Optimization by Monte Carlo Methods
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
KeywordsGenetic Algorithm Monte Carlo Method Travel Salesman Problem Travel Salesman Problem Knapsack Problem
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