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multiobjective evolutionary algorithms: A survey of the state of the art

SWARM AND evolutionary COMPUTATION 2011年第1期1卷 32-49页

作者： Zhou, Aimin Qu, Bo-Yang Li, Hui Zhao, Shi-Zheng Suganthan, Ponnuthurai Nagaratnam Zhang, Qingfu E China Normal Univ Comp Sci & Technol Dept Shanghai 200241 Peoples R China Nanyang Technol Univ Sch Elect & Elect Engn Singapore 639798 Singapore Xi An Jiao Tong Univ Sch Sci Xian 710049 Peoples R China Univ Essex Sch Comp Sci & Elect Engn Colchester CO4 3SQ Essex England

A multiobjective optimization problem involves several conflicting objectives and has a set of Pareto optimal solutions. By evolving a population of solutions, multiobjective evolutionary algorithms (MOEAs) are able to approximate the Pareto optimal set in a single run. MOEAs have attracted a lot of research effort during the last 20 years, and they are still one of the hottest research areas in the field of evolutionary computation. This paper surveys the development of MOEAs primarily during the last eight years. It covers algorithmic frameworks such as decomposition-based MOEAs (MOEA/Ds), memetic MOEAs, coevolutionary MOEAs, selection and offspring reproduction operators, MOEAs with specific search methods, MOEAs for multimodal problems, constraint handling and MOEAs, computationally expensive multiobjective optimization problems (MOPs), dynamic MOPs, noisy MOPs, combinatorial and discrete MOPs, benchmark problems, performance indicators, and applications. In addition, some future research issues are also presented. (C) 2011 Elsevier B.V. All rights reserved.

关键词： multiobjective optimization evolutionary multiobjective optimization multiobjective evolutionary algorithms Multicriteria decision making

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multiobjective evolutionary algorithms for strategic deployment of resources in operational units

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2020年第2期282卷 729-740页

作者： Drake, John H. Starkey, Andrew Owusu, Gilbert Burke, Edmund K. Queen Mary Univ London Operat Res Grp Mile End Rd London E1 4NS England British Telecommun PLC Business Modelling & Operat Transformat Practice Adastral Pk Ipswich Suffolk England Univ Leicester Univ Rd Leicester LE1 7RH Leics England

Large-scale infrastructure networks require frequent maintenance, often performed by a team of skilled engineers spread over a large area. The set of tasks allocated to an engineer can have a huge impact on overall efficiency, whether that be in terms of time taken to complete all tasks, staffing costs or environmental costs in terms of emissions. When required to efficiently allocate a set of geographically distributed tasks to a maintenance engineering workforce, one approach is to define working areas for which teams of engineers are responsible. Often a key obstacle to overcome when looking for solutions is ensuring a balance between multiple competing objectives. In this paper, we employ a number of multiobjective evolutionary algorithms to analyse a simulation model for a real-world workforce optimisation problem used by BT. We provide a detailed analysis of the class of problems to be solved, where the workforce and a set of service distribution points must be split into smaller working areas, referred to as operational units. As the choice of how many operational units to split a larger working area into is critical, some of the practical considerations that must be made when addressing such problems are highlighted. This research has allowed the planning team at BT to understand the unique complexities of the nature of the problems they face in different areas of the UK, particularly with respect to the choice of number of operational units, and has strengthened their ability to design operational units effectively. (C) 2019 The Authors. Published by Elsevier B.V.

关键词： Decision support systems Workforce optimisation multiobjective optimisation multiobjective evolutionary algorithms Work area optimisation

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multiobjective evolutionary algorithms Are Still Good: Maximizing Monotone Approximately Submodular Minus Modular Functions

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evolutionary COMPUTATION 2021年第4期29卷 463-490页

作者： Qian, Chao Nanjing Univ State Key Lab Novel Software Technol Nanjing 210023 Peoples R China

As evolutionary algorithms (EAs) are general-purpose optimization algorithms, recent theoretical studies have tried to analyze their performance for solving general problem classes, with the goal of providing a general theoretical explanation of the behavior of EAs. Particularly, a simple multiobjective EA, that is, GSEMO, has been shown to be able to achieve good polynomial-time approximation guarantees for submodular optimization, where the objective function is only required to satisfy some properties and its explicit formulation is not needed. Submodular optimization has wide applications in diverse areas, and previous studies have considered the cases where the objective functions are monotone submodular, monotone non-submodular, or non-monotone submodular. To complement this line of research, this article studies the problem class of maximizing monotone approximately submodular minus modular functions (i.e., g-c) with a size constraint, where g is a so-called non-negative monotone approximately submodular function and c is a so-called non-negative modular function, resulting in the objective function (g-c) being non-monotone non-submodular in general. Different from previous analyses, we prove that by optimizing the original objective function (g-c) and the size simultaneously, the GSEMO fails to achieve a good polynomial-time approximation guarantee. However, we also prove that by optimizing a distorted objective function and the size simultaneously, the GSEMO can still achieve the best-known polynomial-time approximation guarantee. Empirical studies on the applications of Bayesian experimental design and directed vertex cover show the excellent performance of the GSEMO.

