{"type":"ScholarlyArticle","title":"Quality-Diversity Algorithms Can Provably Be Helpful for Optimization","authors":[{"name":"Chao Qian","slug":"chao-qian","given":"Chao","family":"Qian","affiliation":"National Key Laboratory for Novel Software Technology , Nanjing University , Nanjing 210023 , China School of Artificial Intelligence ,"},{"name":"Ke Xue","slug":"ke-xue","given":"Ke","family":"Xue","affiliation":"National Key Laboratory for Novel Software Technology , Nanjing University , Nanjing 210023 , China School of Artificial Intelligence ,"},{"name":"Ren-Jian Wang","slug":"ren-jian-wang","given":"Ren-Jian","family":"Wang","affiliation":"National Key Laboratory for Novel Software Technology , Nanjing University , Nanjing 210023 , China School of Artificial Intelligence ,; Nanjing University , Nanjing 210023 , China"}],"abstract":"Quality-Diversity (QD) algorithms are a new type of Evolutionary Algorithms (EAs), aiming to find a set of high-performing, yet diverse solutions. They have found many successful applications in reinforcement learning and robotics, helping improve the robustness in complex environments. Furthermore, they often empirically find a better overall solution than traditional search algorithms which explicitly search for a single highest-performing solution. However, their theoretical analysis is far behind, leaving many fundamental questions unexplored. In this paper, we try to shed some light on the optimization ability of QD algorithms via rigorous runtime analysis. By comparing the popular QD algorithm MAP-Elites with (\\mu+1)-EA (a typical EA focusing on finding better objective values only), we prove that on two NP-hard problem classes with wide applications, i.e., monotone approximately submodular maximization with a size constraint, and set cover, MAP-Elites can achieve the (asymptotically) optimal polynomial-time approximation ratio, while (\\mu+1)-EA requires exponential expected time on some instances. This provides theoretical justification for that QD algorithms can be helpful for optimization, and discloses that the simultaneous search for high-performing solutions with diverse behaviors can provide stepping stones to good overall solutions and help avoid local optima.","doi":"10.24963/ijcai.2024/773","url":"https://ijcai.org/proceedings/2024/773","pdf":"https://ijcai.org/proceedings/2024/0773.pdf","markdown":"https://ijcai.org/proceedings/2024/773.md","bibtex":"https://ijcai.org/proceedings/2024/bibtex/773","volume":{"slug":"2024","title":"Proceedings of the Thirty-Third International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2024","url":"https://ijcai.org/proceedings/2024/","year":2024,"location":"Jeju, Korea","dates":"3-9 August 2024","editors":"Kate Larson","isbn":"978-1-956792-04-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2024"},"section":"Search","track":"Main Track","number":773,"pages":{"first":6994,"last":7002},"keywords":["Search: S: Evolutionary computation"],"videos":[],"references":[{"position":1,"raw":"[Auger and Doerr, 2011] A. Auger and B. Doerr. Theory of Randomized Search Heuristics -Foundations and Recent Developments. World Scientific, Singapore, 2011.","title":"Theory of Randomized Search Heuristics -Foundations and Recent Developments","authors":"A Auger, B Doerr","year":"2011","venue":null,"doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Bhatt et al., 2022] V. Bhatt, B. Tjanaka, M. C. Fontaine, and S. Nikolaidis. Deep surrogate assisted generation of envi- ronments. In NeurIPS, New Orleans, LA, 2022.","title":"Deep surrogate assisted generation of environments","authors":"V Bhatt, B Tjanaka, M C Fontaine, S Nikolaidis","year":"2022","venue":"NeurIPS","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Bossek