Investigation of Advanced Metaheuristic Techniques for Simultaneous Size, Shape, and Topology Optimization of Truss Structures

Abstract

The truss optimization can be classified into three categories: size optimization, shape optimization, and topology optimization. Size optimization works to find the optimal element cross-sectional areas, whereas shape optimization works to find the optimal nodal positions of definite nodes of the truss. Topology optimization deals with element addition and removal, so it is more challenging as it includes consideration of all the generated different topologies rather than a particular topology to search the finest topology. The effect of topology, shape, and size (TSS) variables on both the objective function and constraints are fairly unlike. Therefore, simultaneous TSS optimization is a challenging problem for optimization algorithms. The optimal design of a truss subjected to dynamic behavior is a challenging area of study that has been an active research area for many years. The fundamental natural frequencies of a truss are a useful parameter to improve the dynamic behavior of the truss. Therefore, some convinced restrictions on the natural frequencies of the truss can avoid resonance with the external excitations. Also, trusses should be as light as possible. On the other hand, weight reduction conflicts with the frequency constraints and induces complexity in the truss optimization. Therefore, simultaneous TSS optimization with multiple natural frequency constraints adds further complexity and often lead to divergence. Thus, an efficient optimization method is required to design trusses subjected to fundamental frequency constraints and several researchers have been employing various metaheuristics in this aspect, yet this field has not been addressed so far. In this study, ten benchmark trusses (i.e. 10-bar, 14-bar, 15-bar, 24-bar, 20-bar, 72-bar (3D), 39-bar, 45-bar truss, 25-bar (3D), and 39-bar (3D) trusses) subjected to static (i.e. stress, displacement, and buckling) and dynamic (i.e. natural frequency) constraints are proposed. These algorithms are also investigated on ten functions extracted from the CEC2014 test suite to demonstrate effectiveness of the proposed algorithms. This thesis aims to study and enhance the search performance of metaheuristic algorithms developed after 2011 for truss optimization problems by use of various modification concepts. Three categories of modified algorithms, such as a mutation model, a migration model, an adaptive method, and a simultaneous search method, will be developed and x studied. This work includes various metaheuristic methods, namely the dragonfly algorithm (DA), multi-verse optimizer (MVO), sine cosine algorithm (SCA), whale optimization algorithm (WOA), ant lion optimizer (ALO), heat transfer search (HTS), passing vehicle search (PVS), symbiotic organisms search (SOS), grey wolf optimizer (GWO), and teaching-learning based optimization (TLBO) algorithms are examined for truss optimization problems. A metaheuristic is an art of discovering a new upper-level problemindependent methodology that gives a set of rules to solve optimization problems. The performance of a metaheuristic can be enhanced either by modifying its features or through exert the merits of different original algorithms. Modification of a metaheuristic sets a good balance between exploration and exploitation to maintain diversity in the population, improve robustness, and convergence rate of the algorithm. Thus, in this study, a randommutation-search phase and random-migration-search phase along with simulated annealing based selection proposed to study their effect on the DA, MVO, SCA, WOA, ALO, HTS, PVS, SOS, GWO, and TLBO algorithms. Therefore, ten modified metaheuristics (viz. the MDA, MMVO, MSCA, MWOA, MALO, MHTS, MPVS, MSOS, MGWO, and MTLBO algorithms) which includes random-mutation-search phase with simulated annealing bases selection, whereas ten improved metaheuristics (viz. the IDA, IMVO, ISCA, IWOA, IALO, IHTS, IPVS, ISOS, IGWO, and ITLBO algorithms) which includes random-migrationsearch phase with simulated annealing bases selection. In addition, this research work also includes the algorithm specific modifications in the SOS, TLBO, and HTS algorithms with the incorporation of adaptive search technique and simultaneous search techniques to enhance the effectiveness of the SOS, TLBO, and HTS algorithms. The proposed algorithms are applied successfully on ten benchmark trusses, proposed in this study, for simultaneous TSS optimization in order to examine their search performance. Based on solving ten test problems, it is found that the proposed modifications are the better performer compared to their basic versions except for the SCA, PVS, and SOS algorithms with random-mutation-search phase and random-migration-search phases.