Using multi-objective evolutionary algorithms for single-objective constrained and unconstrained optimization

In recent decades, several multi-objective evolutionary algorithms have been successfully applied to a wide variety of multi-objective optimization problems. Along the way, several new concepts, paradigms and methods have emerged. Additionally, some authors have claimed that the application of multi-objective approaches might be useful even in single-objective optimization. Thus, several guidelines for solving single-objective optimization problems using multi-objective methods have been proposed. This paper offers an updated survey of the main methods that allow the use of multi-objective schemes for single-objective optimization. In addition, several open topics and some possible paths of future work in this area are identified.

[1]  Kalyanmoy Deb,et al.  Uniform adaptive scaling of equality and inequality constraints within hybrid evolutionary-cum-classical optimization , 2016, Soft Comput..

[2]  Xin Yao,et al.  Stochastic ranking for constrained evolutionary optimization , 2000, IEEE Trans. Evol. Comput..

[3]  Rajeev Kumar,et al.  Analysis of a Multiobjective Evolutionary Algorithm on the 0-1 knapsack problem , 2006, Theor. Comput. Sci..

[4]  Souma Chowdhury,et al.  Improvements to single-objective constrained predator–prey evolutionary optimization algorithm , 2010 .

[5]  Ernesto Benini,et al.  Genetic Diversity as an Objective in Multi-Objective Evolutionary Algorithms , 2003, Evolutionary Computation.

[6]  Yong Wang,et al.  MOMMOP: Multiobjective Optimization for Locating Multiple Optimal Solutions of Multimodal Optimization Problems , 2015, IEEE Transactions on Cybernetics.

[7]  Hussein A. Abbass,et al.  Multiobjective optimization for dynamic environments , 2005, 2005 IEEE Congress on Evolutionary Computation.

[8]  V. Cutello,et al.  A multi-objective evolutionary approach to the protein structure prediction problem , 2006, Journal of The Royal Society Interface.

[9]  Tapabrata Ray,et al.  Infeasibility Driven Evolutionary Algorithm for Constrained Optimization , 2009 .

[10]  Xiaodong Li,et al.  Evolutionary algorithms and multi-objectivization for the travelling salesman problem , 2009, GECCO.

[11]  Zbigniew Michalewicz,et al.  Handbook of Evolutionary Computation , 1997 .

[12]  K. Deb,et al.  A bi-objective constrained optimization algorithm using a hybrid evolutionary and penalty function approach , 2013 .

[13]  Gary G. Yen,et al.  A generic framework for constrained optimization using genetic algorithms , 2005, IEEE Transactions on Evolutionary Computation.

[14]  S. Baskar,et al.  Application of NSGA-II Algorithm to Single-Objective Transmission Constrained Generation Expansion Planning , 2009, IEEE Transactions on Power Systems.

[15]  Andres Angantyr,et al.  Constrained optimization based on a multiobjective evolutionary algorithm , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[16]  Arina Buzdalova,et al.  Generation of tests for programming challenge tasks using multi-objective optimization , 2013, GECCO '13 Companion.

[17]  Ingo Wegener,et al.  The analysis of evolutionary algorithms on sorting and shortest paths problems , 2004, J. Math. Model. Algorithms.

[18]  Yaonan Wang,et al.  Multi-objective self-adaptive differential evolution with elitist archive and crowding entropy-based diversity measure , 2010, Soft Comput..

[19]  Frank Neumann,et al.  On the Effects of Adding Objectives to Plateau Functions , 2009, IEEE Transactions on Evolutionary Computation.

[20]  Gara Miranda,et al.  A Multi-Objective Evolutionary Approach for the Antenna Positioning Problem , 2010, KES.

[21]  Jesús María López Lezama,et al.  An efficient constraint handling methodology for multi-objective evolutionary algorithms , 2009 .

[22]  Frank W. Ciarallo,et al.  Helper-objective optimization strategies for the Job-Shop Scheduling Problem , 2011, Appl. Soft Comput..

[23]  Stéphane Doncieux,et al.  Using behavioral exploration objectives to solve deceptive problems in neuro-evolution , 2009, GECCO.

