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SM ISO690:2012 PAŞA, Tatiana, UNGUREANU, Valeriu, PALADI, Florentin. Applying genetic algorithms to solve non-linear transportation problems. In: Mathematics and IT: Research and Education, 1-3 iulie 2021, Chişinău. Chișinău, Republica Moldova: 2021, pp. 110-111. |
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Mathematics and IT: Research and Education 2021 | |||||
Conferința "Mathematics and IT: Research and Education " Chişinău, Moldova, 1-3 iulie 2021 | |||||
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Pag. 110-111 | |||||
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Non-linear transportation problems describe various real situations in the modern economy. These are complex models that can’t be solved in reasonable time by the means of exact algorithms. Here heuristic algorithms come to our aid, a subset of which are genetic algorithms. Despite these algorithms not being able to guarantee a global solution, one can obtain a pseudo-optim in reasonable time even on large-scale problems. The use of these algorithms is recommended because it is not necessary to know the gradient or Hessian information and they are resistant to locks in a local minimum.We consider the transportation problem on a network described by a convex graph G = (V;E); jV j = n; jEj = m. On the finite set of vertices the real function of production and consumption q : V ! R is defined. On the finite set of edges the concave non-decreasing functions of cost 'e(x(e)) are defined. It is required to solve the non-linear optimization problem that consists in determining a flow x¤ that minimizes the cost function:formulaWe must solve the non-linear problem:formulawhere E¡(v) = f(v; u)j(v; u) 2 Eg, E+(v) = f(u; v)j(u; v) 2 Eg and X is the set of admissible solutions witch satisfies the conditions of the existence of the flow in the network. The presented algorithms [1-2] can be used to solve several particular cases of the formulated problem. The algorithms were tested in Wolfram Mathematica. |
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