A Comparative Study of Recent Multi-objective Metaheuristics for Solving Constrained Truss Optimisation Problems

Multi-objective truss optimisation is a research topic that has been less investigated in the literature compared to the single-objective cases. This paper investigates the comparative performance of fourteen new and established multi-objective metaheuristics when solving truss optimisation problems. The optimisers include multi-objective ant lion optimiser, multi-objective dragonfly algorithm, multi-objective grasshopper optimisation algorithm, multi-objective grey wolf optimiser, multi-objective multi-verse optimisation, multi-objective water cycle algorithm, multi-objective Salp swarm algorithm, success history-based adaptive multi-objective differential evolution, success history–based adaptive multi-objective differential evolution with whale optimisation, non-dominated sorting genetic algorithm II, hybridisation of real-code population-based incremental learning and differential evolution, differential evolution for multi-objective optimisation, multi-objective evolutionary algorithm based on decomposition, and unrestricted population size evolutionary multi-objective optimisation algorithm. The design problem is assigned to minimise structural mass and compliance subject to stress constraints. Eight classical trusses found in the literature are used for setting up the design test problems. Various optimisers are then implemented to tackle the problems. A comprehensive comparative study is given to critically analyse the performance of all algorithms in this problem area. The results provide new insights to the pros and cons of evolutionary multi-objective optimisation algorithms when addressing multiple, often conflicting objective in truss optimisation. The results and findings of this work assist with not only solving truss optimisation problem better but also designing customised algorithms for such problems.

[1]  Ali Kaveh,et al.  Ray optimization for size and shape optimization of truss structures , 2013 .

[2]  Ali Kaveh,et al.  Chaotic enhanced colliding bodies algorithms for size optimization of truss structures , 2018 .

[3]  Bogdan Filipic,et al.  DEMO: Differential Evolution for Multiobjective Optimization , 2005, EMO.

[4]  A. Kaveh,et al.  Sizing, geometry and topology optimization of trusses using force method and supervised charged system search , 2014 .

[5]  David Greiner,et al.  Truss topology optimization for mass and reliability considerations—co-evolutionary multiobjective formulations , 2012 .

[6]  Qi Xia,et al.  Bi-directional Evolutionary Structural Optimization on Advanced Structures and Materials: A Comprehensive Review , 2016, Archives of Computational Methods in Engineering.

[7]  Nantiwat Pholdee,et al.  A Comparative Study of Eighteen Self-adaptive Metaheuristic Algorithms for Truss Sizing Optimisation , 2018 .

[8]  Laith Mohammad Abualigah,et al.  Ant Lion Optimizer: A Comprehensive Survey of Its Variants and Applications , 2021 .

[9]  Vivek Patel,et al.  Comparative Performance of Recent Advanced Optimization Algorithms for Minimum Energy Requirement Solutions in Water Pump Switching Network , 2020 .

[10]  Leandro dos Santos Coelho,et al.  Multi-objective grey wolf optimizer: A novel algorithm for multi-criterion optimization , 2016, Expert Syst. Appl..

[11]  Nantiwat Pholdee,et al.  Hybridisation of real-code population-based incremental learning and differential evolution for multiobjective design of trusses , 2013, Inf. Sci..

[12]  Yan Zhen,et al.  Application of Improved Bat Algorithm in Truss Optimization , 2019, KSCE Journal of Civil Engineering.

[13]  Sujin Bureerat,et al.  A novel self-adaptive hybrid multi-objective meta-heuristic for reliability design of trusses with simultaneous topology, shape and sizing optimisation design variables , 2019, Structural and Multidisciplinary Optimization.

[14]  Qingfu Zhang,et al.  MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition , 2007, IEEE Transactions on Evolutionary Computation.

[15]  Hammoudi Abderazek,et al.  A Comparative Study of Recent Non-traditional Methods for Mechanical Design Optimization , 2019, Archives of Computational Methods in Engineering.

[16]  Nantiwat Pholdee,et al.  Many-Objective Optimisation of Trusses Through Meta-Heuristics , 2017, ISNN.

[17]  Jacques Periaux,et al.  Multi-level Hybridized Optimization Methods Coupling Local Search Deterministic and Global Search Evolutionary Algorithms , 2019, Archives of Computational Methods in Engineering.

[18]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[19]  Mustafa Sonmez,et al.  Artificial Bee Colony algorithm for optimization of truss structures , 2011, Appl. Soft Comput..