[24]  Wenyin Gong,et al.  A multiobjective differential evolution algorithm for constrained optimization , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

[25]  Günter Rudolph,et al.  Niching by multiobjectivization with neighbor information: Trade-offs and benefits , 2013, 2013 IEEE Congress on Evolutionary Computation.

[26]  Patrick D. Surry,et al.  A Multi-objective Approach to Constrained Optimisation of Gas Supply Networks: the COMOGA Method , 1995, Evolutionary Computing, AISB Workshop.

[27]  Frank Neumann,et al.  Plateaus can be harder in multi-objective optimization , 2007, IEEE Congress on Evolutionary Computation.

[28]  Tapabrata Ray,et al.  Optimum Oil Production Planning Using Infeasibility Driven Evolutionary Algorithm , 2013, Evolutionary Computation.

[29]  Qingfu Zhang,et al.  Multiobjective evolutionary algorithms: A survey of the state of the art , 2011, Swarm Evol. Comput..

[30]  Hisao Ishibuchi,et al.  Evolutionary many-objective optimization: A short review , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

[31]  Yong Wang,et al.  Locating Multiple Optimal Solutions of Nonlinear Equation Systems Based on Multiobjective Optimization , 2015, IEEE Transactions on Evolutionary Computation.

[32]  Henrik Esbensen,et al.  Finding (Near-)Optimal Steiner Trees in Large Graphs , 1995, International Conference on Genetic Algorithms.

[33]  Ning Dong,et al.  An unbiased bi-objective Optimization Model and Algorithm for constrained Optimization , 2014, Int. J. Pattern Recognit. Artif. Intell..

[34]  David Becerra,et al.  A parallel multi-objective ab initio approach for protein structure prediction , 2010, 2010 IEEE International Conference on Bioinformatics and Biomedicine (BIBM).

[35]  Hod Lipson,et al.  Age-fitness pareto optimization , 2010, Annual Conference on Genetic and Evolutionary Computation.

[36]  Arina Buzdalova,et al.  Adaptive Selection of Helper-Objectives with Reinforcement Learning , 2012, 2012 11th International Conference on Machine Learning and Applications.

[37]  Joshua D. Knowles,et al.  Multiobjectivization by Decomposition of Scalar Cost Functions , 2008, PPSN.

[38]  Yong Wang,et al.  A Multiobjective Optimization-Based Evolutionary Algorithm for Constrained Optimization , 2006, IEEE Transactions on Evolutionary Computation.

[39]  Kenneth O. Stanley,et al.  Exploiting Open-Endedness to Solve Problems Through the Search for Novelty , 2008, ALIFE.

[40]  Eduardo Segredo,et al.  Parallel island-based multiobjectivised memetic algorithms for a 2D packing problem , 2011, GECCO '11.

[41]  Laetitia Vermeulen-Jourdan,et al.  The benefits of using multi-objectivization for mining pittsburgh partial classification rules in imbalanced and discrete data , 2013, GECCO '13.

[42]  Gregorio Toscano Pulido,et al.  Handling constraints in the HP model for protein structure prediction by multiobjective optimization , 2013, 2013 IEEE Congress on Evolutionary Computation.

[43]  Hisao Ishibuchi,et al.  Incorporation of Scalarizing Fitness Functions into Evolutionary Multiobjective Optimization Algorithms , 2006, PPSN.

[44]  Peter J. Fleming,et al.  Genetic Algorithms for Multiobjective Optimization: FormulationDiscussion and Generalization , 1993, ICGA.

[45]  Eckart Zitzler,et al.  Reducing Bloat in GP with Multiple Objectives , 2008, Multiobjective Problem Solving from Nature.

[46]  K. Deb,et al.  Reliable classification of two-class cancer data using evolutionary algorithms. , 2003, Bio Systems.

[47]  C. Coello,et al.  CONSTRAINT-HANDLING USING AN EVOLUTIONARY MULTIOBJECTIVE OPTIMIZATION TECHNIQUE , 2000 .

