CN115801072B - Analog-to-digital converter precision distribution method of network-assisted full duplex system - Google Patents
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Abstract
The invention relates to an analog-to-digital converter precision distribution method of a network-assisted full duplex system, belonging to the technical field of mobile communication. Aiming at the problem of the joint optimization of the frequency spectrum efficiency and the energy efficiency of an uplink non-cellular system with a low-precision analog-to-digital converter equipped with a base station antenna, the method based on the non-dominant genetic algorithm is provided for joint optimization of the frequency spectrum efficiency and the energy efficiency under the constraint of user service quality and total quantization bit, and the problem that the non-convex optimization problem is difficult to solve is solved. The algorithm can quickly solve the quantization precision selection scheme of the low-precision analog-to-digital converter, which maximizes the system spectrum efficiency and energy efficiency, obtains better performance than equal-precision quantization bit allocation, has lower complexity compared with the traditional convex optimization method, and is suitable for other various full-duplex and half-duplex systems.
Description
Technical Field
The invention relates to a low-precision ADC quantization bit number distribution method based on a non-dominant genetic algorithm in a network-assisted full-duplex large-scale MIMO system, belonging to the technical field of mobile communication.
Background
In a network-assisted full duplex massive MIMO system, a plurality of RAUs having a plurality of antennas are densely distributed in one area and connected to a common central processor which performs baseband processing. In one time slot, each RAU may perform uplink or downlink transmission, and different radio access units may have different choices, which enable downlink transmission and uplink reception to occur simultaneously on the same frequency band, in-band full duplex may be achieved with a half duplex base station. In this system, since uplink reception and downlink transmission are performed simultaneously, the downlink transmission interferes with the uplink reception, resulting in interference between RAUs. Although the interference between RAUs can be controlled by the geographical separation part, this interference is still a major factor in reducing the uplink rate, and interference cancellation plays a vital role in improving the spectral efficiency. One common method of interference cancellation is to reconstruct the interference, subtracting the reconstructed interference signal from the received signal to perform interference cancellation, so that a beamforming training mechanism is required to obtain channel state information between the downlink RAU and the uplink RAU, so as to cancel the interference.
For a network-assisted full duplex massive MIMO system employing a large antenna array and a plurality of analog-to-digital converters, although the system has significant performance gain, as the number of antennas increases, the hardware complexity and power consumption of the ADC increase exponentially with the number of quantization bits, and the capacity requirement of the backhaul link between the RAU and the CPU increases linearly with the number of quantization bits, which causes problems of high total power consumption, expensive hardware and large-scale data processing. The use of low precision analog-to-digital converters in network-assisted full duplex massive MIMO systems can reduce energy consumption, hardware costs and load of the backhaul link, but will bring about a reduction in spectral efficiency. There is therefore a need to jointly optimize the spectral efficiency and the energy efficiency in this scenario by means of the RAU quantization bit allocation method.
The simplest quantization bit allocation method is equal precision allocation, i.e. each RAU is allocated the same number of quantization bits regardless of the quality of the channel between the RAU and the user. Although this allocation method is simple and easy, it is not ideal when the quality of the communication channel between each RAU and the user is large. For this reason, a quantization bit allocation method having adaptivity needs to be considered. Most quantization bit allocation methods consider only one of spectral efficiency and energy efficiency and have never been done in network-assisted full duplex systems. In order to jointly optimize the spectral efficiency and the energy efficiency of the network-assisted full-duplex large-scale MIMO system, the quantized bit allocation vector on the RAU is rapidly obtained, and the quantized bits are necessarily optimized by combining intelligent algorithms such as genetic algorithm and the like.
Disclosure of Invention
Technical problems: aiming at the problem of low-precision ADC quantized bit allocation for jointly optimizing the frequency spectrum efficiency and the energy efficiency in a network-assisted full-duplex large-scale distributed MIMO system, the invention provides an analog-to-digital converter precision allocation method of the network-assisted full-duplex system under the constraint of uplink service quality and the total number of quantized bits so as to jointly optimize the frequency spectrum efficiency and the energy efficiency.
