Chapter 38
Genetic Versus Han-Type Algorithms
for Maritime Transportation Problems
Doina Carp, Constantin Popa, and Cristina S ¸ erban
Abstract The maritime transportation problem was first formulated by
T.C. Koopmans (1957) as a transportation problem related to specific maritime
activities. Across time, several classes of Simplex-type algorithms have been
developed to find the numerical solution when the problem has a non-empty set
of feasible solutions. Often, the mathematical model of a real world context will
provide an unbalanced and inconsistent maritime transportation problem, i.e. when
the set of classical feasible solutions is empty and the least squares one must be
considered. In such cases, the linear programming solutions techniques cannot be
applied, and one way to find an optimal solution is to reformulate the problem as an
inconsistent (incompatible) system of linear inequalities, for which several
Han-type iterative algorithms have been proposed. In this paper, we attempt to
solve an unbalanced and inconsistent maritime transportation problem by two
approaches. One of them refers to the application of the MH algorithm, a modified
version of Han’s original algorithm, previously proposed by the authors. The other
one involves a soft computing technique that produces an original formulation of a
genetic algorithm (GA) over a maritime transportation problem. The results are
discussed and a comparative study is given, aiming to provide a cost optimized
solution to some real world maritime transportation problems.
D. Carp (*) • C. S ¸ erban
Faculty of Mathematics and Computer Science, Ovidius University of Constanta, Mamaia
Blvd. 124, Constanta 900527, Romania
e-mail: doina.carp@gmail.com
C. Popa
Faculty of Mathematics and Computer Science, Ovidius University of Constanta, Mamaia
Blvd. 124, Constanta 900527, Romania
Gheorghe Mihoc – “Caius Iacob” Institute of Statistical Mathematics and Applied
Mathematics, Calea 13 Septembrie 13, 050711 Bucharest, Romania
© Springer International Publishing AG 2018
C.W. Finkl, C. Makowski (eds.), Diversity in Coastal Marine Sciences, Coastal
Research Library 23, DOI 10.1007/978-3-319-57577-3_38
631
Genetic Versus Han-Type Algorithms
for Maritime Transportation Problems
Doina Carp, Constantin Popa, and Cristina S ¸ erban
Abstract The maritime transportation problem was first formulated by
T.C. Koopmans (1957) as a transportation problem related to specific maritime
activities. Across time, several classes of Simplex-type algorithms have been
developed to find the numerical solution when the problem has a non-empty set
of feasible solutions. Often, the mathematical model of a real world context will
provide an unbalanced and inconsistent maritime transportation problem, i.e. when
the set of classical feasible solutions is empty and the least squares one must be
considered. In such cases, the linear programming solutions techniques cannot be
applied, and one way to find an optimal solution is to reformulate the problem as an
inconsistent (incompatible) system of linear inequalities, for which several
Han-type iterative algorithms have been proposed. In this paper, we attempt to
solve an unbalanced and inconsistent maritime transportation problem by two
approaches. One of them refers to the application of the MH algorithm, a modified
version of Han’s original algorithm, previously proposed by the authors. The other
one involves a soft computing technique that produces an original formulation of a
genetic algorithm (GA) over a maritime transportation problem. The results are
discussed and a comparative study is given, aiming to provide a cost optimized
solution to some real world maritime transportation problems.
D. Carp (*) • C. S ¸ erban
Faculty of Mathematics and Computer Science, Ovidius University of Constanta, Mamaia
Blvd. 124, Constanta 900527, Romania
e-mail: doina.carp@gmail.com
C. Popa
Faculty of Mathematics and Computer Science, Ovidius University of Constanta, Mamaia
Blvd. 124, Constanta 900527, Romania
Gheorghe Mihoc – “Caius Iacob” Institute of Statistical Mathematics and Applied
Mathematics, Calea 13 Septembrie 13, 050711 Bucharest, Romania
© Springer International Publishing AG 2018
C.W. Finkl, C. Makowski (eds.), Diversity in Coastal Marine Sciences, Coastal
Research Library 23, DOI 10.1007/978-3-319-57577-3_38
631