[48]  Xin Yao,et al.  Search biases in constrained evolutionary optimization , 2005, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

[49]  Gregorio Toscano Pulido,et al.  Multi-objectivization, fitness landscape transformation and search performance: A case of study on the hp model for protein structure prediction , 2015, Eur. J. Oper. Res..

[50]  A. Oyama,et al.  Evolutionary and Deterministic Methods for Design, Optimization and Control with Applications to Industrial and Societal Problems Eurogen 2005 New Constraint-handling Method for Multi-objective Multi-constraint Evolutionary Optimization and Its Application to Space Plane Design , 2022 .

[51]  Francisco Herrera,et al.  Replacement strategies to preserve useful diversity in steady-state genetic algorithms , 2008, Inf. Sci..

[52]  Yuren Zhou,et al.  Multi-objective and MGG evolutionary algorithm for constrained optimization , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[53]  Frank W. Ciarallo,et al.  An analysis of decomposition approaches in multi-objectivization via segmentation , 2014, Appl. Soft Comput..

[54]  Frank W. Ciarallo,et al.  Multi-objectivization Via Decomposition: An analysis of helper-objectives and complete decomposition , 2015, Eur. J. Oper. Res..

[55]  Carlos A. Coello Coello,et al.  Use of Multiobjective Optimization Concepts to Handle Constraints in Genetic Algorithms , 2005, Evolutionary Multiobjective Optimization.

[56]  Tapabrata Ray,et al.  An Evolutionary Algorithm for Constrained Optimization , 2000, GECCO.

[57]  Hisao Ishibuchi,et al.  Multiobjectivization from two objectives to four objectives in evolutionary multi-objective optimization algorithms , 2010, 2010 Second World Congress on Nature and Biologically Inspired Computing (NaBIC).

[58]  Jing J. Liang,et al.  Dynamic Multi-Swarm Particle Swarm Optimizer with a Novel Constraint-Handling Mechanism , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[59]  Kalyanmoy Deb,et al.  A fast and accurate solution of constrained optimization problems using a hybrid bi-objective and penalty function approach , 2010, IEEE Congress on Evolutionary Computation.

[60]  Carlos A. Coello Coello,et al.  Constraint-handling in nature-inspired numerical optimization: Past, present and future , 2011, Swarm Evol. Comput..

[61]  Eduardo Segredo,et al.  Multiobjectivisation of the Antenna Positioning Problem , 2011, DCAI.

[62]  Martin H. Luerssen,et al.  Phenotype Diversity Objectives for Graph Grammar Evolution , 2005 .

[63]  Kalyanmoy Deb,et al.  Multimodal Optimization Using a Bi-Objective Evolutionary Algorithm , 2012, Evolutionary Computation.

[64]  C. Coello.  TREATING CONSTRAINTS AS OBJECTIVES FOR SINGLE-OBJECTIVE EVOLUTIONARY OPTIMIZATION , 2000 .

[65]  Yuren Zhou,et al.  An orthogonal design based constrained evolutionary optimization algorithm , 2007 .

[66]  Marco Laumanns,et al.  Combining Convergence and Diversity in Evolutionary Multiobjective Optimization , 2002, Evolutionary Computation.

[67]  Lothar Thiele,et al.  Comparison of Multiobjective Evolutionary Algorithms: Empirical Results , 2000, Evolutionary Computation.

[68]  Frank Neumann,et al.  Approximating Covering Problems by Randomized Search Heuristics Using Multi-Objective Models , 2010, Evolutionary Computation.

[69]  Kalyanmoy Deb,et al.  Multi-objective optimization using evolutionary algorithms , 2001, Wiley-Interscience series in systems and optimization.

[70]  Kazuaki Masuda,et al.  A constrained global optimization method based on multi-objective particle swarm optimization , 2012 .

[71]  Marjan Mernik,et al.  Exploration and exploitation in evolutionary algorithms: A survey , 2013, CSUR.

[72]  Guoshan Zhang,et al.  Biased multiobjective optimization for constrained single-objective evolutionary optimization , 2014, Proceeding of the 11th World Congress on Intelligent Control and Automation.

[73]  Alexandros Agapitos,et al.  An Investigation of Fitness Sharing with Semantic and Syntactic Distance Metrics , 2012, EuroGP.