The technical scheme is as follows: in order to achieve the above purpose, the method for distributing the precision of the analog-to-digital converter of the network-assisted full duplex system adopts the following technical scheme:
step 1, establishing a system spectrum efficiency and energy efficiency joint maximization problem, which specifically comprises the following steps:
setting a spectrum efficiency function:
wherein,
for the transmission rate of the kth downstream user, is->For the transmission rate of the kth upstream user,
respectively N RAUs and K dl ADC precision equipped at each downstream user, T is system coherence time, T ul T is the number of symbols for uplink transmission dl Is the number of symbols for downlink transmission, wherein, < ->Representing a mathematical expectation of a random variable, a random vector or a random matrix, (. Cndot.) H Representing the conjugate transpose of the matrix or vector,indicating effective downlink interference channel between jth uplink and kth downlink users obtained through beamforming training mechanism during channel estimation>Mu is k,i Is a minimum mean square error, MMSE, estimate, +.>To estimate the error s i Is the signal transmitted by the ith downlink user, x j Is the signal sent by the j-th uplink user; />For all remote access units RAU to kth user channels, M represents the number of antennas on each RAU, N dl Represents the number of downlink RAUs, K represents the total number of users, Kul for the number of upstream users, Kdl for the number of downstream users>Representing a complex matrix or vector with a number of rows m and a number of columns n. u (u) t,k,j Is the interference channel between the jth uplink and kth downlink users; w (w) i Is the precoding vector of the ith downlink user. P is p dl/ul,i Is downlink or uplink transmission power, +.>Representing the variance of the zero-mean additive noise of the downstream gaussian channel; zeta type toy k Is the coefficient related to the quantization accuracy of the kth downstream user ADC. />Correlation matrix representing downstream quantization noise, n q,dl,k Representing the quantization noise of a low-precision ADC,
is the transmission rate of the kth upstream user, wherein,representing a diagonal matrix, alpha, associated with low-precision quantization precision n ADC accuracy b equipped with nth RAU n Related accuracy parameters, I M Representing an identity matrix with dimensions M +.>Is the MMSE channel estimation vector from the ith uplink user to all RAUs, N ul Representing the number of uplink RAUs; />Representing channel estimation error, +.>Conjugate transpose of the receiver vector representing the kth upstream user signal,/or->Is the estimation error of the equivalent interference channel between RAUs. />Representing the variance of the zero mean additive noise of the upstream Gaussian channel,/->A correlation matrix representing the upstream quantization noise;
setting an energy efficiency function:
wherein,respectively N RAUs and K dl ADC precision equipped at each downstream user, W is transmission bandwidth, T is system coherence time, T ul T is the number of symbols for uplink transmission dl P is the number of symbols for downlink transmission total For total power consumption, it can be expressed as P total ＝P TC +P T +P LP +P BH 。P TC For energy of system transceiver link, P TC ＝N(MP BS +P SYN )+KP UE +MP ADC ，P BS ,P SYN ,P UE Are constants related to base station, crystal oscillator and user power consumption, P ADC ＝a 0 ·M·2 b +a 1 Is the power consumption related to the quantization accuracy of the ADC, a 0 ,a 1 Is constant;
the energy required for the system to transmit signals, τ is the frame length occupied by the channel estimation; ζ is amplifier efficiency; />The energy required for the RAU-side linear receiver and precoder. />P, the energy consumed by the backhaul link between the distributed antenna system and the CPU 0 ,P BT Constant values associated with fixed backhaul and variable backhaul power consumption, respectively;
the joint maximization problem objective function is:
the joint maximization problem objective function has the following constraints:
constraint C1: the limited backhaul capacity results in a limit on the total number of bits of ADC on all RAUs. M represents the number of antennas on each RAU, b n Represents the number of antennas on the nth RAU, B t Representing the maximum ADC quantization bit total number over all RAUs;
constraint C2: average user quality of service, qoS, requirements for the uplink;
constraint C3: average user quality of service requirements for the downlink;
constraint C4: power constraints of the system sub-modules.
Step 2, iteratively solving the problem established in the step one through a non-dominant genetic algorithm;
firstly, an initial population is needed to be generated, the population is required to meet constraint C1, namely the limit of the sum of quantized bit numbers, after initial b is generated, an objective function value is calculated based on the current population, and the values of SE and EE are calculated in the joint maximization problem; and then sorting the current population according to the congestion distance of the non-primary level, selecting a father population from the current sorted population by using an elite selection strategy, performing selection, crossing and mutation operations, merging and sorting the first father population and the offspring population, creating a new population and replacing the original population, repeating the cycle until the optimization condition is met, and finally obtaining a set of pareto optimal solutions.
