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Algorithms for solving nonlinear transportation problems


Author: Pașa Tatiana
Degree:doctor of informatics
Speciality: 01.05.04 - Mathematical modelling, mathematical methods, software
Year:2022
Scientific advisers: Valeriu Ungureanu
doctor, associate professor (docent), Moldova State University
Florentin Paladi
doctor habilitat, professor, Moldova State University
Institution: Moldova State University

Status

The thesis was presented on the 15 December, 2021
Approved by NCAA on the 1 March, 2022

Abstract

Adobe PDF document – 1.19 Mb / in romanian

Thesis

CZU 004.728.5:519.85(043.3)

Adobe PDF document 3.00 Mb / in romanian
170 pages

Keywords

transportation problem, nonlinear problem, transportation network, cost function, production and consumption function, graph, spanning tree, algorithm, admissible set

Summary

ANNOTATION Pașa Tatiana “Algorithms for solving nonlinear transportation problems” a PhD degree in Informatics, Chișinău, 2021. Thesis structure: The thesis contains an introduction, three chapters, general conclusions and recommendations, a bibliography of 173 titles, 118 pages of main text, 10 figures, 20 tables. The obtained results were published in 19 scientific papers. Keywords: transportation problem, nonlinear problem, transportation network, cost function, production and consumption function, graph, spanning tree, algorithm, admissible set. The goal of the thesis: is to study and solve large-scale nonlinear transportation problems with concave cost functions. Research objectives: research of transport problems and methods of their solving; elaboration of approximate algorithms for solving non-linear transportation problems; elaboration of genetic algorithms for solving in a reasonable time the large-scale transportation problems described by networks with one or more sources and one or more destinations with concave cost functions; elaboration of genetic algorithms for solving in a reasonable time the large-scale transportation problems described by networks with several indices and concave cost functions; testing and estimating the execution time of the proposed algorithms. The scientific novelty and originality: consists in new theoretical and applicative results that complete those known from specialized literature in the domain of nonlinear transportation problems. The non-linear transportation problems with two, four and five indices were solved through the application of consecutive reductions of the non-linear problems to linear ones; the non-linear problems with a single source and destination, with a single source and several destinations, with several sources and several destinations, with 4 indices and with 5 indices were codified so that genetic algorithms could be applied and admissible solutions are obtained through decoding; the crossover and mutations operators of the genetic algorithms were described so that admissible solution are obtained through decoding; it has been practically proved that each of the proposed algorithms generates a local admissible solution in reasonable time. The obtained results which contribute to solve some important scientic problem: consists in indentification of methods of coding nonlinear transportation problems, which led to the creation of genetic algorithms and of algorithms based on reduction to a linear problem. These algorithms were then implemented to solve applicative problems. The theoretical significance: of the research is determined by the obtained results related to the proposed algorithms with polynomial iterations for solving nonlinear transportation problems. It has been shown that algorithms always converge to a local optimal solution in a reasonable time. The applicative value: of the paper consists in the possibility of using the proposed algorithms to solve real transportation problems and adapting them to a larger set of nonlinear transportation problems. The implementation of the scientific results: the obtained results can serve as a support for some optional courses, related to solving nonlinear optimization problems, for bachelor or master students. The proposed algorithms allow solving the problem of supplying stores with products transported from warehouses, enterprises with raw materials, construction and civil engineering companies with construction мaterials, etc.