[20]  Nantiwat Pholdee,et al.  Simultaneous topology, shape, and size optimization of trusses, taking account of uncertainties using multi-objective evolutionary algorithms , 2018, Engineering with Computers.

[21]  P. Hajela,et al.  Genetic algorithms in truss topological optimization , 1995 .

[22]  M. Ohsaki.  Genetic algorithm for topology optimization of trusses , 1995 .

[23]  Ali Sadollah,et al.  Water cycle algorithm for solving constrained multi-objective optimization problems , 2015, Appl. Soft Comput..

[24]  N. Pholdee,et al.  Performance enhancement of multiobjective evolutionary optimisers for truss design using an approximate gradient , 2012 .

[25]  Sujin Bureerat,et al.  Topology optimization of truss subjected to static and dynamic constraints by integrating simulated annealing into passing vehicle search algorithms , 2019, Eng. Comput..

[26]  Seyedali Mirjalili,et al.  Dragonfly algorithm: a new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems , 2015, Neural Computing and Applications.

[27]  Hossam Faris,et al.  Grasshopper optimization algorithm for multi-objective optimization problems , 2017, Applied Intelligence.

[28]  Jaehong Lee,et al.  An adaptive hybrid evolutionary firefly algorithm for shape and size optimization of truss structures with frequency constraints , 2018 .

[29]  Pradeep Jangir,et al.  Multi-objective ant lion optimizer: a multi-objective optimization algorithm for solving engineering problems , 2016, Applied Intelligence.

[30]  Kaisa Miettinen,et al.  Efficient evolutionary approach to approximate the Pareto-optimal set in multiobjective optimization, UPS-EMOA , 2010, Optim. Methods Softw..

[31]  Nantiwat Pholdee,et al.  Hybrid real-code population-based incremental learning and approximate gradients for multi-objective truss design , 2014 .

[32]  Gun-Shing Chen,et al.  OPTIMAL PLACEMENT OF ACTIVE/PASSIVE MEMBERS IN TRUSS STRUCTURES USING SIMULATED ANNEALING , 1991 .

[33]  Jacques Periaux,et al.  Game Theory Based Evolutionary Algorithms: A Review with Nash Applications in Structural Engineering Optimization Problems , 2017 .

[34]  Carlos A. Coello Coello,et al.  Improving PSO-Based Multi-objective Optimization Using Crowding, Mutation and epsilon-Dominance , 2005, EMO.

[35]  Nantiwat Pholdee,et al.  Multiobjective adaptive symbiotic organisms search for truss optimization problems , 2018, Knowl. Based Syst..

[36]  Indrajit N. Trivedi,et al.  Optimization of problems with multiple objectives using the multi-verse optimization algorithm , 2017, Knowl. Based Syst..

[37]  Sujin Bureerat,et al.  Technical Note: Simultaneous topology, shape and sizing optimisation of a three-dimensional slender truss tower using multiobjective evolutionary algorithms , 2011 .

[38]  Chun-Yin Wu,et al.  Truss structure optimization using adaptive multi-population differential evolution , 2010 .

[39]  Amir Hossein Gandomi,et al.  Krill herd algorithm for optimum design of truss structures , 2013, Int. J. Bio Inspired Comput..

[40]  Daniel Balzani,et al.  Influence of microstructure morphology on multi-scale modeling of low-alloyed TRIP-steels , 2018 .

[41]  Albert A. Groenwold,et al.  Sizing design of truss structures using particle swarms , 2003 .

[42]  Nantiwat Pholdee,et al.  Structural optimization using multi-objective modified adaptive symbiotic organisms search , 2019, Expert Syst. Appl..

[43]  R. Venkata Rao,et al.  Design Optimization of Heat Exchangers with Advanced Optimization Techniques: A Review , 2020, Archives of Computational Methods in Engineering.

[44]  Gary B. Lamont,et al.  Multiobjective Evolutionary Algorithms: Analyzing the State-of-the-Art , 2000, Evolutionary Computation.

[45]  Nantiwat Pholdee,et al.  Multi-objective modified heat transfer search for truss optimization , 2020, Engineering with Computers.

[46]  Hossam Faris,et al.  Salp Swarm Algorithm: A bio-inspired optimizer for engineering design problems , 2017, Adv. Eng. Softw..