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Optimization problems arise in all quantitative disciplines from computer science and engineering [3] to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries.
The optimization of sequential experimentation is studied also in stochastic programming and in systems and control. Popular methods include stochastic approximation and other methods of stochastic optimization. Much of this research has been associated with the subdiscipline of system identification. [30]
Another research trend is to try to alleviate premature convergence (that is, optimization stagnation), e.g. by reversing or perturbing the movement of the PSO particles, [19] [52] [53] [54] another approach to deal with premature convergence is the use of multiple swarms [55] (multi-swarm optimization).
A minimum spanning tree of a weighted planar graph.Finding a minimum spanning tree is a common problem involving combinatorial optimization. Combinatorial optimization is a subfield of mathematical optimization that consists of finding an optimal object from a finite set of objects, [1] where the set of feasible solutions is discrete or can be reduced to a discrete set.
Simulation-based optimization (also known as simply simulation optimization) integrates optimization techniques into simulation modeling and analysis. Because of the complexity of the simulation, the objective function may become difficult and expensive to evaluate. Usually, the underlying simulation model is stochastic, so that the objective ...
An optimization problem with discrete variables is known as a discrete optimization, in which an object such as an integer, permutation or graph must be found from a countable set. A problem with continuous variables is known as a continuous optimization, in which an optimal value from a continuous function must be found.
In finance, management science is instrumental in portfolio optimization, risk management, and investment strategies. By employing mathematical models, analysts can assess market trends, optimize asset allocation, and mitigate financial risks , contributing to more informed and strategic decision-making.
In computer science and operations research, the ant colony optimization algorithm (ACO) is a probabilistic technique for solving computational problems that can be reduced to finding good paths through graphs. Artificial ants represent multi-agent methods inspired by the behavior of real ants.