Efficient solutions to a class of generalized time-dependent combinatorial optimization problems
MATH'05 Proceedings of the 7th WSEAS International Conference on Applied Mathematics
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Researchers (Gargano and Edelson, 2001) developed several theoretical models to study the use of Genetic Algorithms (GAs) on an interesting category of Optimization Problems [19, 20, 21, 22]. Some of these models were implemented in applications of optimal matroid basis models where the element costs are not fixed, but are time dependent. This problem is an extension of the study and research suggested by DeCicco, 2002 [7, 8, 9, 10]. While DeCicco investigated and researched the Sensitivity Analysis of Certain Time Dependent Matroid Base Models Solved by Genetic Algorithms using single coding technique, I propose to implement a Multiple Genome Coding method with a focus towards determining whether a Multiple Genome Coding with forward, reverse and permutation coding in combination works out better than a single coding in stand-alone mode. I also studied the way the GA self adapts and tends to use different codings at various stages of the search. Also, I focus on determining the most advantageous in terms of number of generations, mean and standard deviation parameters as a metric measure for comparing multiple genome coding. This dissertation study while implementing multiple genome coding focused on three objectives for the purposes of comparing with single coding. First the effectiveness of GAs with respect to each of the genome coding depending on the variations in the cost table is investigated, in comparison with standalone coding. In addition, the multiple genome coding content in each generation is evaluated. All studies involve a benchmark comparison of the GAs against the brute force method. A discount component is introduced in the cost table with no loss of generality, leading to the best fitness calculation as a result of which, a company with two accepted bids is given preferential dispensation under the pay-off option. This algorithm is translated into one for solving the widely known NP-Problem, known as the Rooted Hamiltonian Directed Path and the related conclusions are reported for values of S = 5 to 10, 15 and N = 5 to 10, 15.