Optimization is an interdisciplinary branch of mathematics that uses trends such as mathematical programming, statistics, and algorithm design to find the optimal point in optimization problems. Finding the optimal point has different meanings depending on the type of problem and is used in decision-making.
Optimization issues focus on maximization – such as profit, production line speed, more crop production, more bandwidth, etc. – or minimization – such as lower cost and risk reduction, etc., using one or more constraints. The basic idea of optimization is to find the best answers to complex problems modelled in a mathematical language that improve or optimize the performance of a system.
Optimization is widely used in many disciplines today:
Structural engineering, road engineering, traffic, transportation, construction engineering, dam and network engineering, water resources systems, irrigation and drainage networks, water supply and sewerage networks, automotive engineering, aerospace, shipbuilding, military industries, distribution and consumption Energy optimization, design of industrial units, system engineering, various branches of electrical engineering and chemical engineering and materials engineering and operations research.
What topics are discussed in this educational video?
In this video tutorial, the main focus is on solving optimization problems with MATLAB software, and first, an introduction to the concepts is given, and then the various functions and features of MATLAB in optimization are fully explained with various examples.
The general form of an optimization problem
Linear constraint constraints
Boundaries and up and down variables are bounded constraints
How to write an objective function in MATLAB
How to write a multivariate function in MATLAB
Find the maximum of a function
Solve unconstrained problems
Problem-solving with nonlinear constraints
Outputs c and ceq
Show optimization problem-solving process
Unequal linear constraints
Matrix writing constraints
Set the initial guess
Set the maximum number of repetitions
Concept (TolX) Tolerance X
Concept of Tolerance Function (TolFun)
The process of solving an optimization problem
How much optimization settings to get a better answer?
Exit flag concept
Why has optimization stopped?
Which exit flag is correct?
Impact of TolX and TolFun on output