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Computational experiments are conducted to study the performance of the integer program and the solution algorithms.
Therefore, from the results of Theorems 1 and 2, we can obtain the solution of the integer program given in Equation 8 in polynomial time.
Comparison of the solution quality of the integer program IP (CPLEX solver, running time limited to 12 hours) and the greedy set cover algorithm on proteomes of different species, and epitope length settings.
We let I be the solution of the integer program and let e∈ I denote that in I there exists a color j such that s e, j =1 We start by initializing a set S with the two nodes of an edge e∈ I.
Comparison of the solution quality of the integer program (IP), integer multicover (IP MC), the greedy set cover (Greedy) and multicover (Greedy MC, s cov = 1; s mcov = 10 ), integer maximization multicover (IP MC, cost max was set to result of Greedy MC), algorithm on different pathways (subsets of the Homo sapiens proteome), and epitope length settings.
The solutions of the integer program delivered by the industry standard ILP solver CPLEX after a limited running time of 12 hours were, not surprisingly, superior to the solutions provided by the greedy algorithm on all tested proteomes and epitope-length combinations (see Table 2).
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The accuracy of the integer programming approach is compared to existing reaction elimination methods.
The run time of this method was compared with that of the integer programming implementation of the MMSE-optimal algorithm.
In this paper, we show that one can reduce the size of the integer programming formulation to O(nm) triangle inequalities.
Hence, one of the integer programming formulations for the VRP can be written as follows: min ∑ i = 0 n ∑ j = 0 n c ij x ij Open image in new window (3).
To obtain mathematically proven optimal solutions of the integer programming formulation, the CPLEX commercial optimization solver was used.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com