The research reported in this thesis considers the classical combinatorial
optimization problem known as the Generalized Assignment Problem (GAP).
Since the mid 1970's researchers have been developing solution approaches
for this particular type of problem due to its importance both in practical and
theoretical terms. Early attempts at solving GAP tended to use exact integer
programming techniques such as Branch and Bound. Although these tended to
be reasonably successful on small problem instances they struggle to cope
with the increase in computational effort required to solve larger instances.
The increase in available computing power during the 1980's and 1990's
coincided with the development of some highly efficient heuristic approaches
such as Tabu Search (TS), Genetic Algorithms (GA) and Simulated Annealing
(SA). Heuristic approaches were subsequently developed that were able to
obtain high quality solutions to larger and more complex instances of GAP.
Most of these heuristic approaches were able to outperform highly
sophisticated commercial mathematical programming software since the
heuristics tend to be tailored to the problem and therefore exploit its structure.
A new approach for solving GAP has been developed during this research that
combines the exact Branch and Bound approach and the heuristic strategy of
Tabu Search to produce a hybrid algorithm for solving GAP. This approach
utilizes the mathematical programming software Xpress-MP as a Branch and
Bound solver in order to solve sub-problems that are generated by the Tabu
Search guiding heuristic. Tabu Search makes use of memory structures that
record information about attributes of solutions visited during the search. This
information is used to guide the search and in the case of the hybrid algorithm
to generate sub problems to pass to the Branch and Bound solver. The new
algorithm has been developed, imp lemented and tested on benchmark test
problems that are extremely challenging and a comprehensive report and
analysis of the experimentation is reported in this thesis.
A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.