more accurate than those of ECL and of the other state-of-the-art systems, on propositional datasets and on one relational dataset. As such, we believe the MOECL system to constitute a promising approach towards a multi-objective and effective concept learner.

关键词： Pareto optimisation Pareto-based optimization algorithm evolutionary algorithms evolutionary computation fitness assignment learning (artificial intelligence) multiobjective evolutionary concept learner multiobjective optimization problems multiobjective search strategy scoring function search problems

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R2-BEAN: R2 Indicator Based Evolutionary Algorithm for Noisy multiobjective optimization 7

R2-BEAN: R2 Indicator Based Evolutionary Algorithm for Noisy...

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7th IEEE Symposium on Computational Intelligence for Security and Defense Applications (IEEE-CISDA)

作者： Phan, Dung H. Suzuki, Junichi Univ Massachusetts Dept Comp Sci Boston MA 02125 USA

ISBN: (纸本)9781479954315

This paper proposes and evaluates an indicator based and noise-aware dominance operator for evolutionary algorithms to solve the multiobjective optimization problems (MOPs) that contain noise in their objective functions. The proposed operator, U(R)2(-)dominance operator is designed with (1) a quality indicator, called R2 indicator, which quantifies the goodness of a given solution candidate (individual) and (2) a non-parametric (i.e., distribution-free) statistical significance test called the Mann Whitney U-test. The U-R2-dominance operator takes samples of given two individuals in the objective space, calculates the R2 indicator value for each sample, estimates the impacts of noise on the R2 values with a U-test, and determines which individual is statistically superior/inferior. Experimental results show that it operates reliably in noisy MOPs and outperforms existing noise aware dominance operators particularly when many outliers exist under asymmetric noise distributions.

关键词： evolutionary computation nonparametric statistics statistical testing Mann-Whitney U-test R2 indicator R2-BEAN UR2-dominance operator asymmetric noise distributions evolutionary algorithms indicator-based dominance operator multiobjective optimization problems noise-aware dominance operators noisy MOP noisy multiobjective optimization nonparametric statistical significance test objective functions objective space quality indicator Linear programming Noise Noise measurement optimization Sociology Statistics Vectors evolutionary algorithm Noise quality indicator Nonparametric Statistics Noise measurement Statistical tests Objective function Sociology linear programming Mann-Whitney test MOP Mops

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Dini and Hadamard directional derivatives in multiobjective optimization: an overview of some results

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DECISIONS IN ECONOMICS AND FINANCE 2023年第2期46卷 355-377页

作者： Giorgi, Giorgio Jimenez, Bienvenido Novo, Vicente Univ Pavia Dept Econ & Management Via S Felice 5 I-27100 Pavia Italy Univ Nacl Educ Distancia UNED Dept Matemat Aplicada ETSI Ind Calle Juan Rosal 12 Madrid 28040 Spain

An overview is given on the use of Dini and Hadamard directional derivatives in various types of multiobjective optimization problems. Necessary optimality conditions are considered for a problem with an abstract constraint, for a problem with inequality and equality constraints and for a problem with both inequality and equality constraints and an abstract constraint. The issue of constraint qualifications is examined, and several first-order sufficient optimality conditions are presented for the third type of multiobjective optimization problems.

关键词： multiobjective optimization problems Dini derivatives Hadamard derivatives Optimality conditions Constraint qualifications

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Automated Discovery of Vital Knowledge from Pareto-optimal Solutions: First Results from Engineering Design

Automated Discovery of Vital Knowledge from Pareto-optimal S...

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2010 IEEE World Congress on Computational Intelligence

作者： Bandaru, Sunith Deb, Kalyanmoy Indian Inst Technol Dept Mech Engn Kanpur 208016 Uttar Pradesh India

ISBN: (纸本)9781424481262

Real world multi-objective optimization problems are often solved with the only intention of selecting a single trade-off solution by taking up a decision-making task. The computational effort and time spent on obtaining the entire Pareto front is thus not justifiable. The Pareto solutions as a whole contain within them a lot more information than that is used. Extracting this knowledge would not only give designers a better understanding of the system, but also bring worth to the resources spent. The obtained knowledge acts as governing principles which can help solve other similar systems easily. We propose a genetic algorithm based unsupervised approach for learning these principles from the Pareto-optimal dataset of the base problem. The methodology is capable of discovering analytical relationships of a certain type between different problem entities.

关键词： Pareto front Pareto optimisation Pareto-optimal solutions data mining genetic algorithm genetic algorithms knowledge discovery multiobjective optimization problems unsupervised learning unsupervised learning approach

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Performance Comparison of multiobjective Evolutionary Algorithms on problems with Partially Different Properties from Popular Test Suites

Performance Comparison of Multiobjective Evolutionary Algori...

