Advanced Computational Optimization Methods and Algorithms 

The lecture notes will be updated here periodically.

This page is last updated on Oct 03, 2025.

Pre-requisites: 

MA-I (MA001), MA-II (MA002), COMA (ID210), Programming

Course Syllabus: 

[Unit-1] Advanced Mathematical Programming: Revise the previous concepts learnt in COMA; Advanced LPP and related topics, Integer programming, Quadratic Programming, Large-scale linear programming problems, Interior point method, Transportation and Assignment Problems.

[Unit-2] Combinatorial Optimization: Fundamentals of graph theory, minimum spanning tree algorithm, Kruskal algorithm, shortest path, Dijkstra algorithm, Floyd Warshell algorithm, network flows and maximum flow problem, max flow min cut algorithm, Menger’s theorem, minimum cost flow problems; Project Management, Game Theory;  Travelling salesman problem and its variants. 

[Unit-3] Nature-inspired Optimization: Introduction to nature-inspired algorithms and various mostly used algorithms; Genetic algorithm, particle swarm optimization, ant colony optimization.  

[Unit-4] Multi-Objective Optimization: Introduction to multi-objective optimization, pareto optimality, classical methods for multi-objective optimization, introductory evolutionary algorithms.  

Course Outcomes: 

The present course will provide a computational perspective of the advanced optimization methods and algorithmic implementation. By attending the course, students will be able to understand 

1. Advanced methods to solve variants of linear programming problems and their application in transportation & assignment problems.

2. The fundamental concepts of graph theory and associated combinatorial optimization problems.

3. The inspiration for nature-inspired optimization algorithms, especially genetic algorithm, particle swarm and ant colony optimization.

4. The mathematical formulation and application for multi-objective optimization problems.    

Recommended Books:

Text Books:

1. H A Taha, Operations Research: An Introduction, Pearson Prentice Hall, 8th Edition, 2007.

2. J. Nocedal, S. J. Wright, Numerical optimization, Springer, 2nd Edition, 2000.

Reference Books:

1. C. H. Papadimitriou, K. Steiglitz, Combinatorial Optimization Algorithms and Complexity, Dover Publication, 2nd Edition, 1998.

2. K. Deb, Multi-Objective Optimization using Evolutionary Algorithms, John Wiley & Sons, 1st Edition, 2001. 

Evaluation Scheme: 

Students will be evaluated on a scale of 100 = (2/3) * best three of {MTE, ETE, Coding, Project} where

MTE - Open Book Mid Term Exam - 50 Marks for 2 Hr duration

ETE - Open Book End Term Exam - 50 Marks for 2 Hr duration

Coding - MATLAB Coding Exam of 50 Marks for 2 Hr duration

Project - Project (a group of max 4) of 50 Marks (Abstract-10M + Report-25M + Presentation-15M)

Note: A minimum of 20 marks is required to pass the course. The grading will be relative-scaled.

Exam/Test Schedule: 

1. Mid Term Exam (MTE) will be held on 27 Sept 2025 from 10:00 AM to 12:00 PM. Q. Paper

2. Last date to submit the abstract (max 200 words; include objective, methodology, possible outcomes; references) of project report is 6 Oct 2025. 

3. Last date to submit the project report (max 6 pages; include abstract, introduction, methodology/model, results, discussion, conclusion, references) is 31st Oct 2025. The report should be in IEEE format. Similarity index of the report should be less than 15%.