Optimization API

`UQPyL.optimization`

The optimization module searches for optimal decision variables for a Problem.

Import

python

from UQPyL.optimization.soea import GA, PSO, DE
from UQPyL.optimization.moea import NSGAII, MOEAD
from UQPyL.optimization.expensive import EGO
from UQPyL.optimization.runtime import OptReader

Public Objects

Top-level objects:

Object	Role
`AlgorithmABC`	Base class for optimization algorithms.
`Population`	Decision, objective, and constraint population container.
`OptResult`	Standard result object returned by optimization runs.
`OptHistory`	Runtime history stored inside `OptResult`.
`OptReader`	Reader for sqlite results saved with `saveFlag=True`.
`Result`	Alias of the mutable optimization state.
`soea`	Single-objective algorithm subpackage.
`moea`	Multi-objective algorithm subpackage.
`expensive`	Expensive-model optimization subpackage.

Algorithm groups:

Group	Import path	Algorithms
Single-objective	`UQPyL.optimization.soea`	`GA`, `PSO`, `DE`, `SCE_UA`, `ML_SCE_UA`, `CSA`, `ABC`
Multi-objective	`UQPyL.optimization.moea`	`NSGAII`, `NSGAIII`, `MOEAD`, `RVEA`
Expensive optimization	`UQPyL.optimization.expensive`	`ASMO`, `EGO`, `MOASMO`

Optimization Workflow

All standard algorithms run through:

python

result = algorithm.run(problem, seed=None)

Expensive optimization algorithms also accept optional initial data:

python

result = algorithm.run(problem, xInit=None, yInit=None, seed=None)

Shared constructor controls:

Parameter	Meaning
`maxFEs`	Maximum number of function evaluations.
`maxIters`	Maximum number of iterations.
`maxTolerates`	Maximum tolerated non-improving iterations.
`tolerate`	Improvement tolerance.
`verboseFlag`	Print runtime progress and summaries.
`verboseFreq`	Progress output frequency.
`logFlag`	Write text logs when enabled.
`saveFlag`	Persist sqlite snapshots and final result when enabled.
`saveFreq`	Snapshot save frequency.

Example:

python

from UQPyL.optimization.soea import GA
from UQPyL.problem import Sphere


problem = Sphere(nInput=5)
algorithm = GA(maxFEs=200, verboseFlag=False, logFlag=False, saveFlag=False)

result = algorithm.run(problem, seed=123)
print(result.bestDecs)
print(result.bestObjs)

`OptResult`

OptResult is returned by run().

Field	Type	Meaning
`bestDecs`	`np.ndarray` or `None`	Best decision variables. For multi-objective runs this is the current Pareto set.
`bestObjs`	`np.ndarray` or `None`	Best objective values.
`bestCons`	`np.ndarray` or `None`	Constraint values for the best solutions.
`bestMetric`	`float` or `None`	Best metric used for multi-objective progress, currently hypervolume.
`bestFeasible`	`bool`	Whether the best solution set is feasible.
`appearFEs`	`int` or `None`	Function evaluation count when the best result appeared.
`appearIters`	`int` or `None`	Iteration count when the best result appeared.
`FEs`	`int`	Final number of function evaluations.
`iters`	`int`	Final number of iterations.
`runtime`	`float`	Runtime in seconds.
`history`	`OptHistory`	Population and progress history.
`extra`	`dict`	Extra method-specific payload.

Methods:

API	Returns	Meaning
`summary()`	`dict`	Compact runtime summary.
`toDict()`	`dict`	Full result dictionary.

`OptHistory`

OptHistory stores optimization progress.

Field	Meaning
`populations`	Population snapshots.
`bests`	Best-solution snapshots.
`metrics`	Metric values, such as hypervolume for multi-objective runs.
`iterToFEs`	Iteration to function-evaluation mapping.
`bestObjHistory`	Single-objective best-value history.
`numBestHistory`	Number of current best solutions for multi-objective runs.
`bestMetricHistory`	Multi-objective metric history.
`improvedHistory`	Whether each update improved the stored best result.

Method:

API	Returns	Meaning
`toDict()`	`dict`	Dictionary representation of the history.