and Sudholt, 2023] J. Bossek and D. Sudholt. Run- time analysis of quality diversity algorithms. In GECCO, pages 1546-1554, Lisbon, Portugal, 2023.","title":"Runtime analysis of quality diversity algorithms","authors":"J Bossek, D Sudholt","year":"2023","venue":"GECCO","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Chalumeau et al., 2023] F. Chalumeau, R. Boige, B. Lim, V. Macé, M. Allard, A. Flajolet, A. Cully, and T. Pier- rot. Neuroevolution is a competitive alternative to rein- forcement learning for skill discovery. In ICLR, Kigali, Rwanda, 2023.","title":"Neuroevolution is a competitive alternative to reinforcement learning for skill discovery","authors":"F Chalumeau, R Boige, B Lim, V Macé, M Allard, A Flajolet, A Cully, T Pierrot","year":"2023","venue":"ICLR","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Chvatal, 1979] V. Chvatal. A greedy heuristic for the set- covering problem. Mathematics of Operations Research, 4(3):233-235, 1979.","title":"A greedy heuristic for the setcovering problem","authors":"V","year":"1979","venue":"Mathematics of Operations Research","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Clune et al., 2013] J. Clune, J.-B. Mouret, and H. Lip- son. The evolutionary origins of modularity. Pro- ceedings of the Royal Society B: Biological Sciences, 280(1755):20122863, 2013.","title":"The evolutionary origins of modularity","authors":"J Clune, J.-B Mouret, H","year":"2013","venue":"Proceedings of the Royal Society B: Biological Sciences","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Colas et al., 2020] C. Colas, V. Madhavan, J. Huizinga, and J. Clune. Scaling MAP-Elites to deep neuroevolution. In GECCO, pages 67-75, Cancún, Mexico, 2020.","title":"Scaling MAP-Elites to deep neuroevolution","authors":"C Colas, V Madhavan, J Huizinga, J Clune","year":"2020","venue":"GECCO","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Conti et al., 2018] E. Conti, V. Madhavan, F. P. Such, J. Lehman, K. O. Stanley, and J. Clune. Improving ex- ploration in evolution strategies for deep reinforcement learning via a population of novelty-seeking agents. In NeurIPS, pages 5032-5043, Montréal, Canada, 2018.","title":"Improving exploration in evolution strategies for deep reinforcement learning via a population of novelty-seeking agents","authors":"E Conti, V Madhavan, F P Such, J Lehman, K O Stanley, J Clune","year":"2018","venue":"NeurIPS","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Cully and Demiris, 2018] A. Cully and Y. Demiris. Qual- ity and diversity optimization: A unifying modular frame- work. IEEE Transactions on Evolutionary Computation, 22(2):245-259, 2018.","title":"Quality and diversity optimization: A unifying modular framework","authors":"A Cully, Y Demiris","year":"2018","venue":"IEEE Transactions on Evolutionary Computation","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Cully et al., 2015] A. Cully, J. Clune, D. Tarapore, and J.- B. Mouret. Robots that can adapt like animals. Nature, 521(7553):503-507, 2015.","title":"Robots that can adapt like animals","authors":"A Cully, J Clune, D Tarapore, J.-B Mouret","year":"2015","venue":"Nature","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Das and Kempe, 2011] A. Das and D. Kempe. Submodu- lar meets spectral: Greedy algorithms for subset selection, sparse approximation and dictionary selection. In ICML, pages 1057-1064, Bellevue, WA, 2011.","title":"Submodular meets spectral: Greedy algorithms for subset selection, sparse approximation and dictionary selection","authors":"A Das, D Kempe","year":"2011","venue":"ICML","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Doerr and Neumann, 2020] B. Doerr and