Energy Saving Maximization of Balanced and Unbalanced Distribution Power Systems via Network Reconﬁguration and Optimum Capacitor Allocation Using a Hybrid Metaheuristic Algorithm

: The main aim of this work was the maximization of the energy saving of balanced and unbalanced distribution power systems via system reconﬁguration and the optimum capacitor’s bank choice, which were estimated by using a new algorithm: modiﬁed Tabu search and Harper sphere search (MTS-HSSA). The results demonstrated that the proposed method is appropriate for energy saving and improving performance compared with other methods reported in the literature for IEEE 33-bus adopted systems, including large scale systems such as IEEE 119 and the IEEE 123 unbalanced distribution system. Moreover, it can be used for unbalanced distribution systems distributed generators (DGs). The results demonstrated that the proposed method (the optimal choice of shunt capacitor (SC) banks and the optimal reconﬁguration via the proposed algorithm) is appropriate for energy saving compared with different strategies for energy saving, which included distributed generation (DG) at different cost levels.


Introduction
The maximization of energy saving of the distribution system is inspired by many strategies, such as a distribution system reconfiguration and optimum capacitor allocation [1][2][3] where allocation of shunt capacitors offered several benefits to the distribution power systems, not only maximizing energy saving but also improving the voltage profile. System reconfiguration can be used to ease the current feeders, therefore, improving the voltage profile of the system and maximizing energy saving. Several investigators have studied the problem of the reconfiguration and allocation of distribution and power systems and the problem of the sizing of shunt capacitors in distribution power systems separately. The analytical algorithms have been used for solving the problem of shunt capacitor allocation in [4,5]. Recently, heuristic algorithms have been widely used for solving this problem. The simulating annealing algorithm (SAA) [6], Tabu search (TS) [7], the genetic algorithm (GA) [8], cuckoo search algorithms [9,10], particle swarm optimization (PSO) [11], the bee colony algorithm [12], the ant colony algorithm [13], and the firefly algorithm [14] were presented to solve the problem of shunt capacitor allocation placement. The firefly algorithm was presented in [15] for solving the same problem in a radial distribution system via loss of the sensitivity factor. Improved harmony algorithms (IHA)

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A novel meta-heuristic algorithm (HSSA-MTS) was investigated to obtain the optimal solution of the energy-saving problem via the optimal choice of SC banks and the optimal reconfiguration, which ensures convergence. The proposed algorithm collects the advantages of MTS and HSSA, e.g., it can solve a mixed integer programming problem for the system reconfiguration. Moreover, the proposed algorithm restricts the trial solution by checking the system to be radial during the reconfiguration process, and the power loss index (PLI) was used to provide a good initial solution for the optimum allocation of capacitors. High convergence probability was achieved because of the use of the hyper-sphere space idea, which closely restricts the searching space.

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The other novelty of this work is that, unlike previous works about energy saving for unbalanced distribution systems, which were only concerned with the solved reconfiguration problem, the proposed algorithm was used for maximization of energy saving of the unbalanced distribution system via the optimal choice of SC banks and the optimal reconfiguration. Additionally, it was used for unbalanced distribution systems with the presence of distributed generators (DGs).

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The results demonstrate that the proposed method is appropriate for energy saving and improving performance compared with other methods reported in the literature for IEEE 33-bus adopted systems, including large scale systems such as IEEE 119 and the IEEE 123 unbalanced distribution system. Additionally, the results demonstrate that the proposed method (optimal choice of SC banks and optimal reconfiguration via the proposed algorithm) is appropriate for energy saving compared with different strategies for energy saving that included distributed generation (DG) at different cost levels.
The article is organized as follows. Section 1 provides an overview of the approaches and methodologies of maximization of energy saving of the distribution system. Section 2 describes the problem formulation and a new algorithm: modified Tabu search and Harper sphere search. In Section 3, the proposed method is applied and the obtained results are discussed. Section 4 estimates the conclusions of the study.

Materials and Methods
The proposed route, which is described in this section, was used for the maximization of energy saving in different distribution power systems via the system reconfiguration and optimum capacitor's bank choice. The balanced distribution power systems had different sizes such as IEEE 33 and a large number of buses in IEEE 119. The proposed route can be Energies 2021, 14, 3205 4 of 24 applied to unbalanced distribution power systems such as the IEEE 123 distribution power system. In the next section, these systems are modified based on the proposed algorithm to ensure its effectiveness.