关键词： Submodular optimization multiobjective evolutionary algorithms running time analysis computational complexity empirical study

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multiobjective evolutionary algorithms: Analyzing the State-of-the-Art

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evolutionary COMPUTATION 2000年第2期8卷 125-147页

作者： Van Veldhuizen, David A. Lamont, Gary B. USAF Res Lab Opt Radiat Branch Brooks AFB TX 78235 USA USAF Dept Elect & Comp Engn Inst Technol Wright Patterson AFB OH 45433 USA

Solving optimization problems with multiple (often conflicting) objectives is, generally, a very difficult goal. evolutionary algorithms (EAs) were initially extended and applied during the mid-eighties in an attempt to stochastically solve problems of this generic class. During the past decade, a variety of multiobjective EA (MOEA) techniques have been proposed and applied to many scientific and engineering applications. Our discussion's intent is to rigorously define multiobjective optimization problems and certain related concepts, present an MOEA classification scheme, and evaluate the variety of contemporary MOEAs. Current MOEA theoretical developments are evaluated;specific topics addressed include fitness functions, Pareto ranking, niching, fitness sharing, mating restriction, and secondary populations. Since the development and application of MOEAs is a dynamic and rapidly growing activity, we focus on key analytical insights based upon critical MOEA evaluation of current research and applications. Recommended MOEA designs are presented, along with conclusions and recommendations for future work.

关键词： multiobjective optimization multiobjective evolutionary algorithms multiobjective genetic algorithms Pareto optimality

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multiobjective evolutionary algorithms to identify highly autocorrelated areas: the case of spatial distribution in financially compromised farms

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ANNALS OF OPERATIONS RESEARCH 2014年第1期219卷 187-202页

作者： Garcia-Alonso, Carlos R. Perez-Naranjo, Leonor M. Fernandez-Caballero, Juan C. Univ Cordoba SPAIN Fac Business Adm ETEA Cordoba 14004 Spain Univ Pablo de Olavide Dept Business Adm Seville 41013 Spain Univ Cordoba Comp Sci & Numer Anal Dept E-14071 Cordoba Spain

Local Indicators of Spatial Aggregation (LISA) can be used as objectives in a multicriteria framework when highly autocorrelated areas (hot-spots) must be identified and geographically located in complex areas. To do so, a Multi-Objective evolutionary Algorithm (MOEA) based on SPEA2 (Strength Pareto evolutionary Algorithm v.2) has been designed to evaluate three different fitness functions (fine-grained strength, the weighted sum of objectives and fuzzy evaluation of weighted objectives) and three LISA methods. MOEA makes it possible to achieve a compromise between spatial econometric methods as it highlights areas where a specific phenomenon shows significantly high autocorrelation. The spatial distribution of financially compromised olive-tree farms in Andalusia (Spain) was selected for analysis and two fuzzy hot-spots were statistically identified and spatially located. Hot-spots can be considered to be spatial fuzzy sets where the spatial units have a membership degree that can also be calculated.

关键词： multiobjective evolutionary algorithms Spatial analysis Local indicators of spatial aggregation Fuzzy hot-spots Financially compromised areas

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multiobjective evolutionary algorithms for Operational Planning Problems in Open-Pit Mining 17

Multiobjective Evolutionary Algorithms for Operational Plann...

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Genetic and evolutionary Computation Conference (GECCO)

作者： Alexandre, Rafael F. Campelo, Felipe Vasconcelos, Joao A. Univ Fed Ouro Preto Dept Exact & Appl Sci BR-35931026 Joao Monlevade Brazil Univ Fed Minas Gerais Grad Progr Elect Engn Dept Elect Engn BR-31270901 Belo Horizonte MG Brazil

ISBN: (纸本)9781450349390

This paper addresses the problem of planning and allocation of trucks in open-pit mines in terms of three conflicting objectives, and adapts three algorithms for its solution: NSGA-II, SPEA2, and a variant of the Pareto Iterated Local Search using Reduced Variable Neighborhood Search as its local exploration mechanism. Results on four different mining scenarios are also reported and compared.

