Mathematical Sciences: Theoretical and Algorithmic Studies in Combinatorial Problem-Solving

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Mathematical programming is concerned with the optimization of functions in many variables subject to side constraints. Combinatorial optimization addresses the same problem with an additional complication brought about by the inclusion of indivisible activities, i.e., by variables that must assume integer values. In purely combinatorial problems, all variables must be integer. Since its inception shortly after World War II, mathematical programming ideas have been successfully utilized to formulate and to solve many complex planning problems, with applications covering the entire range from the quantitative social sciences to engineering science. The increased ability to numerically solve mathematical programming problems has brought about a greater demand to incorporate indivisible activities into the planning models. This research aims to extend the computational frontiers of combinatorial problem-solving as well as to achieve a better mathematical understanding of combinatorial optimization problems.