🛠️ Simplex Solver - Desktop App (Linux)

Core Solver and Functionality

The heart of the project uses the powerful scipy.optimize.linprog module to provide accurate linear programming solutions. It robustly handles:

• Maximization and Minimization objectives.
• Inequality constraints (\(\le, \ge\)).
• Equality constraints (\(=\)).
• Automatic conversion of Free Variables (without non-negativity constraint).

Advanced User Interfaces

1. Domain Specific Languages (DSLs)

Define optimization problems programmatically or in a human-readable way:

• String-based DSL: To load problems from .lp files or directly from a text string in a standard format.
• Pythonic DSL: An elegant syntax, inspired by mathematical libraries, that uses Python objects and operators to build the model natively.

2. Graphical User Interface (GUI) - PySide6

A complete desktop application built with PySide6 (Qt) that offers an interactive experience. It includes an editor, results table, and a logging console.

• Graphical Visualization: Displays the feasible region and the optimal point for 2-variable problems.
• Responsive UI: The solver runs in a separate thread to prevent the application from freezing.

Practical Example: Profit Maximization

The following optimization example (products A and B) is defined concisely using the String-based DSL, which reads a format similar to a traditional .lp file:

from dsl import DSL
problem_lp = DSL("""
MAXIMIZE
    Z = 3*A + 4*B
SUBJECT TO
    2*A + 3*B <= 100
    1*A + 2*B <= 80
BOUNDS
    A >= 0
    B >= 0
""")
# 2*A + 3*B <= 100 # Work hours
# 1*A + 2*B <= 80 # Raw material
solver = problem_lp.to_simplex()
solver.solve_problem()
solver.show_results()
# Optimal solution: A=20, B=30, Z_max = $180

Quick Installation and Usage

Dependency Installation

After cloning the repository, use pip to install everything needed:

git clone https://github.com/xeland314/simplex.git
cd simplex
pip install -r requirements.txt

Launching Interfaces

Run your preferred interface with a single command:

• GUI (Desktop Application):

python app.py

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• Interactive Command Line (CLI):

python simplex.py

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