An Effective Improved Multi-objective Evolutionary Algorithm (IMOEA) for Solving Constraint Civil Engineering Optimization Problems

Abstract

This paper introduces a new metaheuristic optimization method based on evolutionary algorithms to solve single-objective engineering optimization problems faster and more efficient. By considering constraints as a new objective function, problems turned to multi objective optimization problems. To avoid regular local optimum, different mutations and crossovers are studied and the best operators due their performances are selected as main operators of algorithm. Moreover, certain infeasible solutions can provide useful information about the direction which lead to best solution, so these infeasible solutions are defined on basic concepts of optimization and uses their feature to guide convergence of algorithm to global optimum. Dynamic interference of mutation and crossover are considered to prevent unnecessary calculation and also a selection strategy for choosing optimal solution is introduced. To verify the performance of the proposed algorithm, some CEC 2006 optimization problems which prevalently used in the literatures, are inspected. After satisfaction of acquired result by proposed algorithm on mathematical problems, four popular engineering optimization problems are solved. Comparison of results obtained by proposed algorithm with other optimization algorithms show that the suggested method has a powerful approach in finding the optimal solutions and exhibits significance accuracy and appropriate convergence in reaching the global optimum.

Keywords

• evolutionary algorithm
• single objective optimization problem
• multi objective optimization algorithm
• constraint handling
• Constraint optimization
• civil optimization problem

References

1. Rao, S.S., Engineering optimization: theory and practice. 2009: John Wiley & Sons.
2. Bazaraa, M.S., J.J. Jarvis, and H.D. Sherali, Linear programming and network flows. 2011: John Wiley & Sons.
3. Holland, J.H.J.S.a., Genetic algorithms. 1992. 267(1): p. 66-73.
4. Eberhart, R. and J. Kennedy. A new optimizer using particle swarm theory. in Micro Machine and Human Science, 1995. MHS'95., Proceedings of the Sixth International Symposium on. 1995. IEEE.
5. Atashpaz-Gargari, E. and C. Lucas. Imperialist competitive algorithm: an algorithm for optimization inspired by imperialistic competition. in Evolutionary computation, 2007. CEC 2007. IEEE Congress on. 2007. IEEE.
6. Rao, R. and V. Patel, An elitist teaching-learning-based optimization algorithm for solving complex constrained optimization problems. International Journal of Industrial Engineering Computations, 2012. 3(4): p. 535-560.
7. Ghaemi, M. and M.-R. Feizi-Derakhshi, Forest optimization algorithm. Expert Systems with Applications, 2014. 41(15): p. 6676-6687.
8. Jordehi, A.R., Brainstorm optimisation algorithm (BSOA): An efficient algorithm for finding optimal location and setting of FACTS devices in electric power systems. International Journal of Electrical Power & Energy Systems, 2015. 69: p. 48-57.