F. Neumann. The- ory of Evolutionary Computation: Recent Developments in Discrete Optimization. Springer, Cham, Switzerland, 2020.","title":"Theory of Evolutionary Computation: Recent Developments in Discrete Optimization","authors":"B Doerr, F Neumann","year":"2020","venue":null,"doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Doerr et al., 2012] B. Doerr, D. Johannsen, and C. Winzen. Multiplicative drift analysis. Algorithmica, 64(4):673- 697, 2012.","title":"Multiplicative drift analysis","authors":"B Doerr, D Johannsen, C Winzen","year":"2012","venue":"Algorithmica","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Doncieux et al., 2019] S. Doncieux, A. Laflaquière, and A. Coninx. Novelty search: A theoretical perspective. In GECCO, pages 99-106, Prague, Czech Republic, 2019.","title":"Novelty search: A theoretical perspective","authors":"S Doncieux, A Laflaquière, A Coninx","year":"2019","venue":"GECCO","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Ecoffet et al., 2021] A. Ecoffet, J. Huizinga, J. Lehman, K. O. Stanley, and J. Clune. First return, then explore. Nature, 590(7847):580-586, 2021.","title":"First return, then explore","authors":"A Ecoffet, J Huizinga, J Lehman, K O Stanley, J Clune","year":"2021","venue":"Nature","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Eysenbach et al., 2018] B. Eysenbach, A. Gupta, J. Ibarz, and S. Levine. Diversity is all you need: Learning skills without a reward function. In ICLR, Vancouver, Canada, 2018.","title":"Diversity is all you need: Learning skills without a reward function","authors":"B Eysenbach, A Gupta, J Ibarz, S Levine","year":"2018","venue":"ICLR","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Faldor et al., 2023] M. Faldor, F. Chalumeau, M. Flageat, and A. Cully. MAP-Elites with descriptor-conditioned gradients and archive distillation into a single policy. In GECCO, pages 138-146, Lisbon, Portugal, 2023.","title":"MAP-Elites with descriptor-conditioned gradients and archive distillation into a single policy","authors":"M Faldor, F Chalumeau, M Flageat, A Cully","year":"2023","venue":"GECCO","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Feige, 1998] U. Feige. A threshold of ln n for approximat- ing set cover. Journal of the ACM, 45(4):634-652, 1998.","title":"A threshold of ln n for approximating set cover","authors":"U Feige","year":"1998","venue":"Journal of the ACM","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Feng et al., 2019] C. Feng, C. Qian, and K. Tang. Unsuper- vised feature selection by Pareto optimization. In AAAI, pages 3534-3541, Honolulu, HI, 2019.","title":"Unsupervised feature selection by Pareto optimization","authors":"C Feng, C Qian, K Tang","year":"2019","venue":"AAAI","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Fontaine et al., 2021] M. C. Fontaine, R. Liu, A. Khalifa, J. Modi, J. Togelius, A. K. Hoover, and S. Nikolaidis. Illu- minating Mario scenes in the latent space of a generative adversarial network. In AAAI, pages 5922-5930, Virtual, 2021.","title":"Illuminating Mario scenes in the latent space of a generative adversarial network","authors":"M C Fontaine, R Liu, A Khalifa, J Modi, J Togelius, A K Hoover, S Nikolaidis","year":"2021","venue":"AAAI","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Friedrich and Neumann, 2015] T. Friedrich and F. Neu- mann. Maximizing submodular functions under ma- troid constraints by evolutionary algorithms. Evolutionary Computation, 23(4):543-558, 2015.","title":"Maximizing submodular functions under matroid constraints by evolutionary algorithms","authors":"T Friedrich, F Neumann","year":"2015","venue":"Evolutionary Computation","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Friedrich