Recent Results and Open Problems in Evolutionary Multiobjective Optimization

Evolutionary algorithms (as well as a number of other metaheuristics) have become a popular choice for solving problems having two or more (often conflicting) objectives (the so-called multi-objective optimization problems). This area, known as EMOO (Evolutionary Multi-Objective Optimization) has had an important growth in the last 20 years, and several people (particularly newcomers) get the impression that it is now very difficult to make contributions of sufficient value to justify, for example, a PhD thesis. However, a lot of interesting research is still under way. In this paper, we will briefly review some of the research topics on evolutionary multi-objective optimization that are currently attracting a lot of interest (e.g., indicator-based selection, many-objective optimization and use of surrogates) and which represent good opportunities for doing research. Some of the challenges currently faced by this discipline will also be delineated.

[1]  Kalyanmoy Deb,et al.  Dynamic multiobjective optimization problems: test cases, approximations, and applications , 2004, IEEE Transactions on Evolutionary Computation.

[2]  Kent McClymont,et al.  Markov chain hyper-heuristic (MCHH): an online selective hyper-heuristic for multi-objective continuous problems , 2011, GECCO '11.

[3]  Andreas Zell,et al.  Model-Assisted Steady-State Evolution Strategies , 2003, GECCO.

[4]  Carlos A. Coello Coello,et al.  Evolutionary Many-Objective Optimization Based on Kuhn-Munkres' Algorithm , 2015, EMO.

[5]  H. Kuhn The Hungarian method for the assignment problem , 1955 .

[6]  Michel Gendreau,et al.  Hyper-heuristics: a survey of the state of the art , 2013, J. Oper. Res. Soc..

[7]  Tapabrata Ray,et al.  Performance of kriging and cokriging based surrogate models within the unified framework for surrogate assisted optimization , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[8]  Rajib Mall,et al.  Parallel Single and Multiple Objectives Genetic Algorithms: A Survey , 2011, Int. J. Appl. Evol. Comput..

[9]  Carlos A. Coello Coello,et al.  Evolutionary multiobjective optimization using a cultural algorithm , 2003, Proceedings of the 2003 IEEE Swarm Intelligence Symposium. SIS'03 (Cat. No.03EX706).

[10]  Kok Wai Wong,et al.  Surrogate-Assisted Evolutionary Optimization Frameworks for High-Fidelity Engineering Design Problems , 2005 .

[11]  Junichi Suzuki,et al.  R2-IBEA: R2 indicator based evolutionary algorithm for multiobjective optimization , 2013, 2013 IEEE Congress on Evolutionary Computation.

[12]  Carlos A. Coello Coello,et al.  A Review of Techniques for Handling Expensive Functions in Evolutionary Multi-Objective Optimization , 2010 .

[13]  Christian Blum,et al.  Metaheuristics in combinatorial optimization: Overview and conceptual comparison , 2003, CSUR.

[14]  Yang Liu,et al.  Collaborative Security , 2015, ACM Comput. Surv..

[15]  Enrique Alba,et al.  Parallel metaheuristics: recent advances and new trends , 2012, Int. Trans. Oper. Res..

[16]  Khaled Rasheed,et al.  Comparison of methods for developing dynamic reduced models for design optimization , 2002, Soft Comput..

[17]  Nicola Beume,et al.  SMS-EMOA: Multiobjective selection based on dominated hypervolume , 2007, Eur. J. Oper. Res..

[18]  Andries Petrus Engelbrecht,et al.  Performance measures for dynamic multi-objective optimisation algorithms , 2013, Inf. Sci..

[19]  Francesco di Pierro,et al.  Many-objective evolutionary algorithms and applications to water resources engineering , 2006 .

[20]  David W. Corne,et al.  Techniques for highly multiobjective optimisation: some nondominated points are better than others , 2007, GECCO '07.

[21]  Hussein A. Abbass,et al.  Tackling Dynamic Problems with Multiobjective Evolutionary Algorithms , 2008, Multiobjective Problem Solving from Nature.

[22]  Patrick M. Reed,et al.  Borg: An Auto-Adaptive Many-Objective Evolutionary Computing Framework , 2013, Evolutionary Computation.

[23]  Kalyanmoy Deb,et al.  An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point-Based Nondominated Sorting Approach, Part I: Solving Problems With Box Constraints , 2014, IEEE Transactions on Evolutionary Computation.

[24]  Amos H. C. Ng,et al.  Tuning of Multiple Parameter Sets in Evolutionary Algorithms , 2016, GECCO.

[25]  Yuping Wang,et al.  An evolutionary algorithm for dynamic multi-objective optimization , 2008, Appl. Math. Comput..

[26]  Zbigniew Michalewicz,et al.  Using Cultural Algorithms for Constraint Handling in GENOCOP , 1995, Evolutionary Programming.