Single-Objective Algorithms

Import:

python

from UQPyL.optimization.soea import GA, PSO, DE, SCE_UA, ML_SCE_UA, CSA, ABC

`GA`

python

GA(
    nPop=50,
    proC=1,
    disC=20,
    proM=1,
    disM=20,
    maxFEs=50000,
    maxIters=1000,
    maxTolerates=None,
    tolerate=1e-6,
    verboseFlag=True,
    verboseFreq=10,
    logFlag=False,
    saveFlag=True,
    saveFreq=100,
)

Parameter	Meaning
`nPop`	Population size.
`proC`	Crossover probability.
`disC`	Crossover distribution index.
`proM`	Mutation probability.
`disM`	Mutation distribution index.

`PSO`

python

PSO(w=0.1, c1=0.5, c2=0.5, nPop=50, ...)

Parameter	Meaning
`w`	Inertia weight.
`c1`	Cognitive coefficient.
`c2`	Social coefficient.
`nPop`	Population size.

`DE`

python

DE(cr=0.9, f=0.5, nPop=50, ...)

Parameter	Meaning
`cr`	Crossover probability.
`f`	Differential weight.
`nPop`	Population size.

`SCE_UA`

python

SCE_UA(ngs=3, npg=7, nps=4, nspl=7, alpha=1.0, beta=0.5, ...)

Parameter	Meaning
`ngs`	Number of complexes.
`npg`	Number of points in each complex.
`nps`	Number of points in each sub-complex.
`nspl`	Number of evolution steps before shuffling.
`alpha`	Reflection coefficient.
`beta`	Contraction coefficient.

`ML_SCE_UA`

python

ML_SCE_UA(ngs=3, npg=7, nps=4, nspl=7, alpha=1.0, beta=0.5, sita=0.2, ...)

ML_SCE_UA uses the same parameters as SCE_UA, plus:

Parameter	Meaning
`sita`	Multi-level SCE-UA control parameter.

`CSA`

python

CSA(alpha=0.1, beta=0.15, M=3, nPop=25, ...)

Parameter	Meaning
`alpha`	CSA control parameter.
`beta`	CSA control parameter.
`M`	CSA memory or search-control parameter.
`nPop`	Population size.

`ABC`

python

ABC(employedRate=0.3, limit=50, nPop=50, ...)

Parameter	Meaning
`employedRate`	Fraction of employed bees.
`limit`	Trial limit before abandoning a source.
`nPop`	Population size.

Multi-Objective Algorithms

Import:

python

from UQPyL.optimization.moea import NSGAII, NSGAIII, MOEAD, RVEA

`NSGAII`

python

NSGAII(proC=1.0, disC=20.0, proM=1.0, disM=20.0, nPop=50, ...)

Parameter	Meaning
`proC`	Crossover probability.
`disC`	Crossover distribution index.
`proM`	Mutation probability.
`disM`	Mutation distribution index.
`nPop`	Population size.

`NSGAIII`

python

NSGAIII(proC=1.0, disC=20.0, proM=1.0, disM=20.0, nPop=50, ...)

NSGAIII uses the same public constructor parameters as NSGAII.

`MOEAD`

python

MOEAD(aggregation="TCH", nPop=50, ...)

Parameter	Meaning
`aggregation`	Decomposition aggregation method. One of `"PBI"`, `"TCH"`, `"TCH_N"`, or `"TCH_M"`.
`nPop`	Population size.

`RVEA`

python

RVEA(alpha=2.0, fr=0.1, nPop=50, ...)

Parameter	Meaning
`alpha`	RVEA penalty parameter.
`fr`	Reference-vector adaptation frequency.
`nPop`	Population size.

Example:

python

from UQPyL.optimization.moea import NSGAII
from UQPyL.problem import ZDT1


problem = ZDT1(nInput=5)
algorithm = NSGAII(maxFEs=200, verboseFlag=False, logFlag=False, saveFlag=False)

result = algorithm.run(problem, seed=123)
print(result.bestDecs.shape)
print(result.bestObjs.shape)

Expensive Optimization Algorithms

Import:

python

from UQPyL.optimization.expensive import ASMO, EGO, MOASMO

`EGO`

python

EGO(nInit=50, maxFEs=1000, maxIters=1000, maxTolerates=None, ...)

Parameter	Meaning
`nInit`	Number of initial samples.
`xInit`	Optional initial decision matrix passed to `run()`.
`yInit`	Optional initial objective matrix passed to `run()`.

