4.2 The BA-TLS Framework
4.2.3 Genetic Algorithm Strategy for Robustness Level SelectionSelection
Genetic algorithm [24, 84] is an optimization search procedure which samples the solution space of the problem iteratively and tries to locate a globally optimal solution after examining a limited number of candidates in the solution space.
Effectiveness and efficiency of genetic algorithm comes from its potential to ana- lyze the search space and maintain the traits of the best candidates already found while searching through the state space.
As depicted in Figure 4.2, the genetic algorithm selects a solution providing candidate robustness levels for each flow in five steps, namely, (1) Initialization, (2) Reproductors Selection, (3) Crossover, (4) Mutation Operator and (5) Sub-
4.2 The BA-TLS Framework
stitution. The steps 2-5 are repeated until the solutions converge. Once, the solutions are converged, the algorithm determines a final solution which has the highest fitness value. Now, we discuss each step of our genetic algorithm strategy in detail.
Initialization: In this step, initial candidate solutions are generated. Here, a solution represents a distinct set of selected robustness levels for the flows. Ini- tialization may be done through a random strategy or using thefirst fit scheme.
However, with the random strategy, the candidate solutions are selected without investigating their feasibility. On the other hand,best-fit scheme only selects fea- sible candidate solutions. A solution is feasible if the total number of RBs required to transmit all flows do not surpass the total available RBs (B) at eNodeB. It may be noted that the first fit process is myopically greedy in choosing feasible candi- date solutions and may induce poor overall performance of the genetic algorithm.
On the other hand, random generation may provide good candidate solutions, but the chances for their infeasibility are also high. To ensure a good variety of selected robustness levels in the initial solutions, we have selected 30% of the can- didate robustness levels in the initial configuration by the first-fit method while robustness levels for the rest of the candidates have been generated randomly.
Reproductors Selection: This step identifies the better solutions within a given generation using a metric called Fitness Value (FV). These identified solutions act as reproductors for the creation of a new population. Feasible candidate solutions with relatively higher fitness values are closer to the optimal solution.
The fitness value (F Vz) for the zthcandidate solution is defined as the sum of the rewards of all flows at their selected robustness levels i.e.
F Vz =
N
X
i=1 Li
X
l=1
Ril×xzil (4.4)
It may be noted that FV is same as the expression for the objective function of the ILPin equation 4.3.
Figure 4.3: Single-point Crossover procedure
Crossover: One of the principal motivations towards the use of a genetic al- gorithm approach is to transfer the best traits in the parent solutions to the subsequent candidate generations. This is achieved through the mechanism of crossover where new child solutions are generated by combining parts of the con- figurations from two different parent solutions. For example, in the scenario shown in Figure 4.3, two offspring solutions Oa and Ob have been generated through a crossover operation on the parent solutions Sa and Sb. Here, both Oa and Ob are obtained by combining half of the robustness levels from Sa and remaining fromSb. The Primary goal of the crossover operation is to generate a good variety for a new population. This is typically referred to as “Survival of the fittest”. However, good offspring candidates can only be generated by intel- ligently choosing parents having the best traits. This is achieved by assigning a selection probability to each parent solution based on its goodness/fitness. This work calculates selection probability SPz of the zth candidate using its fitness value as:
SPz = F Vz
P
P
z=1
F Vz
(4.5)
where, P denotes the size of the population.
It may be observed from the above equation that higher the fitness value of a candidate solution, higher will be its selection probability. Then, roulette wheel [24] selection scheme has been used to choose the parents based on their selection probability and traits of the parents are combined to generate new can- didates. As shown in Fig 4.3, the algorithm calculates a single crossover point [85]
4.2 The BA-TLS Framework
on both parents’ and then, a new candidate solution is generated using robust- ness levels from the beginning of the chromosome to the crossover point from one parent, the rest being copied from the second parent. After that, a second child solution is generated from the remaining robustness levels of both the parent so- lutions.
Mutation Operator: It may be noted that just selecting the best solutions based on their fitness values is not enough for obtaining the global maximum reward because the approach may get stuck at a local maxima. The main pur- pose of the mutation operator is to maintain diversity by perturbing the solutions within a population and avoid premature convergence. The mutation operator randomly selects a flow (also called mutation flow) from the candidate solutions and assigns all possible robustness levels to it. Then, the algorithm calculates the fitness values corresponding to all newly assigned robustness levels to the mutation flow. The robustness level which corresponds to highest fitness value is assigned to the mutation flow.
Substitution: The improved solutions which are obtained by the crossover and mutation steps are included in the population, and the solutions which are infea- sible are removed. Then, the algorithm repeats steps 2-5 until the solutions are converged.
GA thus produces good solutions at appreciably lower computational cost with respect to DP. However, insight obtained through a deeper look into the structure of the problem revealed that it is possible to design a poised propor- tionally balanced step by step heuristic solution approach which is capable of providing comparable performance with that of GA while incurring drastically lower computational overheads. This approach, which we call the Proportionally Balanced Robustness-level Allocator (PBRA) is discussed next.