et al., 2010] T. Friedrich, J. He, N. Hebbinghaus, F. Neumann, and C. Witt. Approximating covering problems by randomized search heuristics using multi- objective models. Evolutionary Computation, 18(4):617- 633, 2010.","title":"Approximating covering problems by randomized search heuristics using multiobjective models","authors":"T Friedrich, J He, N Hebbinghaus, F Neumann, C Witt","year":"2010","venue":"Evolutionary Computation","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Grillotti and Cully, 2022] L. Grillotti and A. Cully. Unsu- pervised behavior discovery with quality-diversity opti- mization. IEEE Transactions on Evolutionary Computa- tion, 26(6):1539-1552, 2022.","title":"Unsupervised behavior discovery with quality-diversity optimization","authors":"L Grillotti, A Cully","year":"2022","venue":"IEEE Transactions on Evolutionary Computation","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Harshaw et al., 2019] C. Harshaw, M. Feldman, J. Ward, and A. Karbasi. Submodular maximization beyond non- negativity: Guarantees, fast algorithms, and applications. In ICML, pages 2634-2643, Long Beach, CA, 2019.","title":"Submodular maximization beyond nonnegativity: Guarantees, fast algorithms, and applications","authors":"C Harshaw, M Feldman, J Ward, A Karbasi","year":"2019","venue":"ICML","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Jansen and Wegener, 2001] T. Jansen and I. Wegener. On the utility of populations in evolutionary algorithms. In GECCO, pages 1034-1041, San Francisco, CA, 2001.","title":"On the utility of populations in evolutionary algorithms","authors":"T Jansen, I Wegener","year":"2001","venue":"GECCO","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Kempe et al., 2003] D. Kempe, J. Kleinberg, and É. Tardos. Maximizing the spread of influence through a social net- work. In KDD, pages 137-146, Washington, DC, 2003.","title":"Maximizing the spread of influence through a social network","authors":"D Kempe, J Kleinberg, É Tardos","year":"2003","venue":"KDD","doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Krause et al., 2008] A. Krause, A. Singh, and C. Guestrin. Near-optimal sensor placements in Gaussian processes: Theory, efficient algorithms and empirical studies. Jour- nal of Machine Learning Research, 9:235-284, 2008.","title":"Near-optimal sensor placements in Gaussian processes: Theory, efficient algorithms and empirical studies","authors":"A Krause, A Singh, C Guestrin","year":"2008","venue":"Journal of Machine Learning Research","doi":null,"url":null,"internal_url":null},{"position":28,"raw":"[Kumar et al., 2020] S. Kumar, A. Kumar, S. Levine, and C. Finn. One solution is not all you need: Few-shot ex- trapolation via structured MaxEnt RL. In NeurIPS, pages 8198-8210, Virtual, 2020.","title":"One solution is not all you need: Few-shot extrapolation via structured MaxEnt RL","authors":"S Kumar, A Kumar, S Levine, C Finn","year":"2020","venue":"NeurIPS","doi":null,"url":null,"internal_url":null},{"position":29,"raw":"[Lehman and Stanley, 2011a] J. Lehman and K. O. Stanley. Abandoning objectives: Evolution through the search for novelty alone. Evolutionary Computation, 19(2):189-223, 2011.","title":"Abandoning objectives: Evolution through the search for novelty alone","authors":"Stanley ; Lehman, ] J Lehman, K O Stanley","year":"2011","venue":"Evolutionary Computation","doi":null,"url":null,"internal_url":null},{"position":30,"raw":"[Lehman and Stanley, 2011b] J. Lehman and K. O. Stanley. Evolving a diversity of virtual creatures through novelty search and local competition. In GECCO, pages 211-218, Dublin, Ireland, 2011.","title":"Evolving a diversity of virtual creatures through novelty search and local