9. Dai, T., et al., Stiffness optimisation of coupled shear wall structure by modified genetic algorithm. 2016. 20(8): p. 861-876.
10. Mirjalili, S. and A. Lewis, The whale optimization algorithm. Advances in Engineering Software, 2016. 95: p. 51-67.
11. Varaee, H. and M.R. Ghasemi, Engineering optimization based on ideal gas molecular movement algorithm. Engineering with Computers, 2017. 33(1): p. 71-93.
12. Tabari, A. and A. Ahmad, A new optimization method: Electro-Search algorithm. Computers & Chemical Engineering, 2017. 103: p. 1-11.
13. TOĞAN, V. and M.A.J.T.D. EIRGASH, Time-Cost Trade-Off Optimization with a New Initial Population Approach. 2018. 30(6).
14. Muhammad, A.A., et al., Adoption of Virtual Reality (VR) for Site Layout Optimization of Construction Projects. 2019. 31(2).
15. AZAD, S.K. and A.J.T.D. Ebru, Cost Efficient Design of Mechanically Stabilized Earth Walls Using Adaptive Dimensional Search Algorithm. 31(4).
16. Coello, C.A.C., Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art. Computer methods in applied mechanics and engineering, 2002. 191(11): p. 1245-1287.
17. Kucukkoc, I. and D.Z. Zhang, Balancing of parallel U-shaped assembly lines. Computers & Operations Research, 2015. 64: p. 233-244.
18. Chou, C.-H., S.-C. Hsieh, and C.-J. Qiu, Hybrid genetic algorithm and fuzzy clustering for bankruptcy prediction. Applied Soft Computing, 2017. 56: p. 298-316.
19. Araghi, S., et al., Influence of meta-heuristic optimization on the performance of adaptive interval type2-fuzzy traffic signal controllers. Expert Systems with Applications, 2017. 71: p. 493-503.
20. 0]Tosta, T.A.A., et al., Computational method for unsupervised segmentation of lymphoma histological images based on fuzzy 3-partition entropy and genetic algorithm. Expert Systems with Applications, 2017. 81: p. 223-243.
21. Yang, G., Y. Wang, and L. Guo, A sparser reduced set density estimator by introducing weighted l 1 penalty term. Pattern Recognition Letters, 2015. 58: p. 15-22.
22. Dong, Z. and W. Zhu, An improvement of the penalty decomposition method for sparse approximation. Signal Processing, 2015. 113: p. 52-60.
23. Kia, S.S., Distributed optimal resource allocation over networked systems and use of an e-exact penalty function. IFAC-PapersOnLine, 2016. 49(4): p. 13-18.
24. Tang, K.-Z., T.-K. Sun, and J.-Y. Yang, An improved genetic algorithm based on a novel selection strategy for nonlinear programming problems. Computers & Chemical Engineering, 2011. 35(4): p. 615-621.
25. Long, Q., A constraint handling technique for constrained multi-objective genetic algorithm. Swarm and Evolutionary Computation, 2014. 15: p. 66-79.
26. de Paula Garcia, R., et al., A rank-based constraint handling technique for engineering design optimization problems solved by genetic algorithms. Computers & Structures, 2017. 187: p. 77-87.
27. Coello, C.A.C., G.B. Lamont, and D.A. Van Veldhuizen, Evolutionary algorithms for solving multi-objective problems. Vol. 5. 2007: Springer.
28. Dhiman, G. and V.J.K.-B.S. Kumar, Multi-objective spotted hyena optimizer: A Multi-objective optimization algorithm for engineering problems. 2018. 150: p. 175-197.
29. Deb, K., et al., A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE transactions on evolutionary computation, 2002. 6(2): p. 182-197.
30. 0]Monfared, S.A.H., et al., Water Quality Planning in Rivers: Assimilative Capacity and Dilution Flow. Bulletin of environmental contamination and toxicology, 2017. 99(5): p. 531-541.
31. Hashemi Monfared, S. and M. Dehghani Darmian, Evaluation of Appropriate Advective Transport Function for One-Dimensional Pollutant Simulation in Rivers. International Journal of Environmental Research, 2016. 10(1): p. 77-84.
32. Noura, A. and F.J.A.M.S. Saljooghi, Determining feasible solution in imprecise linear inequality systems. 2008. 2(36): p. 1789-1797.
33. Mostaghim, S. and J. Teich. Strategies for finding good local guides in multi-objective particle swarm optimization (MOPSO). in Swarm Intelligence Symposium, 2003. SIS'03. Proceedings of the 2003 IEEE. 2003. IEEE.
34. Coello Coello, C. and M. Lechuga. MOPSO: a proposal for multiple objective particle swarm optimization. in Proc., Evolutionary Computation, 2002. CEC'02. Proceedings of the 2002 Congress on.
35. Zhang, Q. and H.J.I.T.o.e.c. Li, MOEA/D: A multiobjective evolutionary algorithm based on decomposition. 2007. 11(6): p. 712-731.