In the first step, the auxiliary variable { beta }, is introduced dl,n,k ,η dl,n,k ，β ul,n,k ,η ul,n,k ，λ t,k,j ，λ ul,n,m Using gamma theorem, if the maximum ratio combining MRC receiver is considered, converting the downlink spectrum efficiency into:
wherein the auxiliary parameter is，Definition of the definition<x> Γ =Γ (x+0.5)/Γ (x) is a quasi-normalized Gamma distribution operator, ++>MMSE estimation for downstream channel>Error of estimation->Statistical correlation coefficient of>
Converting the uplink spectral efficiency into:
wherein t is ul ＝(N ul M-K ul +1)/N ul M，In the above, p ul,k Representing the transmission power of the kth user, p dp,i Representing the power of the ith user transmitting downlink pilot, beta ul,n,k Representing estimated large-scale fading, lambda, between the nth uplink RAU and the kth user I,n,m Representing the true large-scale fading, eta, between the nth uplink RAU and the mth downlink RAU ul,n,i Representing the large-scale estimation error, alpha, between the nth uplink RAU and the ith user n Representing quantized coefficients on the nth uplink RAU related to the number of bits bn, when b n When the temperature is less than or equal to 5, the relation between the two is shown in the table 1; b n At the time of > 5 a, the number of the cells,
table 1 relation between quantization coefficient α and quantization bit number b.
In the second step, the genetic algorithm includes the following steps:
step 2.1, randomly generating an initial value of the number of quantization bits on the RAU according to the constraint C1,
step 2.2, calculating the spectral efficiency and energy efficiency of the system,
step 2.3, calculating a non-dominant ranking and crowding distance, ranking the population based on the calculated non-dominant ranking and crowding distance,
step 2.4, repeating the above steps,
step 2.5, selecting a parent population by elite selection strategy,
step 2.6, parent population selection, hybridization, mutation, generation of offspring population,
step 2.7, calculating the frequency spectrum efficiency and the energy efficiency of the offspring population,
step 2.8, merging the offspring population and the parent population, calculating the non-dominant ranking and crowding distance of the merged population, ranking the merged population based on the calculated non-dominant ranking and crowding distance,
and 2.9, selecting a superior population to replace the parent population.
The beneficial effects are that: the invention solves the multi-objective optimization problem by utilizing the genetic algorithm, converts the complex mathematical solving problem into the biological population evolution problem, and the proposed algorithm can quickly solve the RAU quantization bit allocation scheme of the spectrum efficiency and the energy efficiency of the combined optimization system, has the self-adaptability of large-scale information, and obtains better performance than equal-precision quantization bit allocation.
Compared with the existing full duplex and half duplex equipment network, the network-assisted full duplex distributed large-scale multi-input multi-output system has the advantage that the spectrum efficiency is remarkably improved. The invention designs an effective bit allocation algorithm for a low-resolution analog-to-digital converter of a network-assisted full-duplex distributed large-scale multi-input multi-output system aiming at the influence of the low-resolution analog-to-digital converter on the system performance. The present invention mitigates heavy pilot overhead for downlink channel estimation through a beamforming training mechanism. Aiming at multi-objective joint optimization of energy efficiency and spectrum efficiency, the invention utilizes a genetic algorithm to solve the multi-objective optimization problem, converts the complex mathematical solution problem into a biological population evolution problem, and the proposed algorithm can quickly solve an RAU quantization bit allocation scheme of the spectrum efficiency and the energy efficiency of the joint optimization system, has the self-adaptability of large-scale information, and obtains better performance than equal-precision quantization bit allocation. Simulation results confirm the effectiveness of theoretical derivation and verification of the introduction of low resolution analog-to-digital converters in network-assisted full duplex distributed large-scale multiple-input multiple-output systems. Meanwhile, a pareto optimal set with precision distribution provides valuable references for actually deploying the analog-to-digital converter.
Drawings
Fig. 1 is a schematic diagram of the relationship between spectral efficiency and energy efficiency.
Detailed Description
The invention will be further described with reference to the accompanying drawings and specific examples.
