Optimization of laminate stacking sequence for maximum buckling load using the ant colony optimization (ACO) metaheuristic

doi:10.1016/j.compositesa.2007.10.011

Composites Part A: Applied Science and Manufacturing

Volume 39, Issue 2, February 2008, Pages 262-272

https://doi.org/10.1016/j.compositesa.2007.10.011 Get rights and content

Abstract

The paper illustrates the application of the ant colony optimization (ACO) metaheuristic to the lay-up design of laminated panels for maximization of buckling load with strength constraints. A specific problem previously studied by different researchers using genetic algorithms (GA) and Tabu search (TS) was chosen as a test-case to characterize the computational efficiency and the quality of results provided by the developed ACO algorithm. The results of numerical experiments, based on the use of a single ant per search run, show that the average performance and the robustness of the ACO search strategy is comparable or better than that of optimization procedures based on GA or TS.

Introduction

Laminated composite materials have been increasingly used in primary load bearing structures because of their good mechanical and physical properties and of their ability to be tailored to satisfy the requirements of the specific application [1]. However, as a direct consequence of the number of variables involved (such as ply thicknesses, ply-orientations and fibre architecture) and of the intrinsic anisotropy of the individual layers, the design problem of laminate structures is usually more involved than that associated to isotropic material structures.

Practical manufacturing issues typically require the designer to assume ply-thicknesses as fixed and ply-orientations as limited to a finite set of predefined angles; the design of composite laminates reduces thus to a combinatorial optimization problem [2], which can be attacked by many complete or approximate algorithms [3].

As opposed to complete algorithms, which provide guaranteed optimal solutions but often require extremely large computation times, approximate algorithms have received growing attention, in the last decades, as practical tools capable of obtaining near-optimal solutions in an acceptable amount of time. In particular, a new class of approximate methods, called metaheuristics, consisting of high-level strategies which guide low-level subordinate heuristic search processes in the exploration of the solution space, have emerged in recent years as the most promising approaches for dealing with combinatorial optimization problems [4], [5], [6], [7]. One of the key issues of metaheuristics, which include techniques such as genetic algorithms, Tabu search, simulated annealing, scatter search, ant colony optimization [4], [5] resides in the balance between intensification (exploitation of past search experience) and diversification (exploration of the entire solution space), which controls the ability of the search process to escape from local optima and efficiently sample the most promising regions of the search space [7].

Various investigations have been conducted on the use of metaheuristic methodologies for stacking sequence optimization of composite laminates under different loading and constraint conditions. Most of the studies published in the open literature adopt genetic algorithms optimization procedures [8], [9], [10], [11], [12], [13], [14] while only quite recently different metaheuristics such as Tabu search [15] or scatter search [16] have been applied to the design of composite laminates.

In a recent study [17], the authors examined the potential of the ant colony optimization (ACO) metaheuristic for lay-up design of composite laminates and demonstrated the robustness of the technique for stiffness maximization of laminated plates under in-plane and out-of-plane loads.

The performance of the ACO search strategy is further investigated in this paper by analyzing the problem of buckling load maximization of composite laminates under strength and ply-contiguity constraints. The computational efficiency of the developed ACO procedure, based on the use of a single ant during each search run, is assessed by comparison with published results of numerical experiments carried out for the same optimization problem by other metaheuristic techniques.

Section snippets

Ant colony optimization

ACO algorithms are a class of approximate heuristic search techniques, introduced in early 1990s by Dorigo [18], [19], that were inspired by the foraging behaviour of real ants and, in particular, by their ability to find the shortest paths between their nest and the food source.

As demonstrated by laboratory observations [20], when searching for food, ants deposit on the ground along their tracks a volatile chemical (pheromone) and tend to probabilistically choose paths marked by high pheromone

Formulation of the optimization problem

The problem of stacking sequence optimization of a simply supported fixed-thickness laminated plate under biaxial compression and subject to strength constraints was chosen in this study in order to assess the performance of the developed ACO procedure. This specific optimum problem has been examined in the recent past by different research groups with the use of various heuristic search techniques. Haftka and co-workers, in particular, extensively tested the application of genetic algorithms

Implementation of ACO metaheuristic

The lay-up design problem described in the previous section may be formulated as a combinatorial optimization problem consisting in the maximization of an objective function J, given a set of candidate solutions S and a set of constraints Ω. In particular, the specific optimization problem may be mapped to a problem characterized by the following items:

•
A finite set C consisting of m = 3 orientation components c_i : C = {(0°₂), (±45°), (90°₂)}.
•
A set S of candidate solutions, which are defined by

Results and discussion

The buckling problem of a simply supported laminated plate, as described in Section 3, was investigated for three different loading cases. Solution quality and performance of the ACO algorithm were compared with those reported in the literature for GA [8], [9] and TS [15] optimization techniques applied to the same test-case.

The following load configurations were examined for the 48-ply laminate (Fig. 1):

N_x = 175 N/m; N_y/N_x = 0.125 (load case 1)
N_x = 175 N/m; N_y/N_x = 0.25 (load case 2)
N_x = 175 N/m; N_y/N_x = 0.5 (load

Conclusions

This work describes the application of the ant colony optimization (a recent metaheuristic technique inspired by the behaviour of real ant colonies) to the problem of lay-up design of laminated composite panels for buckling load maximization under strength constraints. Implementation aspects and details on special daemon action schemes introduced in the algorithm to improve the performance of the ACO exploration are discussed in the paper.

Numerical experiments were carried out to assess, with

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Optimization of laminate stacking sequence for maximum buckling load using the ant colony optimization (ACO) metaheuristic

Abstract

Introduction

Section snippets

Ant colony optimization

Formulation of the optimization problem

Implementation of ACO metaheuristic

Results and discussion

Conclusions

Compos Part B: Eng

Comput Struct

Compos Struct

Compos Part B: Eng

Compos Struct

Phys Life Rev

Future Generat Comput Syst

Comput Methods Appl Mech Eng

Design and optimization of laminated composite materials

Combinatorial optimization: algorithms and complexity

Metaheuristics for hard optimization