Fitness Evaluation (First Stage)

The fitness value is an indicator of the performance of the solutions. The algorithm sorts the solutions according to the fitness value. This step is the most important part of the algorithm. The objective in the first stage is to cover all site-specific users. Therefore, the fitness value is the number of covered site-specific users, 𝑁_𝑛. A solution is regarded as a better solution if the value of 𝑁_𝑠 is larger. When two solutions have the same values of 𝑁_𝑠, the one with a higher number of covered neutral host users, 𝑁_𝑛, is considered as a better solution. By doing so, when more than one solution that covers all site-specific users, we can select the one with the highest profit. Figure 13 is an example of calculating the fitness values. The small cells from solution 1 in Figure 12 are used. The coordinate of the micro cell is (11,7), and the coordinate of the pico cell is (5,4). The yellow crosses in Figure 13 are the users that are in the coverage of both small cells but cannot access to the small cells due to inter-cell interference. To better demonstrate the example, the sector splitting is not used in the solution description. In this case, 7 site-specific users are served so that the fitness value of the solution is 7.

Figure 13: Fitness value in the first stage

However, the inter-cell interference is able to be reduced. The dynamic power allocation in Section 2.4 is adopted to reduce interference. The micro operator tries all combinations (100%, 80%, 60%, 40% and 20% of the original power of each small cell) to have the highest fitness value. In this case, there are one micro cell and one pico cell so that 5×5 combinations are tried. When the power of the micro cell does not change and the power of the pico cell is set to 80% of the original, the small cells have the highest fitness value. After modifying the power, a site-specific user and a neutral host user are recovered by the micro cell as shown in Figure 14. The black dotted circle is the original pico cell and the black circle is the pico cell after power allocation. Hence, the final fitness value of this solution is 8.

Figure 14: Power adjustment of the example 3.1.4 Offspring Generation (First Stage)

After the fitness values are calculated, the offspring generation is executed. Table 8 lists the fitness value of all the solutions in Figure 12. According to the elite number we set in Table 6, the best two solutions are regarded as elites.The solution of the elites will directly pass to the next generation. Figure 15 is an example of the elite selection. Solution 1 and solution 6 have the two highest fitness value in all 6 solutions so that they will become new solutions in the next generation.

Table 8: Fitness value of the solutions

Figure 15: The elite selection

In the genetic algorithm, each generation has 6 solutions. The elite selection procedure decides two new solutions from the 6 generated solutions. The rest of the new solutions (i.e. 4 new solutions) are generated by the parent selection, the crossover and the mutation. In Table 6, the tournament selection is used in parent selection. Figure 16 shows an example to demonstrate how parents are selected. First, randomly choose two solutions from the 6 solutions. Second, the solution with a higher fitness value is chosen as a father. If the fitness values of the two chosen solutions are the same, the solution that

covers more neutral host users is chosen as a father. If the fitness value and the number of covered neutral host users of the two solutions are all the same, we randomly choose one of the solutions as a father. In this example, solution 3 and solution 4 are chosen. The fitness values of the two solutions are the same so that we compare the numbers of covered neutral host users. Therefore, solution 3 is chosen as a father.

Figure 16: The parent selection

After that, we randomly choose two solutions from the 6 solutions again and compare their fitness values to decide a mother. If solution 1 and solution 2 are chosen, solution 1 is selected as a mother because the fitness value of solution 1 is higher. So far, a set of parents are selected. The parent selection will be executed until 4 sets of parents are generated. Once we have 4 sets of parents, we can generate 4 offsprings by the parents with the crossover and the mutation. Table 9 lists the 4 sets of parents after the parent selection.

Table 9: Four sets of parents after the parent selection

After the parent selection, the crossover is applied to the parents to decide which genes of the parents will be passed to their offsprings. The crossover uses single point method and has a probability 0.5 in Table 6. Figure 17 shows an example of the crossover of the first set of parents. In this case, the father is solution 3 and the mother is solution 1. Because each solution includes two coordinates of small cells, two numbers are randomly generated between 0 to 1 to decide which coordinates are passed to the offspring.

