
StatusThe thesis was presented on the 15 December, 2021Approved by NCAA on the 1 March, 2022 Abstract– 1.19 Mb / in romanianThesisCZU 004.728.5:519.85(043.3)
3.00 Mb /
in romanian 
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 largescale nonlinear transportation problems
with concave cost functions.
Research objectives: research of transport problems and methods of their solving;
elaboration of approximate algorithms for solving nonlinear transportation problems; elaboration
of genetic algorithms for solving in a reasonable time the largescale 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 largescale
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 nonlinear transportation problems with two, four and five indices were solved
through the application of consecutive reductions of the nonlinear problems to linear ones; the
nonlinear 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.
Under consideration [1] :
Theses Archive: