Genetic Algorithm (GA) — CAE Terminology Guide

In a nutshell, it is an optimization technique that mimics biological evolution. You create a population of design candidates and advance through generations using three operations—selection, crossover, and mutation—gradually evolving toward better designs. A classical method proposed by Holland in 1975, it remains a primary tool in CAE today.

Great question. Gradient-based methods (derivative-based) are efficient when the objective function is smooth and differentiable, but in CAE, we encounter nonlinear, discontinuous, and multimodal problems all the time. For example, in crash analysis, a small parameter change can cause the response to change discontinuously. Since GA does not use gradient information at all, it can find optimal solutions even for such "rough" problems.

Let me explain in order. First, Selection is the operation of choosing "superior parents" from the population. A common approach is tournament selection, where k individuals are randomly selected and the one with the highest fitness is chosen as a parent. Roulette selection (selecting with probability proportional to fitness) is also well-known.

Exactly. Crossover is the operation of combining genes (design variables) from two parent individuals to create offspring. In real-valued GA, SBX (Simulated Binary Crossover) is commonly used. Since design variables in CAE optimization are typically continuous values like plate thickness, material constants, and shape parameters, SBX is well-suited. Increasing the distribution index $\eta_c$ makes offspring closer to parents, while decreasing it produces offspring farther from parents.

Exactly. Mutation is the operation of randomly perturbing an individual's genes, serving to prevent convergence to local optima. For real values, Polynomial Mutation is the standard, with mutation rate typically set to $p_m = 1/n$ (where $n$ is the number of design variables). For example, with 20 design variables, it would be around 5%. If too large, it becomes random search and won't converge, so care is needed.

A typical application is structural optimization. For example, optimizing the plate thickness of an automotive crash box to minimize weight while satisfying constraints on energy absorption capacity. Running the FEA solver (such as LS-DYNA) once corresponds to "evaluating one individual."

That is exactly the biggest challenge with GA. With a population size of 100 and 50 generations, you need 5,000 analyses. If each analysis takes 2 hours, that is 10,000 hours just by simple calculation. That is why in practice, we insert a surrogate model (metamodel) to dramatically reduce the number of evaluations. We limit the actual FEA to dozens to hundreds of runs and use the surrogate to predict the rest. I will explain this in detail later.

That is where multi-objective optimization comes in. The most famous is NSGA-II (Non-dominated Sorting Genetic Algorithm II, Deb et al., 2002), which is essentially the de facto standard for multi-objective optimization in CAE.

Consider a problem minimizing two objective functions $f_1, f_2$. Individual A is "dominated by" individual B when $f_1(B) \leq f_1(A)$ and $f_2(B) \leq f_2(A)$, with at least one being strictly smaller. The set of individuals not dominated by anyone becomes the first front (Pareto front approximation). NSGA-II ranks individuals based on this front and further maintains solution diversity via Crowding Distance.

Good point. All solutions on the Pareto front are "optimal" in the sense that neither objective can be improved simultaneously, so the final choice is up to the engineer's judgment. For example, you might narrow down with a criterion like "weight can increase by 5%, but maximum displacement must be under 10 mm." This process is sometimes called MCDM (Multi-Criteria Decision Making). In practice, engineers examine the Pareto front with visualization tools and select solutions that look well-balanced.

SIMP is gradient-based and excels at single-objective, continuous density variables, but struggles with multiple objectives or discrete material selection (aluminum vs. CFRP vs. titanium). That is where GA shines. You encode the density or material of each element as a bit string and explore with GA.

The B-pillar design of an automobile body is a clear example. You optimize two objectives—weight minimization and minimization of intrusion in side impact—using NSGA-II, simultaneously determining plate thickness distribution and rib layout. A "two-stage approach" is common in practice: first, SIMP provides the general topological direction, then GA performs size optimization and material selection. With the rise of additive manufacturing (3D printing), the free-form shapes produced by GA are increasingly manufacturable.

A surrogate model is a "low-cost proxy function." The most commonly used are Kriging (Gaussian Process Regression) and RBF (Radial Basis Function) networks. You start by running a few real FEA samples (50–100 points via DOE) to create a response surface, then replace GA evaluations with the surrogate. When promising solutions are found, you validate them with real FEA and update the surrogate with those results—this cycle is the EGO (Efficient Global Optimization) approach.

That risk exists. For kriging, we use not just the predicted value but also its uncertainty (prediction variance) with an Expected Improvement (EI) acquisition function to balance exploring "promising regions" and "unexplored regions with high uncertainty." In practice, final candidates are always validated with real FEA, so surrogate errors rarely become critical.