To mention some, among others, conic programming, semi definite programming, semi infinite programming and some meta heuristic techniques. For now, much software help is needed to solve the wrong problem found to get the optimal solution with computation time not too long. Successful application of optimization techniques requires at least three conditions. These requirements are the ability to make mathematical models of problems encountered, knowledge of optimization techniques and knowledge of computer programs.
Optimization is a problem associated with the best decision that is effective and efficient decisions whether it is worth maximum or minimum by way of determining a satisfactory solution. Optimization is not a new science. It has grown even since Newton in the 17th century discovered how to count roots. Currently the science of optimization is still evolving in terms of techniques and applications. Many cases or problems in everyday life that involve optimization to solve them.
Artificial Intelligence has an important place in the scientific community as a result of its successful outputs in terms of different fields. In time, the field of Artificial Intelligence has been divided into many sub-fields because of increasing number of different solution approaches, methods, and techniques. Machine Learning has the most remarkable role with its functions to learn from samples from the environment. On the other hand, intelligent optimization done by inspiring from nature and swarms had its own unique scientific literature, with effective solutions provided for optimization problems from different fields. Because intelligent optimization can be applied in different fields effectively, this study aims to provide a general discussion on multidisciplinary effects of Artificial Intelligence by considering its optimization oriented solutions. The study briefly focuses on background of the intelligent optimization briefly and then gives application examples of intelligent optimization from a multidisciplinary perspective.
Nonlinear constrained optimization problems are an important class of problems with a broad range of engineering, and scientific applications. In this article, we will see how the refashioning of simple unconstrained Optimization techniques leads to a hybrid algorithm for constrained optimization problems. Later, we will observe the robustness of the algorithm through a detailed analysis of a problem set and monitor the performance of optima by comparing the results with some of the inbuilt functions in python. Many engineering design and decision making problems have an objective of optimizing a function and simultaneously have a requirement for satisfying some constraints arising due to space, strength, or stability considerations. So, Constrained optimization refers to the process of optimizing an objective function with respect to some variables in the presence of constraint of those variables.
Resource allocation and transceivers in wireless networks are usually designed by solving optimization problems subject to specific constraints, which can be formulated as variable or functional optimization. If the objective and constraint functions of a variable optimization problem can be derived, standard numerical algorithms can be applied for finding the optimal solution, which however incur high computational cost when the dimension of the variable is high. To reduce the on-line computational complexity, learning the optimal solution as a function of the environment's status by deep neural networks (DNNs) is an effective approach. DNNs can be trained under the supervision of optimal solutions, which however, is not applicable to the scenarios without models or for functional optimization where the optimal solutions are hard to obtain. If the objective and constraint functions are unavailable, reinforcement learning can be applied to find the solution of a functional optimization problem, which is however not tailored to optimization problems in wireless networks. In this article, we introduce unsupervised and reinforced-unsupervised learning frameworks for solving both variable and functional optimization problems without the supervision of the optimal solutions. When the mathematical model of the environment is completely known and the distribution of environment's status is known or unknown, we can invoke unsupervised learning algorithm. When the mathematical model of the environment is incomplete, we introduce reinforced-unsupervised learning algorithms that learn the model by interacting with the environment. Our simulation results confirm the applicability of these learning frameworks by taking a user association problem as an example.