GESO: Genetic Evolutionary Structural Optimization

Description

GESO (Genetic Evolutionary Structural Optimization) is a hybrid algorithm that combines evolutionary structural optimization with genetic algorithm concepts. Unlike BESO which uses sensitivity-based element removal/addition, GESO employs binary encoding of design variables and genetic operators (crossover, mutation) to explore the design space.

This tutorial solves the same HalfMBB beam problem as the BESO tutorial, but using the GESO algorithm. GESO is particularly useful when dealing with discrete design variables and can escape local minima through its stochastic search strategy.

Setup

Load the TopOpt package:

using TopOpt
using WGLMakie
WGLMakie.activate!(; resize_to=:parent)
using Bonito
if haskey(ENV, "QUARTO_PROJECT_DIR")
    Bonito.Page(exportable=true, offline=true)
else
    Bonito.browser_display()
end
display_app(app) = display(app)

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display_app (generic function with 1 method)

WGLMakie.activate!(; resize_to=:parent) selects the browser renderer and fills the Quarto output column. Bonito.Page(exportable=true, offline=true) embeds the assets needed by visualize(...; static=true) in the Quarto output, so the visualization does not require a running Julia process.

Define the problem

We use the same 2D HalfMBB benchmark with 160×40 elements:

E = 1.0 # Young's modulus (normalized)
v = 0.3 # Poisson's ratio
f = 1.0 # downward force magnitude

nels = (160, 40)  # 160 elements in x, 40 in y
problem = HalfMBB(nels, (1.0, 1.0), E, v, f)

TopOpt half MBB problem

Define the FEA solver and apply material penalization

The FEA solver uses power-law penalization to drive toward 0/1 designs:

solver = FEASolver(DirectSolver, problem; xmin=0.01, penalty=PowerPenaltyFun(3.0))

TopOpt direct structural solver (GenericFEASolver)

Define the compliance objective and volume constraint

GESO requires:

1. Objective: Compliance to minimize
2. Constraint: Volume fraction limit
3. Filter: Sensitivity filter for mesh independence

comp = ComplianceFun(solver)
volfrac = VolumeFun(solver)
sensfilter = SensFilterFun(solver; rmin=4.0)
geso = GESO(comp, volfrac, 0.5, sensfilter)  # target volume = 50%

TopOpt GESO algorithm

The GESO algorithm uses:

• Binary encoding of design variables (string length = 4 bits per element)
• Crossover probability (Pcmin=0.6, Pcmax=1.0)
• Mutation probability (Pmmin=0.5, Pmmax=1.0)
• Penalty parameter (Pen=3.0) for constraint handling

Run the GESO optimization

The GESO algorithm iterates:

1. Encode current design as binary strings
2. Evaluate fitness (compliance + penalty for constraint violation)
3. Apply genetic operators: selection, crossover, mutation
4. Decode binary strings to get new design
5. Filter sensitivities for stability
6. Check convergence

x0 = ones(length(solver.vars))  # start from fully solid design
result = geso(x0)

TopOpt.Algorithms.GESOResult{Float64, Vector{Float64}}([1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], 355.348478842284, 0.0005875080850982552, true, 132)

GESO typically requires more iterations than BESO (100-200+) due to its stochastic nature, but can find better global optima for complex problems.

Visualize the result

fig = visualize(problem; static=true, topology=result.topology)
display_app(fig)

undeformed mesh

load arrows

support arrows

Figure 1: GESO optimization result showing the evolved beam structure

The result shows a truss-like structure optimized for minimum compliance under the 50% volume constraint.