competition","authors":"Stanley ; Lehman, ] J Lehman, K O Stanley","year":"2011","venue":"GECCO","doi":null,"url":null,"internal_url":null},{"position":31,"raw":"[Lengler and Zou, 2021] J. Lengler and X. Zou. Exponential slowdown for larger populations: The (µ+1)-EA on mono- tone functions. Theoretical Computer Science, 875:28-51, 2021.","title":"Exponential slowdown for larger populations: The (µ+1)-EA on monotone functions","authors":"J Lengler, X Zou","year":"2021","venue":"Theoretical Computer Science","doi":null,"url":null,"internal_url":null},{"position":32,"raw":"[Lim et al., 2022] B. Lim, M. C. Flageat, and A. Cully. Effi- cient exploration using model-based quality-diversity with gradients. arXiv:2211.12610, 2022.","title":"Efficient exploration using model-based quality-diversity with gradients","authors":"B Lim, M C Flageat, A Cully","year":"2022","venue":null,"doi":null,"url":null,"internal_url":null},{"position":33,"raw":"[Lupu et al., 2021] A. Lupu, H. Hu, and J. Foerster. Trajec- tory diversity for zero-shot coordination. In ICML, pages 7204-7213, Virtual, 2021.","title":"Trajectory diversity for zero-shot coordination","authors":"A Lupu, H Hu, J Foerster","year":"2021","venue":"ICML","doi":null,"url":null,"internal_url":null},{"position":34,"raw":"[Mouret and Clune, 2015] J.-B. Mouret and J. Clune. Illuminating search spaces by mapping elites. arXiv:1504.04909, 2015.","title":"Illuminating search spaces by mapping elites","authors":"J.-B Mouret, J Clune","year":"2015","venue":null,"doi":null,"url":null,"internal_url":null},{"position":35,"raw":"[Nemhauser et al., 1978] G. L. Nemhauser, L. A. Wolsey, and M. L. Fisher. An analysis of approximations for max- imizing submodular set functions -I. Mathematical Pro- gramming, 14(1):265-294, 1978.","title":"An analysis of approximations for maximizing submodular set functions -I","authors":"G L Nemhauser, L A Wolsey, M L Fisher","year":"1978","venue":"Mathematical Programming","doi":null,"url":null,"internal_url":null},{"position":36,"raw":"[Neumann and Wegener, 2006] F. Neumann and I. Wegener. Minimum spanning trees made easier via multi-objective optimization. Natural Computing, 3(5):305-319, 2006.","title":"Minimum spanning trees made easier via multi-objective optimization","authors":"F Neumann, I Wegener","year":"2006","venue":"Natural Computing","doi":null,"url":null,"internal_url":null},{"position":37,"raw":"[Neumann and Witt, 2010] F. Neumann and C. Witt. Bioin- spired Computation in Combinatorial Optimization -Al- gorithms and Their Computational Complexity. Springer, Berlin, Germany, 2010.","title":"Bioinspired Computation in Combinatorial Optimization -Algorithms and Their Computational Complexity","authors":"F Neumann, C Witt","year":"2010","venue":null,"doi":null,"url":null,"internal_url":null},{"position":38,"raw":"[Nikfarjam et al., 2022a] A. Nikfarjam, A. Neumann, and F. Neumann. On the use of quality diversity algorithms for the traveling thief problem. In GECCO, pages 260-268, Boston, MA, 2022.","title":"On the use of quality diversity algorithms for the traveling thief problem","authors":"Nikfarjam","year":"2022","venue":"GECCO","doi":null,"url":null,"internal_url":null},{"position":39,"raw":"[Nikfarjam et al., 2022b] A. Nikfarjam, A. Viet Do, and F. Neumann. Analysis of quality diversity algorithms for the knapsack problem. In PPSN, pages 413-427, Dort- mund, Germany, 2022.","title":"Analysis of quality diversity algorithms for the knapsack problem","authors":"Nikfarjam","year":"2022","venue":"PPSN","doi":null,"url":null,"internal_url":null},{"position":40,"raw":"[Nilsson and Cully, 2021] O. Nilsson and A. Cully. Policy gradient assisted MAP-Elites. In GECCO, page 866-875, Lille, France, 