SDMA

Semidefinite‐Based Metaheuristic Algorithm

Multi-Objective Optimization Comparison (SDMA vs Weighted Sum vs NSGA-II)

This MATLAB project compares three multi-objective optimization algorithms — SDMA, Weighted Sum Scalarization, and NSGA-II — on a constrained 2D polynomial problem. The code generates Pareto front visualizations and evaluates multiple performance metrics.

Problem Statement

Objective Functions:

$$ \begin{aligned} f_1(x) &= \frac{(x_1 + x_2 - 7.5)^2}{4} + (x_2 - x_1 + 3)^2 \\ f_2(x) &= 0.4(x_1 - 1)^2 + 0.4(x_2 - 4)^2 \end{aligned} $$ Constraints: $$ \begin{aligned} g_1(x) &= -\frac{(x_1 - 2)^3}{2} - x_2 + 2.5 \geq 0 \\ g_2(x) &= -x_1 - x_2 + 8(x_2 - x_1 + 0.65)^2 + 3.85 \geq 0 \\ & x_1, x_2 \in [0, 5] \end{aligned} $$

Algorithms Compared

SDMA: Sequential Decomposition-based Multi-objective Algorithm Weighted Sum Scalarization NSGA-II: Non-dominated Sorting Genetic Algorithm II

Installation

Clone the repository: git clone https://github.com/kanchan999/SDMA.git

MATLAB Requirements: MATLAB R2020b or later Optimization Toolbox (for fmincon)

Usage

Open MATLAB and navigate to the project directory. Run the main script: SDMA

Outputs

Console:

Performance tables (Hypervolume, Spread, Domination %, Computation Time, etc.)

Figure: pareto_front_comparison.png showing Pareto fronts of all methods

Tunable Parameters

SDMA: maxBoxIter (box subdivisions), popSize (population per box)

Weighted Sum: numWeights (number of weights)

NSGA-II: popSize, maxGen (population size and generations)

License

This project is licensed under the MIT License. See the LICENSE file for details.

Contributing

We welcome contributions! You can:

Report bugs or request features via GitHub Issues Fork the repository and submit a pull request

Contact

For questions or collaboration, feel free to contact:

Author: Kanchan Rajwar

Email: kanchanrajwar1519@gmail.com