Topology Design of Planar Cross-Sections with a Genetic Algorithm: Part 1--Overcoming the Obstacles

Tai

Int. J. Numer. Meth. Engng

2005

119

SUMMARYGenetic algorithms (GAs) have become a popular optimization tool for many areas of research and topology optimization an effective design tool for obtaining efficient and lighter structures. In this paper, a versatile, robust and enhanced GA is proposed for structural topology optimization by using problemspecific knowledge. The original discrete black-and-white (0 -1) problem is directly solved by using a bit-array representation method. To address the related pronounced connectivity issue effectively, the four-neighbourhood connectivity is used to suppress the occurrence of checkerboard patterns. A simpler version of the perimeter control approach is developed to obtain a well-posed problem and the total number of hinges of each individual is explicitly penalized to achieve a hinge-free design. To handle the problem of representation degeneracy effectively, a recessive gene technique is applied to viable topologies while unusable topologies are penalized in a hierarchical manner. An efficient FEM-based function evaluation method is developed to reduce the computational cost. A dynamic penalty method is presented for the GA to convert the constrained optimization problem into an unconstrained problem without the possible degeneracy. With all these enhancements and appropriate choice of the GA operators, the present GA can achieve significant improvements in evolving into near-optimum solutions and viable topologies with checkerboard free, mesh independent and hinge-free characteristics. Numerical results show that the present GA can be more efficient and robust than the conventional GAs in solving the structural topology optimization problems of minimum compliance design, minimum weight design and optimal compliant mechanisms design. It is suggested that the present enhanced GA using problem-specific knowledge can be a powerful global search tool for structural topology optimization.

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An enhanced genetic algorithm for structural topology optimization

Tai

Int. J. Numer. Meth. Engng

2005

119

Int. J. Simul. Multidisci. Des. Optim.

“…Hence, the original '0-1' optimization problem was attacked directly by using a bit-array representation and a genetic algorithm. The work of Sandgren and his co-workers, using bit-array representation, has been extended by Jakiela and his coworkers [3][4][5], by Schoenauer and his co-workers [6,7,9], by Fanjoy and Crossley [8,10], and, more recently, by Wang and Tai [11]. Although all these extensions can well prevent checkerboard patterns by exploiting a connectiva Corresponding author: matthieu.domaszewski@utbm.fr ity restriction, the other numerical instabilities in structural topology optimization such as mesh dependency and one-node connections still exist.…”

Section: Introductionmentioning

confidence: 99%

“…and Δx ie = rand · (−1) round(rand) (8) where x ie is density variable,x ie is the ie element density computed using the expression 7 and Δx ie is real value randomly generated using expression (8).…”

Section: Mutationmentioning

confidence: 99%

An adjacency representation for structural topology optimization using genetic algorithm

Sid

Domaszewski

Peyraut

2007

-A new approach for continuum structural topology optimization using genetic algorithms is presented in this paper. The proposed approach is based on a representation by adjacency where the principle is founded on the concept of connectivity of finite elements, considered as cells. This principle is expressed by an adjacency matrix similar to that used in the graph theory. The encoding of the structure solutions uses this matrix by transforming it into a binary string. The research of optimal solution, i.e. the optimal material distribution, is interpreted in this approach by the determination of the connectivity of elements (cells). Using density variable, the approach has some common points with the homogenization techniques. The proposed approach is tested with simple benchmark applications.

Journal of Mechanical Design

“…( 1 1 ) To enhance the search efficiency of GA, a "direct" crossover [16,[33][34][35][36][37][38] scheme is adopted, which directly acts on phenotype (structures in 3D space in our case) rather than on genotype (a linear list of numbers in Equation (11) in our case) as the conventional crossovers. As in [16], this is achieved by:…”

Section: Optimization Algorithmmentioning

confidence: 99%

Decomposition-Based Assembly Synthesis Based on Structural Considerations

Yetis

Saitou

2002

An extension of decomposition-based assembly synthesis for structural modularity is presented where the early identification of shareable components within multiple structures is posed as an outcome of the minimization of estimated production costs. The manufacturing costs of components are estimated under given production volumes considering the economies of scale. Multiple structures are simultaneously decomposed and the types of welded joints at component interfaces are selected from a given library, in order to minimize the overall production cost and the reduction of structural strength due to the introduction of joints. A multiobjective genetic algorithm is utilized to allow effective examination of trade-offs between manufacturing cost and structural strength. A new joint-oriented representation of structures combined with a "direct" crossover is introduced to enhance the efficiency of the search. A case study with two aluminum space frame automotive bodies is presented to demonstrate that not all types of component sharing are economically justifiable under a certain production scenario.