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Learning Value Functions in Interactive evolutionary multiobjective optimization

IEEE TRANSACTIONS ON evolutionary COMPUTATION 2015年第1期19卷 88-102页

作者： Branke, Juergen Greco, Salvatore Slowinski, Roman Zielniewicz, Piotr Univ Warwick Warwick Business Sch Coventry CV4 7AL W Midlands England Univ Catania Dept Econ & Business I-95124 Catania Italy Univ Portsmouth Portsmouth Business Sch Portsmouth PO1 2UP Hants England Poznan Univ Tech Inst Comp Sci PL-60965 Poznan Poland Polish Acad Sci Syst Res Inst PL-01447 Warshaw Poland

This paper proposes an interactive multiobjective evolutionary algorithm (MOEA) that attempts to learn a value function capturing the users' true preferences. At regular intervals, the user is asked to rank a single pair of solutions. This information is used to update the algorithm's internal value function model, and the model is used in subsequent generations to rank solutions incomparable according to dominance. This speeds up evolution toward the region of the Pareto front that is most desirable to the user. We take into account the most general additive value function as a preference model and we empirically compare different ways to identify the value function that seems to be the most representative with respect to the given preference information, different types of user preferences, and different ways to use the learned value function in the MOEA. Results on a number of different scenarios suggest that the proposed algorithm works well over a range of benchmark problems and types of user preferences.

关键词： evolutionary multiobjective optimization interactive procedure ordinal regression preference learning

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An Efficient Approach to Nondominated Sorting for evolutionary multiobjective optimization

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IEEE TRANSACTIONS ON evolutionary COMPUTATION 2015年第2期19卷 201-213页

作者： Zhang, Xingyi Tian, Ye Cheng, Ran Jin, Yaochu Anhui Univ Sch Comp Sci & Technol Minist Educ Key Lab Intelligent Comp & Signal Proc Hefei 230039 Peoples R China Univ Surrey Dept Comp Guildford GU2 7XH Surrey England

evolutionary algorithms have been shown to be powerful for solving multiobjective optimization problems, in which nondominated sorting is a widely adopted technique in selection. This technique, however, can be computationally expensive, especially when the number of individuals in the population becomes large. This is mainly because in most existing nondominated sorting algorithms, a solution needs to be compared with all other solutions before it can be assigned to a front. In this paper we propose a novel, computationally efficient approach to nondominated sorting, termed efficient nondominated sort (ENS). In ENS, a solution to be assigned to a front needs to be compared only with those that have already been assigned to a front, thereby avoiding many unnecessary dominance comparisons. Based on this new approach, two nondominated sorting algorithms have been suggested. Both theoretical analysis and empirical results show that the ENS-based sorting algorithms are computationally more efficient than the state-of-the-art nondominated sorting methods.

关键词： Computational complexity evolutionary multiobjective optimization nondominated sorting Pareto-optimality

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Visualization of Pareto Front Approximations in evolutionary multiobjective optimization: A Critical Review and the Prosection Method

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IEEE TRANSACTIONS ON evolutionary COMPUTATION 2015年第2期19卷 225-245页

作者： Tusar, Tea Filipic, Bogdan Jozef Stefan Inst Dept Intelligent Syst SI-1000 Ljubljana Slovenia Jozef Stefan Int Postgrad Sch SI-1000 Ljubljana Slovenia

In evolutionary multiobjective optimization, it is very important to be able to visualize approximations of the Pareto front (called approximation sets) that are found by multiobjective evolutionary algorithms. While scatter plots can be used for visualizing 2-D and 3-D approximation sets, more advanced approaches are needed to handle four or more objectives. This paper presents a comprehensive review of the existing visualization methods used in evolutionary multiobjective optimization, showing their outcomes on two novel 4-D benchmark approximation sets. In addition, a visualization method that uses prosection (projection of a section) to visualize 4-D approximation sets is proposed. The method reproduces the shape, range, and distribution of vectors in the observed approximation sets well and can handle multiple large approximation sets while being robust and computationally inexpensive. Even more importantly, for some vectors, the visualization with prosections preserves the Pareto dominance relation and relative closeness to reference points. The method is analyzed theoretically and demonstrated on several approximation sets.