If the first number is larger than 0.5, the first coordinate of the father will be passed to the offspring. Otherwise, the first coordinate of the mother will be passed to the offspring. If the second number is larger than 0.5, the second coordinate of the father will be passed to the offspring. Otherwise, the second coordinate of the mother will be passed to the offspring. Figure 18 shows the results after the crossover of the 4 set of parents.

Figure 17: An example of the crossover of the first set of parents

Figure 18:The crossover of all the parents

After the crossover, the mutation is applied to the offspring. The mutation performs with a uniform method and has a mutation probability 0.1 in Table 6. For example, as shown in Figure 19, the mutation will occur with a 0.1 probability of each gene. When the mutation happens (the red circle), the coordinate (8,2) will be regenerated randomly.

The new coordinate is (12,7) in this example. It is worth noting that the new coordinates do not need to satisfy the constraint as shown in Figure 11. This ensures the solutions have diverse coordinates so that the algorithm searches more solutions instead leading to a local optimal. Figure 20 shows the mutation of all the offsprings.

Figure 19: An example of the mutation

Figure 20:The mutation of all the offsprings

After the mutation, the final offsprings will be the new solutions of the next generation. A generation is finished after generating 6 new solutions as shown in Figure 21. New solution 1 and new solution 2 are generated by the elite selection. The others are generated by the parent selection, the crossover and the mutation. The algorithm will keep generating new generations until it reaches the generation threshold, as shown in Table 6.

Once the algorithm reaches the generation threshold, it records the solution with the highest fitness values. If not all the combinations of small cells are performed by the algorithm, the algorithm will go back to step 1 with those combinations. In this example, the algorithm will go back to step 1 with combination (0,3). After the algorithm is executed over all combination for a given cost, the solution with the highest fitness value will be recorded. If the solution achieves the constraint (all site-specific users are covered), the first stage ends. Otherwise, the algorithm increases the total cost by the cost of the pico cell and goes back to step 0. The new combinations of micro cells and pico cells are calculated. The algorithm will be performed over all possible combinations of small cells.

Figure 21:New solutions after a generation

3.2 The Second Stage of the Genetic Algorithm

Figure 22 illustrates the flowchart of the second stage of the genetic algorithm. Most of the steps in this stage are the same as the first stage. In this section, we only introduce the difference in each step.

Figure 22: Flowchart of the second stage of the genetic algorithm

3.2.1 Parameter Setting (Second Stage)

Same as the first stage, the micro operator will have some information before starting to deploy small cells. The parameter of the genetic algorithm is equivalent to Table 6. The original configuration of the user distribution is the same. The micro operator will also have the final result of the first stage, including the numbers and the positions of micro

included. The cost of the small cells and the revenues of site-specific services and neutral host services are listed in Table 10. The algorithm will be performed over all combinations of small cells for a deployment cost in the second which is represented as the additional cost. The addition cost will increase from 0 by the cost of the pico cell. By doing so, the micro operator can gradually increase the numbers of small cells until the profit stop increasing. In this case, we set the addition cost as 1 so that the micro operator can deploy one additional pico cell to serve neutral host users. According to the cost and revenue, the current profit can be calculated. In this example, there are 9 site-specific users and 4 neutral host users covered by one micro cell and one pico cell. Therefore, the profit is 15 + (4 ∙ 0.2) − (2 + 1) = 12.8 . The profit will be the baseline in the following procedure.

Figure 23: Original configuration in the second stage

Table 10: Parameters of the small cells and the revenues

3.2.2 Solution Initialization (Second Stage)

The representation in the second stage is equivalent to the first stage as shown in Figure 10, and the generation of the initial solutions is similar to the first stage. The objective in the first stage is to cover all site-specific users. The coordinates of the solutions are generated near the hotspots of site-specific users. However, the objective in the second stage is to earn additional profit from neutral host users. The coordinates of the solutions are randomly generated close to the center of the hotspots of neutral host users. The distances between the initial solutions and the nearest hotspot are less than the width of the hotspot of neutral host users. The constraint is similar to the constraint in Section 3.1.2. The only difference is that the hotspots of the site-specific users are changed to the hotspots of neutral host users.