[74]  Yuping Wang,et al.  Preference Bi-objective Evolutionary Algorithm for Constrained Optimization , 2005, CIS.

[75]  Pascal Bouvry,et al.  A Novel Multi-objectivisation Approach for Optimising the Protein Inverse Folding Problem , 2015, EvoApplications.

[76]  Vincenzo Cutello,et al.  A Class of Pareto Archived Evolution Strategy Algorithms Using Immune Inspired Operators for Ab-Initio Protein Structure Prediction , 2005, EvoWorkshops.

[77]  Xavier Blasco Ferragud,et al.  Multiobjective optimization algorithm for solving constrained single objective problems , 2010, IEEE Congress on Evolutionary Computation.

[78]  Edwin D. de Jong,et al.  Multi-objective diversity maintenance , 2006, GECCO '06.

[79]  Stéphane Doncieux,et al.  Overcoming the bootstrap problem in evolutionary robotics using behavioral diversity , 2009, 2009 IEEE Congress on Evolutionary Computation.

[80]  Ingo Wegener,et al.  Real royal road functions--where crossover provably is essential , 2001, Discret. Appl. Math..

[81]  Riccardo Poli,et al.  New ideas in optimization , 1999 .

[82]  Bilel Derbel,et al.  Multiobjectivization with NSGA-ii on the noiseless BBOB testbed , 2013, GECCO.

[83]  Carlos A. Coello Coello,et al.  Handling Constraints in Genetic Algorithms Using Dominance-based Tournaments , 2002 .

[84]  Edwin D. de Jong,et al.  Objective Set Compression , 2008, Multiobjective Problem Solving from Nature.

[85]  Eduardo Rodriguez-Tello,et al.  An Improved Multiobjectivization Strategy for HP Model-Based Protein Structure Prediction , 2012, PPSN.

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

[87]  Richard A. Watson,et al.  Reducing Local Optima in Single-Objective Problems by Multi-objectivization , 2001, EMO.

[88]  Xin Yao,et al.  Performance Scaling of Multi-objective Evolutionary Algorithms , 2003, EMO.

[89]  K. Matsui.  New selection method to improve the population diversity in genetic algorithms , 1999, IEEE SMC'99 Conference Proceedings. 1999 IEEE International Conference on Systems, Man, and Cybernetics (Cat. No.99CH37028).

[90]  Roman Neruda,et al.  Multi-objectivization and Surrogate Modelling for Neural Network Hyper-parameters Tuning , 2013, ICIC.

[91]  Carlos Segura,et al.  A Novel Diversity-based Evolutionary Algorithm for the Traveling Salesman Problem , 2015, GECCO.

[92]  Ahmad Alhindi,et al.  Guided Local Search , 2010, Handbook of Heuristics.

[93]  Gary B. Lamont,et al.  Solving the Protein Structure Prediction Problem Through a Multiobjective Genetic Algorithm , 2002 .

[94]  Gara Miranda,et al.  Improving the diversity preservation of multi-objective approaches used for single-objective optimization , 2013, 2013 IEEE Congress on Evolutionary Computation.

[95]  Lothar Thiele,et al.  Multiobjective genetic programming: reducing bloat using SPEA2 , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[96]  Tapabrata Ray,et al.  Society and civilization: An optimization algorithm based on the simulation of social behavior , 2003, IEEE Trans. Evol. Comput..

[97]  Edmund K. Burke,et al.  USING DIVERSITY TO GUIDE THE SEARCH IN MULTI-OBJECTIVE OPTIMIZATION , 2004 .

[98]  Ajith Abraham,et al.  A New Approach for Solving Nonlinear Equations Systems , 2008, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[99]  Mikkel T. Jensen,et al.  Guiding Single-Objective Optimization Using Multi-objective Methods , 2003, EvoWorkshops.

[100]  Jouni Lampinen,et al.  Constrained Real-Parameter Optimization with Generalized Differential Evolution , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[101]  Yuren Zhou,et al.  Multiobjective Optimization and Hybrid Evolutionary Algorithm to Solve Constrained Optimization Problems , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[102]  Hisao Ishibuchi,et al.  Optimization of Scalarizing Functions Through Evolutionary Multiobjective Optimization , 2007, EMO.

