Comparison of Multiobjective Evolutionary Algorithms: Empirical Results

By Eckart Zitzler, Kalyanmoy Deb, Lothar Thiele. Evolutionary Computation, 2000

6,070 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/3cf23da3fb520ab78477648e53dc3d8dbbd690a7

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Citations in the corpus

Bat algorithm for multi-objective optimisation (2011, methodology): “ZDT1 function with a convex front (Zitzler and Thiele, 1999; Zitzler et al., 2000)”
A survey on multi-objective evolutionary algorithms for many-objective problems (2014, methodology): “…N S GA -II [ 24 ] w it h s ub s tit u t e s ec ond a r y d i s t a n ce s d e ﬁ n e d i n [ 60 ] C onv e r g e n ce [ 26 , 62 ] , C ov e r a g e [ 109 , 111 ] [ 58 ] NK - l a nd s ca p e s [ 55 ] 2 , 5 , 10 P E S A -II [ 21 ] , R a ndo m C ov e r a g e [ 109 , 111 ] [ 100 ] D TLZ ( 1 , 2 ) [ 25…”
Multi-Objective Particle Swarm Optimizers: A Survey of the State-of-the-Art (2006, background): “In general, when solving a multi-objective problem, three are the main goals to achieve [73]:”
Performance indicators in multiobjective optimization (2018, background): “4 3 3 3 3 Hypervolume indicator (or S-metric) [6] 3.”
An easy-to-use real-world multi-objective optimization problem suite (2020, methodology): “Representative examples include the ZDT [8], DTLZ [9], WFG [10], and LZ [11] problem suites.”
Multi-objective ant lion optimizer: a multi-objective optimization algorithm for solving engineering problems (2016, methodology): “Appendix A shows that the well-known ZDT test suite is employed [42].”
Direct Multisearch for Multiobjective Optimization (2011, neutral): “Problem n m Problem n m Problem n m BK1 [25] 2 2 I5 [24] 8 3 MOP3 [25] 2 2 CL1 [6] 4 2 IKK1 [25] 2 3 MOP4 [25] 3 2 Deb41 [15] 2 2 IM1 [25] 2 2 MOP5 [25] 2 3 Deb512a [15] 2 2 Jin1 [48] 2 2 MOP6 [25] 2 2 Deb512b [15] 2 2 Jin2 [48] 2 2 MOP7 [25] 2 3 Deb512c [15] 2 2 Jin3 [48] 2 2 OKA1 [39] 2 2 Deb513 [”
A Strength Pareto Evolutionary Algorithm Based on Reference Direction for Multiobjective and Many-Objective Optimization (2017, methodology): “The test problems used here are the MOP [34] test suite, which is a modification of ZDT [52] and DTLZ [15] but more difficult than its predecessors.”
Test Problems for Large-Scale Multiobjective and Many-Objective Optimization (2017, background): “The ZDT test suite is one of the most popular test suites in the multi-objective optimization literature [20].”
M-PAES: a memetic algorithm for multiobjective optimization (2000, methodology): “More recently, elitism has been shown to improve the performance of multiobjective GAs, for example see [22], and a very elegant method of exploiting co-evolution to perform fitness assignment in an elitist GA was put forward by Zitzler and Thiele [30, 32, 31].”
PESA-II: region-based selection in evolutionary multiobjective optimization (2001, methodology): “We encode the functions herein precisely the same way as done in Zitzler et al (1999)and Corne et al (2000).”
A Survey on Evolutionary Constrained Multiobjective Optimization (2023, methodology): “On the basis of the unconstrained test set ZDT [144], the constrained test suite CZDT was proposed in [54].”
Evaluating the -Domination Based Multi-Objective Evolutionary Algorithm for a Quick Computation of Pareto-Optimal Solutions (2005, methodology): “First, we consider five two-objective ZDT test problems (Deb, 1999; Zitzler et al., 2000), each providing a different kind of difficulty for MOEAs.”
Benchmark Problems and Performance Indicators for Search of Knee Points in Multiobjective Optimization (2020, background): “Note, however, that neither ZDT nor DTLZ pays particular attention to the complexity of the PoF, and it is assumed that there is no correlation between the position and distance variables.”
A taxonomy and an empirical analysis of multiple objective ant colony optimization algorithms for the bi-criteria TSP (2007, background): “in [47], are reviewed as follows: Given a set of pairwise non-dominated decision vectors X 0 X, a neighborhood parameter r > 0 (to be chosen appropriately), and a distance metric kÆk:”