(5/5)

SUMMARY

• In order to advance the state of the art in algorithms for the generalised assignment problem a benchmark set of relatively large test problems is solved and made publically available to others.

• For the more difficult highlycapacitated problems, exact algorithms can only solve problems involving up to a few hundred decision variables before the search trees g r o w prohibitively large.

• Since we solve the GAP as a minimisation problem, we changed the sign of the costs in the original data such that all costs become negative and the problems are solved as minimisation problems.

• For the 24 'large-size' problems the optimal solutions are not known, except for type A problems for which we were able to obtain the optimal solutions by using the CPLEX general purpose mixed integer solver.

• In Table 3, we compare the performance of our GA heuristic with other existing heuristic algorithms in terms of the average percentage deviation for each problem set, the average percentage deviation for all problems, the average percentage deviation of the best solutions and the number of optimal solutions obtained for each of the 12 'small-sized' problem sets.

In order to advance the state of the art in algorithms for the generalised assignment problem a benchmark set of relatively large test problems is solved and made publically available to others.

For the more difficult highlycapacitated problems, exact algorithms can only solve problems involving up to a few hundred decision variables before the search trees g r o w prohibitively large.

For each problem type, we generate one problem for each agent/job combination, giving a total of 24 problems.

Since we solve the GAP as a minimisation problem, we changed the sign of the costs in the original data such that all costs become negative and the problems are solved as minimisation problems.

For the 24 'large-size' problems the optimal solutions are not known, except for type A problems for which we were able to obtain the optimal solutions by using the CPLEX general purpose mixed integer solver.

For the Type D problems in particular, the average number of non-duplicate children generated is approximately 3 10 6 before termination, indicating that the solution quality in Type D improves more slowly during the course of a trial than in A genetic algorithm for the generalised assignment problem 23 the other problem types.

In Table 3, we compare the performance of our GA heuristic with other existing heuristic algorithms in terms of the average percentage deviation for each problem set, the average percentage deviation for all problems, the average percentage deviation of the best solutions and the number of optimal solutions obtained for each of the 12 'small-sized' problem sets.

(5/5)

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