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IEEE International Conference on Systems, Man, and Cybernetics (SMC)

作者： Matsumoto, Takashi Masuyama, Naoki Nojima, Yusuke Ishibuchi, Hisao Osaka Prefecture Univ Dept Comp Sci & Intelligent Syst Sakai Osaka 5998531 Japan Southern Univ Sci & Technol SUSTech Dept Comp Sci & Engn Shenzhen Peoples R China

ISBN: (纸本)9781538666500

A multiobjective Evolutionary Algorithm (MOEA) is one of the effective approaches for solving multiobjective optimization problems (MOPs). The performance of MOEAs is evaluated mainly by scalable MOP test suites where the number of objectives can be arbitrarily specified. However, the number of scalable MOP test suites is quite limited and their properties are similar. Thus, there is a risk that the current research on MOEAs is specialized for some properties (i.e., a shape of feasible regions, a shape of the Pareto front, and a distance function) of existing scalable MOP test suites. In this paper, we focus on the above properties of two popular MOP test suites (i.e., DTLZ and WFG). Based on DTLZ and WFG, we create 12 MOPs which have partially different properties from those of DTLZ and WFG. Computational experiments show that the search performance of the state-of-the-art MOEAs strongly depends on three properties.

关键词： multiobjective optimization problems many-objective optimization scalable test suites evolutionary multiobjective optimization algorithms

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Balancing Convergence and Diversity in multiobjective Immune Algorithm 12

Balancing Convergence and Diversity in Multiobjective Immune...

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12th International Conference on Advanced Computational Intelligence (ICACI)

作者： Li, Lingjie Lin, Wu Lin, Qiuzhen Ming, Zhong Shenzhen Univ Coll Comp Sci & Software Engn Shenzhen Peoples R China

ISBN: (纸本)9781728142487

Recently, multiobjective immune algorithms (MOIAs) become popular, which are designed for multiobjective optimization problems (MOPs). However, most existing MOIAs put more attention on maintaining diversity as the used clonal selection strategy will allocate more cloning for the sparse areas, which may hamper the convergence to speed to the optimal Pare-to front, especially for some complicated MOPs. To alleviate the phenomenon mentioned above, we propose a dynamic mechanism into traditional MOIAs in this paper, aiming to balance convergence and diversity, called BCD-MOIA. First, MOP will be decomposed into several single subproblems by decomposition method, and then these subproblems will be optimized simultaneously. Second, we propose a novel measure metric instead of the crowding distance to assign the clone number for each solution, which includes two main parts. The first part focuses on the diversity performance, i.e., the perpendicular distance between solution and its associated weight vectors. The second part uses the aggregated function values quantified by the decomposition method, which is more efficient for accelerating the convergence speed and maintaining diversity as well. Moreover, a dynamic mechanism is performed during the whole evolutionary process, focusing on diversity and convergence at different stages. By this way, our proposed algorithm can tradeoff the performance on convergence and diversity dynamically. The effectiveness of our proposed algorithm BCD-MOIA is validated by comparing with three competitive MOIAs and three multi-objective evolutionary algorithms for tackling two sets of complicated problems.

关键词： immune algorithm multiobjective optimization problems convergence and diversity

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Many-Objective Test problems to Visually Examine the Behavior of multiobjective Evolution in a Decision Space

Many-Objective Test Problems to Visually Examine the Behavio...

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11th International Conference on Parallel Problem Solving from Nature

作者： Ishibuchi, Hisao Hitotsuyanagi, Yasuhiro Tsukamoto, Noritaka Nojima, Yusuke Osaka Prefecture Univ Dept Comp Sci & Intelligent Syst Grad Sch Engn Naka Ku Osaka 5998531 Japan

ISBN: (纸本)9783642158704

Many-objective optimization is a hot issue in the EMO (evolutionary multiobjective optimization) community. Since almost all solutions in the current population are non-dominated with each other in many-objective EMO algorithms, we may need a different fitness evaluation scheme from the case of two and three objectives. One difficulty in the design of many-objective EMO algorithms is that we cannot visually observe the behavior of multiobjective evolution in the objective space with four or more objectives. In this paper, we propose the use of many-objective test problems in a two- or three-dimensional decision space to visually examine the behavior of multiobjective evolution. Such a visual examination helps us to understand the characteristic features of EMO algorithms for many-objective optimization. Good understanding of existing EMO algorithms may facilitates their modification and the development of new EMO algorithms for many-objective optimization.

