Fig 1.
A Virtual Data Center (VDC) has at least 2 physical data centers composed by 2 server nodes.
A combination of 3 or more VDC’s is a geographic Region.
Fig 2.
Computing provider’s distributed over a network of machines with the respective published service’s and available nodes.
Fig 3.
A sample cost matrix for 4 nodes and the Euclidian distance between each pair of nodes.
Table 1.
Solution sample of valid and invalid candidates for a given string schema.
Fig 4.
Diagram representation for the many categories of computational complexity.
Fig 5.
Hamiltonian cycle from a super graph.
Table 2.
Cost matrix for graph G with 5 nodes.
Fig 6.
Example of Hamiltonian and Eulerian graphs.
Fig 7.
Generating 2-opt moves.
Fig 8.
Temperature decay relative to the iterations of the SA algorithm.
Fig 9.
Simulated annealing algorithm flowchart.
Fig 10.
Chromosome for a sample of individual candidate solutions.
Fig 11.
Offspring representation for the genetic algorithm mutation and crossover operators.
Fig 12.
Basic genetic algorithm.
Fig 13.
Ant colony pheromone representation.
Fig 14.
Entropy decrease process.
Table 3.
Relation between the level of uncertainty and knowledge about possible string outcomes.
Fig 15.
Entropy H(X) vs Probality Pr(X = 1).
Fig 16.
The probability density function for cost function g(X).
Fig 17.
The normal distribution with mean 49.65 and standard deviation 0.91.
Then P (X<48; X < min g(X)) = 0.0349.
Table 4.
Statistical metrics for function g(X) distribution.
Table 5.
Example of representation of strings X1 and X2 using substring Y.
Fig 18.
Examples of representations of a given input string set using regex and an automaton.
Fig 19.
Maximization of entropy in random events.
Table 6.
Yield returns from bernoulli process P(1) and P(0).
Fig 20.
Flowchart for the Quantitative TSP algorithm based in information theory.
Table 7.
Proposed pseudo-code algorithm to solve the TSP.
Table 8.
Example calculation for the Kelly criterion for P (1) = 90, 50 and 10 and net-odds b = 1.
Fig 21.
Decision Criterion 1 is implemented as an evaluation of the IF logical statement for the Simulated Kelly Criterion and the Uniform Random Number output value.
Fig 22.
P(X) for the Bernoulli distribution with P(1) = 0.2 and P(0) = 1—P(1) = 0.8.
Table 9.
Examples of random events and the respective binary outcome.
Fig 23.
Decision Criterion 2 is implemented as a OR gate using the input bernoulli distribution Trial B and The output A of the IF statement from the Simulated Kelly Criterion and the uniform random number output value.
Fig 24.
TSP target objectives.
Table 10.
Auxiliary theorems for the proposed model based in information theory.
Fig 25.
Utility function.
Fig 26.
Tour construction for a weighted graph with a probability function p ∈ [0,1].
Fig 27.
Candidate solution production and path decision.
Fig 28.
Edge crossing between nodes.
Fig 29.
Hill-Climbing problem.
Table 11.
Classes of computational complexity.
Table 12.
Subset of the simulation results for 50 nodes with trial length of N = 60.
Fig 30.
QA sample: Normal distribution for n = 50 and N = 60.
Fig 31.
Histogram for the initial tour cost in the QA method.
Fig 32.
QQ-Plot for the initial tour cost in the QA method.
Fig 33.
SA Sample: Normal distribution for n = 50 and N = 60.
Fig 34.
Histogram for the initial tour cost in the SA method.
Fig 35.
QQ-Plot for the initial tour cost in the SA method.
Fig 36.
Boxplot for the QA simulation.
Fig 37.
Boxplot for the SA simulation.
Table 13.
Node coordinates with size n = 20.
Table 14.
Node coordinates with size n = 30.
Table 15.
Node coordinates with size n = 50.
Fig 38.
Chart with results for test cases with n = 20 nodes with sample size N = 60.
Fig 39.
Chart with results for test cases with n = 30 nodes with sample size N = 60.
Fig 40.
Chart with results for test cases with n = 50 nodes with sample size N = 60.
Table 16.
T-test for n = 20 nodes and N = 60 trials–total distance cost variable.
Table 17.
T-test for n = 20 nodes and N = 60 trials—execution time variable.
Table 18.
T-test for n = 30 nodes and N = 60 trials–total distance cost variable.
Table 19.
T-test for n = 30 nodes and N = 60 trials—execution time variable.
Table 20.
T-test for n = 50 nodes and N = 60 trials–total distance cost variable.
Table 21.
T-test for n = 50 nodes and N = 60 trials—execution time variable.
Table 22.
Execution results for 20 nodes (n = 20) with samples size N = 60.
Table 23.
Execution results for 30 nodes (n = 30) with samples size N = 60.
Table 24.
Execution results for 50 nodes (n = 50) with samples size N = 60.
Table 25.
Comparison matrix for the two-tailed t-test independent means p-values for the test cases with nodes with n = 20, 30, 50 and sample size N = 60.
Fig 41.
Example of TSP applications.