2021.","title":"Policy gradient assisted MAP-Elites","authors":"O Nilsson, A Cully","year":"2021","venue":"GECCO","doi":null,"url":null,"internal_url":null},{"position":41,"raw":"[Pugh et al., 2016] J. K. Pugh, L. B. Soros, and K. O. Stan- ley. Quality diversity: A new frontier for evolutionary computation. Frontiers Robotics AI, 3:40, 2016.","title":"Quality diversity: A new frontier for evolutionary computation","authors":"J K Pugh, L B Soros, K O Stanley","year":"2016","venue":"Frontiers Robotics AI","doi":null,"url":null,"internal_url":null},{"position":42,"raw":"[Qian et al., 2015a] C. Qian, Y. Yu, and Z.-H. Zhou. On constrained Boolean Pareto optimization. In IJCAI, pages 389-395, Buenos Aires, Argentina, 2015.","title":"On constrained Boolean Pareto optimization","authors":"Qian","year":"2015","venue":"IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2015/61"},{"position":43,"raw":"[Qian et al., 2015b] C. Qian, Y. Yu, and Z.-H. Zhou. Subset selection by Pareto optimization. In NeurIPS, pages 1765- 1773, Montreal, Canada, 2015.","title":"Subset selection by Pareto optimization","authors":"Qian","year":"2015","venue":"NeurIPS","doi":null,"url":null,"internal_url":null},{"position":44,"raw":"[Qian et al., 2016] C. Qian, J.-C. Shi, Y. Yu, K. Tang, and Z.- H. Zhou. Parallel Pareto optimization for subset selection. In IJCAI, pages 1939-1945, New York, NY, 2016.","title":"Parallel Pareto optimization for subset selection","authors":"C Qian, J.-C Shi, Y Yu, K Tang, Z.-H Zhou","year":"2016","venue":"IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2016/277"},{"position":45,"raw":"[Qian et al., 2019] C. Qian, Y. Yu, K. Tang, X. Yao, and Z.- H. Zhou. Maximizing submodular or monotone approx- imately submodular functions by multi-objective evolu- tionary algorithms. Artificial Intelligence, 275:279-294, 2019.","title":"Maximizing submodular or monotone approximately submodular functions by multi-objective evolutionary algorithms","authors":"C Qian, Y Yu, K Tang, X Yao, Z.-H Zhou","year":"2019","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":46,"raw":"[Salehi et al., 2022] A. Salehi, A. Coninx, and S. Doncieux. Few-shot quality-diversity optimization. IEEE Robotics and Automation Letters, 7(2):4424-4431, 2022.","title":"Few-shot quality-diversity optimization","authors":"A Salehi, A Coninx, S Doncieux","year":"2022","venue":"IEEE Robotics and Automation Letters","doi":null,"url":null,"internal_url":null},{"position":47,"raw":"[Sfikas et al., 2021] K. Sfikas, A. Liapis, and G. N. Yan- nakakis. Monte Carlo elites: Quality-diversity selection as a multi-armed bandit problem. In GECCO, pages 180- 188, Lille, France, 2021.","title":"Monte Carlo elites: Quality-diversity selection as a multi-armed bandit problem","authors":"K Sfikas, A Liapis, G N Yannakakis","year":"2021","venue":"GECCO","doi":null,"url":null,"internal_url":null},{"position":48,"raw":"[Storch, 2008] T. Storch. On the choice of the parent pop- ulation size. Evolutionary Computation, 16(4):557-578, 2008.","title":"On the choice of the parent population size","authors":"T Storch","year":"2008","venue":"Evolutionary Computation","doi":null,"url":null,"internal_url":null},{"position":49,"raw":"[Strouse et al., 2021] DJ Strouse, K. McKee, M. Botvinick, E. Hughes, and R. Everett. Collaborating with humans without human data. In NeurIPS, pages 14502-14515, Vir- tual, 2021.","title":"Collaborating with humans without human data","authors":"K Dj Strouse, M Mckee, E Botvinick, R Hughes, Everett","year":"2021","venue":"NeurIPS","doi":null,"url":null,"internal_url":null},{"position":50,"raw":"[Tjanaka et al., 2022] B. Tjanaka, M. C. Fontaine, J. To- gelius, and S. Nikolaidis. Approximating gradients for differentiable quality diversity in reinforcement learning. In GECCO, page 1102-1111, Boston, MA, 2022.","title":"Approximating gradients for differentiable quality diversity in reinforcement learning","authors":"B Tjanaka, M C Fontaine, J Togelius, S Nikolaidis","year":"2022","venue":"GECCO","doi":null,"url":null,"internal_url":null},{"position":51,"raw":"[Vassiliades et al., 2018] V. Vassiliades, K. I. Chatzilyger- oudis, and J.