[27]  Carlos A. Coello Coello,et al.  Use of cooperative coevolution for solving large scale multiobjective optimization problems , 2013, 2013 IEEE Congress on Evolutionary Computation.

[28]  Sanaz Mostaghim,et al.  Distance Based Ranking in Many-Objective Particle Swarm Optimization , 2008, PPSN.

[29]  Eckart Zitzler,et al.  Indicator-Based Selection in Multiobjective Search , 2004, PPSN.

[30]  Robert E. Smith,et al.  Fitness inheritance in genetic algorithms , 1995, SAC '95.

[31]  David W. Corne,et al.  Approximating the Nondominated Front Using the Pareto Archived Evolution Strategy , 2000, Evolutionary Computation.

[32]  David W. Corne,et al.  Properties of an adaptive archiving algorithm for storing nondominated vectors , 2003, IEEE Trans. Evol. Comput..

[33]  Frederico G. Guimarães,et al.  Multi-Objective Differential Evolution on the GPU with C-CUDA , 2012, SOCO.

[34]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems , 2002, Genetic Algorithms and Evolutionary Computation.

[35]  Bernhard Sendhoff,et al.  Structure optimization of neural networks for evolutionary design optimization , 2005, Soft Comput..

[36]  Stefan Roth,et al.  Covariance Matrix Adaptation for Multi-objective Optimization , 2007, Evolutionary Computation.

[37]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[38]  Tobias Friedrich,et al.  The maximum hypervolume set yields near-optimal approximation , 2010, GECCO '10.

[39]  Alain Ratle,et al.  Accelerating the Convergence of Evolutionary Algorithms by Fitness Landscape Approximation , 1998, PPSN.

[40]  P. Hajela,et al.  Genetic search strategies in multicriterion optimal design , 1991 .

[41]  Lothar Thiele,et al.  Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach , 1999, IEEE Trans. Evol. Comput..

[42]  Carlos A. Coello Coello,et al.  A new multi-objective evolutionary algorithm based on a performance assessment indicator , 2012, GECCO.

[43]  Carlos A. Coello Coello,et al.  MOMBI: A new metaheuristic for many-objective optimization based on the R2 indicator , 2013, 2013 IEEE Congress on Evolutionary Computation.

[44]  Adriana Menchaca-Mendez,et al.  Selection mechanisms based on the maximin fitness function to solve multi-objective optimization problems , 2016, Inf. Sci..

[45]  Carolina P. de Almeida,et al.  MOEA/D-HH: A Hyper-Heuristic for Multi-objective Problems , 2015, EMO.

[46]  Carlos A. Coello Coello,et al.  IGD+-EMOA: A multi-objective evolutionary algorithm based on IGD+ , 2016, CEC.

[47]  Nicola Beume,et al.  Effects of 1-Greedy -Metric-Selection on Innumerably Large Pareto Fronts , 2009, EMO.

[48]  H. T. Kung,et al.  On the Average Number of Maxima in a Set of Vectors and Applications , 1978, JACM.

[49]  Günter Rudolph,et al.  Parallel Approaches for Multiobjective Optimization , 2008, Multiobjective Optimization.

[50]  Carlos A. Coello Coello,et al.  Objective reduction using a feature selection technique , 2008, GECCO '08.

[51]  Marc Schoenauer,et al.  Surrogate Deterministic Mutation: Preliminary Results , 2001, Artificial Evolution.

[52]  Andreas Zell,et al.  Evolution strategies assisted by Gaussian processes with improved preselection criterion , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[53]  Carlos A. Coello Coello,et al.  Indicator-based cooperative coevolution for multi-objective optimization , 2016, 2016 IEEE Congress on Evolutionary Computation (CEC).

[54]  Carlos A. Coello Coello,et al.  Fitness inheritance in multi-objective particle swarm optimization , 2005, Proceedings 2005 IEEE Swarm Intelligence Symposium, 2005. SIS 2005..

[55]  Carlos A. Brizuela,et al.  A survey on multi-objective evolutionary algorithms for many-objective problems , 2014, Comput. Optim. Appl..

[56]  Bernhard Sendhoff,et al.  Evolutionary Multi-objective Optimization for Simultaneous Generation of Signal-Type and Symbol-Type Representations , 2005, EMO.

[57]  Hisao Ishibuchi,et al.  Mutation operators based on variable grouping for multi-objective large-scale optimization , 2016, 2016 IEEE Symposium Series on Computational Intelligence (SSCI).

[58]  Kiyoshi Tanaka,et al.  Controlling Dominance Area of Solutions and Its Impact on the Performance of MOEAs , 2007, EMO.

[59]  Rolf Drechsler,et al.  Robust Multi-Objective Optimization in High Dimensional Spaces , 2007, EMO.

