truss_optimization.md

Truss optimization

Introduction

After slientruss3d v1.2.x, you could use slientruss3d.ga module to do member type selection optimization conveniencely with Genetic Algorithm (GA)! Just simply define the topology of the truss and what member types you want to use, and then you could start the optimization.

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Gene data structure

A gene in slientruss3d is a list of integers. Each integer is a index of the member type in the member type list input by the user. And the length of a gene is equal to Truss.nMember. Example:

[0, 3, 1, 8, 9, 15, 0, 3]

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Fitness function

The following is the default fitness function:

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Crossover

The following is the default crossover policy:

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Mutation

The following is the default mutation policy:

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Evolution policy

The following is the default evolution policy (only for one step):

Where p is probability.

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Example

The following is the example code of GA:

from slientruss3d.truss import Truss
from slientruss3d.type  import MemberType
from slientruss3d.ga    import GA
import random


def TestGA():
    # Allowable stress and displacement:
    ALLOWABLE_STRESS         = 30000.
    ALLOWABLE_DISPLACEMENT   = 10.

    # Type the member types you want to use here:
    MEMBER_TYPE_LIST = [MemberType(inch, random.uniform(1e7, 3e7), random.uniform(0.1, 1.0)) for inch in range(1, 21)]

    # GA settings:
    MAX_ITERATION      = None  # When [MAX_ITERATION] is None, do infinite iteration until convergence (reach [PATIENCE_ITERATION]).
    PATIENCE_ITERATION = 50

    # Truss object:
    truss = Truss(3)
    truss.LoadFromJSON('./data/bar-120_input_0.json')

    # Do GA:
    ga = GA(truss, MEMBER_TYPE_LIST, ALLOWABLE_STRESS, ALLOWABLE_DISPLACEMENT, nIteration=MAX_ITERATION, nPatience=PATIENCE_ITERATION)
    minGene, (fitness, isInternalAllowed, isDisplaceAllowed), finalPop, bestFitnessHistory = ga.Evolve()

    # Translate optimal gene to member types:
    truss.SetMemberTypes(ga.TranslateGene(minGene))

    # Save result:
    truss.Solve()
    truss.DumpIntoJSON(f'bar-120_ga_0.json')

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Geneic algorithm

(Not every method or property is listed here)

Constructor

GA(truss, memberTypeList, allowStress=30000., allowDisplace=10., nIteration=None, nPatience=50, nPop=200, nElite=50, pCrossover=0.7, pMutate=0.1, pOrigin=0.1, isCheckWorst=False) -> None

• truss : Truss object.
• memberTypeList : A list which contains what member type you want to use as the options to be optimized.
• allowStress : Allowable stress.
• allowDisplace : Allowable displacement.
• nIteration : Maximum number of iterations for updating the population (When it's None, GA will do infinite iteration until convergence ( no more improvement for nPatience iterations).)
• nPatience : Maximun number of iterations for no improvement.
• nPop : Number of individuals in the population.
• nElite : Individuals whose fitness value are ranked last nElite will be selected as elites for crossover or mutation.
• pCrossover : Probability to crossover.
• pMutate : Probability to mutate.
• pOrigin : Probability to do neither crossover nor mutate.
• isCheckWorst : Whether to check the two worst cases (assign max cross-sectional area (A) and max cross-sectional area * Young's modulus (EA) to all members) both do not violate the allowable stress and allowable displacement before executing GA.

Execute generic algorithm

GA.Evolve(isPrintMessage=True) -> tuple[list[int], tuple[int, bool, bool], list[list[int]], list[float]]

• isPrintMessage : Whether to print optimization messages in the screen or not.

• Return: (1., 2. is the same output as GA.GetBestFeasibleGene.)

  1. Best and *feasible* gene
  2. Tuple(Fitness corresponding to i. , Is all internal stresses allowed ? , Is all displacements allowed ?)
  3. Final population
  4. History of best fitness value at each iteration

Translate gene to member types

GA.TranslateGene(gene) -> dict[int, MemberType]

• gene : Gene, which is a list of integers.

• Return:

  A dictionary whose key is member ID and value is MemberType object.

Set member types of the truss by a gene

GA.SetMemberTypesByGene(gene, truss) -> Truss

• gene : Gene, which is a list of integers.

• truss : Truss object.

  This method is equivalent to truss.SetMemberTypes(ga.TranslateGene(gene)).
  The reference of the output truss is the same as the input truss.

Get the best and feasible gene

GA.GetBestFeasibleGene(pop) -> tuple[list[int], tuple[int, bool, bool]

• pop : Population, which is a list of genes.

  If there is no feasible gene, this method will return the None, (inf, False, False).

Return a random gene

GA.GetRandomGene() -> list[int]

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Customization

As long as you comply with the function signiture and the meaning of every input, output variable, it's possible to customize your own generic algorithm by inheriting class GA in slientruss3d. The following are the methods you could perhaps override them to make your own custom GA.

class CustomGA(GA):

    ...

    def GetFitness(self, gene: list[int]) -> tuple[float, bool, bool]:
        ## ...... something to do ...... ##
        return fitness, isInternalAllowed, isDisplaceAllowed
    
    def Initialize(self) -> list[list[int]]:
        ## ...... something to do ...... ##
        return pop
    
    def Select(self, pop: list[list[int]]) -> tuple[list[list[int]], float]:
        ## ...... something to do ...... ##
        return elitePop, bestFitness
    
    def Crossover(self, gene0: list[int], gene1: list[int]) -> list[int]:
        ## ...... something to do ...... ##
        return newGene
    
    def Mutate(self, gene: list[int]) -> list[int]:
        ## ...... something to do ...... ##
        return newGene
    
    def UpdatePop(self, pop: list[list[int]], elitePop: list[list[int]]) -> list[list[int]]:
        ## ...... something to do ...... ##
        return newPop
    
    ...

Here is an example:

from slientruss3d.ga import GA

class CustomGA(GA):
    def GetFitness(self, gene):
        truss = self.SetMemberTypesByGene(gene, self.truss)
        truss.Solve()

        isInternalAllowed, internalViolation = truss.IsInternalStressAllowed(self.allowStress, True)
        isDisplaceAllowed, displaceViolation = truss.IsDisplacementAllowed(self.allowDisplace, True)

        fitness = truss.weight
        if not isInternalAllowed: fitness += internalViolation / self.allowStress   * 1e3
        if not isDisplaceAllowed: fitness += displaceViolation / self.allowDisplace * 1e3
        return fitness, isInternalAllowed, isDisplaceAllowed

This example shows that if you don't want to use default fitness function, you can customize it by overriding the origin method GetFitness. The new fitness function just adjusts the penalty weights for the sum of exceeding quantities of stresses and displacements (1e5 -> 1e3).