Two Arch2: An Improved Two-Archive Algorithm for Many-Objective Optimization

IEEE Transactions on Evolutionary Computation

Volumn 19, Issue 4, 2015, Pages 524-541

  Wang, Handing ^a   Jiao, Licheng ^a   Yao, Xin ^b  

^a XIDIAN UNIVERSITY   (China)

^b UNIVERSITY OF BIRMINGHAM   (United Kingdom)

Author keywords

Evolutionary algorithm; Lp norm; manyobjective optimization; two archive algorithm (Two Arch)

Indexed keywords

ALGORITHMS; ARCHES; BENCHMARKING; COMPUTATIONAL COMPLEXITY; MULTIOBJECTIVE OPTIMIZATION; OPTIMIZATION; PARETO PRINCIPLE;

DIVERSITY MAINTENANCE; LOW COMPLEXITY ALGORITHM; LP-NORM; MANY-OBJECTIVE OPTIMIZATIONS; MULTI-OBJECTIVE PROBLEM; MULTIOBJECTIVE EVOLUTIONARY ALGORITHMS; SELECTION PRINCIPLES; TWO-ARCHIVE ALGORITHM (TWO-ARCH);

EVOLUTIONARY ALGORITHMS;

EID: 84938564711     PISSN: 1089778X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TEVC.2014.2350987     Document Type: Article

References (58)

