Improved ant colony optimization algorithms for continuous ... - CoDE

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52 Ant Colony Optimization for Mixed Variable Problems vestigation of the performance of mixed-variable optimization algorithms, and they provide a training environment for parameter tuning. Based on the benchmark functions, a rigorous comparison between ACOMV-o and ACOMV-c was conducted, so that we can conclude from these results of this comparision that ACOMV-o is better than ACOMV-c in the case that the discrete variables of mixed-variable problems are ordered, while ACOMV-c is better than ACOMV-o in the case that discrete variables of mixed-variable problems are categorical variables. The experiments illustrate the advantage of combining of ACOMV-o and ACOMV-c, and also suggest that discarding of scratching one of them to handle mixed-variable optimization problems is not a good idea. The experimental results for real-world engineering problems illustrate that ACOMV not only can tackle various classes of decision variables robustly, but also it is efficient in finding high-quality solutions. In the welded beam design case A and the pressure vessel design problem case A, B, C, ACOMV is the only available algorithm that obtains the best-so-far solution with a 100% success rate as well as the required smallest number of function evaluations. In the pressure vessel design problem case D, ACOMV obtains the best-so-far solution with a 100% success rate. In the coil spring design problem, ACOMV is the only one that obtains the best-so-far solution with a 100% success rate. In the thermal insulation systems design problem, ACOMV obtains the new best-so-far solution. In the welded beam design problem case B, ACOMV obtained the new best-so-far solution with a 100% success rate and the smallest number of function evaluations.
4.7 Conclusions 53 Table 4.11: Comparison of the best solutions for the thermal insulation systems Solution information MVP [52] FMGPS [3] ACOMV Continuous variable xi(cm) 1 0.3125 4.5313 4.9506 2 5.4688 6.7188 7.9729 3 3.9062 4.8437 12.8448 4 6.5625 4.2188 17.07978 5 5.7812 7.3438 9.4420 6 5.1562 9.8438 10.1077 7 13.2812 24.948 0.02811 8 21.4062 12.135 7.3080 9 8.5938 7.5 11.9592 10 9.2188 6.4063 12.1872 11 20.3125 11.5105 6.1197 Ti(K) 1 4.2188 6.125 6.1003 2 7.3438 10.55 11.0841 3 10 14.35 21.2509 4 15 17.994 38.2608 5 20 24.969 51.8508 6 25 36.006 70.1000 7 40 71.094 71.0001 8 71.0938 116.88 99.4475 9 101.25 156.88 153.1701 10 146.25 198.44 236.8358 11 300 300 300 Categorical variable Ii 1 N N N 2 N N N 3 N N N 4 N N N 5 N N T 6 N N E 7 N T T 8 E E E 9 E E E 10 E T T 11 T T T Power( )) 25.294 25.58 24.299 P L A ( W cm
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Université Libre de Bruxelles Facu
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Acknowledgements I thank Prof. Marc
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Contents Abstract iii Acknowledgeme
Page 11 and 12: Chapter 1 Introduction Metaheuristi
Page 13: them in the smallest function evalu
Page 16 and 17: 6 Ant Colony Optimization Algorithm
Page 18 and 19: 8 Ant Colony Optimization Algorithm
Page 20 and 21: 10 Ant Colony Optimization of Sep-A
Page 22 and 23: 12 Ant Colony Optimization Average
Page 25 and 26: Chapter 3 An Incremental Ant Colony
Page 27 and 28: 3.2 IACOR with Local Search 17 3.2
Page 29 and 30: 3.3 Experimental Study 19 Algorithm
Page 31 and 32: 3.3 Experimental Study 21 Table 3.2
Page 33 and 34: 3.4 Conclusions 23 3.4 Conclusions
Page 35 and 36: 3.4 Conclusions 25 G−CMA−ES (5
Page 37: 3.4 Conclusions 27 Table 3.4: The m
Page 40 and 41: 30 Ant Colony Optimization for Mixe
Page 66 and 67: 56 Conclusions and Future Work of t
Page 69 and 70: Chapter 6 Appendix 6.1 Mathematical
Page 71 and 72: 6.1 Mathematical formulation of eng
Page 73 and 74: 6.1 Mathematical formulation of eng
Page 75 and 76: Bibliography [1] K. Abhishek, S. Le
Page 77 and 78: BIBLIOGRAPHY 67 [20] D. Datta and J
Page 79 and 80: BIBLIOGRAPHY 69 [44] Q. He and L. W
Page 81 and 82: BIBLIOGRAPHY 71 [65] S. Lucidi, V.
Page 83 and 84: BIBLIOGRAPHY 73 [87] Thomas Stützl
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