关键词： Approximation set evolutionary algorithm evolutionary multiobjective optimization Pareto front projection visualization

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evolutionary multiobjective optimization with hybrid selection principles

Evolutionary multiobjective optimization with hybrid selecti...

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Congress on evolutionary Computation

作者： Ke Li Kalyanmoy Deb Qingfu Zhang Department of Electrical and Computer Engineering Michigan State University East Lansing MI USA Department of Computer Science City University of Hong Kong Hong Kong

ISBN: (纸本)9781479974931

Achieving balance between convergence and diversity is a basic issue in evolutionary multiobjective optimization (EMO). In this paper, we propose a hybrid EMO algorithm that assigns different selection principles to two separate and co-evolving archives. Particularly, one archive maintains a repository with a competitive selection pressure towards the Pareto-optimal front (PF), the other preserves a population with a satisfied distribution in the objective space. Furthermore, to exploit guidance information towards the Pareto-optimal set (PS), we develop a restricted mating selection mechanism to select mating parents from each archive for offspring generation. Empirical studies are conducted on a set of benchmark problems with complicated PSs. Experimental results demonstrate the effectiveness and competitiveness of our proposed algorithm in balancing convergence and diversity.

关键词： evolutionary multiobjective optimization Hybrid Selection Principles PF

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Adaptive directional local search strategy for hybrid evolutionary multiobjective optimization

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APPLIED SOFT COMPUTING 2014年 19卷 290-311页

作者： Kim, Hyoungjin Liou, Meng-Sing Sci Applicat Int Corp Cleveland OH 44135 USA NASA Glenn Res Ctr Cleveland OH 44135 USA

A novel adaptive local search method is developed for hybrid evolutionary multiobjective algorithms (EMOA) to improve convergence to the Pareto front in multiobjective optimization. The concepts of local and global effectiveness of a local search operator are suggested for dynamic adjustment of adaptation parameters. Local effectiveness is measured by quantitative comparison of improvements in convergence made by local and genetic operators based on a composite objective. Global effectiveness is determined by the ratio of number of local search solutions to genetic search solutions in the nondominated solution set. To be consistent with the adaptation strategy, a new directional local search operator, eLS (efficient Local Search), minimizing the composite objective function is designed. The search direction is determined using a centroid solution of existing neighbor solutions without making explicit calculations of gradient information. The search distance of eLS decreases adaptively as the optimization process converges. Performances of hybrid methods NSGA-II + eLS are compared with the baseline NSGA-II and NSGA-II + HCS1 for multiobjective test problems, such as ZDT and DTLZ functions. The neighborhood radius and local search probability are selected as adaptation parameters. Results show that the present adaptive local search strategy can provide significant convergence enhancement from the baseline EMOA by dynamic adjustment of adaptation parameters monitoring the properties of multiobjective problems on the fly. (C) 2014 Elsevier B.V. All rights reserved.

关键词： evolutionary multiobjective optimization Memetic algorithms Directional operator Adaptive local search

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GECCO'2014 tutorial on evolutionary multiobjective optimization 14

GECCO'2014 tutorial on evolutionary multiobjective optimizat...