1. E. Hughes, "Radar waveform optimisation as a many-objective application benchmark, " in Evolutionary Multi-Criterion Optimization. Berlin, Germany: Springer, 2007, pp. 700-714.
2. P. Fleming, R. Purshouse, and R. Lygoe, "Many-objective optimization: An engineering design perspective, " in Evolutionary Multi-Criterion Optimization. Berlin, Germany: Springer, 2005, pp. 14-32.
3. V. Khare, X. Yao, and K. Deb, "Performance scaling of multi-objective evolutionary algorithms, " in Evolutionary Multi-Criterion Optimization (Lecture Notes in Computer Science), vol. 2632, C. Fonseca, P. Fleming, E. Zitzler, L. Thiele, and K. Deb, Eds. Berlin, Germany: Springer, 2003, pp. 376-390.
4. K. Praditwong and X. Yao, "How well do multi-objective evolutionary algorithms scale to large problems, " in Proc. IEEE Congr. Evol. Comput. (CEC), Singapore, Sep. 2007, pp. 3959-3966.
5. K. Miettinen, Nonlinear Multiobjective Optimization. Berlin, Germany: Springer, 1999.
6. K. Deb, Multi-Objective Optimization Using Evolutionary Algorithms, vol. 16. New York, NY, USA: Wiley, 2001.
7. D. Hadka and P. Reed, "Diagnostic assessment of search controls and failure modes in many-objective evolutionary optimization, " Evol. Comput., vol. 20, no. 3, pp. 423-452, 2012.
8. E. Hughes, "Evolutionary many-objective optimisation: Many once or one many?" in Proc. IEEE Congr. Evol. Comput. (CEC), vol. 1. Edinburgh, U.K., 2005, pp. 222-227.
9. H. Ishibuchi, N. Akedo, H. Ohyanagi, and Y. Nojima, "Behavior of EMO algorithms on many-objective optimization problems with correlated objectives, " in Proc. IEEE Congr. Evol. Comput. (CEC), New Orleans, LA, USA, Jun. 2011, pp. 1465-1472.
10. T. Wagner, N. Beume, and B. Naujoks, "Pareto-, aggregation-, and indicator-based methods in many-objective optimization, " in Evolutionary Multi-Criterion Optimization. Berlin, Germany: Springer, 2007, pp. 742-756.
11. H. Ishibuchi, N. Tsukamoto, Y. Hitotsuyanagi, and Y. Nojima, "Effectiveness of scalability improvement attempts on the performance of NSGA-II for many-objective problems, " in Proc. 10th Annu. Conf. Genet. Evol. Comput. (GECCO), 2008, pp. 649-656.
12. R. C. Purshouse and P. J. Fleming, "On the evolutionary optimization of many conflicting objectives, " IEEE Trans. Evol. Comput., vol. 11, no. 6, pp. 770-784, Dec. 2007.
13. H. Ishibuchi, N. Tsukamoto, and Y. Nojima, "Evolutionary manyobjective optimization: A short review, " in Proc. IEEE Congr. Evol. Comput. (CEC), Hong Kong, Jun. 2008, pp. 2419-2426.
14. M. Köppen and K. Yoshida, "Substitute distance assignments in NSGA-II for handling many-objective optimization problems, " in Evolutionary Multi-Criterion Optimization. Berlin, Germany: Springer, 2007, pp. 727-741.
15. S. F. Adra and P. J. Fleming, "Diversity management in evolutionary many-objective optimization, " IEEE Trans. Evol. Comput., vol. 15, no. 2, pp. 183-195, Apr. 2011.
16. Q. Zhang and H. Li, "MOEA/D: A multiobjective evolutionary algorithm based on decomposition, " IEEE Trans. Evol. Comput., vol. 11, no. 6, pp. 712-731, Dec. 2007.
17. H. Ishibuchi, Y. Hitotsuyanagi, H. Ohyanagi, and Y. Nojima, "Effects of the existence of highly correlated objectives on the behavior of MOEA/D, " in Evolutionary Multi-Criterion Optimization. Berlin, Germany: Springer, 2011, pp. 166-181.
18. I. Giagkiozis, R. C. Purshouse, and P. J. Fleming, "Generalized decomposition and cross entropy methods for many-objective optimization, " Dept. Autom. Control Syst. Eng., Univ. Sheffield, Sheffield, U.K., Res. Rep. 1029, 2012.
19. E. Zitzler and S. Künzli, "Indicator-based selection in multiobjective search, " in Parallel Problem Solving from Nature-PPSN VIII. Berlin, Germany: Springer, 2004, pp. 832-842.
20. J. Bader and E. Zitzler, "HypE: An algorithm for fast hypervolume-based many-objective optimization, " Evol. Comput., vol. 19, no. 1, pp. 45-76, 2011.
21. J. Bader and E. Zitzler, "A hypervolume-based optimizer for highdimensional objective spaces, " in New Developments in Multiple Objective and Goal Programming. Berlin, Germany: Springer, 2010, pp. 35-54.
22. E. Zitzler and L. Thiele, "Multiobjective evolutionary algorithms: A comparative case study and the strength Pareto approach, " IEEE Trans. Evol. Comput., vol. 3, no. 4, pp. 257-271, Nov. 1999.
23. K. Bringmann, "Bringing order to special cases of Klee's measure problem, " in Mathematical Foundations of Computer Science. Berlin, Germany: Springer, 2013, pp. 207-218.
24. D. Brockhoff and E. Zitzler, "Are all objectives necessary? On dimensionality reduction in evolutionary multiobjective optimization, " in Parallel Problem Solving from Nature-PPSN IX. Berlin, Germany: Springer, 2006, pp. 533-542.
25. D. Brockhoff and E. Zitzler, "Objective reduction in evolutionary multiobjective optimization: Theory and applications, " Evol. Comput., vol. 17, no. 2, pp. 135-166, 2009.
26. A. López Jaimes, C. C. Coello, and D. Chakraborty, "Objective reduction using a feature selection technique, " in Proc. 10th Annu. Conf. Genet. Evol. Comput. (GECCO), 2008, pp. 673-680.
27. K. Deb and D. Saxena, "On finding Pareto-optimal solutions through dimensionality reduction for certain large-dimensional multi-objective optimization problems, " vol. 11, Indian Institute of Technology, Kharagpur, India, Kangal Rep. 2005011, 2005.
28. D. Saxena and K. Deb, "Non-linear dimensionality reduction procedures for certain large-dimensional multi-objective optimization problems: Employing correntropy and a novel maximum variance unfolding, " in Evolutionary Multi-Criterion Optimization. Berlin, Germany: Springer, 2007, pp. 772-787.
29. D. K. Saxena, J. A. Duro, A. Tiwari, K. Deb, and Q. Zhang, "Objective reduction in many-objective optimization: Linear and nonlinear algorithms, " IEEE Trans. Evol. Comput., vol. 17, no. 1, pp. 77-99, Feb. 2013.
