Multi-objective Optimization Problems and Algorithms

Name: Multi-objective Optimization Problems and Algorithms
Rating: 4.4 (581 reviews)

How to handle multiple objectives using a wide range of optimization algorithms

Created bySeyedali Mirjalili

Last updated 10/2018

English

What you'll learn

Able to solve multi-objective problems
Able to use multi-objective optimization algorithms
Visualize the results of a multi-objective optimization
Analyze the results of a multi-objective optimization
Able to solve multi-objective optimization problems with a wide range of multi-objective techniques

Course content

5 sections • 20 lectures • 4h 6m total length

Introduction9:41
This lesson gives you some tips on how to get the most of this course. It shows you how to download Matlab and SciLab too.

Multi-objective Optimization Problems16:55
Multi-objective problems have more than one objective. This video shows you the main components of such problems and how to formulate them.
Coding A Multi-objective Benchmark Function10:48
This video shows you the steps of formulating and implementing a benchmark multi-objective test function in Matlab.
Coding A Real-world Multi-objective Function11:48
This video shows you the steps of formulating and implementing a real-world multi-objective problem in Matlab.
Decision Variable Space and Objective Space10:25
Decision Variable Space and Objective Space are two of the most fundamental concepts in the field of optimization. This lesson allows you to understand their meanings with intuitive examples.
Search Space and Objective Space of ZDT113:46
This lesson shows you how to visualize the search space and objective space of a multi-objective test function in Matlab.
Search Space and Objective Space of The Cantilever Beam Design Problem6:36
This lesson shows you how to visualize the search space and objective space of a real-world multi-objective problem (cantilever beam design) in Matlab.
Feasible and Infeasible Areas in Parameter and Objective Spaces20:26
The constraints of a problem change its search space and objective space. This video allows you to see the impacts of constraints.

Pareto Optimal Dominance and Pareto Optimality19:01
This lesson includes the most important theory video, which is about Pareto Optimal dominance and Pareto optimality. These concepts are covered in detail.
Pareto Optimal Solution Set and Pareto Optimal Front6:15
This video covers the concepts of Pareto Optimal Solution Set and Pareto Optimal Front.
Coding A Function for Pareto Optimal Dominance11:42
This lesson shows you the steps of implementing a function to compare solutions of a multi-objective problem using Pareto Optimal dominance.

A Classification of Multi-objective Optimization Algorithms8:54
This video shows you the classification of multi-objective algorithms in the fields of Artificial Intelligence and Mathematics.
No Preference Methods: theory and coding28:21
A Priori Multi-objective Algorithms: theory20:33
This lesson covers the details of a priori multi-objective algorithms, in which objectives are aggregated using a set of weights.
A Priori Multi-objective Algorithms: coding16:54
This video uses Particle Swarm Optimization (PSO) to solve a multi-objective problem as a priori algorithm. If you have never used PSO, I have provided the details of this algorithm in an announcement. Make sure to watch it.
A Posteriori Multi-objective Algorithms: Theory13:09
This vide takes you through the definitions and main components and posteriori multi-objective algorithms, in which the objectives ARE NOT aggregated anymore.
A Posteriori Multi-objective Algorithms: Coding9:48
This video uses an Evolutionary Algorithm to find Pareto optimal solutions for a multi-objective problem. The multi-objective formulation is maintained, so the algorithm is considered as a posteriori multi-objective optimization algorithm.
Progressive Multi-objective Algorithms: Theory4:45
Progressive Multi-Objective Algorithms refer to the algorithms that involve humans (decision makers) during the optimization process. This video shows you how such methods works.
Progressive Multi-objective Algorithms: Coding5:24
Progressive Multi-Objective Algorithms refer to the algorithms that involve humans (decision makers) during the optimization process. This video shows you an examples of such methods.

Requirements

Basic understanding of single-objective optimization
Familiar with Matlab programming language
Basic knowledge of Genetic Algorithms
Basic knowledge of Particle Swarm Optimization

Description

This is an introductory course to multi-objective optimization using Artificial Intelligence search algorithms. We start with the details and mathematical models of problems with multiple objectives. Then, we focus on understanding the most fundamental concepts in the field of multi-objective optimization including but not limited to: search space, objective space, Pareto optimality, Pareto optimal solution set, Pareto optimal front, Pareto dominance, constraints, objective function, local fronts, local solutions, true Pareto optimal solutions, true Pareto optimal front, etc.

In the second part of this course, several optimization methods will be given to solve multi-objective optimization problems as follows:

No preference methods
A priori methods
A posteriori methods
Progressive methods

The course also includes a large number of coding videos to give you enough opportunity to practice the theory covered in the lecture. There are also several case studies including real-world problems that allow you to learn the process of solving challenging multi-objective optimization problems using multi-objective optimization algorithms.

For the search methods, we will be using stochastic optimization algorithms including Particle Swarm Optimization and Genetic Algorithms. This means that we develop Multi-Objective Particle Swarm Optimization (MOPSO) and multi-Objective Genetic Algorithms (MOGA).

Some of the reviews for this course are as follows:

Femi said: "As always, the instructor is expert in the course and explained in details with real-life examples, and I love his teaching style, even though the course is a bit tough, he made it fun!"

Pankaj said: "Dr Mirjalili teaches with a very good pace and conveys the concept clearly. The examples he uses are very relatable and he makes learning tricky concepts really fun."

Oyakhilome said: "Another great course by Dr. Seyedali. All components of the course were well structured and tailored to meet the educational needs of the students. I strongly recommend this course to everyone new to the field of optimization."

Join 1000+ students and start your optimization journey with us. If you are in any way not satisfied, for any reason, you can get a full refund from Udemy within 30 days. No questions asked. But I am confident you won't need to. I stand behind this course 100% and am committed to help you along the way.

Who this course is for:

Anyone who wants to solve multi-objective optimizations
Anyone who wants to use multi-objective algorithms

Multi-objective Optimization Problems and Algorithms

What you'll learn

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Course content

Part 1: Introduction1 lecture • 10min

Part 2: Multi-objective Optimization Problems7 lectures • 1hr 31min

Part 3: Preliminaries and Essential Definitions in Multi-objective Optimization3 lectures • 37min

Part 4: Multi-objective Algorithms8 lectures • 1hr 48min

Bonus Video1 lecture • 2min

Requirements

Description

Who this course is for: