Topological design of structures using population-based optimization methods

Abstract

In this article, a number of well-established population-based optimization methods i.e. genetic algorithms, simulated annealing and population-based incremental learning are briefly reviewed and compared in terms of their philosophical basis. The use of the optimization methods for topology optimization is demonstrated. The article also presents an efficient numerical technique to prevent checkerboard formation in topology design. A number of design test-cases are assigned to measure the performances of the population-based methods. The optimum solutions obtained using these methods are illustrated and compared. Advantages and disadvantages of the optimization methods are discussed. It is shown that, based upon the convergence rate and consistency measure, simulated annealing is the best technique for this type of structural design.

Evolutionary Black-Box Topology Optimization: Challenges and Promises

“…In addition, a structure's specifications and manufacturability are constraints that should be satisfied [81], [80], [147], [8], [163], [164], [165], [166]. Nonlinear constraints can be handled in two ways: (1) implicitly by using repair/filtering mechanisms, e.g., [42], [80], [81], [21], [68], [73], [46], [112], [101], [37] or assigning a penalty function to the objective function value, e.g., [81], [59], [79], [25], [19], and (2) coupled explicitly with the optimization algorithm [25], [35], [95], [102], [82], [52], [44] incorporating constraint-handling techniques, e.g., [167], [154], [168], [169], [170], [171], [172].…”

“…• Explicit bit array representation [16], [17], [18], [19], [20], [21], [22], [23], [24], [25] • Voronoi representation [26], [27], [28], [29], [30] • Dipole representation [26] • H-representation [27] • Parametric curves and graph [31], [32], [33], [34], [35], [36] • Map Lyndenmayer systems [37], [38], [39], [40] • Moving morphable components and solid geometries [26], [41], [42], [43], [44], [45] • Material mask overlay [46], [47], [48], [49], [50] • Ground element filtering and multi-resolution design variables [51], [52], [53], [54] • Spectral level-set formulation [55], [56]. • Interpolated level-sets [57], [58], [59] • Parameterized B-spline surface…”

Structural topology optimisation using simulated annealing with multiresolution design variables

“…It can also be used for suppression of checkerboard patterns on the resulting topologies [3]. Furthermore, from the numerical investigation in [16,17], it has been shown that the mutation-based optimisation methods such as simulated annealing (SA) are more efficient than the other EAs when solving largescale topological design problems with single objective functions. The results obtained from using such methods can even be compared to the optimum results from the gradient-based approaches, although they still require more function evaluations.…”

Structural Optimization Using Simulated Annealing

“…A number of researchers applied simulated annealing to topologyoptimization problems. (Dhingra & Bennage, 1995;Topping et al, 1996;Shim & Manoochehri, 1997;Liu et al, 1997;Bureerat & Kunakote, 2006;Lamberti & Pappalettere, 2007). Their results show the promise of SA to solve topology optimization problems.…”

“…The optimal topology designs for torque arm (Shim & Manoochehri, 1997). Bureerat & Kunakote (2006) considered a multi -objective optimization problem of minimizing both compliance and mass of an MBB beam depicted in Fig. 26.…”