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Optimization by Monte Carlo Methods

  • Ronald W. Shonkwiler
  • Franklin Mendivil
Chapter
Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

It may be that the problem of optimization entails more time and effort by mankind than any other mathematical problem. For example, it permeates nearly all design and engineering projects.

When formalized, the problem consists of a given function f called the objective function together with a domain Ω of its arguments x. It is required to find a value of x ∈ Ω that minimizes or maximizes f(x). The problem may also impose certain constraints on the admissible or feasible x’s. In the formalization above, Ω would (usually) exclude infeasible states. However, it is often better to leave infeasible states in the domain, since they can be useful in searching for a feasible solution. In fact, one method of attacking a constrained optimization problem is to penalize infeasible states, and to an increasing degree as the run progresses

Keywords

Genetic Algorithm Monte Carlo Method Travel Salesman Problem Travel Salesman Problem Knapsack Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA
  2. 2.Department of Mathematics and StatisticsAcadia UniversityWolfvilleCanada

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