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Abstract:
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Constrain satisfaction problems including the optimisation problems are among the
most important problems of discrete mathematics with wide area of application
in mathematics itself and in the applied mathematics.
Dissertation study optimisation problem and presents an original method for
finding its exact solution. The name of the method is Sedimentation Algorithm,
which is introduced together with two heuristics. It belongs to the class of
branch-and-bound algorithms, which uses backtracking and forward checking
techniques. The Sedimentation Algorithm is proven to be totally correct.
Ability of the Sedimentation Algorithm to solve different type of problems is
demonstrated in dissertation by its application on the Boolean satisfiability problems,
the Whitehead Minimisation Problem and the Berth Allocation Problem in
container port. The best results are obtained for Berth Allocation Problem, because
its modelling for Sedimentation Algorithm includes all available optimisation
techniques of the method. The precise complexity estimation of the Sedimentation
Algorithm for the Berth Allocation Problem is established. Experimental
results verify that the Sedimentation Algorithm is capable to solve the
Berth Allocation Problem on the state of art level. |