Objective Function Definition
The main objective of optimal allocations, sizing of shunt capacitors, and feeder reconfiguration of the distribution system is to minimize the annual energy losses, which is the objective function. This is formulated in Equation (1) [17,41].
where To obtain the optimal solution, the following conditions should be achieved: 1.
Real power and reactive power constraints. The power flows of the slack bus must be balanced with the generated power and the load demand.

2.
Injection reactive power constraint. Constraint (4) states the boundary condition of the reactive power limit: 3.
Voltage magnitude constraints.

4.
Current of lines constraints.

MTS-HSSA Algorithm for Optimum Operation of Distribution System
The Tabu search algorithm was used to find the best solution for system reconfiguration problems [28], and this problem was very confident with this method. The standard Tabu search algorithm is described in Appendix A. HSSA, which is described in Appendix B, achieved the best solutions for optimal allocations and the sizing of shunt capacitors (Xc) in [18]. This section explains a compound algorithm between three methods, which were the power loss index, the HSSA algorithm, and the Tabu algorithm, to find the best values of (Xr) and (Xc). The complete flow chart of the proposed algorithm is shown in Figure 1. Also, the following steps describe the proposed algorithm to find (Xr) and (Xc), which minimize the cost function in Equation (1) Step 1: Estimate the set of the distribution power system configuration Ω [28].
where Ω 1 : set of the sectionalizing switches. Ω 2 : set of the switches of tie lines.
Step 2: Input initial values of Tabu parameters and initial solutions of X r .
Step 3: Choose a tie line (T) for the exchange operation.
Step 4: Execute a branch exchange between a tie line T and a branch P.
is not incident to bus no (j).
Step 6: Check if the system is still radial after step 4 as follows: Go to the next step, or else go to step 3.
Step 7: Calculate the cost function for the current configuration using a power flow study via the Newton-Raphson method.
Step 8: Move the current solution to the best one in the candidate neighborhood while meeting the Tabu restriction and update the Tabu list.
Step 9: Go to step 10 if the stop criterion is satisfied. Otherwise, return to step 3.
Step 10: Restore the best reconfiguration of the distribution power system.
Step 11: Calculate the power loss index for all buses via the next equation [17]: P Losses , i: power losses of line i. P max : maximum real power reduction through all buses. P min : minimum real power reduction through all busses.
Step 12: Estimate the initial location of the capacitors corresponding to the buses with the highest PLI values and initialize particle values via step 11.
Step 13: Initial set of solutions (particles) are generated randomly X ci (X ci,min :X ci,max ) and Nsc hyper-sphere centers (HSCs) are selected corresponding to the smallest values of the objective function [18].
The initial set of solutions is generated randomly in the specified band. For each solution (particle) and N-dimensional problem, each particle is 1 *N vector, (p 1 , p 2 , . . . , p N ). The following items should be defined: Two parameters of the dummy process, which are zeta and the number of dummy particles/iteration.
Step 14: Each particle is represented by using spherical coordinates (r, θ, and ϕ), which are shown in Figure A2 (Appendix B). Npop particles are reproduced, and the stay particles are allocated surrounded by HSCs via the -sphere centers dominance [18]. The particles were divided proportionally so the normalized dominant sphere center (D sc ) is defended as follows: where OFD sc : objective function difference, which is: The number of particles among hyper-spheres is calculated according to Equation (11).
where N pop is the number of the initial population. The initial number of particles is chosen randomly by each sphere center from the remaining particles.
Step 15: The position of particles is changed via probability Pr angle and r (r min , r max ). Figure A2 shows the searching region of the particle (dashed-space) The procedure of searching is achieved through moving in a (r, θ, ϕ) dimension, as shown in Figure A2. θ and ϕ varied uniformly between (0, 2π) and reproduced a new movement of the particle. These angles (θ and ϕ) varied with the probability Pr angle for each iteration.
Step 16: The sphere centers with the largest value of the objective function should be varied. The dummy particle is shown in Figure A3 (Appendix B). It should have been allocated to a new sphere center via a set of objective functions (SOF). Dummy particles re selected to look for the new sphere centers via the assignment probability (AP) of the sphere centers.
The AP is given by the next Equation: where Step 17: The particles (N newpar ) with the worst are eliminated. Such particles are r placed by a new group of particles with the same number N newpar described in step 14.
Step 18: Go to step 19 if the stop criterion is satisfied. Otherwise, return to step 14.

