sktopt.core.optimizers.common
- class sktopt.core.optimizers.common.DensityMethod(cfg: DensityMethodConfig, tsk: TaskConfig)
Bases:
objectBase class for sensitivity-based topology optimization routines.
This class provides common functionality shared by multiple optimization strategies (e.g., OC, LDMOC, EUMOC), including finite element analysis (FEA), sensitivity filtering, and density projection using Heaviside-type functions. It does not perform the optimization update itself — that logic is delegated to subclasses.
Typical usage involves: - Assembling the global stiffness matrix - Solving the displacement field under given loads and boundary conditions - Computing the compliance and its sensitivity with respect to density - Applying density or sensitivity filters (e.g., Helmholtz, cone filters) - Projecting intermediate densities using smooth Heaviside functions
This class is designed for reuse and extension. All algorithm-specific update steps (e.g., density changes, Lagrange multiplier updates) should be implemented in derived classes such as OC_Optimizer, LDMOC_Optimizer, or ` EUMOC_Optimizer`.
Responsibilities
Manage problem configuration (e.g., material parameters, mesh, basis)
Provide filtered sensitivities for stable optimization
Apply projection functions for sharp interface control
Evaluate objective functions such as compliance
Notes
This class serves as the backbone of sensitivity-based topology optimization. Subclasses are expected to override methods such as rho_update() to implement specific optimization logic.
- tsk
Contains FEM mesh, basis, boundary condition data, and load vectors.
- Type:
TaskConfig
- config
Holds numerical and algorithmic settings like filtering radius, penalization power, projection beta, etc.
- Type:
DensityMethodConfig
- init_schedulers(export: bool = True)
- initialize_density()
- initialize_params()
- load_parameters()
- optimize()
- parameterize()
- rho_update(iter_loop: int, rho_candidate: ndarray, rho_projected: ndarray, dC_drho_ave: ndarray, u_dofs: ndarray, strain_energy_ave: ndarray, scaling_rate: ndarray, move_limit: float, eta: float, tmp_lower: ndarray, tmp_upper: ndarray, lambda_lower: float, lambda_upper: float, percentile: float, elements_volume_design: ndarray, elements_volume_design_sum: float, vol_frac: float)
- scale()
- unscale()
- class sktopt.core.optimizers.common.DensityMethodConfig(dst_path: str = './result/pytests', interpolation: Literal['SIMP', 'RAMP'] = 'SIMP', record_times: int = 20, max_iters: int = 200, p_init: float = 1.0, p: float = 3.0, p_step: int = -1, vol_frac_init: float = 0.8, vol_frac: float = 0.4, vol_frac_step: int = -3, beta_init: float = 1.0, beta: float = 2, beta_step: int = -1, beta_curvature: float = 2.0, beta_eta: float = 0.5, eta: float = 0.6, percentile_init: float = 60, percentile: float = -90, percentile_step: int = -1, filter_radius_init: float = 2.0, filter_radius: float = 1.2, filter_radius_step: int = -3, E0: float = 210000000000.0, E_min: float = 210000000.0, rho_min: float = 0.01, rho_max: float = 1.0, move_limit_init: float = 0.3, move_limit: float = 0.1, move_limit_step: int = -3, restart: bool = False, restart_from: int = -1, export_img: bool = False, export_img_opaque: bool = False, design_dirichlet: bool = False, lambda_lower: float = 1e-07, lambda_upper: float = 10000000.0, sensitivity_filter: bool = False, solver_option: Literal['spsolve', 'cg_pyamg'] = 'spsolve', scaling: bool = False)
Bases:
objectConfiguration class for controlling parameters in topology optimization.
This class defines optimization parameters, filtering and projection settings, continuation schedules, and numerical solver options. It is designed to support sensitivity-based topology optimization algorithms such as SIMP and RAMP.
- dst_path
Directory to which results and logs are saved.
- Type:
str
- interpolation
Interpolation method for material penalization.
- Type:
{“SIMP”, “RAMP”}
- record_times
Number of snapshots to record during optimization.
- Type:
int
- max_iters
Maximum number of optimization iterations.
- Type:
int
- p_init
Initial penalization power in SIMP/RAMP interpolation.
- Type:
float
- p
Final value of the penalization power.
- Type:
float
- p_step
Number of steps to continue p from p_init to p. If negative, p is fixed at p_init.
- Type:
int
- vol_frac_init
Initial volume fraction for continuation.
- Type:
float
- vol_frac
Final volume fraction constraint.