[103]  Hisao Ishibuchi,et al.  Comparison between Single-Objective and Multi-Objective Genetic Algorithms: Performance Comparison and Performance Measures , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[104]  R. Courant.  Variational methods for the solution of problems of equilibrium and vibrations , 1943 .

[105]  Enrique Alba,et al.  Parallel Metaheuristics: A New Class of Algorithms , 2005 .

[106]  Stéphane Doncieux,et al.  Behavioral diversity measures for Evolutionary Robotics , 2010, IEEE Congress on Evolutionary Computation.

[107]  Sanyang Liu,et al.  A Dual-Population Differential Evolution With Coevolution for Constrained Optimization , 2015, IEEE Transactions on Cybernetics.

[108]  Rolf Drechsler,et al.  Applications of Evolutionary Computing, EvoWorkshops 2008: EvoCOMNET, EvoFIN, EvoHOT, EvoIASP, EvoMUSART, EvoNUM, EvoSTOC, and EvoTransLog, Naples, Italy, March 26-28, 2008. Proceedings , 2008, EvoWorkshops.

[109]  Gara Miranda,et al.  Using multi-objective evolutionary algorithms for single-objective optimization , 2013, 4OR.

[110]  Yong Wang,et al.  A Dynamic Hybrid Framework for Constrained Evolutionary Optimization , 2012, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[111]  Andrew Philippides,et al.  Multi-objectivization of the Tool Selection Problem on a Budget of Evaluations , 2013, EMO.

[112]  Anabela Simões,et al.  Memory-based CHC algorithms for the dynamic traveling salesman problem , 2011, GECCO '11.

[113]  Joshua D. Knowles,et al.  Investigations into the Effect of Multiobjectivization in Protein Structure Prediction , 2008, PPSN.

[114]  Michel Gendreau,et al.  A hybrid genetic algorithm with adaptive diversity management for a large class of vehicle routing problems with time-windows , 2013, Comput. Oper. Res..

[115]  Eduardo Segredo,et al.  Memetic algorithms and hyperheuristics applied to a multiobjectivised two-dimensional packing problem , 2014, J. Glob. Optim..

[116]  Efrn Mezura-Montes,et al.  Constraint-Handling in Evolutionary Optimization , 2009 .

[117]  Frank Neumann,et al.  Do additional objectives make a problem harder? , 2007, GECCO '07.

[118]  Carlos A. Coello Coello,et al.  Handling constraints using multiobjective optimization concepts , 2004 .

[119]  Hongbin Dong,et al.  A Novel Genetic Algorithm using Helper Objectives for the 0-1 Knapsack Problem , 2014, ArXiv.

[120]  Gary B. Lamont,et al.  Applications Of Multi-Objective Evolutionary Algorithms , 2004 .

[121]  Joshua D. Knowles,et al.  Multiobjective Optimization in Bioinformatics and Computational Biology , 2007, IEEE/ACM Transactions on Computational Biology and Bioinformatics.

[122]  Martin H. Luerssen,et al.  Chapter 12 Phenotype Diversity Objectives for Graph Grammar Evolution , 2005, Recent Advances in Artificial Life.

[123]  Tapabrata Ray,et al.  Performance of infeasibility empowered memetic algorithm for CEC 2010 constrained optimization problems , 2010, IEEE Congress on Evolutionary Computation.

[124]  Lothar Thiele,et al.  Maximizing population diversity in single-objective optimization , 2011, GECCO '11.

[125]  Samir W. Mahfoud.  Crowding and Preselection Revisited , 1992, PPSN.

[126]  Carlos A. Coello Coello,et al.  Constrained Optimization via Multiobjective Evolutionary Algorithms , 2008, Multiobjective Problem Solving from Nature.

[127]  Stéphane Doncieux,et al.  Encouraging Behavioral Diversity in Evolutionary Robotics: An Empirical Study , 2012, Evolutionary Computation.