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The proposed route was applied to one of the distribution power systems with a large 265 number of buses to ensure its effectiveness. This system was a 119 IEEE distribution power 266 system and its data is contained in [27]. There is a scarcity of references that have used a 267

Results and Discussion
The proposed route was applied to one of the distribution power systems with a large number of buses to ensure its effectiveness. This system was a 119 IEEE distribution power system and its data is contained in [27]. There is a scarcity of references that have used a large distribution system for optimal reconfiguration and capacitor allocation simultaneously, so model 33 IEEE [55] had to be used to conduct the comparison process.
The Newton-Raphson method was used to study the flow of power and to calculate the total lost power in the lines of 33 IEEE and 119 IEEE systems; the base data is tabulated in The cost calculations can be recalculated based on Equation (1) and the data of Tables 1 and 2. The proposed method, which is explained in detail in the previous section of this article, was applied. Its outputs are included in Table 3 as follows: 1.
The reconfiguration only of IEEE119 and IEEE 33 power distributions systems; 2.
The optimal places and values of capacitors only of IEEE119 and IEEE 33 power distributions systems; 3.
The reconfiguration and optimal places and values of capacitors simultaneously of the IEEE119 and IEEE 33 power distributions systems.
The IEEE 33 system consisted of 37 switches; switches from 1 to 32 are normally closed, and switches from 33 to 37 are open. This system had a V nominal = 12.66 kV with the V min = 0.9 pu and the V max = 1.0 pu The best open switches and optimal capacitor allocations for case 1, case 2, and case 3 to minimizes the objective in Equation (1) are given in Table 3. The voltage profile and the VSI profile were improved for the 33-bus at different cases via the proposed algorithm, as shown in Figure 2. Additionally, the maximum voltage deviation and voltage deviation index were reduced. Power losses and energy costs were reduced for three modified IEEE 33 systems SC only, reconfiguration only, and SC with reconfiguration) via the proposed algorithm. It was noticed that the performance of the IEEE 33 system with reconfiguration via the MTS-HSSA algorithm was better than its performance with the optimal choice of capacitors. The IEEE 33 system with reconfiguration and optimal choice of capacitors.  The IEEE 33 system consisted of 37 switches; switches from 1 to 32 are normally 287 closed, and switches from 33 to 37 are open. This system had a Vnominal = 12.66 kV with the 288 Vmin =0.9 pu and the Vmax = 1.0 pu The best open switches and optimal capacitor 289 allocations for case 1, case 2, and case 3 to minimizes the objective in Equation (1) are given 290 in Table 3. The voltage profile and the VSI profile were improved for the 33-bus at 291 different cases via the proposed algorithm, as shown in Figure 2. Additionally, the 292 maximum voltage deviation and voltage deviation index were reduced. Power losses and 293 energy costs were reduced for three modified IEEE 33 systems SC only, reconfiguration 294 only, and SC with reconfiguration) via the proposed algorithm. It was noticed that the 295 performance of the IEEE 33 system with reconfiguration via the MTS-HSSA algorithm 296 was better than its performance with the optimal choice of capacitors. The IEEE 33 system 297 with reconfiguration and optimal choice of capacitors  The performance of the distribution power system can be estimated by using the 305 voltage deviation (VD) index [56,57], which was calculated by using Equation (16).
The voltage stability index (VSI) was used for monitoring the stability of the 307 distribution power system and detecting the weak buses. It can be calculated by using 308 Equation (17).
via the MTS-HSSA algorithm gave the best performance compared with the other 310 cases. 311 The modified systems were compared with previous works at six cases, which are: 312 Case1: IEEE 33 system with reconfiguration only, as shown in Table 4. 313 Case 2: IEEE 33 system with capacitor allocation only, as shown in Table 5 314 Case 3: IEEE 33 system with reconfiguration and capacitor allocation, as shown in 315 Table 6. 316 Case 4: IEEE 119 system with reconfiguration only, as shown in Table 7 317 Case 5: IEEE 119 system with capacitor allocation only, as shown in Table 8 318 Case 6: IEEE 119 system with reconfiguration and capacitors allocation, as shown in 319 Table 9. 