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16th Genetic and evolutionary Computation Conference Companion, GECCO 2014 Companion

作者： Brockhoff, Dimo Inria Lille - Nord Europe Villeneuve d'Ascq France

ISBN: (纸本)9781450328814

Many optimization problems are multiobjective in nature in the sense that multiple, conflicting criteria need to be optimized simultaneously. Due to the conflict between objectives, usually, no single optimal solution exists. Instead, the optimum corresponds to a set of so-called Pareto-optimal solutions for which no other solution has better function values in all *** multiobjective optimization (EMO) algorithms are widely used in practice for solving multiobjective optimization problems due to several reasons. As stochastic blackbox algorithms, EMO approaches allow to tackle problems with nonlinear, nondifferentiable, or noisy objective functions. As set-based algorithms, they allow to compute or approximate the full set of Pareto-optimal solutions in one algorithm run---opposed to classical solution-based techniques from the multicriteria decision making (MCDM) field. Using EMO approaches in practice has two other advantages: they allow to learn about a problem formulation, for example, by automatically revealing common design principles among (Pareto-optimal) solutions (innovization) and it has been shown that certain single-objective problems become easier to solve with randomized search heuristics if the problem is reformulated as a multiobjective one (multiobjectivization).This tutorial aims at giving a broad introduction to the EMO field and at presenting some of its recent research results in more detail. More specifically, we are going to (i) introduce the basic principles of EMO algorithms in comparison to classical solution-based approaches, (ii) show a few practical examples which motivate the use of EMO in terms of the mentioned innovization and multiobjectivization principles, and (iii) present a general overview of state-of-the-art algorithms and techniques. Moreover, we will present some of the most important research results in areas such as indicator-based EMO, preference articulation, and performance *** classifi

关键词： tutorial emo multi-criteria decision making evolutionary multiobjective optimization

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evolutionary multiobjective optimization for Selecting Members of an Ensemble Streamflow Forecasting Model 13

Evolutionary Multiobjective Optimization for Selecting Membe...

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15th Genetic and evolutionary Computation Conference (GECCO)

作者： Brochero, Darwin Gagne, Christian Anctil, Francois Univ Laval Chaire Rech EDS Previs & Act Hydrol Dep Genie Civil & Genie Eaux Quebec City PQ G1V 0A6 Canada Univ Laval Dept Gen Elect & Gen Informat Lab Vis & Syst Numeriques Quebec City PQ G1V 0A6 Canada

ISBN: (纸本)9781450319638

We are proposing to use the Nondominated Sorting Genetic Algorithm II (NSGA-II) for optimizing a hydrological forecasting model of 800 simultaneous streamflow predictors. The optimization is based on the selection of the best 48 predictors from the 800 that jointly define the "best" ensemble in terms of two probabilistic criteria. Results showed that the difficulties in simplifying the ensembles mainly originate from the preservation of the system reliability. We conclude that Pareto fronts generated with NSGA-II allow the development of a decision process based explicitly on the trade-off between different probabilistic properties. In other words, evolutionary multiobjective optimization offers more flexibility to the operational hydrologists than a priori methods that produce only one selection.

关键词： evolutionary multiobjective optimization Probabilistic forecasting Streamflow forecasting Hydrological ensemble prediction system Uncertainty cascade model

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PRIMAL-DUAL TYPE evolutionary multiobjective optimization

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FOUNDATIONS OF COMPUTING AND DECISION SCIENCES 2013年第4期38卷 267-275页

作者： Kaliszewski, Ignacy Miroforidis, Janusz Polish Acad Sci Syst Res Inst PL-01447 Warsaw Poland Treeffect Co PL-32420 Gdow Poland

A new, primal-dual type approach for derivation of Pareto front approximations with evolutionary computations is proposed. At present, evolutionary multiobjective optimization algorithms derive a discrete approximation of the Pareto front (the set of objective maps of efficient solutions) by selecting feasible solutions such that their objective maps are close to the Pareto front. As, except of test problems, Pareto fronts are not known, the accuracy of such approximations is known neither. Here we propose to exploit also elements outside feasible sets with the aim to derive pairs of Pareto front approximations such that for each approximation pair the corresponding Pareto front lies, in a certain sense, in-between. Accuracies of Pareto front approximations by such pairs can be measured and controlled with respect to distance between such approximations. A rudimentary algorithm to derive pairs of Pareto front approximations is presented and the viability of the idea is verified on a limited number of test problems.

