Topological Genetic Algorithm
Topological optimization tool using genetic algorithm for optimization is known to be very expensive in computation time. Still, it continues to be one of the important research areas today that can bring a big change in technology. This may bring many break-throughs in the near future. Let’s see how.
More often, during the design phase of a new device, optimization holds a significant place to bring out the best of all solutions. These methods differentiate themselves from the design variables on which they are performed. We witness three main categories of different methods. The first one named Dimensional optimization, uses design parameters to size a solution whose geometry has been predefined by the designer. The second, Shape optimization, changes the boundary between each sub-domain of material whose topology is defined by the designer. And the last, Topology optimization, uses parameters describing the material distribution inside a design space.
With this, let’s dive into our main topic.
Genetic algorithms are an optimization strategy where points in the design space are analogous to organisms involved in a process of natural selection.
Each organism is represented by a character string analogous to a chromosome, with each character position and value analogous to a gene and allele respectively. These chromosomes are created in generations and child designs are created when parent designs, chosen from the best designs in a generation, group in pairs to produce offspring via genetic reproduction and crossover.
Crossover
Parents: 111111111111 000000000000
Children: 111111110000 000000001111
Crossover: 11111111 00000000 1111 0000
Mutation
1011100101100010110100 BEFORE
1011101101100010110100 AFTER
Genetic algorithms are a compromise between weak and strong methods.
Strong methods perform search in an informed manner through the use of function gradients (numerical optimization), while weak methods search in an uninformed manner by extensively sampling the design space (random/exhausted procedures). Weak methods are expensive but find the global optima, in contrast to strong methods, which more likely settle for local sub-optima and are inexpensive. Genetic algorithms, in contrast to both, operate with a strong progression toward improved designs, together with the weak operations of probabilistic pairing, crossover and mutation.
Several parameters constitute genetic algorithm — Probability of crossover, Probability of Mutation, Fitness Scaling Coefficient, Population Size, Crossover Operator, Selection Scheme etc. They have a great effect on the search performance and efficiency.
For your knowledge, Shape and Topology Optimization have been active research areas for some time. Some of the recent works that caught my sight are Homogenization-Based, Simulated Annealing, Genetic Algorithms, etc. The main advantage of using genetic algorithms is due to the fact that they return an optimal or at least near optimal solutions on every run regardless of problem instance, problem size or random number seed.
As David Edward quotes, “Genetic algorithms (GAs) are defined as search procedures based on the mechanics of natural selection and genetics, and we think we know what innovation is — at least in some sort of qualitative way — but what does one have to do with the other?” Explore!
