Mathematical Optimization | Chapter 5.4 : Random Search | Indonesian

Summary

This video explains the random search method for solving multivariable optimization problems. The method involves randomly generating values for variables within specified bounds to find the optimal solution. The example maximizes the function f(x, y) = y - x - 2x^2 - 2xy - y^2, with x ranging from -2 to 2 and y from 1 to 3. Through trial and error, the optimal values of x = -1 and y = 1.5 are found, yielding a maximum function value of 1.25. The video demonstrates the utility of random search for complex optimization problems.

Takeaways

• 😀 The script introduces the second numerical method for multivariable optimization problems: Random Search method.
• 😀 Random Search involves evaluating the objective function using random values for the decision variables.
• 😀 A specific example of a function (x, y) = y - x - 2x^2 - 2xy - y^2 is provided to demonstrate the process of maximizing the function.
• 😀 The domain for the function is constrained with x values ranging from -2 to 2, and y values ranging from 1 to 3.
• 😀 The method uses random numbers between 0 and 1 to generate random values for x and y within their respective domains.
• 😀 The formula for generating random values for x and y is given as: x = a + (b - a) * R, where R is a random number between 0 and 1.
• 😀 The random search process involves substituting different random values for x and y into the objective function to evaluate the function's output.
• 😀 For example, a set of random values for R (such as 0.0025, 0.50, 0.75, and 1) are used to calculate possible values for x and y.
• 😀 Once the random values are substituted, the function's output is computed, and the optimal values of x and y are selected based on the maximum function value.
• 😀 In the example, the optimal solution is found with x = -1 and y = 1.5, yielding a maximum objective function value of 1.25.
• 😀 The script concludes by stating that the Random Search method is one of several numerical methods (including Golden Section and others) for solving nonlinear programming problems.

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