A New Constraint Handling Approach Based on Enhanced Quadratic Approximation: Tested on Optimal Design of Mechanical Systems and Truss Structures

Year 2024, Volume: 9 Issue: 2, 85 - 112, 30.08.2024

Mahsa Moloodpoor , Ali Mortazavi

https://doi.org/10.30931/jetas.1331636

Abstract

Optimization refers to the process of identifying the optimal state of a system while ensuring all constraints and requirements are met. In engineering problems, the feasibility of solutions is typically assured by imposing relevant constraints. Since these constraints have different properties, utilizing more systematic and logical methods to handle them has the potential to enhance the search performance of the optimization algorithms. According to this fact, in the current study, a new constraint handling mechanism based on combining the fly-back method, weighted average concept and quadratic approximation approach is developed. The proposed mechanism is then merged with three distinct well-established metaheuristic optimization methods. The effectiveness of the enhanced techniques is evaluated through comparative analysis in solving various mathematical and engineering optimization problems subjected to different constraints. Furthermore, non-parametric statistical tests are conducted to compare the quality of the obtained results. The results show that the developed approach can considerably improve the performance of the search algorithms with regards to accuracy, stability, and computational cost.

Keywords

Metaheuristic algorithm, constrained optimization problems, fly-back method, quadratic approximation, structural and mechanical problems