36. Coello, C.A.C., Use of a self-adaptive penalty approach for engineering optimization problems. Computers in Industry, 2000. 41(2): p. 113-127.
37. Segura, C., et al., Using multi-objective evolutionary algorithms for single-objective constrained and unconstrained optimization. Annals of Operations Research, 2016. 240(1): p. 217-250.
38. Fonseca, C.M. and P.J. Fleming. Genetic Algorithms for Multiobjective Optimization: FormulationDiscussion and Generalization. in Icga. 1993.
39. Srinivas, N. and K. Deb, Muiltiobjective optimization using nondominated sorting in genetic algorithms. Evolutionary computation, 1994. 2(3): p. 221-248.
40. 0]Deb, K., et al. A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. in International Conference on Parallel Problem Solving From Nature. 2000. Springer.
41. Ngatchou, P., A. Zarei, and A. El-Sharkawi. Pareto multi objective optimization. in Intelligent systems application to power systems, 2005. Proceedings of the 13th international conference on. 2005. IEEE.
42. Smith, J. and T.C. Fogarty. Self adaptation of mutation rates in a steady state genetic algorithm. in Evolutionary Computation, 1996., Proceedings of IEEE International Conference on. 1996. IEEE.
43. Moon, C., et al., An efficient genetic algorithm for the traveling salesman problem with precedence constraints. European Journal of Operational Research, 2002. 140(3): p. 606-617.
44. Ho, W., et al., A hybrid genetic algorithm for the multi-depot vehicle routing problem. Engineering Applications of Artificial Intelligence, 2008. 21(4): p. 548-557.
45. Juang, C.-F., A hybrid of genetic algorithm and particle swarm optimization for recurrent network design. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 2004. 34(2): p. 997-1006.
46. Mühlenbein, H. and D. Schlierkamp-Voosen, Predictive models for the breeder genetic algorithm i. continuous parameter optimization. Evolutionary computation, 1993. 1(1): p. 25-49.
47. Liang, J., et al., Problem definitions and evaluation criteria for the CEC 2006 special session on constrained real-parameter optimization. Journal of Applied Mechanics, 2006. 41(8).
48. Horn, J., N. Nafpliotis, and D.E. Goldberg. A niched Pareto genetic algorithm for multiobjective optimization. in Evolutionary Computation, 1994. IEEE World Congress on Computational Intelligence., Proceedings of the First IEEE Conference on. 1994. Ieee.
49. Deep, K. and M. Thakur, A new crossover operator for real coded genetic algorithms. Applied mathematics and computation, 2007. 188(1): p. 895-911.
50. 0]Herrera, F., M. Lozano, and A.M. Sánchez, A taxonomy for the crossover operator for real‐coded genetic algorithms: An experimental study. International Journal of Intelligent Systems, 2003. 18(3): p. 309-338.
51. Weile, D.S. and E. Michielssen, Genetic algorithm optimization applied to electromagnetics: A review. IEEE Transactions on Antennas and Propagation, 1997. 45(3): p. 343-353.
52. Schott, J.R., Fault Tolerant Design Using Single and Multicriteria Genetic Algorithm Optimization. 1995, AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH.
53. Patel, V.K. and V.J. Savsani, Heat transfer search (HTS): a novel optimization algorithm. Information Sciences, 2015. 324: p. 217-246.
54. Hamida, S.B. and M. Schoenauer. ASCHEA: New results using adaptive segregational constraint handling. in Evolutionary Computation, 2002. CEC'02. Proceedings of the 2002 Congress on. 2002. IEEE.
55. Karaboga, D. and B. Akay, A modified artificial bee colony (ABC) algorithm for constrained optimization problems. Applied soft computing, 2011. 11(3): p. 3021-3031.
56. Topal, U., et al., Buckling load optimization of laminated plates resting on Pasternak foundation using TLBO. J Structural Engineering and Mechanics, 2018. 67(6): p. 617-628.
57. Zhiyi, Y., Z. Kemin, and Q. Shengfang, Topology optimization of reinforced concrete structure using composite truss-like model. J Structural Engineering and Mechanics, 2018. 67(1): p. 79-85.
58. Noura, A. and F. Saljooghi, Ranking decision making units in Fuzzy-DEA Using entropy. Applied Mathematical Sciences, 2009. 3(6): p. 287-295.
59. Saljooghi, F.H. and M.M.J.A.J.o.A.S. Rayeni, Distinguishing congestion and technical inefficiency in presence undesirable output. 2011. 8(9): p. 903.