Considering a network assisted full duplex system, the emulated region is limited to a circular region with radius r=1 km, all n=6 RAUs being randomly distributed over the region (containing 3 upstream 3 downstream RAUs). Within the region is K ul =2 uplink users and K dl =3 downlink users are randomly distributed. The minimum access distance between the user and the RAUs is r 0 =30m, path loss index set to α ul ＝α dl =3.7, the path loss index between uplink and downlink users is α t =4, the path loss index between the uplink RAUs and the downlink RAUs is α I The coherence time is t=196 symbols, the length of the uplink pilot sequence is τ 1 =k symbols, the length of the downlink pilot sequence is τ 2 ＝K dl And a symbol. With power consumptionThe parameters are shown in Table 2.
TABLE 2 Power consumption parameters
The implementation method of the invention in the system is as follows:
step one, establishing a system spectrum efficiency and energy efficiency joint maximization problem;
setting a spectrum efficiency function:
wherein,
is the transmission rate of the kth downlink user. Wherein,representing a mathematical expectation of a random variable, a random vector or a random matrix, (. Cndot.) H Representing the conjugate transpose of the matrix or vector. />Representing the effective interfering channel obtained by the beamforming training mechanism during channel estimation, +.>Mu is k,i MMSE estimate of>In order to estimate the error of the signal,
for all RAUs to kthChannels of individual users, M denotes the number of antennas on each RAU, N dl Represents the number of downlink RAUs, K represents the total number of users,/-the number of users>Representing a complex matrix or vector with a number of rows m and a number of columns n. u (u) t,k,j Is the interference channel between the jth uplink and kth downlink users; w (w) i Is the precoding vector of the ith downlink user. P is p dl/ul I is the downlink or uplink transmission power, < > and->Representing the variance of the zero-mean additive noise of the downstream gaussian channel; zeta type toy k Is the coefficient related to the quantization accuracy of the kth downstream user ADC. />Correlation matrix representing downstream quantization noise, n q,dl,k Representing quantization noise of the low-precision ADC.
Is the transmission rate of the kth uplink user. Wherein,representing a diagonal matrix, alpha, associated with low-precision quantization precision n ADC accuracy b equipped with nth RAU n Related accuracy parameters, I M Representing an identity matrix with dimensions M +.>Is the MMSE channel estimation vector from the ith uplink user to all RAUs, N ul Representing the number of uplink RAUs; />Representing channel estimation error, +.>Receiver vector representing kth upstream user signal,/->Is the estimation error of the equivalent interference channel between RAUs. />Representing the variance of the zero-mean additive noise of the upstream gaussian channel. />Representing the correlation matrix of the upstream quantization noise.
Setting an energy efficiency function:
wherein,respectively N RAUs and K dl ADC precision equipped at each downstream user, W is transmission bandwidth, T is system coherence time, T ul T is the number of symbols for uplink transmission dl P is the number of symbols for downlink transmission total For total power consumption, it can be expressed as P total ＝P TC +P T +P LP +P BH 。P TC For energy of system transceiver link, P TC ＝N(MP BS +P SYN )+KP UE +MP ADC ，P BS ,P SYN ,P UE Are constants related to base station, crystal oscillator and user power consumption, P ADC ＝a 0 ·M·2 b +a 1 Is the power consumption related to the quantization accuracy of the ADC, a 0 ,a 1 Is constant.
Transmitting a message for a systemThe energy required by the number, τ, is the frame length occupied by the channel estimation; ζ is the amplifier efficiency. />The energy required for the RAU-side linear receiver and precoder. />P, the energy consumed by the backhaul link between the distributed antenna system and the CPU 0 ,P BT Constant values for fixed backhaul and variable backhaul power consumption, respectively.
The joint maximization problem objective function is:
the joint maximization problem objective function has the following constraints:
constraint C1: the limited backhaul capacity results in a limit on the total number of bits of ADC on all RAUs. M represents the number of antennas on each RAU, b n Represents the number of antennas on the nth RAU, B t Representing the maximum ADC quantization bit total number over all RAUs;
constraint C2: average user quality of service requirements for the uplink;
constraint C3: average user quality of service requirements for the downlink;
constraint C4: power constraints of the system sub-modules.