关键词： Evolutionary multiobjective optimization (EMO) many-objective optimization multiobjective optimization problems test problems

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multiobjective approximate gradient projection method for constrained vector optimization: Sequential optimality conditions without constraint qualifications

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2022年 410卷 114122-114122页

作者： Lai, Kin Keung Maurya, J. K. Mishra, S. K. Jinan Univ Sch Intelligent Syst Sci & Engn Zhuhai Campus Zhuhai Peoples R China Kashi Naresh Govt Post Grad Coll Gyanpur Bhadohi 221304 India Banaras Hindu Univ Inst Sci Dept Math Varanasi 221005 India

In this paper, we establish multiobjective approximate gradient projection (MAGP) and linear multiobjective approximate gradient projection (LMAGP) sequential optimality conditions without constraint qualification for multiobjective constrained optimization problems. Further, we introduce constraint qualifications under which a point that satisfies established optimality conditions also satisfies Karush-Kuhn-Tucker optimality conditions. Such constraint qualifications are called strict constraint qualifications. We discuss the relationship between introduced constraint qualifications and validate it by suitable examples. (c) 2022 Elsevier B.V. All rights reserved.

关键词： multiobjective optimization problems Sequential optimality conditions Constraints qualification Approximate gradient projection method

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Assessing the Performance of Interactive multiobjective optimization Methods: A Survey

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ACM COMPUTING SURVEYS 2021年第4期54卷 85-85页

作者： Afsar, Bekir Miettinen, Kaisa Ruiz, Francisco Univ Jyvaskyla Fac Informat Technol POB 35 Agora FI-40014 Jyvaskyla Finland Univ Malaga Dept Appl Econ Math Fac Comercio & Gest Campus Teatinos Malaga 29071 Spain

Interactive methods are useful decision-making tools for multiobjective optimization problems, because they allow a decision-maker to provide her/his preference information iteratively in a comfortable way at the same time as (s)he learns about all different aspects of the problem. A wide variety of interactive methods is nowadays available, and they differ from each other in both technical aspects and type of preference information employed. Therefore, assessing the performance of interactive methods can help users to choose the most appropriate one for a given problem. This is a challenging task, which has been tackled from different perspectives in the published literature. We present a bibliographic survey of papers where interactive multiobjective optimization methods have been assessed (either individually or compared to other methods). Besides other features, we collect information about the type of decision-maker involved (utility or value functions, artificial or human decision-maker), the type of preference information provided, and aspects of interactive methods that were somehow measured. Based on the survey and on our own experiences, we identify a series of desirable properties of interactive methods that we believe should be assessed.

关键词： Interactive methods multiobjective optimization problems performance assessment decision-makers preference information

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multiobjective ensemble surrogate-based optimization algorithm for groundwater optimization designs

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JOURNAL OF HYDROLOGY 2022年第PartB期612卷

作者： Wu, Mengtian Wang, Lingling Xu, Jin Wang, Zhe Hu, Pengjie Tang, Hongwu Hohai Univ State Key Lab Hydrol Water Resources & Hydraul Eng Nanjing Peoples R China Hohai Univ Coll Water Conservancy & Hydropower Engn Nanjing Peoples R China Hohai Univ Coll Agr Sci & Engn Nanjing Peoples R China Hohai Univ Coll Hydrol & Water Resources Nanjing Peoples R China

Simulation technique is an increasingly focused method for conveniently evaluating a solution or scenario in the field of groundwater. However, traditional evolutionary algorithms require at least thousands of simulation executions when addressing groundwater simulation-based optimization problems to find reasonable solutions. Intensive simulations usually yield a prohibitive computational burden if the simulation involved is time-consuming. To defeat the issue, this paper proposes a multiobjective ensemble surrogate-based optimization algorithm named MESOA for groundwater optimization designs. Surrogate models can reduce the continual usage of expensive-cost models in a way that approximates objective functions. Unlike existing surrogate-assisted evolutionary algorithms, MESOA employs surrogates with various basis functions (RBFs) and Kriging as available surrogates, and presents an adaptive switching technique to construct surrogate models in an online way. In addition, MESOA involves three sample infill criteria and a novel population filter. With the assistance of these techniques, MESOA can fully depict the outline of the true Pareto front, although the times of invoking simu-lation are limited. Some representative benchmark cases are provided to test the applicability and effectiveness of the proposed algorithm at first. Afterward, MESOA is applied to solve some practical groundwater multi -objective optimization designs, such as groundwater remediation and requirement optimization. All empirical results indicate that the proposed algorithm obtains more availability and effectiveness than other algorithms and has wide universality for groundwater optimization designs.

关键词： multiobjective optimization problems Surrogate -assisted evolutionary algorithm Groundwater optimization designs Pumping and treatment optimization

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