Global Optimization Algorithm

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One of the most fundamental principles in our world is the search for an optimal state. Many real life applications in operations research and computer science are formulated as optimization problem.These real life problems are non-linear in nature having the characteristics like multi-mode, non-continuous etc. So, it is very difficult to solve these problems by tools like gradient descent, Secant method etc. Here comes the concept of global optimization.\\
Global optimization is a branch of applied mathematics and numerical analysis that deals with the global optimization of a function or a set of functions according to some criteria.
Global optimization is distinguished from regular optimization by its focus on finding the maximum or minimum …show more content…

Then we can efficiently explore our search space. If there is no relationship observed or the dimentionability of search space is high then it become very hard to solve any problem deterministically. Then we have to do large number of enumerations even for a very small problem. Then comes the role of probabilistic algorithms.\\ \item \textbf{Probabilistic Algorithms:} These are generally referred as Monte-Carlo algorithms which provides a good solution in shorter time. They doesn't provide exact solution of a problem but a good solution near to optima which would have taken years by deterministic algorithms.\\\\
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\includegraphics[scale=1]{1}\\ \caption{Different Optimization algorithms (Source:\text{[1]})} …show more content…

It is a part of optimization algorithm which uses the information gathered by the algorithm to decide which solution candidate to be tested next or how to reach the next solution candidate.It is a local search. Heuristic are problem dependent. Heuristics can be used by both deterministic and probabilistic algorithms.
\item \textbf{Meta-heuristics:} It is a Heuristic method for solving general class of problem. It is generalized local search. Meta-heuristic are problem independent that can be applied to wide range of problems. Generally all the probabilistic algorithms uses Meta-heuristics. \end{enumerate} The algorithm that we are trying to implement is a probabilistic algorithm. In our algorithm either we are randomly picking points from domain of function or applying gradient descent method with probability p and 1-p respectively. There are four different versions of algorithms that we have implemented. The algorithm is tested by simulations performed on benchmark function in MATLAB.

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