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In addition, we expand upon the relation of lexicase selection to many-objective optimization methods to describe the behavior of lexicase selection, which is to select individuals on the boundaries of Pareto fronts in high-dimensional space. We show analytically why lexicase selection performs more poorly for certain sizes of population and training cases, and show why it has been shown to perform more poorly in continuous error spaces. To address this last concern, we propose new variants of [Formula: see text]-lexicase selection, a method that modifies the pass condition in lexicase selection to allow near-elite individuals to pass cases, thereby improving selection performance with continuous errors. We show that [Formula: see text]-lexicase outperforms several diversity\u2013maintenance strategies on a number of real-world and synthetic regression problems.<\/jats:p>","DOI":"10.1162\/evco_a_00224","type":"journal-article","created":{"date-parts":[[2018,5,10]],"date-time":"2018-05-10T19:51:51Z","timestamp":1525981911000},"page":"377-402","source":"Crossref","is-referenced-by-count":82,"title":["A Probabilistic and Multi-Objective Analysis of Lexicase Selection and \u03b5-Lexicase Selection"],"prefix":"10.1162","volume":"27","author":[{"given":"William","family":"La Cava","sequence":"first","affiliation":[{"name":"Institute for Bioinformatics, University of Pennsylvania, Philadelphia, PA, 19104, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Thomas","family":"Helmuth","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Hamilton College, Clinton, NY, 13323, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lee","family":"Spector","sequence":"additional","affiliation":[{"name":"School of Cognitive Science, Hampshire College, Amherst, MA, 01002, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jason H.","family":"Moore","sequence":"additional","affiliation":[{"name":"Institute for Bioinformatics, University of Pennsylvania, Philadelphia, PA, 19104, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"281","reference":[{"key":"B1","doi-asserted-by":"publisher","DOI":"10.1145\/1527125.1527138"},{"key":"B2","author":"Burks A. 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