References

• [1] Mortazavi, A., Moloodpoor, M., "Differential evolution method integrated with a fuzzy decision-making mechanism and Virtual Mutant agent: Theory and application", Applied Soft Computing 112 (2021) : 107808.
• [2] Rajeev, S., Krishnamoorthy, C.S., "Discrete Optimization of Structures Using Genetic Algorithms", Journal of Structural Engineering 118(5) (1992).
• [3] Yadav, A., Kumar, N., "Artificial electric field algorithm for engineering optimization problems", Expert Systems with Applications 149 (2020) : 113308.
• [4] Moloodpoor, M., Mortazavi, A., "Simultaneous optimization of fuel type and exterior walls insulation attributes for residential buildings using a swarm intelligence", International Journal of Environmental Science and Technology (2022).
• [5] Gandomi, A.H., Alavi, A.H., "An introduction of Krill Herd algorithm for engineering optimization", Journal of Civil Engineering and Management 22(3) (2016) : 302-310.
• [6] Hayyolalam, V., Pourhaji Kazem, A.A., "Black Widow Optimization Algorithm: A novel meta-heuristic approach for solving engineering optimization problems", Engineering Applications of Artificial Intelligence 87 (2020) : 103249.
• [7] Houssein, E.H., Saad, M.R., Hashim, F.A., Shaban, H., Hassaballah, M., "Lévy flight distribution: A new metaheuristic algorithm for solving engineering optimization problems", Engineering Applications of Artificial Intelligence 94 (2020) : 103731.
• [8] Moloodpoor, M., Mortazavi, A., "Thermo-Economic optimization for saving energy in residential bildings using population-based optimization techniques", Journal of Construction Engineering, Management & Innovation 5(1) (2022) : 45-63.
• [9] Lee, K.S., Geem, Z.W., "A new meta-heuristic algorithm for continuous engineering optimization: harmony search theory and practice", Computer Methods in Applied Mechanics and Engineering 194(36) (2005) : 3902-33.
• [10] Liu, H., Cai, Z., Wang, Y., "Hybridizing particle swarm optimization with differential evolution for constrained numerical and engineering optimization", Applied Soft Computing 10(2) (2010) : 629-640.
• [11] Rao, S.S., "Engineering optimization: theory and practice. 4th edition", John Wiley & Sons, Inc., Hoboken, New Jersey (2009).
• [12] Moloodpoor, M., Mortazavi, A., Ozbalta, N., "Thermo-economic optimization of double-pipe heat exchanger using a compound swarm intelligence", Heat Tansfer Research 52(6) (2021) : 1-20.
• [13] Zamani, H., Nadimi-Shahraki, M.H., Gandomi, A.H., "Starling murmuration optimizer: A novel bio-inspired algorithm for global and engineering optimization", Computer Methods in Applied Mechanics and Engineering 392 (2022) : 114616.
• [14] Toğan, V., Mortazavi, A., "Sizing optimization of skeletal structures using teaching-learning based optimization", An International Journal of Optimization and Control: Theories & Applications (IJOCTA) 7(2) (2017) : 130-141.
• [15] Mendi, F., Baskal, T., Külekci, M.K., "Application of Genetic Algorithm (GA) for Optimum Design of Module, Shaft Diameter and Bearing for Bevel Gearbox", Materials Testing 54(6) (2012) : 431-436.
• [16] Liu, H., Duan, S., Luo, H., "A hybrid engineering algorithm of the seeker algorithm and particle swarm optimization", Materials Testing 64(7) (2022) : 1051-1089.
• [17] Moloodpoor, M., Mortazavi, A., Ozbalta, N., "Performance Assessment of Parabolic Trough Collectors under Climatic Conditions of Izmir, Turkey: A Case Study", Heat Transfer Research 55(4) (2024) : 47-76.
• [18] Abd Elaziz, M., Yousri, D., Mirjalili, S., "A hybrid Harris hawks-moth-flame optimization algorithm including fractional-order chaos maps and evolutionary population dynamics", Advances in Engineering Software 154 (2021) : 102973.
• [19] Tsipianitis, A., Tsompanakis, Y., "Improved Cuckoo Search algorithmic variants for constrained nonlinear optimization", Advances in Engineering Software 149 (2020) : 102865.
• [20] Zhengtong, H., Zhengqi, G., Xiaokui, M., Wanglin, C., "Multimaterial layout optimization of truss structures via an improved particle swarm optimization algorithm", Computers & Structures 222 (2019) : 10-24.
• [21] Tejani, G.G., Savsani, V.J., Patel, V.K., Savsani, P.V., "Size, shape, and topology optimization of planar and space trusses using mutation-based improved metaheuristics", Journal of Computational Design and Engineering 5(2) (2018) : 198-214.
• [22] Javidi, A., Salajegheh, E., Salajegheh, J., "Enhanced crow search algorithm for optimum design of structures", Applied Soft Computing 77 (2019) : 274-289.
• [23] Rao, R.V., Savsani, V.J., Vakharia, D.P., "Teaching–learning-based optimization: A novel method for constrained mechanical design optimization problems", Computer-Aided Design 43(3) (2011) : 303-315.
• [24] Heidari, A.A., Mirjalili, S., Faris, H., Aljarah, I., Mafarja, M., Chen, H., "Harris hawks optimization: Algorithm and applications", Future Generation Computer Systems 97 (2019) : 849-872.
• [25] Arora, S., Singh, S., "Butterfly optimization algorithm: a novel approach for global optimization", Soft Computing 23(3) (2019) : 715-734.
• [26] He, S., Prempain, E., Wu, Q.H., "An improved particle swarm optimizer for mechanical design optimization problems", Engineering Optimization 36(5) (2004) : 585-605.
• [27] Mortazavi, A., "Bayesian Interactive Search Algorithm: A New Probabilistic Swarm Intelligence Tested on Mathematical and Structural Optimization Problems", Advances in Engineering Software 155 (2021) : 102994.
• [28] Mortazavi, A., "Interactive fuzzy Bayesian search algorithm: A new reinforced swarm intelligence tested on engineering and mathematical optimization problems", Expert Systems with Applications 187 (2022) : 115954.
• [29] Mortazavi, A., "Comparative assessment of five metaheuristic methods on distinct problems", Dicle University Journal of Engineering 10(3) (2019) : 879-898.
• [30] Mortazavi, A., "The Performance Comparison of Three Metaheuristic Algorithms On the Size, Layout and Topology Optimization of Truss Structures", Mugla Journal of Science and Technology 5(2) (2019) : 28-41.
• [31] Mortazavi, A., "Size and layout optimization of truss structures with dynamic constraints using the interactive fuzzy search algorithm", Engineering Optimization (2021) : 1-23.
• [32] Guohua, W., Mallipeddi, R., Suganthan, P., "Problem Definitions and Evaluation Criteria for the CEC 2017 Competition and Special Session on Constrained Single Objective Real-Parameter Optimization", Nanyang Technological Universityr: Singapore (2016).
• [33] Belegundu, A.D., "A study of mathematical programming methods for structural optimization", [Ph.D.]. Ann Arbor: The University of Iowa (1982).
• [34] Siddall, J.N., "Optimal Engineering Design. Principles and Applications", CRC Press (1982).
• [35] Osyczka, A.. "Evolutionary Algorithms for Single and Multicriteria Design Optimization", Heidelberg: Physica-Verlag (2002).
• [36] Youn, B.D., Choi, K.K., Yang, R.J., Gu, L., "Reliability-based design optimization for crashworthiness of vehicle side impact", Structural and Multidisciplinary Optimization 26(3) (2004) : 272-283.
• [37] Gandomi, A.H., Yang, X.S., Alavi, A.H., "Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems", Engineering with Computers 29(1) (2013) : 17-35.
• [38] Gupta, S., Tiwari, R., Nair, S.B., "Multi-objective design optimisation of rolling bearings using genetic algorithms", Mechanism and Machine Theory 42(10) (2007) : 1418-1443.
• [39] Mortazavi, A., "A fuzzy reinforced Jaya algorithm for solving mathematical and structural optimization problems", Soft Computing 28(3) (2024) : 2181-2206.