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

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54 Ant Colony Optimization for Mixed Variable Problems Table 4.12: Comparison of the best solutions for welded beam design design problem case B Methods x1(h) x2(l) x3(t) x4(b) x5(M) x6(Joint) f(x) GeneAS [21] 0.1875 1.6849 8.2500 0.2500 Steel 4-sided 1.9422 PSOA [23] 0.2500 2.2219 8.2500 0.2500 Steel 2-sided 1.7631 RSPSO [95] 0.1875 1.6842 8.25 0.25 Steel 4-sided 1.9421 ACOMV 0.225 1.272373 8.25 0.225 Steel 4-sided 1.502942 Table 4.13: Statistical results for welded beam design design problem case B Methods fMean Sd F Es GeneAS [21] N/A N/A N/A RSPSO [95] N/A N/A N/A PSOA [23] 1.7631 0 6570 ACOMV 1.502942 0 1436 Table 4.14: Constrains analysis for welded beam design design problem case B Constraints GeneAS [21] PSOA [23] RSPSO [95] ACOMV g1 -0.1621 0 N/A 0 g2 -380.1660 N/A -380.1653 -148.8186 g3 -0.0625 0 N/A 0 g4 -3.4399 -3.3838 N/A -3.562618 g5 -0.0625 -0.1250 N/A -0.1 g6 -0.2346 -0.2344 N/A -0.2349907 g7 -402.0473 -412.5254 N/A -1630.64
Chapter 5 Conclusions and Future Work 5.1 Conclusions In this thesis, we have proposed two improved ant colony optimization algorithms for continuous and mixed discrete-continuous optimization problems. These are IACOR-LS and ACOMV, respectively. In Chapter 2, based on the new C++ implementation of ACOR and Sep-ACOR, we further investigated their performance and addressed their possible drawbacks. Then, we proposed IACOR-LS, an ACOR algorithm with growing solution archive hybridized with a local search procedure in Chapter 3. Three different local search procedures, Powell’s conjugate directions set, Powell’s BOBYQA, and Mtsls1, were tested with IACOR-LS in order to enhance its search intensification. The very good performance of IACOR-Mtsls1 is a clear indication of the high potential hybrid ACO algorithms have for the continuous domain. In fact, IACOR-Mtsls1 is clearly competitive with state-of-the-art continuous optimizers. In Chapter 4 , we have shown how ACOR is extended to ACOMV for tackling mixed-variable optimization problems. Based on the solution archive framework of ACOMV, ACOMV integrates a component of a continuous optimization solver (ACOR), a continuous relaxation approach (ACOMV-o) and a native mixed-variable optimization approach (ACOMVc) to solve continuous and mixed-variable optimization problems. In addition, we proposed artificial mixed-variable benchmark functions as well as constructive methods. They provide a sufficiently controlled environment for the investigation 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 ACOMVo and ACOMV-c was conducted, so that we can conclude from these results
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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
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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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