CN111814251A - Multi-target multi-modal particle swarm optimization method based on Bayesian adaptive resonance - Google Patents
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Abstract
The invention discloses a multi-target multi-modal particle swarm optimization method based on Bayesian adaptive resonance, which divides all particles into a plurality of groups by utilizing a Bayesian adaptive resonance theory; sorting the particles of each population according to a non-dominated sorting method and a special crowding distance; updating the particles in the population by utilizing the individual optimization of the particles and the global optimization of the population; connecting the non-dominated solution sets of each population end to form a closed ring topology, and performing local exploration by using a particle swarm optimization algorithm based on the ring topology; and repeating the two updating and exploring processes until a termination condition is met, and outputting all the non-dominated solution sets and the pareto frontier. The invention is suitable for solving the optimization of multi-objective multi-modal problems, can find the distribution of the front edge of pareto in the objective space, and can also find the corresponding pareto optimal solution set in the decision variable space, thereby providing a redundant backup method and improving the reliability of engineering practice activities.
Description
Technical Field
The invention relates to the technical field of optimization algorithms, in particular to a multi-target multi-modal particle swarm optimization method based on Bayesian adaptive resonance.
Background
In real life, a plurality of optimization targets which conflict with each other and are mutually restricted often exist, for example, in the design process of an aircraft, the stability of the aircraft is required to be ensured, the maneuverability of the aircraft is required to be pursued, the stability and the maneuverability are two mutually restricted targets, meanwhile, the solution of the same target may contain a plurality of schemes, for example, different aircraft design schemes may obtain the same stability and maneuverability, and the problem is called a multi-target multi-mode problem. The space made up of the objective functions is called the target space, and the space made up of the variables used to generate the objective functions is called the decision space.
For the multi-objective problem, the conventional research generally focuses only on finding the pareto frontier of the target space, but neglects a plurality of variable combinations of which one pareto frontier may correspond to the decision space, and besides ensuring the diversity of the target space solution, ensuring the diversity of the decision space is also important for solving the multi-objective problem, so in recent years, people pay more and more attention to the optimization method of the multi-objective multi-modality problem.
At present, algorithms such as an intelligent algorithm based on self-organizing mapping, an evolutionary algorithm based on a reorganization strategy, a multi-mode multi-target difference algorithm, a multi-target multi-mode algorithm based on ring topology, a particle swarm optimization algorithm based on clustering and the like are successively proposed to solve the multi-target multi-mode optimization problem. Due to high efficiency and strong robustness of the particle swarm optimization algorithm, the particle swarm optimization algorithm is widely applied to academic and engineering circles in the last two decades. For the multi-modal problem, the niche particle swarm algorithm is a better solution; for multi-objective problems, particle swarm optimization algorithms based on k-means clustering and Euclidean distance clustering are also proposed, however, the existing particle swarm optimization algorithm based on clustering needs to set the clustering number in advance according to the number of solutions, but in reality, the number of solutions of a multi-objective multi-modal function is difficult to know in advance, so that the past method generally adopts the clustering numbers with different numbers to perform experiments, selects the optimal clustering number according to the experiment results, and brings great uncertainty and problem dependency to the optimization problem.
Therefore, how to provide a multi-objective multi-modal particle swarm optimization method capable of accurately ensuring the diversity of solutions of a target space and a decision space is a problem that needs to be solved by those skilled in the art.
Disclosure of Invention
In view of this, the present invention provides a multi-objective multi-modal particle swarm optimization method based on bayesian adaptive resonance, and aims to better solve the multi-objective multi-modal optimization problem, obtain pareto frontier of a target space and pareto optimal solution sets of a decision space as many as possible, and ensure the diversity of solutions of the target space and the decision space.
In order to achieve the purpose, the invention adopts the following technical scheme:
the multi-target multi-modal particle swarm optimization method based on Bayesian adaptive resonance comprises the following steps of:
s1, dividing a particle swarm into a plurality of populations through a Bayes self-adaptive resonance theory;
s2, sorting the particles of each population according to a non-dominated sorting method and a special crowding distance: according to a non-dominant sorting method, all particles in various groups are sorted in a layered mode in a target space, and the particles which are located in a first non-dominant layer after sorting are sorted in a descending mode according to the size of a special crowding distance;
s3, storing the sorted non-dominant solutions of the various populations in a non-dominant solution set of the various populations;
s4, evolving the particles of each population by using a global optimal particle swarm optimization algorithm;
s5, local search is carried out by utilizing a particle swarm optimization algorithm based on ring topology;
s6, repeating the evolution of each population and the local search process based on the ring topology until a termination condition is met;
and S7, outputting the non-dominant particles in each non-dominant solution set and corresponding pareto fronts.
