Continuous optimization

Continuous optimization refers to the process of finding the optimal values of a function by adjusting a set of continuous variables or parameters. The goal is to minimize or maximize the function, and this is achieved by iteratively adjusting the values of the variables until the optimal solution is found. This approach is used in a wide range of applications, including engineering, finance, and machine learning.From: Nature-Inspired Computing [2017]

Water Drop Algorithm

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Published in Nazmul Siddique, Hojjat Adeli, Nature-Inspired Computing, 2017

Nazmul Siddique, Hojjat Adeli

It is also possible to solve continuous optimization problems by the WDA. In a continuous optimization problem, a number of continuous variables (parameters) are needed such that a function is minimized or maximized. Shah-Hosseini (2012) applied WD-CO by encoding real continuous variables into binary strings like binary chromosomes in the standard GA. The WDA then tries to optimize the given function in the binary representation. Finally, the best solution is reported as the final solution.

Asymptotic behaviour of a dynamical system governed by non-monotone potential and non-potential operators

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Published in Optimization, 2022

B. Djafari Rouhani, H. Khatibzadeh, M. Rahimi Piranfar, J. Rooin

In the following, we illustrate Theorem 4.1 by a concrete example from quantum chemistry. The minimum-energy configuration of a small cluster of atoms, molecules, or ions is known as the molecular conformation problem. It is a central problem in the study of cluster statics, or the topography of a potential energy function in an internal configuration space. From the viewpoint of mathematical optimization, it is a difficult global optimization problem which does not yield easily either to discrete or continuous optimization methods. See [16] and the references therein. In the following example, we consider the simple case of a molecule with two atoms. The interested reader may consult [17,18] for more details.

Continuous optimization

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Water Drop Algorithm

Asymptotic behaviour of a dynamical system governed by non-monotone potential and non-potential operators