[60]  Qingfu Zhang,et al.  Multiobjective Memetic Algorithms , 2012, Handbook of Memetic Algorithms.

[61]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[62]  Kalyanmoy Deb,et al.  Multi-objective test problems, linkages, and evolutionary methodologies , 2006, GECCO.

[63]  Wali Khan Mashwani,et al.  Multiobjective memetic algorithm based on decomposition , 2014, Appl. Soft Comput..

[64]  Pierre Collet,et al.  Implementation Techniques for Massively Parallel Multi-objective Optimization , 2013, Massively Parallel Evolutionary Computation on GPGPUs.

[65]  Enrique Alba,et al.  A Multi-Objective Evolutionary Algorithm based on Parallel Coordinates , 2016, GECCO.

[66]  Julian F. Miller,et al.  Genetic and Evolutionary Computation — GECCO 2003 , 2003, Lecture Notes in Computer Science.

[67]  Jie Zhang,et al.  A Simple and Fast Hypervolume Indicator-Based Multiobjective Evolutionary Algorithm , 2015, IEEE Transactions on Cybernetics.

[68]  Kazutoshi Sakakibara,et al.  A proposal on a decomposition-based evolutionary multiobjective optimization for large scale vehicle routing problems , 2015, 2015 IEEE Congress on Evolutionary Computation (CEC).

[69]  Carlos A. Coello Coello,et al.  Using the Averaged Hausdorff Distance as a Performance Measure in Evolutionary Multiobjective Optimization , 2012, IEEE Transactions on Evolutionary Computation.

[70]  Dimo Brockhoff A Bug in the Multiobjective Optimizer IBEA: Salutary Lessons for Code Release and a Performance Re-Assessment , 2015, EMO.

[71]  Adriana Menchaca-Mendez,et al.  An alternative hypervolume-based selection mechanism for multi-objective evolutionary algorithms , 2017, Soft Comput..

[72]  Bernabé Dorronsoro,et al.  A Survey of Decomposition Methods for Multi-objective Optimization , 2014, Recent Advances on Hybrid Approaches for Designing Intelligent Systems.

[73]  Adriana Menchaca-Mendez,et al.  A More Efficient Selection Scheme in iSMS-EMOA , 2014, IBERAMIA.

[74]  Marco Laumanns,et al.  Performance assessment of multiobjective optimizers: an analysis and review , 2003, IEEE Trans. Evol. Comput..

[75]  Kalyanmoy Deb,et al.  Muiltiobjective Optimization Using Nondominated Sorting in Genetic Algorithms , 1994, Evolutionary Computation.

[76]  R. Lyndon While,et al.  A faster algorithm for calculating hypervolume , 2006, IEEE Transactions on Evolutionary Computation.

[77]  Lothar Thiele,et al.  Multiobjective Optimization Using Evolutionary Algorithms - A Comparative Case Study , 1998, PPSN.

[78]  Peter J. Bentley,et al.  Finding Acceptable Solutions in the Pareto-Optimal Range using Multiobjective Genetic Algorithms , 1998 .

[79]  Kevin Tucker,et al.  Response surface approximation of pareto optimal front in multi-objective optimization , 2004 .

[80]  Thomas Bäck,et al.  Metamodel-Assisted Evolution Strategies , 2002, PPSN.

[81]  Michael T. M. Emmerich,et al.  Faster Exact Algorithms for Computing Expected Hypervolume Improvement , 2015, EMO.

[82]  Saúl Zapotecas Martínez,et al.  A nonlinear simplex search approach for multi-objective optimization , 2011, 2011 IEEE Congress of Evolutionary Computation (CEC).

[83]  Lucas Bradstreet,et al.  A Fast Way of Calculating Exact Hypervolumes , 2012, IEEE Transactions on Evolutionary Computation.

[84]  Carlos Cruz,et al.  Optimization in dynamic environments: a survey on problems, methods and measures , 2011, Soft Comput..

[85]  José António Tenreiro Machado,et al.  Entropy Diversity in Multi-Objective Particle Swarm Optimization , 2013, Entropy.

[86]  Xin Yao,et al.  Many-Objective Evolutionary Algorithms , 2015, ACM Comput. Surv..

[87]  Carlos A. Coello Coello,et al.  Ranking Methods for Many-Objective Optimization , 2009, MICAI.

[88]  Marco Laumanns,et al.  A Tutorial on Evolutionary Multiobjective Optimization , 2004, Metaheuristics for Multiobjective Optimisation.

[89]  Heike Trautmann,et al.  On the properties of the R2 indicator , 2012, GECCO '12.

[90]  Min-Jea Tahk,et al.  Acceleration of the convergence speed of evolutionary algorithms using multi-layer neural networks , 2003 .

[91]  Bernard De Baets,et al.  Is Fitness Inheritance Useful for Real-World Applications? , 2003, EMO.