`ASMO`

python

ASMO(
    nInit=50,
    surrogate=None,
    optimizer=None,
    euclidThres=1e-5,
    maxFEs=1000,
    maxIters=1000,
    maxTolerates=None,
    ...
)

Parameter	Meaning
`nInit`	Number of initial samples.
`surrogate`	Optional surrogate model.
`optimizer`	Optional optimizer used on the surrogate problem.
`euclidThres`	Minimum Euclidean distance threshold for accepting new samples.
`oneStep`	Optional `run()` flag for one-step execution.

`MOASMO`

python

MOASMO(
    surrogates=None,
    optimizer=None,
    pct=0.2,
    nInit=50,
    nPop=50,
    advance_infilling=False,
    maxFEs=1000,
    maxIters=100,
    ...
)

Parameter	Meaning
`surrogates`	Optional multi-surrogate object.
`optimizer`	Optional optimizer used on surrogate problems.
`pct`	Infill selection fraction.
`nInit`	Number of initial samples.
`nPop`	Population size used by the internal optimizer.
`advance_infilling`	Whether to use advanced infill selection.

`Population`

Population stores decisions and optional evaluation outputs.

python

Population(decs, objs=None, cons=None, conWgt=None)

Field	Meaning
`decs`	Decision matrix.
`objs`	Objective matrix, or `None` before evaluation.
`cons`	Constraint matrix, or `None` when unavailable.
`conWgt`	Optional constraint weights.
`nPop`	Population size.
`D`	Number of decision variables.
`nOutput`	Number of objective columns when evaluated.
`frontNo`	Non-dominated front number for multi-objective populations.
`crowdDis`	Crowding distance for multi-objective populations.

Common methods:

Method	Returns	Meaning
`copy()`	`Population`	Deep copy.
`add(pop)` / `merge(pop)`	`Population`	Append another population in place.
`merged(pop)`	`Population`	Return merged copy.
`getBest(k=None)`	`Population`	Return best solution or Pareto front.
`getParetoFront()`	`Population`	Return current Pareto front.
`argsort()`	`np.ndarray`	Sort solution indices.
`clip(lb, ub)`	`Population`	Clip decisions in place.
`replace(index, pop)`	`Population`	Replace members in place.
`assignEval(objs, cons=None)`	`Population`	Attach objective and constraint values.
`size()`	`(int, int)`	Return `(nPop, D)`.

`OptReader`

Use OptReader to read sqlite snapshots saved with saveFlag=True.

python

from UQPyL.optimization.runtime import OptReader


reader = OptReader("Result/ga_Sphere_20260509_1200_0000.sqlite3")
summary = reader.get_run_summary()
best = reader.load_last_best()
reader.close()

Method	Returns	Meaning
`OptReader.list_runs(result_dir)`	table-like data	List saved optimization runs in a result directory.
`get_run()`	`dict` or `None`	Return raw run metadata.
`get_run_params()`	`dict`	Return stored algorithm parameters.
`get_run_summary()`	`dict`	Return compact run summary.
`load_algorithm()`	algorithm object	Reconstruct the saved algorithm class with stored parameters.
`load_problem()`	problem object	Load the saved problem payload.
`list_snapshots()`	`list[dict]`	List saved snapshots.
`load_population(snapshotId)`	`Population`	Load population for a snapshot.
`load_best(snapshotId)`	`Population`	Load best or Pareto population for a snapshot.
`load_last_population()`	`Population`	Load the latest population snapshot.
`load_last_best()`	`Population`	Load the latest best or Pareto snapshot.
`close()`	`None`	Close the sqlite connection.

Optimization API

Optimization API ​

UQPyL.optimization ​

Import ​

Public Objects ​

Optimization Workflow ​

OptResult ​

OptHistory ​

Single-Objective Algorithms ​

GA ​

PSO ​

DE ​

SCE_UA ​

ML_SCE_UA ​

CSA ​

ABC ​

Multi-Objective Algorithms ​

NSGAII ​

NSGAIII ​

MOEAD ​

RVEA ​

Expensive Optimization Algorithms ​

EGO ​

ASMO ​

MOASMO ​

Population ​

OptReader ​

Optimization API

`UQPyL.optimization`

Import

Public Objects

Optimization Workflow

`OptResult`

`OptHistory`

Single-Objective Algorithms

`GA`

`PSO`

`DE`

`SCE_UA`

`ML_SCE_UA`

`CSA`

`ABC`

Multi-Objective Algorithms

`NSGAII`

`NSGAIII`

`MOEAD`

`RVEA`

Expensive Optimization Algorithms

`EGO`

`ASMO`

`MOASMO`

`Population`

`OptReader`