关键词： evolutionary multiobjective optimization lower and upper Pareto front approximation

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Indicator-based Selection in evolutionary multiobjective optimization Algorithms Based On the Desirability Index

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JOURNAL OF MULTI-CRITERIA DECISION ANALYSIS 2013年第5-6期20卷 319-337页

作者： Trautmann, Heike Wagner, Tobias Biermann, Dirk Weihs, Claus Univ Munster Informat Syst & Stat Grp D-48149 Munster Germany TU Dortmund Chair Computat Stat D-44221 Dortmund Germany TU Dortmund Inst Machining Technol ISF D-44227 Dortmund Germany

In multiobjective optimization, the identification of practically relevant solutions on the Pareto-optimal front is an important research topic. Desirability functions (DFs) allow the preferences of the decision maker to be specified in an intuitive way. Recently, it has been shown for continuous optimization problems that an a priori transformation of the objectives by means of DFs can be used to focus the search of a hypervolume-based evolutionary algorithm on the desired part of the front. In many-objective optimization, however, the computational complexity of the hypervolume can become a crucial part. Thus, an alternative to this approach will be presented in this paper. The new algorithm operates in the untransformed objective space, but the desirability index (DI), that is, a DF-based scalarization, will be used as the second-level selection criterion in the non-dominated sorting. The diversity and uniform distribution of the resulting approximation are ensured by the use of an external archive. In the experiments, different preferences are specified as DFs, and their effects are investigated. It is shown that trade-off solutions are generated in the desired regions of the Pareto-optimal front and with a density adaptive to the DI. The efficiency of the approach with respect to increasing objective space dimension is also analysed using scalable test functions. The convergence speed is superior to other set-based and preference-based evolutionary multiobjective algorithms while the approach is of low computational complexity due to cheap DI evaluations. Copyright (C) 2013 John Wiley & Sons, Ltd.

关键词： decision making desirability function desirability index evolutionary multiobjective optimization hypervolume preferences epsilon-MOEA archive

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Difficulty in evolutionary multiobjective optimization of Discrete Objective Functions with Different Granularities

Difficulty in Evolutionary Multiobjective Optimization of Di...

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7th International Conference on evolutionary Multi-Criterion optimization (EMO)

作者： Ishibuchi, Hisao Yamane, Masakazu Nojima, Yusuke Osaka Prefecture Univ Dept Comp Sci & Intelligent Syst Grad Sch Engn Naka Ku Sakai Osaka 5998531 Japan

ISBN: (纸本)9783642371400

Objective functions are discrete in combinatorial optimization. In general, the number of possible values of a discrete objective is totally different from problem to problem. That is, discrete objectives have totally different granularities in different problems (In this paper, "granularity" means the width of discretization intervals). In combinatorial multiobjective optimization, a single problem has multiple discrete objectives with different granularities. Some objectives may have fine granularities with many possible values while others may have very coarse granularities with only a few possible values. Handling of such a combinatorial multiobjective problem has not been actively discussed in the EMO community. In our former study, we showed that discrete objectives with coarse granularities slowed down the search by NSGA-II, SPEA2, MOEA/D and SMS-EMOA on two-objective problems. In this paper, we first discuss why such a discrete objective deteriorates the search ability of those EMO algorithms. Next we propose the use of strong Pareto dominance in NSGA-II to improve its search ability. Then we examine the effect of discrete objectives on the performance of the four EMO algorithms on many-objective problems. An interesting observation is that discrete objectives with coarse granularities improve the search ability of NSGA-II and SPEA2 on many-objective problems whereas they deteriorate their search ability on two-objective problems. The performance of MOEA/D and SMS-EMOA is always deteriorated by discrete objectives with coarse granularities. These observations are discussed from the following two viewpoints: One is the difficulty of many-objective problems for Pareto dominance-based EMO algorithms, and the other is the relation between discrete objectives and the concept of epsilon-dominance.

关键词： evolutionary multiobjective optimization many-objective problems discrete objectives epsilon-dominance combinatorial multiobjective optimization

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