关键词： multiobjective evolutionary algorithms Open-Pit Mine Dispatch

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Survey of multiobjective evolutionary algorithms for Data Mining: Part II

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IEEE TRANSACTIONS ON evolutionary COMPUTATION 2014年第1期18卷 20-35页

作者： Mukhopadhyay, Anirban Maulik, Ujjwal Bandyopadhyay, Sanghamitra Coello Coello, Carlos A. Univ Kalyani Dept Comp Sci & Engn Kalyani 741235 W Bengal India Jadavpur Univ Dept Comp Sci & Engn Kolkata 700032 India Indian Stat Inst Machine Intelligence Unit Kolkata 700108 India CINVESTAV IPN Dept Comp Evolutionary Computat Grp Mexico City 07360 DF Mexico

This paper is the second part of a two-part paper, which is a survey of multiobjective evolutionary algorithms for data mining problems. In Part I [1], multiobjective evolutionary algorithms used for feature selection and classification have been reviewed. In this part, different multiobjective evolutionary algorithms used for clustering, association rule mining, and other data mining tasks are surveyed. Moreover, a general discussion is provided along with scopes for future research in the domain of multiobjective evolutionary algorithms for data mining.

关键词： Association rule mining biclustering clustering ensemble learning multiobjective evolutionary algorithms

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Experimental analysis of design elements of scalarizing function-based multiobjective evolutionary algorithms

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SOFT COMPUTING 2019年第21期23卷 10769-10780页

作者： Aghabeig, Mansoureh Jaszkiewicz, Andrzej Poznan Univ Tech Fac Comp Inst Comp Sci Ul Piotrowo 2 PL-60965 Poznan Poland

In this paper, we systematically study the influence of the main design elements of scalarizing function-based multiobjective evolutionary algorithms (MOEAs) on the performance of these algorithms. Such algorithms proved to be very successful in multiple computational experiments and practical applications. Well-known examples of this class of MOEAs are Jaszkiewicz's multiobjecitve genetic local search and multiobjective evolutionary algorithm based on decomposition (MOEA/D). The two algorithms share the same common structure and differ in two aspects, i.e., the selection of parents for recombination and the selection of weight vectors of scalarizing functions. Using three different multiobjective combinatorial optimization problems, i.e., the multiobjective symmetric traveling salesperson problem, the traveling salesperson problem with profits, and the multiobjective set covering problem, we show that the design element with the highest influence on the performance is the choice of a mechanism for parents selection, while the selection of weight vectors, either random or evenly distributed, has practically negligible influence if the number of evenly distributed weight vectors is sufficiently large.

关键词： Metaheuristics multiobjective evolutionary algorithms Combinatorial optimization Traveling salesperson problem Set covering problem

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Adaptive, convergent, and diversified archiving strategy for multiobjective evolutionary algorithms

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EXPERT SYSTEMS WITH APPLICATIONS 2010年第12期37卷 8462-8470页

作者： Jin, Huidong Wong, Man-Leung Lingnan Univ Dept Comp & Decis Sci Tuen Mun Hong Kong Peoples R China CSIRO Math Informat & Stat Canberra ACT 2601 Australia

It is crucial to obtain automatically and efficiently a well-distributed set of Pareto optimal solutions in multiobjective evolutionary algorithms (MOEAs). Many studies have proposed different evolutionary algorithms that can progress toward the Pareto front with a widely spread distribution of solutions. However, most theoretically, convergent MOEAs necessitate certain prior knowledge about the Pareto front in order to efficiently maintain widespread solutions. In this paper, we propose, based on the new E-dominance concept, an Adaptive Rectangle Archiving (ARA) strategy that overcomes this important problem. The MOEA with this archiving technique provably converges to well-distributed Pareto optimal solutions without prior knowledge about the Pareto front. ARA complements the existing archiving techniques and is useful to both researchers and practitioners. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： evolutionary computation multiobjective evolutionary algorithms Diversified archiving Convergence epsilon-Pareto set

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An improved robust topology optimization approach using multiobjective evolutionary algorithms

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COMPUTERS & STRUCTURES 2013年 125卷 1-10页

作者： Garcia-Lopez, N. P. Sanchez-Silva, M. Medaglia, A. L. Chateauneuf, A. Univ Los Andes Dept Ingn Civil Bogota Colombia Univ Los Andes Dept Ingn Ind Bogota Colombia Univ Blaise Pascal LaMI F-63174 Aubiere France

Robust topology optimization has gained importance during the last years. This paper presents a robust approach to topology optimization using multiobjective evolutionary algorithms. A key contribution of our approach is that our optimization model handles structural robustness through the first two objectives, namely, the expected compliance and its variance: whereas a third objective incorporates the volume of the structure and tackles the sizing optimization problem. Finally, a major contribution of the proposed approach is that it returns a Pareto frontier showing the designer an array of possible solutions and unveiling the existing tradeoff between the different problem objectives, namely the expected compliance, variance of compliance, and volume of the structure. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Robust optimization Topology optimization multiobjective evolutionary algorithms MOEA NSGA-II Sizing optimization

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