30. H. Singh, A. Isaacs, and T. Ray, "A Pareto corner search evolutionary algorithm and dimensionality reduction in many-objective optimization problems, " IEEE Trans. Evol. Comput., vol. 15, no. 4, pp. 539-556, Aug. 2011.
31. L. Thiele, K. Miettinen, P. Korhonen, and J. Molina, "A preference-based evolutionary algorithm for multi-objective optimization, " Evol. Comput., vol. 17, no. 3, pp. 411-436, 2009.
32. D. Cvetkovic and I. C. Parmee, "Preferences and their application in evolutionary multiobjective optimization, " IEEE Trans. Evol. Comput., vol. 6, no. 1, pp. 42-57, Feb. 2002.
33. K. Sindhya, A. B. Ruiz, and K. Miettinen, "A preference based interactive evolutionary algorithm for multi-objective optimization: PIE, " in Evolutionary Multi-Criterion Optimization. Berlin, Germany: Springer, 2011, pp. 212-225.
34. L. Ben Said, S. Bechikh, and K. Ghédira, "The r-dominance: A new dominance relation for interactive evolutionary multicriteria decision making, " IEEE Trans. Evol. Comput., vol. 14, no. 5, pp. 801-818, Oct. 2010.
35. M. Koksalan and I. Karahan, "An interactive territory defining evolutionary algorithm: iTDEA, " IEEE Trans. Evol. Comput., vol. 14, no. 5, pp. 702-722, Oct. 2010.
36. R. Wang, R. Purshouse, and P. Fleming, "Preference-inspired coevolutionary algorithms for many-objective optimization, " IEEE Trans. Evol. Comput., vol. 17, no. 4, pp. 474-494, Aug. 2013.
37. J.-H. Kim, J.-H. Han, Y.-H. Kim, S.-H. Choi, and E.-S. Kim, "Preference-based solution selection algorithm for evolutionary multiobjective optimization, " IEEE Trans. Evol. Comput., vol. 16, no. 1, pp. 20-34, Feb. 2012.
38. I. Karahan and M. Koksalan, "A territory defining multiobjective evolutionary algorithms and preference incorporation, " IEEE Trans. Evol. Comput., vol. 14, no. 4, pp. 636-664, Aug. 2010.
39. M. Farina and P. Amato, "On the optimal solution definition for manycriteria optimization problems, " in Proc. Annu. Meeting North Amer. Fuzzy Inf. Process. Soc. (NAFIPS), 2002, pp. 233-238.
40. K. Deb, M. Mohan, and S. Mishra, "Evaluating the ?-domination based multi-objective evolutionary algorithm for a quick computation of Pareto-optimal solutions, " Evol. Comput., vol. 13, no. 4, pp. 501-525, 2005.
41. K. Bringmann, T. Friedrich, F. Neumann, and M. Wagner, "Approximation-guided evolutionary multi-objective optimization, " in Proc. 22nd Int. Joint Conf. Artif. Intell., 2011, pp. 1198-1203.
42. M. Wagner and F. Neumann, "A fast approximation-guided evolutionary multi-objective algorithm, " in Proc. 15th Annu. Conf. Genet. Evol. Comput. Conf. (GECCO). Amsterdam, The Netherlands, 2013, pp. 687-694.
43. H. Sato, H. E. Aguirre, and K. Tanaka, "Controlling dominance area of solutions and its impact on the performance of MOEAs, " in Evolutionary Multi-Criterion Optimization. Berlin, Germany: Springer, 2007, pp. 5-20.
44. S. Kukkonen and J. Lampinen, "Ranking-dominance and many-objective optimization, " in Proc. IEEE Congr. Evol. Comput. (CEC), Singapore, 2007, pp. 3983-3990.
45. M. Köppen, R. Vicente-Garcia, and B. Nickolay, "Fuzzy-Paretodominance and its application in evolutionary multi-objective optimization, " in Evolutionary Multi-Criterion Optimization. Berlin, Germany: Springer, 2005, pp. 399-412.
46. K. Deb and S. Tiwari, "Omni-optimizer: A procedure for single and multi-objective optimization, " in Evolutionary Multi-Criterion Optimization. Berlin, Germany: Springer, 2005, pp. 47-61.
47. H. Wang and X. Yao, "Corner sort for Pareto-based many-objective optimization, " IEEE Trans. Cybern., vol. 44, no. 1, pp. 92-102, Jan. 2014.
48. K. McClymont and E. Keedwell, "Deductive sort and climbing sort: New methods for non-dominated sorting, " Evol. Comput., vol. 20, no. 1, pp. 1-26, 2012.
49. K. Deb and H. Jain, "An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, part I: Solving problems with box constraints, " IEEE Trans. Evol. Comput., vol. 18, no. 4, pp. 577-601, Aug. 2014.
50. K. Praditwong and X. Yao, "A new multi-objective evolutionary optimization algorithm: The two-archive algorithm, " in Proc. Int. Conf. Comput. Intell. Security, vol. 1. Guangzhou, China, 2006, pp. 286-291.
51. G. Rudolph, H. Trautmann, S. Sengupta, and O. Schütze, "Evenly spaced Pareto front approximations for tricriteria problems based on triangulation, " in Evolutionary Multi-Criterion Optimization. Berlin, Germany: Springer, 2013, pp. 443-458.
52. Z. Wang, K. Tang, and X. Yao, "Multi-objective approaches to optimal testing resource allocation in modular software systems, " IEEE Trans. Rel., vol. 59, no. 3, pp. 563-575, Sep. 2010.
53. C. C. Aggarwal, A. Hinneburg, and D. A. Keim, On the Surprising Behavior of Distance Metrics in High Dimensional Space. New York, NY, USA: Springer, 2001.
54. R. Morgan and M. Gallagher, "Sampling techniques and distance metrics in high dimensional continuous landscape analysis: Limitations and improvements, " IEEE Trans. Evol. Comput., vol. 18, no. 3, pp. 456-461, Jun. 2014.
55. K. Deb, L. Thiele, M. Laumanns, and E. Zitzler, "Scalable multiobjective optimization test problems, " in Proc. IEEE Congr. Evol. Comput. (CEC), Honolulu, HI, USA, 2002, pp. 825-830.
56. S. Huband, P. Hingston, L. Barone, and L. While, "A review of multiobjective test problems and a scalable test problem toolkit, " IEEE Trans. Evol. Comput., vol. 10, no. 5, pp. 477-506, Oct. 2006.
57. Q. Zhang et al., "Multiobjective optimization test instances for the CEC 2009 special session and competition, " School Comput. Sci. Elect. Eng., Univ. Essex, Tech. Rep. CES-887, 2008, pp. 1-30.
58. M. Hollander and D. Wolfe, Nonparametric Statistical Methods. New York, NY, USA: Wiley, 1999.