3.2.3 Fitness Evaluation (Second Stage)

Profit maximization is the main consideration in the second stage. Therefore, the fitness value is the profit of the current solution. In addition to the profit, it is important to notice whether all site-specific users are covered because the micro operator needs to

guarantee that all site-specific users are covered. It is assumed that we want to select a better solution from two solutions. If both of them cover all site-specific users, the one with a higher profit will be regarded as a better solution. If only one of the solutions covers all site-specific users, the solution that covers all site-specific users will be regarded as a better solution no matter its profit is higher or lower than the profit of the other one. If both solutions do not cover all site-specific users, the one with a higher profit will be regarded as a better solution. Figure 24 is an example of calculating the fitness value of two solution in the second stage. According to Table 10, the micro operator can deploy one pico cell. As shown in Figure 24 (a), it is assumed that the coordinate of the pico cell is (16,16). In this step, the dynamic power allocation in Section 2.4 is also adopted. However, the micro operator can only adjust the power of small cells that generated in the second stage. In this example, only the power of the pico cell at (16,16) can be adjusted. The micro operator tries all combinations of the power (i.e. 100%, 80%, 60%, 40% and 20% of the original power) to have the highest profit. After adjustment, there are 3 additional neutral host users covered by all the small cells. According to the revenues in Table 10. The profit of the solution is 15 + (7 ∙ 0.2) − (2 + 1 ∙ 2) = 12.4.

As shown in Figure 24 (b), it is assumed that a pico cell is located at (5,7). After power allocation, one additional neutral host user is covered. However, one site-specific user cannot access to the small cells due to interference. In this case, the micro operator does not cover all the site-specific users. Therefore, the solution (a) is better than the solution (b) in Figure 24 regardless of the profit of solution (b).

Figure 24: Two examples of fitness evaluation in the second stage 3.2.4 Offspring Generation (Second Stage)

The offsprings are also generated by the elite selection, the parent selection, the crossover and the mutation. The procedures are all the same as the first stage and the parameters are listed in Table 6. If not all the combinations of small cells are performed by the algorithm, the algorithm goes back to step 1 with the unused combinations of small cells. In this example, the additional cost is 1 so that the micro operator can only deploy small cells with one combination (0,1). After the algorithm is performed over all combinations of small cells, the solution with the highest profit will be compared with the baseline profit. If the profit of the solution is higher than the baseline profit, the numbers and the positions of the small cells of the solution will be recorded, and the profit of the solution will be the new baseline profit. The algorithm will increase the additional cost by the cost of the pico cell and go back to step 0. If the profit of the solution is less than the baseline profit, the algorithm will be terminated. By comparing the baseline profit with the profit of the solutions and updating the baseline profit, the micro operator can maximize its profit.

Chapter 4 PERFORMANCE EVALUATION

In this chapter, we evaluate the performance in terms of profit of the genetic algorithm in three scenarios. The greedy algorithm is adopted for comparison. Parameters of the genetic algorithm we used in this thesis are listed in Table 11. The performance metric is formulated as Eq. (2.5) in Section 2.6. The revenue setting of (𝑅_𝑁, 𝑅_𝑆 ) is introduced in Section 4.1. The simulation results and numerical comparison are described in Section 4.2.

4.1 Three Scenarios

The values of 𝑅_𝑆 and 𝑅_𝑁 are all different in different scenarios. Each scenario may correspond to an actual scene in the real world. We will give a brief introduction to the scenarios in the following paragraph. Table 12 lists the values of the revenues in different scenarios.

Scenario 1: Because the entry barrier to become a micro operator is low, a venue owner can provide services as a micro operator easily. Therefore, a venue owner can serve its people and charge low prices. The venue owner may try to serve neutral host users and charge them at a high price. By doing so, the venue owner can compensate its deployment cost and earn additional profit.