In the step (2), the problem is solved iteratively by a non-dominant genetic algorithm:
(1) According to the constraint C1, an initial value of the number of quantization bits on the RAU is randomly generated,
(2) The spectral efficiency and energy efficiency of the system are calculated,
(3) Calculating a non-dominant ranking and crowding distance, ranking the population based on the calculated non-dominant ranking and crowding distance,
(4) The parental population is selected by elite selection strategy,
(5) Parent population selection, hybridization, mutation, generation of offspring population,
(6) Calculating the spectrum efficiency and energy efficiency of the offspring population,
combining the offspring population with the parent population, calculating a non-dominant ranking and crowding distance of the combined population, ranking the combined population based on the calculated non-dominant ranking and crowding distance,
(7) A preferred population is selected to replace the parent population.
An initial value of the number of quantization bits on the RAUs is randomly generated according to the constraint C1,
outputting a series of pareto optimal solutions of the problem 1,
calculating the spectral efficiency and energy efficiency of the system,
2 calculating non-dominant ranking and crowding distance,
3 ranking the population based on the calculated non-dominant ranking and crowding distance,
4, repeating:
a parent population is selected by elite selection strategy,
6, parent population selection, hybridization and mutation,
7, generating a offspring population,
8, calculating the spectrum efficiency and energy efficiency of the offspring population,
9. Combining the offspring population with the parent population,
calculating non-dominant ranking and crowding distance of the combined population,
based on the calculated non-dominant ranking and crowding distance to rank the combined population,
selecting a preferred population to replace the parent population,
and 13, until the optimization stopping standard is met.
The foregoing is only a preferred embodiment of the invention, it being noted that: it will be apparent to those skilled in the art that various modifications and adaptations can be made without departing from the principles of the present invention, and such modifications and adaptations are intended to be comprehended within the scope of the invention.
Claims (3)
1. A network-assisted full duplex system analog-to-digital converter precision distribution method is characterized in that: the method comprises the following steps:
step 1, establishing a system spectrum efficiency and energy efficiency joint maximization problem, which specifically comprises the following steps:
setting a spectrum efficiency function:
wherein,
for the transmission rate of the kth downstream user, is->For the transmission rate of the kth upstream user, is->Respectively N RAUs and K dl ADC precision equipped at each downstream user, T is system coherence time, T ul T is the number of symbols for uplink transmission dl Is the number of symbols for downlink transmission, wherein, < ->Representing a mathematical expectation of a random variable, a random vector or a random matrix, (. Cndot.) H Representing the conjugate transpose of a matrix or vector, +.>Indicating effective downlink interference channel between jth uplink and kth downlink users obtained through beamforming training mechanism during channel estimation>Mu is k,i Is a minimum mean square error, MMSE, estimate, +.>To estimate the error s i Is the signal transmitted by the ith downlink user, x j Is the signal sent by the j-th uplink user; />For all remote access units RAU to kth user channels, M represents the number of antennas on each RAU, N dl Represents the number of downlink RAUs, K represents the total number of users, K ul K is the number of uplink users dl For the number of downstream users>Representing a complex matrix or vector with a number of rows of m and a number of columns of n; u (u) t,k,j Is the interference channel between the jth uplink and kth downlink users; w (w) i Is the precoding vector of the ith downlink user; p is p dl/ul,i Is the downlink or uplink transmission power,representing the variance of the zero-mean additive noise of the downstream gaussian channel; zeta type toy k Is a coefficient related to the quantization accuracy of the kth downstream user ADC; />Correlation matrix representing downstream quantization noise, n q,dl,k Representing the quantization noise of a low-precision ADC,
is the transmission rate of the kth upstream user, wherein,representing a diagonal matrix, alpha, associated with low-precision quantization precision n ADC accuracy b equipped with nth RAU n Related accuracy parameters, I M Representing an identity matrix with dimensions M +.>Is the MMSE channel estimation vector from the ith uplink user to all RAUs, N ul Representing the number of uplink RAUs; />Representing channel estimation error, +.>Conjugate transpose of the receiver vector representing the kth upstream user signal,/or->An estimation error of an equivalent interference channel between RAUs; />Representing the variance of the zero mean additive noise of the upstream Gaussian channel,/->A correlation matrix representing the upstream quantization noise;
setting an energy efficiency function:
