Multi-Objective Optimization with Pymoo / PHV_optimizer /

This repository contains a multi-objective optimization script for prosthetic heart valve leaflet design improvement using the pymoo library. The custom problem is described by parameters, multiple objectives, and constraints. The algorithm used is NSGA-II.

Table of Contents

• Key Components
• Problem Definition
• Optimization Process
• Visualization Functions
• Dependencies
• TODO

Key Components

• optimizer.py: Contains an optimization algorithm based on the class Problem. Custom class Problem (derived from pymoo's ElementwiseProblem) defines objectives, parameters, and constraints, along with the _evaluate method to calculate them.
• test_problem.py: Contains optimization_problem_test, which evaluates a specific problem ("welded_beam") based on given parameters and returns objective and constraint results.
• visualization.py: Contains functions to create various plots, such as Pareto fronts, objective convergence, hypervolume, scatter plots, and parallel coordinates.

Problem Definition

The custom problem class Problem is defined with:

• Parameters: Dictionary of parameter names and their lower and upper bounds (e.g., 'param1': (0.01, 10.0)).
• Objectives: List of objective names to optimize (e.g., ['objective1', 'objective2']).
• Constraints: List of constraint names representing conditions to meet (e.g., ['constraint1', 'constraint2', 'constraint3', 'constraint4']):
  • Constraints are defined numerically, where each constraint function outputs a value representing the degree of violation.
  • A constraint value less than or equal to zero (<= 0) indicates that the constraint is satisfied (non-violated).
  • A positive constraint value (> 0) indicates a violation.

Optimization Process

The optimization is using the following components:

• Algorithm Initialization: Defines population size, crossover, mutation, and other parameters.
• Termination Criteria: Conditions for ending the optimization, such as maximum generations and evaluations.
• Results Extraction: A function extract_optimization_results that extracts optimization results into DataFrames for analysis and storage.

Visualization Functions

The repository contains several visualization functions to analyze the optimization results:

• Pareto Front: Shows the Pareto-optimal solutions.
• Objective Convergence: Displays how objectives improve over generations.
• Hypervolume: Shows convergence by hypervolume.
• Scatter Plots: Plots objectives against parameters and constraints.
• Parallel Coordinates: Plots multiple variables on parallel axes to understand relationships.

Dependencies

Necessary dependencies are listed in requirements.txt.

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TODO

• Try R-NSGA-II.
• Try NSGA-III.
• Try U-NSGA-III.
• Try R-NSGA-III.
• Try MOEA/D.

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For more information about pymoo and its multi-objective optimization features, refer to the [pymoo documentation] (https://pymoo.org/documentation.html).