320 The comparison in Tables 4, 5, and 6 shows the effectiveness of the proposed method 321 for three cases (1, 2, and 3) in terms of total power losses, minimum voltage, and energy-322 saving total power losses for case 1, case 2, and case 3 via the proposed algorithm was the 323 lowest when compared to the other best previous algorithms. Moreover, the proposed 324 method achieved a clear increase in the value of energy savings compared to the other 325 methods, as evidenced by Figure 3. The IEEE 33 system with reconfiguration and optimal 326 choice of capacitors via the MTS-HSSA algorithm provided the best energy saving 327 compared with the other algorithms. On the other hand, it provided the lowest value of 328 maximum voltage deviation. 329   The performance of the distribution power system can be estimated by using the voltage deviation (VD) index [56,57], which was calculated by using Equation (16).
The voltage stability index (VSI) was used for monitoring the stability of the distribution power system and detecting the weak buses. It can be calculated by using Equation (17).
via the MTS-HSSA algorithm gave the best performance compared with the other cases. The modified systems were compared with previous works at six cases, which are: Case 1: IEEE 33 system with reconfiguration only, as shown in Table 4. Case 2: IEEE 33 system with capacitor allocation only, as shown in Table 5. Case 3: IEEE 33 system with reconfiguration and capacitor allocation, as shown in Table 6. Case 4: IEEE 119 system with reconfiguration only, as shown in Table 7. Case 5: IEEE 119 system with capacitor allocation only, as shown in Table 8. Case 6: IEEE 119 system with reconfiguration and capacitors allocation, as shown in Table 9.    The comparison in Tables 4-6 shows the effectiveness of the proposed method for three cases (1, 2, and 3) in terms of total power losses, minimum voltage, and energy-saving total power losses for case 1, case 2, and case 3 via the proposed algorithm was the lowest when compared to the other best previous algorithms. Moreover, the proposed method achieved a clear increase in the value of energy savings compared to the other methods, as evidenced by Figure 3. The IEEE 33 system with reconfiguration and optimal choice of capacitors via the MTS-HSSA algorithm provided the best energy saving compared with the other algorithms. On the other hand, it provided the lowest value of maximum voltage deviation.      Table 3. 341 The performance of the distribution power system can be estimated by using the 342 voltage deviation index [57], which is calculated by using Equation (16). The voltage 343  The main objective of this study was to maximize the energy saving of large power systems such as the IEEE 119 system, which consists of 133 switches; switches 1 to 118 are normally closed, and 119 to 133 are open. This system had a V nominal = 11 kV with the V min = 0.9 and V max = 1.0 The best open switches and optimal capacitor allocation for case 4, case 5, and case 6 to minimize the objective in Equation (1) are provided in Table 3. The performance of the distribution power system can be estimated by using the voltage deviation index [57], which is calculated by using Equation (16). The voltage stability index is used for monitoring the stability of the distribution power system and detecting the weak buses. It can be calculated by using Equation (17) The voltage profile and the VSI profile were improved for the 119-bus at different cases via the proposed algorithm shown in Figure 4. Additionally, the maximum voltage deviation and the voltage deviation index were reduced. Power losses and energy costs were reduced for the three modified IEEE 119 systems (SC only, reconfiguration only, and SC with reconfiguration) via the proposed algorithm. It was observed that the performance of the IEEE 119 system with reconfiguration via the MTS-HSSA algorithm was better than its performance with the optimal choice of capacitors. Moreover, the IEEE 119 system with reconfiguration and optimal choice of capacitors via the MTS-HSSA algorithm provided the best performance compared with the other cases.     