[92]  Hisao Ishibuchi,et al.  Modified Distance Calculation in Generational Distance and Inverted Generational Distance , 2015, EMO.

[93]  Ricardo Landa Becerra,et al.  A hybrid local search operator for multiobjective optimization , 2013, 2013 IEEE Congress on Evolutionary Computation.

[94]  Xin Yao,et al.  Dynamic Multi-objective Optimization: A Survey of the State-of-the-Art , 2013 .

[95]  Nicola Beume,et al.  Pareto-, Aggregation-, and Indicator-Based Methods in Many-Objective Optimization , 2007, EMO.

[96]  David W. Corne,et al.  Quantifying the Effects of Objective Space Dimension in Evolutionary Multiobjective Optimization , 2007, EMO.

[97]  Lamjed Ben Said,et al.  Many-objective Optimization Using Evolutionary Algorithms: A Survey , 2017, Recent Advances in Evolutionary Multi-objective Optimization.

[98]  Xin Yao,et al.  How well do multi-objective evolutionary algorithms scale to large problems , 2007, 2007 IEEE Congress on Evolutionary Computation.

[99]  Stephane Pierret,et al.  Turbomachinery Blade Design Using a Navier–Stokes Solver and Artificial Neural Network , 1999 .

[100]  Petros Koumoutsakos,et al.  Accelerating evolutionary algorithms with Gaussian process fitness function models , 2005, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

[101]  Qingfu Zhang,et al.  MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition , 2007, IEEE Transactions on Evolutionary Computation.

[102]  David E. Goldberg,et al.  Fitness Inheritance In Multi-objective Optimization , 2002, GECCO.

[103]  Kaisa Miettinen,et al.  Nonlinear multiobjective optimization , 1998, International series in operations research and management science.

[104]  Thomas Stützle,et al.  Automatic Configuration of Multi-Objective ACO Algorithms , 2010, ANTS Conference.

[105]  Fang Liu,et al.  A Multiobjective Evolutionary Algorithm Based on Decision Variable Analyses for Multiobjective Optimization Problems With Large-Scale Variables , 2016, IEEE Transactions on Evolutionary Computation.

[106]  Adriana Menchaca-Mendez,et al.  Δp-MOEA: A new multi-objective evolutionary algorithm based on the Δp indicator , 2016, 2016 IEEE Congress on Evolutionary Computation (CEC).

[107]  Eckart Zitzler,et al.  Are All Objectives Necessary? On Dimensionality Reduction in Evolutionary Multiobjective Optimization , 2006, PPSN.

[108]  Carlos A. Coello Coello,et al.  The Micro Genetic Algorithm 2: Towards Online Adaptation in Evolutionary Multiobjective Optimization , 2003, EMO.

[109]  Evan J. Hughes,et al.  Evolutionary many-objective optimisation: many once or one many? , 2005, 2005 IEEE Congress on Evolutionary Computation.

[110]  Kay Chen Tan,et al.  Multi-Objective Memetic Algorithms , 2009 .

[111]  Carlos A. Coello Coello,et al.  Improved Metaheuristic Based on the R2 Indicator for Many-Objective Optimization , 2015, GECCO.

[112]  M. Farina A neural network based generalized response surface multiobjective evolutionary algorithm , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[113]  Günter Rudolph,et al.  Convergence properties of some multi-objective evolutionary algorithms , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[114]  Jasper A Vrugt,et al.  Improved evolutionary optimization from genetically adaptive multimethod search , 2007, Proceedings of the National Academy of Sciences.

[115]  Nicola Beume,et al.  An EMO Algorithm Using the Hypervolume Measure as Selection Criterion , 2005, EMO.

[116]  Carlos A. Coello Coello,et al.  HCS: A New Local Search Strategy for Memetic Multiobjective Evolutionary Algorithms , 2010, IEEE Transactions on Evolutionary Computation.

[117]  Eckart Zitzler,et al.  HypE: An Algorithm for Fast Hypervolume-Based Many-Objective Optimization , 2011, Evolutionary Computation.

[118]  Mark Fleischer,et al.  The measure of pareto optima: Applications to multi-objective metaheuristics , 2003 .

[119]  Joshua D. Knowles,et al.  ParEGO: a hybrid algorithm with on-line landscape approximation for expensive multiobjective optimization problems , 2006, IEEE Transactions on Evolutionary Computation.

[120]  Robert G. Reynolds,et al.  Multi-objective Cultural Algorithms , 2010, IEEE Congress on Evolutionary Computation.

[121]  Tea Tusar,et al.  Visualization of Pareto Front Approximations in Evolutionary Multiobjective Optimization: A Critical Review and the Prosection Method , 2015, IEEE Transactions on Evolutionary Computation.