Scenario 2: Besides the fundamental services, the micro operator can provide extra site-specific services (e.g. reliability, security or low latency) to site venues. Hence, the micro operator can take high revenue from the site-specific services. When the micro operator tries to serve neutral host users, it can give some discounts to the users. The MNOs of the users only need to spend little money to buy supplemental services from the

micro operator. Therefore, the revenue from the site-specific services is high and the revenue from the neutral host services is relatively low.

Scenario 3: The micro operator is not a venue owner and only provides fundamental services to site-specific users. The revenue of site-specific services can compensate its deployment cost and have a little profit. The micro operator can also earn additional profit from neutral host users. Therefore, the revenues from site-specific services and neutral host services of scenario 3 are between the revenues of scenario 1 and scenario 2.

Table 11: Parameters of the genetic algorithm

Table 12: Parameters of the scenarios

4.2 Simulation Results of the Three Scenarios

We use the same 15 topologies with different revenues, as shown in Table 12, to deploy small cells. Figure 25 to Figure 27 show the performance in terms of profit of

Figure 25: Simulation results of scenario 1

Figure 26: Simulation results of scenario 2

Figure 27: Simulation results of scenario 3

The orange line represents the genetic algorithm and the blue line represents the greedy algorithm. The genetic algorithm outperforms the greedy algorithm in all scenarios. The result of scenario 1 shows a significant difference between the genetic algorithm and the greedy algorithm. The average absolute difference in profits is 47 and the average percentage difference in profit is 16%. For scenario 2, the performances of the two algorithms are relatively close. The average absolute difference is 16 and the average percentage difference is 4%. For scenario 3, the genetic algorithm also outperforms the greedy algorithm. However, the difference is not that great compared to scenario 1. The average absolute difference is 27 and the average percentage difference is 12%. The performance of the algorithms in different scenarios varies a lot. Table 13 lists the numerical results in different scenarios.

Table 13: Numerical comparison in different scenarios

In simulation, the performance of the two algorithms depends on the revenue of neutral host services and the properties of the algorithms. We give an explanation in an example.

Figure 28: Original configuration

Figure 28 is the original configuration of a simulation result. The users are distributed in an 800m * 800m region. The red dots are site-specific users and the black dots are neutral host users. The distribution and parameters of the users are described in Sector 2.1 and Section 2.6. In the beginning, the micro operator provides service to the site-specific users. Figure 29 is the configuration when the micro operator covers all the site-specific users with the greedy algorithm and the genetic algorithm, respectively.

Figure 29: Configuration when all the site-specific users are covered with (a) the greedy (b) the genetic

The blue dots are the covered site-specific users. The green dots are the covered neutral host users. The black dots are the unserved neutral host users. In the current stage, all the site-specific users are served so that there are no red dots in the figures. The red triangles

and the red crosses are the positions of micro and pico cells, respectively. After covering all the site-specific users, the micro operator provides service to the neutral host users to earn additional profit. Figure 30 to Figure 32 are the deployment results in different scenarios. It is worth noting that the small cells are deployed densely to serve neutral host users in scenario 1. In scenario 2, the number of extra small cells to serve neutral host users are much fewer than scenario 1. In scenario 3, the number of additional small cells are larger than scenario 2 but smaller than scenario 1. Table 14 lists the numerical results of profit in three scenarios. The disparity between the two algorithms is in proportion to the number of deployed small cells. The larger the number of small cells are deployed, the greater the gap of the performance is.

Figure 30: Scenario 1 with (a) the greedy algorithm (b) the genetic algorithm

Figure 31: Scenario 2 with (a) the greedy algorithm (b) the genetic algorithm

Figure 32: Scenario 3 with (a) the greedy algorithm (b) the genetic algorithm Table 14: Numerical results of the example

From Figure 30 to Figure 32, the number of small cells varies a lot. The number of

From Figure 30 to Figure 32, the number of small cells varies a lot. The number of