The comparison in Tables 7-9 shows the effectiveness of the proposed method for the three cases and is also shown in Figure 5. The proposed algorithm achieves energy-saving better than the best previous algorithms, especially in case 6, as evidenced by Figure 5c. The IEEE 119 system with reconfiguration and optimal choice of capacitors via the MTS-HSSA algorithm provided the best energy saving compared with the other algorithms. On the other hand, it provided the lowest value of maximum voltage deviation, as shown in Figure 5d. In this case, the percentage of energy-saving via the MTS-HSSA algorithm increased 33.649% more than the best one. The comparison in Tables 7, 8, and 9 shows the effectiveness of the proposed method 362 for the three cases and is also shown in Figure 5. The proposed algorithm achieves energy-363 saving better than the best previous algorithms, especially in case 6, as evidenced by 364 Figure 5c. The IEEE 119 system with reconfiguration and optimal choice of capacitors via 365 the MTS-HSSA algorithm provided the best energy saving compared with the other 366 algorithms. On the other hand, it provided the lowest value of maximum voltage 367 deviation, as shown in Figure 5d. In this case, the percentage of energy-saving via the 368 MTS-HSSA algorithm increased 33.649% more than the best one.   In Figures 6 and 7 an economic comparison was made between the proposed method and different strategies for energy saving, which included distributed generation. The cost calculations and data contained in [58] were used to calculate the energy saving for different methods. This data could be applied only to the specified case (the cost per KWh was $0.057). It was clear that, in this case, the proposed method was the best out of all to save the cost of energy for each of the model IEEE 33 and IEEE 119 systems. The cost per Kwh was $0.035 for another study case [59]. In this case, although the energy saving was better, the proposed method was the best out of all to save the cost of energy for each of the model IEEE 33 and IEEE 119 systems. Furthermore, it can also be extended for many maximization of energy saving strategies such as networks with soft open points and distributed generation [60]. The cost of distributed generation units has a wide range variation via the uncertainties of renewable energy source generation and energy demand [61,62]; it needs more study in the future to estimate general objective function to apply the proposed algorithm.
was $0.057). It was clear that, in this case, the proposed method was the best out of all to 381 save the cost of energy for each of the model IEEE 33 and IEEE 119 systems. The cost per 382 Kwh was $0.035 for another study case [59]. In this case, although the energy saving was 383 better, the proposed method was the best out of all to save the cost of energy for each of 384 the model IEEE 33 and IEEE 119 systems. Furthermore, it can also be extended for many 385 maximization of energy saving strategies such as networks with soft open points and 386 distributed generation [60]. The cost of distributed generation units has a wide range 387 variation via the uncertainties of renewable energy source generation and energy demand 388 [61][62]; it needs more study in the future to estimate general objective function to apply 389 the proposed algorithm. 390 391 Figure 6 Comparison of % energy savings for the IEEE   The proposed route was applied to one of the unbalanced distribution power 398 systems. This system was an IEEE 123 distribution power system, and its data is contained 399 in [63] and its base data is tabulated in Table 10. The proposed route was also applied to 400 the unbalanced distribution power systems influenced with DGs, which can be taken as a 401 constant value and which were integrated at the weak buses according to a penetration 402 level of 20%, as presented in [45]. The results of the proposed mathematical analysis of the 403 IEEE 123 distribution power system were placed in Table 11. 404  The proposed route was applied to one of the unbalanced distribution power systems. This system was an IEEE 123 distribution power system, and its data is contained in [63] and its base data is tabulated in Table 10. The proposed route was also applied to the unbalanced distribution power systems influenced with DGs, which can be taken as a constant value and which were integrated at the weak buses according to a penetration level of 20%, as presented in [45]. The results of the proposed mathematical analysis of the IEEE 123 distribution power system were placed in Table 11.  The comparison in Table 12 shows the effectiveness of MTS-HSSA for the IEEE 123 unbalance system with and without DG integration in terms of total power losses, minimum voltage, and energy-saving. Total power losses via the proposed algorithm were the lowest, and the proposed method achieved a clear increase in the value of energy savings compared to the other methods, as evidenced by Figure 8. The IEEE 123 system with reconfiguration and optimal choice of capacitors via the MTS-HSSA algorithm provided the best energy saving out of all the algorithms. However, it provided the lowest value of maximum voltage deviation, and the voltage profile was improved for the 123-bus in different cases as shown in Figure 9.