wherein,respectively N RAUs and K dl ADC precision equipped at each downstream user, W is transmission bandwidth, T is system coherence time, T ul T is the number of symbols for uplink transmission dl P is the number of symbols for downlink transmission total For total power consumption, it can be expressed as P total ＝P TC +P T +P LP +P BH ；P TC For energy of system transceiver link, P TC ＝N(MP BS +P SYN )+KP UE +MP ADC ，P BS ,P SYN ,P UE Are constants related to base station, crystal oscillator and user power consumption, P ADC ＝a 0 ·M·2 b +a 1 Is the power consumption related to the quantization accuracy of the ADC, a 0 ,a 1 Is constant; />The energy required for the system to transmit signals, τ is the frame length occupied by the channel estimation; ζ is amplifier efficiency; />The energy required by the linear receiver and the precoder at the RAU end; />P, the energy consumed by the backhaul link between the distributed antenna system and the CPU 0 ,P BT Constant values associated with fixed backhaul and variable backhaul power consumption, respectively;
the joint maximization problem objective function is:
the joint maximization problem objective function has the following constraints:
constraint C1: limitation of the total number of bits of ADC on all RAUs due to limited backhaul capacity; m represents the number of antennas on each RAU, b n Represents the number of antennas on the nth RAU, B t Representing the maximum ADC quantization bit total number over all RAUs;
constraint C2: average user quality of service, qoS, requirements for the uplink;
constraint C3: average user quality of service requirements for the downlink;
constraint C4: power constraint of the system sub-module;
step 2, iteratively solving the problem established in the step one through a non-dominant genetic algorithm;
firstly, an initial population is needed to be generated, the population is required to meet constraint C1, namely the limit of the sum of quantized bit numbers, after initial b is generated, an objective function value is calculated based on the current population, and the values of SE and EE are calculated in the joint maximization problem; and then sorting the current population according to the congestion distance, selecting a father population from the current sorted population by using an elite selection strategy, performing selection, crossing and mutation operations, merging and sorting the first father population and the offspring population, creating a new population and replacing the original population, repeating the cycle until the optimization condition is met, and finally obtaining a pareto optimal solution.
2. The method for distributing precision of an analog-to-digital converter of a network-assisted full duplex system according to claim 1, wherein the method comprises the steps of: in the first step, the auxiliary variable { beta }, is introduced dl,n,k ,η dl,n,k ，β ul,n,k ,η ul,n,k ，λ t,k,j ，λ ul,n,m Using gamma theorem, if the maximum ratio combining MRC receiver is considered, converting the downlink spectrum efficiency into:
wherein, the auxiliary parameters are as follows,definition of the definition<x> Γ =Γ (x+0.5)/Γ (x) is a quasi-normalized Gamma distribution operator, ++>MMSE estimation for downstream channel>Error of estimation->Statistical correlation coefficient of>
Converting the uplink spectral efficiency into:
wherein t is ul ＝(N ul M-K ul +1)/N ul M，
In the above, p ul,k Representing the transmission power of the kth user, p dp,i Representing the power of the ith user transmitting downlink pilot, beta ul,n,k Representing estimated large-scale fading, lambda, between the nth uplink RAU and the kth user I,n,m Representing the true large-scale fading, eta, between the nth uplink RAU and the mth downlink RAU ul,n,i Representing the large-scale estimation error, alpha, between the nth uplink RAU and the ith user n Representing the upper sum ratio of the nth uplink RAUThe quantization factor associated with the number bn of bits, b n When the temperature is less than or equal to 5, the relation between the two is shown in the table 1; b n At the time of > 5 a, the number of the cells,
table 1 relation between quantization coefficient α and quantization bit number b
3. The method for distributing precision of an analog-to-digital converter of a network-assisted full duplex system according to claim 1, wherein the method comprises the steps of: in the step 2, the genetic algorithm includes the following steps:
step 2.1, randomly generating an initial value of the number of quantization bits on the RAU according to the constraint C1,
step 2.2, calculating the spectral efficiency and energy efficiency of the system,
step 2.3, calculating a non-dominant ranking and crowding distance, ranking the population based on the calculated non-dominant ranking and crowding distance,
step 2.4, repeating the above steps,
step 2.5, selecting a parent population by elite selection strategy,
step 2.6, parent population selection, hybridization, mutation, generation of offspring population,
step 2.7, calculating the frequency spectrum efficiency and the energy efficiency of the offspring population,
step 2.8, merging the offspring population and the parent population, calculating the non-dominant ranking and crowding distance of the merged population, ranking the merged population based on the calculated non-dominant ranking and crowding distance,
and 2.9, selecting a superior population to replace the parent population.
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