[128]  Gregorio Toscano Pulido,et al.  Constraint-handling through multi-objective optimization: The hydrophobic-polar model for protein structure prediction , 2015, Comput. Oper. Res..

[129]  Kazutoshi Sakakibara,et al.  Multi-objective approaches in a single-objective optimization environment , 2005, 2005 IEEE Congress on Evolutionary Computation.

[130]  Kalyanmoy Deb,et al.  An Investigation of Niche and Species Formation in Genetic Function Optimization , 1989, ICGA.

[131]  Carlos A. Coello Coello,et al.  A simple multimembered evolution strategy to solve constrained optimization problems , 2005, IEEE Transactions on Evolutionary Computation.

[132]  Hisao Ishibuchi,et al.  Evolutionary many-objective optimization , 2008, 2008 3rd International Workshop on Genetic and Evolving Systems.

[133]  Hisao Ishibuchi,et al.  A multi-objective genetic local search algorithm and its application to flowshop scheduling , 1998, IEEE Trans. Syst. Man Cybern. Part C.

[134]  Eduardo Segredo,et al.  Scalability and robustness of parallel hyperheuristics applied to a multiobjectivised frequency assignment problem , 2013, Soft Comput..

[135]  Yong Wang,et al.  Combining Multiobjective Optimization With Differential Evolution to Solve Constrained Optimization Problems , 2012, IEEE Transactions on Evolutionary Computation.

[136]  Eduardo Segredo,et al.  A multiobjectivised memetic algorithm for the Frequency Assignment Problem , 2011, 2011 IEEE Congress of Evolutionary Computation (CEC).

[137]  Carlos A. Coello Coello,et al.  Constraint-handling in genetic algorithms through the use of dominance-based tournament selection , 2002, Adv. Eng. Informatics.

[138]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems (Genetic and Evolutionary Computation) , 2006 .

[139]  R. Storn,et al.  Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series) , 2005 .

[140]  Günter Rudolph,et al.  Solving multimodal problems via multiobjective techniques with Application to phase equilibrium detection , 2007, 2007 IEEE Congress on Evolutionary Computation.

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

[142]  Yuren Zhou,et al.  An Adaptive Tradeoff Model for Constrained Evolutionary Optimization , 2008, IEEE Transactions on Evolutionary Computation.

[143]  Kay Chen Tan,et al.  Multimodal Optimization Using a Biobjective Differential Evolution Algorithm Enhanced With Mean Distance-Based Selection , 2013, IEEE Transactions on Evolutionary Computation.

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

[145]  Graham Kendall,et al.  Diversity in genetic programming: an analysis of measures and correlation with fitness , 2004, IEEE Transactions on Evolutionary Computation.

[146]  Dipti Srinivasan,et al.  Multi-objectivization of short-term unit commitment under uncertainty using evolutionary algorithm , 2012, 2012 IEEE Congress on Evolutionary Computation.

[147]  Frank W. Ciarallo,et al.  Multiobjectivization via Helper-Objectives With the Tunable Objectives Problem , 2012, IEEE Transactions on Evolutionary Computation.

[148]  Kalyanmoy Deb,et al.  Customized evolutionary optimization procedure for generating minimum weight compliant mechanisms , 2014 .

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

[150]  Anikó Ekárt,et al.  Selection Based on the Pareto Nondomination Criterion for Controlling Code Growth in Genetic Programming , 2001, Genetic Programming and Evolvable Machines.

[151]  David Greiner,et al.  Improving Computational Mechanics Optimum Design Using Helper Objectives: An Application in Frame Bar Structures , 2007, EMO.

[152]  Jean-Baptiste Mouret.  Novelty-Based Multiobjectivization , 2011 .

[153]  Amarda Shehu,et al.  Multi-Objective Stochastic Search for Sampling Local Minima in the Protein Energy Surface , 2013, BCB.

[154]  Enrique Alba,et al.  Design Issues in a Multiobjective Cellular Genetic Algorithm , 2007, EMO.

[155]  Aimin Zhou,et al.  Dynamic multi-objective differential evolution for solving constrained optimization problem , 2011, 2011 IEEE Congress of Evolutionary Computation (CEC).