453
This study investigated a compound algorithm (MTS-HSSA) for reconfiguration and 454 capacitor allocation of distribution power systems. The MTS-HSSA algorithm was 455 explained in the previous section and has many advantages. The MTS-HSSA algorithm 456 has a variable size of the reconfiguration problem for escaping from cycling and a local 457 minimum. The MTS-HSSA algorithm restricts the trial solution by checking the system to 458 be radial during the reconfiguration process. The results demonstrate that the proposed 459 method is appropriate for energy saving and improving performance compared with 460

Conclusions
This study investigated a compound algorithm (MTS-HSSA) for reconfiguration and capacitor allocation of distribution power systems. The MTS-HSSA algorithm was explained in the previous section and has many advantages. The MTS-HSSA algorithm has a variable size of the reconfiguration problem for escaping from cycling and a local minimum. The MTS-HSSA algorithm restricts the trial solution by checking the system to be radial during the reconfiguration process. The results demonstrate that the proposed method is appropriate for energy saving and improving performance compared with other methods reported in the literature for IEEE 33-bus adopted systems, including large scale systems such as IEEE 119 and the IEEE 123 unbalanced distribution system. Moreover, the results demonstrate that the proposed method (the optimal choice of SC banks and the optimal reconfiguration via the proposed algorithm) is appropriate for energy saving compared with different strategies for energy saving, which included distributed generation (DG) at different levels of cost. In the proposed method, the power loss index was used to provide a good initial solution to the optimum allocation capacitor. The hyper-sphere space idea (HSC and its particle) in the proposed algorithm achieved the high convergence probability because of the space of searching was closely restricted.
From the comparison results, the following conclusions can be drawn: the effectiveness of the modified system in terms of low power losses (56.78% reduction for the IEEE 119 bus) improved the voltage level (minimum voltage (0.9602 pu for the IEEE 119 bus), and the modified system had the lowest annual cost of energy losses (50.64% net saving for the IEEE 119 bus). For the IEEE 119 distribution system with reconfiguration and shunt capacitor allocation, the percentage of energy-saving via the MTS-HSSA algorithm increased 33.649% more than the MFPA method. Additionally, the effectiveness of the modified system was demonstrated for unbalanced systems (IEEE 123) in terms of the reduction in power losses, the improvement in voltage level, and the reduction in annual cost of energy losses. For the IEEE 123 distribution system with reconfiguration and shunt capacitor allocation, the percentage of energy-saving via the MTS-HSSA algorithm increased about 70% more than the Pareto-optimization-based NR method.
End while. The above actions are repeated up to the maximum iteration number. The modified TS algorithm is described in the following section. It has the variable size to escape from cycling and the local minimum. The hyper-spherical search algorithm is investigated for the optimum solution to 520 different problems [65], and it is used for the optimum choice of shunt capacitors in 521 distribution power systems [18]. In this algorithm, the solutions are generated randomly 522 in the specified band. For each solution (particle), and for each N-dimensional problem, 523 Figure A1. Tabu search flowchart.

Appendix B Overview of the Hyper-Spherical Search Algorithm
The hyper-spherical search algorithm is investigated for the optimum solution to different problems [65], and it is used for the optimum choice of shunt capacitors in distribution power systems [18]. In this algorithm, the solutions are generated randomly in the specified band. For each solution (particle), and for each N-dimensional problem, each particle is 1 x N vector, (p 1 , p 2 , . . . , p N ). The number of particles among hyper-spheres is distributed accordingly.
A better solution will be sought in spherical coordinates, and this is done by repositioning the particles. We found that the spherical coordinates of the solution change by changing both the radius and the angle in the predetermined framework. Each particle is represented by using spherical coordinates (r, θ, and ϕ), which are shown in Figure A2. Each point has N-1 angles in N-dimension space in spherical coordinates, as shown in Figure A2. Each point has two angles in three-dimensional space. The position of particles is changed via probability Pr angle and r (r min , r max ) [65]. Figure A2 shows the searching region of the particle (dashed-space); the procedure of searching is achieved through moving in a (r, θ, ϕ). θ and ϕ varied uniformly between (0, 2π), reproducing a new movement of the particle. These angles (θ and ϕ) were varied with the probability Pr angl for each iteration. After the total objective function was calculated for all particles, the SCs with the largest value of the objective function should be varied. The dummy particle [65] is shown in Figure A3. It should be allocated to a new SC via a set of objective functions (SOF). Dummy particles are selected to look for the new SC via the assignment probability of the SCs. Dummy particles that have the worst set objective function (SOF) ( Figure A3) were selected to look for the new SC via the assignment probability. Then, the worst particles were eliminated, and new particles were generated until the best one was reached. The complete flow chart of the HASSA algorithm is shown in Figure A4. objective function (SOF) ( Figure B2) were selected to look for the new SC via the 541 assignment probability. Then, the worst particles were eliminated, and new particles were 542 generated until the best one was reached. The complete flow chart of the HASSA 543 algorithm is shown in Figure B3. 544 545 Figure B1. The searching region of the particle (dashed-space). 546 547 Figure B2. Dummy particle recovery.
548 Figure A2. The searching region of the particle (dashed-space).
, 14, x FOR PEER REVIEW 22 of 26 objective function (SOF) ( Figure B2) were selected to look for the new SC via the 541 assignment probability. Then, the worst particles were eliminated, and new particles were 542 generated until the best one was reached. The complete flow chart of the HASSA 543 algorithm is shown in Figure B3.