-B. Mouret. Using centroidal voronoi tessel- lations to scale up the multidimensional archive of pheno- typic elites algorithm. IEEE Transactions on Evolutionary Computation, 22(4):623-630, 2018.","title":"Using centroidal voronoi tessellations to scale up the multidimensional archive of phenotypic elites algorithm","authors":"V Vassiliades, K I Chatzilygeroudis, J.-B Mouret","year":"2018","venue":"IEEE Transactions on Evolutionary Computation","doi":null,"url":null,"internal_url":null},{"position":52,"raw":"[Wang et al., 2022] Y. Wang, K. Xue, and C. Qian. Evolu- tionary diversity optimization with clustering-based selec- tion for reinforcement learning. In ICLR, Virtual, 2022.","title":"Evolutionary diversity optimization with clustering-based selection for reinforcement learning","authors":"Y Wang, K Xue, C Qian","year":"2022","venue":"ICLR, Virtual","doi":null,"url":null,"internal_url":null},{"position":53,"raw":"[Wang et al., 2023] R.-J. Wang, K. Xue, H. Shang, C. Qian, H. Fu, and Q. Fu. Multi-objective optimization-based se- lection for quality-diversity by non-surrounded-dominated sorting. In IJCAI, pages 4335-4343, Macao, SAR, China, 2023.","title":"Multi-objective optimization-based selection for quality-diversity by non-surrounded-dominated sorting","authors":"R.-J Wang, K Xue, H Shang, C Qian, H Fu, Q Fu","year":"2023","venue":"IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2023/482"},{"position":54,"raw":"[Wiegand, 2024] R. P. Wiegand. Preliminary analysis of sim- ple novelty search. Evolutionary Computation, pages 1- 25, 2024.","title":"Preliminary analysis of simple novelty search","authors":"R P Wiegand","year":"2024","venue":"Evolutionary Computation","doi":null,"url":null,"internal_url":null},{"position":55,"raw":"[Witt, 2006] C. Witt. Runtime analysis of the (µ+1) EA on simple pseudo-Boolean functions. Evolutionary Compu- tation, 14(1):65-86, 2006.","title":"Runtime analysis of the (µ+1) EA on simple pseudo-Boolean functions","authors":"C Witt","year":"2006","venue":"Evolutionary Computation","doi":null,"url":null,"internal_url":null},{"position":56,"raw":"[Xue et al., 2024] K. Xue, R.-J. Wang, P. Li, D. Li, J. Hao, and C. Qian. Sample-efficient quality-diversity by cooper- ative coevolution. In ICLR, Vienna, Austria, 2024.","title":"Sample-efficient quality-diversity by cooperative coevolution","authors":"K Xue, R.-J Wang, P Li, D Li, J Hao, C Qian","year":"2024","venue":"ICLR","doi":null,"url":null,"internal_url":null},{"position":57,"raw":"[Zhang et al., 2023] Y. Zhang, M. C. Fontaine, V. Bhatt, S. Nikolaidis, and J. Li. Multi-robot coordination and lay- out design for automated warehousing. In IJCAI, pages 5503-5511, Macao, SAR, China, 2023.","title":"Multi-robot coordination and layout design for automated warehousing","authors":"Y Zhang, M C Fontaine, V Bhatt, S Nikolaidis, J Li","year":"2023","venue":"IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2023/611"},{"position":58,"raw":"[Zhou et al., 2019] Z.-H. Zhou, Y. Yu, and C. Qian. Evolu- tionary Learning: Advances in Theories and Algorithms. Springer, Singapore, 2019.","title":"Evolutionary Learning: Advances in Theories and Algorithms","authors":"Z.-H Zhou, Y Yu, C Qian","year":"2019","venue":null,"doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}