Abstract
In this paper we propose a genetic algorithm for solving the nonlinear transportation problem on a network with multiple sinks and concave piecewise cost functions. We prove that the complexity of one iteration of the algorithm is O(n2) and the algorithm converges to a local optimum solution. We show that the algorithm can be used to solve large-scale problems and present the implementation and several testing examples of the algorithm using Wolfram Language.
Highlights
There are often situations where a manufacturer of a type of product has sale contracts with traders from various cities and/or countries
After the product is transported through several intermediary points, it is placed on store shelves and bought by the customer. This structure can be described by a transportation network with one source, several destinations and a set of intermediary points
There are no known polynomial algorithms that would provide the solution to these largescale problems. This is due to the NP-difficult problem with concave cost functions, which can have several local minima, to which, in most cases, the algorithm often converges
Summary
There are often situations where a manufacturer of a type of product has sale contracts with traders from various cities and/or countries. After the product is transported through several intermediary points, it is placed on store shelves and bought by the customer This structure can be described by a transportation network with one source, several destinations and a set of intermediary points. Even if no genetic algorithms [5] are known that are able to deliver the exact solution for all optimization problems, their use is recommended, because they do not need the gradient or Hessian information. These algorithms are resistant to blockages in an optimal local even if the structure of the restrictions that describe the range of admissible solutions is quite complex. Incorporating techniques that improve the solution in the genetic algorithm produces a hybrid that can obtain better results [8]
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