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

[157]  N. Hansen,et al.  Markov Chain Analysis of Cumulative Step-Size Adaptation on a Linear Constrained Problem , 2015, Evolutionary Computation.

[158]  Gunar E. Liepins,et al.  Genetic Algorithms Applications to Set Covering and Traveling Salesman Problems , 1990 .

[159]  Gregorio Toscano Pulido,et al.  Locality-based multiobjectivization for the HP model of protein structure prediction , 2012, GECCO '12.

[160]  Sushil J. Louis,et al.  Pareto OptimalityGA-Easiness and Deception (Extended Abstract) , 1993, International Conference on Genetic Algorithms.

[161]  Hussein A. Abbass,et al.  Searching under Multi-evolutionary Pressures , 2003, EMO.

[162]  M. Jensen.  Helper-Objectives: Using Multi-Objective Evolutionary Algorithms for Single-Objective Optimisation , 2004 .

[163]  Kalyanmoy Deb,et al.  A parameterless-niching-assisted bi-objective approach to multimodal optimization , 2013, 2013 IEEE Congress on Evolutionary Computation.

[164]  Gregorio Toscano Pulido,et al.  Optimal Triangulation in 3D Computer Vision Using a Multi-objective Evolutionary Algorithm , 2007, EvoWorkshops.

[165]  Peter J. Fleming,et al.  On the Evolutionary Optimization of Many Conflicting Objectives , 2007, IEEE Transactions on Evolutionary Computation.

[166]  Kalyanmoy Deb,et al.  Reference point based multi-objective optimization using evolutionary algorithms , 2006, GECCO.

[167]  Jie Yao,et al.  Bi-Objective Multipopulation Genetic Algorithm for Multimodal Function Optimization , 2010, IEEE Transactions on Evolutionary Computation.

[168]  Patrick D. Surry,et al.  The COMOGA Method: Constrained Optimisation by Multi-Objective Genetic Algorithms , 1997 .

[169]  Frank Neumann,et al.  Approximating Minimum Multicuts by Evolutionary Multi-objective Algorithms , 2008, PPSN.

[170]  Edwin D. de Jong,et al.  Reducing bloat and promoting diversity using multi-objective methods , 2001 .

[171]  David E. Goldberg,et al.  A niched Pareto genetic algorithm for multiobjective optimization , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[172]  Kalyanmoy Deb,et al.  A Hybrid Evolutionary Multi-objective and SQP Based Procedure for Constrained Optimization , 2007, ISICA.

[173]  R. Haftka,et al.  Constrained particle swarm optimization using a bi-objective formulation , 2009 .

[174]  Risto Miikkulainen,et al.  Effective diversity maintenance in deceptive domains , 2013, GECCO '13.

[175]  Pietro Simone Oliveto,et al.  Design and Management of Complex Technical Processes and Systems by Means of Computational Intelligence Methods Theoretical Analysis of Diversity Mechanisms for Global Exploration Theoretical Analysis of Diversity Mechanisms for Global Exploration , 2022 .

[176]  El-Ghazali Talbi,et al.  Metaheuristics - From Design to Implementation , 2009 .

[177]  Abel García-Nájera.  Preserving population diversity for the multi-objective vehicle routing problem with time windows , 2009, GECCO '09.

[178]  David H. Wolpert,et al.  No free lunch theorems for optimization , 1997, IEEE Trans. Evol. Comput..

[179]  Kazutoshi Sakakibara,et al.  A Multiobjectivization Approach for Vehicle Routing Problems , 2007, EMO.

[180]  Eduardo Segredo,et al.  Analysing the Robustness of Multiobjectivisation Approaches Applied to Large Scale Optimisation Problems , 2013, EVOLVE.

[181]  Carlos A. Coello Coello,et al.  THEORETICAL AND NUMERICAL CONSTRAINT-HANDLING TECHNIQUES USED WITH EVOLUTIONARY ALGORITHMS: A SURVEY OF THE STATE OF THE ART , 2002 .

[182]  Frank Neumann,et al.  Computing Minimum Cuts by Randomized Search Heuristics , 2008, GECCO '08.