- Type:
float
- vol_frac_step
Number of continuation steps from vol_frac_init to vol_frac. If negative, vol_frac is fixed at vol_frac_init.
- Type:
int
- beta_init
Initial sharpness parameter for Heaviside projection.
- Type:
float
- beta
Final beta value for projection.
- Type:
float
- beta_step
Number of continuation steps from beta_init to beta. If negative, beta is fixed at beta_init.
- Type:
int
- beta_curvature
Controls the curvature of the Heaviside projection function.
- Type:
float
- beta_eta
Threshold parameter for Heaviside projection; determines where the projection function switches rapidly between 0 and 1.
- Type:
float
- eta
Threshold density used in projection. Often used to define intermediate region in Heaviside or filtering.
- Type:
float
- percentile_init
Initial percentile used to scale sensitivity fields.
- Type:
float
- percentile
Final percentile value. If set to a negative value, percentile-based scaling is disabled, resulting in a more “exact” optimization behavior.
- Type:
float
- percentile_step
Number of continuation steps for the percentile value. If negative, fixed at percentile_init.
- Type:
int
- filter_radius_init
Initial radius of the sensitivity or density filter.
- Type:
float
- filter_radius
Final filter radius.
- Type:
float
- filter_radius_step
Number of continuation steps for filter radius. If negative, filter_radius is fixed at initial value.
- Type:
int
- E0
Young’s modulus of the solid material.
- Type:
float
- E_min
Minimum Young’s modulus (used for void regions).
- Type:
float
- rho_min
Minimum density value (to avoid singular stiffness).
- Type:
float
- rho_max
Maximum density value (usually 1.0 for full material).
- Type:
float
- move_limit_init
Initial move limit for density update.
- Type:
float
- move_limit
Final move limit.
- Type:
float
- move_limit_step
Number of continuation steps for move limit. If negative, move limit is fixed.
- Type:
int
- restart
Whether to resume optimization from an existing state.
- Type:
bool
- restart_from
Iteration index to restart from.
- Type:
int
- export_img
Whether to export images during optimization.
- Type:
bool
- export_img_opaque
If True, image export uses opaque rendering.
- Type:
bool
- design_dirichlet
If True, Dirichlet boundary elements are included in the design domain.
- Type:
bool
- lambda_lower
Lower bound for the Lagrange multiplier in constrained optimization.
- Type:
float
- lambda_upper
Upper bound for the Lagrange multiplier.
- Type:
float
- sensitivity_filter
If True, applies filtering to the sensitivity field.
- Type:
bool
- solver_option
Linear solver to be used in analysis. “cg_pyamg” enables multigrid acceleration.
- Type:
{“spsolve”, “cg_pyamg”}
- scaling
If True, length and force scaling are applied to normalize the mesh geometry and load magnitudes. This helps improve numerical stability by making the system dimensionless or better conditioned.
- Type:
bool
- E0: float = 210000000000.0
- E_min: float = 210000000.0
- beta: float = 2
- beta_curvature: float = 2.0
- beta_eta: float = 0.5
- beta_init: float = 1.0
- beta_step: int = -1
- design_dirichlet: bool = False
- dst_path: str = './result/pytests'
- eta: float = 0.6
- export(path: str)
- export_img: bool = False
- export_img_opaque: bool = False
- filter_radius: float = 1.2
- filter_radius_init: float = 2.0
- filter_radius_step: int = -3
- classmethod from_defaults(**args)
- image_path(iter: int, prefix: str)
- classmethod import_from(path: str) DensityMethodConfig
- interpolation: Literal['SIMP', 'RAMP'] = 'SIMP'
- lambda_lower: float = 1e-07
- lambda_upper: float = 10000000.0
- max_iters: int = 200
- move_limit: float = 0.1
- move_limit_init: float = 0.3
- move_limit_step: int = -3
- p: float = 3.0
- p_init: float = 1.0
- p_step: int = -1
- percentile: float = -90
- percentile_init: float = 60
- percentile_step: int = -1
- record_times: int = 20
- restart: bool = False
- restart_from: int = -1
- rho_max: float = 1.0
- rho_min: float = 0.01
- scaling: bool = False
- sensitivity_filter: bool = False
- solver_option: Literal['spsolve', 'cg_pyamg'] = 'spsolve'
- vol_frac: float = 0.4
- vol_frac_init: float = 0.8
- vol_frac_step: int = -3
- vtu_path(iter: int)
- sktopt.core.optimizers.common.interpolation_funcs(cfg: DensityMethodConfig)