60. 0]Artar, M. and A.J.T.D. Daloglu, The Optimization of Multi-Storey Composite Steel Frames with Genetic Algorithm Including Dynamic Constraints. 2015. 26(2): p. 7077-7098.
61. Mustafa, O., et al., Construction Site Layout Planning: Application of Multi-Objective Particle Swarm Optimization. 29(6).
62. Rayeni, M.M., F.H.J.I.J.o.S. Saljooghi, and O. Management, Ranking and measuring efficiency using secondary goals of cross-efficiency evaluation–a study of railway efficiency in Iran. 2014. 17(1): p. 1-16.
63. Bulut, B. and M.T.J.T.D. Yilmaz, Analysis of the 2007 and 2013 Droughts in Turkey by NOAH Hydrological Model. 2016. 27(4): p. 7619-7634.
64. Mahallati, M. and F.J.J.o.A.S. Saljooghi, Performance assessment of education institutions through interval DEA. 2010. 10: p. 2945-2949.
65. Tözer, K.D., T. Çelik, and G.E.J.T.D. Gürcanlı, Classification of Construction Accidents in Northern Cyprus. 2018. 29(2): p. 8295-8316.
66. Coello, C.A.C. and C.S.P. Zacatenco, List of references on constraint-handling techniques used with evolutionary algorithms. Information Sciences, 2012. 191: p. 146-168.
67. He, Q. and L. Wang, An effective co-evolutionary particle swarm optimization for constrained engineering design problems. Engineering Applications of Artificial Intelligence, 2007. 20(1): p. 89-99.
68. Mezura-Montes, E. and C.A.C. Coello, An empirical study about the usefulness of evolution strategies to solve constrained optimization problems. International Journal of General Systems, 2008. 37(4): p. 443-473.
69. Mirjalili, S., S.M. Mirjalili, and A. Lewis, Grey wolf optimizer. Advances in Engineering Software, 2014. 69: p. 46-61.
70. 0]Kaveh, A. and S. Talatahari, An improved ant colony optimization for constrained engineering design problems. Engineering Computations, 2010. 27(1): p. 155-182.
71. Belegundu, A.D. and J.S. Arora, A study of mathematical programming methods for structural optimization. Part I: Theory. International Journal for Numerical Methods in Engineering, 1985. 21(9): p. 1583-1599.
72. Arora, J., Introduction to optimum design. 2004: Academic Press.
73. Eskandar, H., et al., Water cycle algorithm–A novel metaheuristic optimization method for solving constrained engineering optimization problems. Computers & Structures, 2012. 110: p. 151-166.
74. Kaveh, A. and S. Talatahari, A novel heuristic optimization method: charged system search. Acta Mechanica, 2010. 213(3): p. 267-289.
75. Kaveh, A. and V. Mahdavi, Colliding bodies optimization: a novel meta-heuristic method. Computers & Structures, 2014. 139: p. 18-27.
76. Svanberg, K., The method of moving asymptotes—a new method for structural optimization. International journal for numerical methods in engineering, 1987. 24(2): p. 359-373.
77. Chickermane, H. and H. Gea, Structural optimization using a new local approximation method. International journal for numerical methods in engineering, 1996. 39(5): p. 829-846.
78. Mirjalili, S., Moth-flame optimization algorithm: A novel nature-inspired heuristic paradigm. Knowledge-Based Systems, 2015. 89: p. 228-249.
79. Cheng, M.-Y. and D. Prayogo, Symbiotic organisms search: a new metaheuristic optimization algorithm. Computers & Structures, 2014. 139: p. 98-112.
80. 0]Liu, H., Z. Cai, and Y. Wang, Hybridizing particle swarm optimization with differential evolution for constrained numerical and engineering optimization. Applied Soft Computing, 2010. 10(2): p. 629-640.
81. Ray, T. and K.M. Liew, Society and civilization: An optimization algorithm based on the simulation of social behavior. IEEE Transactions on Evolutionary Computation, 2003. 7(4): p. 386-396.
82. Javidrad, F. and M. Nazari, A new hybrid particle swarm and simulated annealing stochastic optimization method. Applied Soft Computing, 2017. 60: p. 634-654.
83. Yılmaz, M., et al., Uydu Kaynaklı Yağmur Verilerinin Hata Oranlarının Deniz Kıyılarına Olan Uzaklığa Bağlı Analizi. 2017. 28(3): p. 7993-8005.
84. Dorigo, M. and G. Di Caro. Ant colony optimization: a new meta-heuristic. in Proceedings of the 1999 congress on evolutionary computation-CEC99 (Cat. No. 99TH8406). 1999. IEEE.
85. Shafigh, P., S.Y. Hadi, and E.J.I.s. Sohrab, Gravitation based classification. 2013. 220: p. 319-330.
86. Lin, Y., et al., A hybrid differential evolution algorithm for mixed-variable optimization problems. 2018. 466: p. 170-188.
87. Deng, H., et al., Ranking-based biased learning swarm optimizer for large-scale optimization. 2019. 493: p. 120-137.