It should be noted that:
a decision space of the particle, that is, a space formed by a value range of each dimension of the particle; the target space is a space formed by the value ranges of the target function determined by the decision space.
"non-dominant" at S2 means that: in the multi-objective problem, if one solution a is better than the other solution B on all objectives, solution a dominates solution B; if one solution A is not dominated by other solutions, then solution A is referred to as a non-dominated solution.
The crowding distance is: in the target space, the higher the crowding distance is, the more distributed the target solution distribution of the particles is, the more the solution diversity can be ensured.
Preferably, the specific contents of S1 include:
s11, selecting a population: in order to divide different particles into proper populations, the maximum posterior probability of each particle relative to all existing populations is calculated, and the population corresponding to the maximum posterior probability is used as a winning population;
the posterior probability of the particles to the existing population is calculated by the following method:
wherein,
representing particle x for yjPosterior probability of population, K represents the number of already existing populations, ylRepresents the j-th population of the plant,
representing the estimated prior probability of the jth population,
representing the probability of a population j being a particle x;
wherein,
sum ΣjAn estimated mean vector and a covariance matrix representing the j population;
and (3) selecting a winning population j according to the population with the maximum posterior probability:
s12, matching test: if the sample point capacity of the winning population is less than the warning threshold SMAXThen execution proceeds to S13; otherwise, the next winning population is found according to S11; if the sample point capacity of all the populations is larger than the warning threshold value SMAXIf so, establishing a new population, wherein the mean vector of the new population is the particle itself, and the covariance matrix is a very small value;
population sample capacity usage hypervolume SJThe representation is a determinant of a gaussian covariance matrix, for a diagonal covariance matrix, the hyper-volume is the product of the variances per dimension:
wherein d represents the dimension of the particle,
represents the variance;
s13, learning and updating: and adjusting the mean vector and the covariance matrix of the winning population according to the new particles:
wherein,
and
respectively representing the population mean vector and covariance after the addition of new particles, MJDenotes the number of particles in the J population, and I denotes the identity matrix.
Preferably, the non-dominated ranking method comprises the following:
(4) substituting the particles into a plurality of objective functions to obtain a target solution represented by the particles;
(5) if the particles in the population are not dominated by other particles, dividing the target solution of the particles into a first layer of non-dominated layer in a target space;
if the particles in the population are not dominated by other particles except the particles of the first non-dominated layer, dividing the target solution of the particles into a second non-dominated layer in the target space;
and (3) sequentially carrying out layering sequencing on all particles in the population according to the method in the step (2).
Preferably, the calculation method of the special congestion distance is as follows:
(1) calculating a target space crowding distance CDi，obj：
Where M represents the number of all objective functions, CDim，objRepresenting the particle i at the objective function fm(x) The calculation method of the congestion distance of the dimension comprises the following steps:
wherein f ism(xi+1) And fm(xi-1) To representObjective function solution f for particle im(xi) Of the neighboring target solution, fm(xmax) And fm(xmin) Representing an objective function fm(x) Maximum and minimum values of;
the similar method is used for obtaining the decision space congestion distance CDi，dec；
(2) Carrying out normalization processing on the crowding distance between the decision space and the target space;
wherein, CDi，obj' represents the target space crowding distance, CD, of the particle i after normalizationi，obj' represents the decision space congestion distance of the particle i after normalization, wherein M represents a target space dimension, and N represents a decision space dimension;
(6) calculating the special crowding distance of the particle i:
wherein, CDavg，obj' and CDavg，dec' represents the normalized average congestion distance of the target space and the average congestion distance of the decision space, respectively.
Preferably, the specific steps of S4 are:
(1) creating an archive of each particle for storing historical information of each particle, regarding the first-ranked particle in the non-dominant solution set of each population as a population global optimal subGbest, and then updating the speed and position of each particle in the population by the following method:
V′i＝wVi+c1r1(Pbesti-Xi)+c2r2(Gbest-Xi)
X′i＝Xi+Vi
wherein, XiIs the position of the current particle, Xi' is the updated position of the particle, ViIs the velocity, V, of the current particlei' is the updated particle speed, Pbest is the individual best for each particle, and Gbest is the global best for the population, subGbest;
(2) storing the updated particles into a particle file, and deleting the particles dominated by the updated particles in the file;
(3) when the particle file contains particles which can govern the individual best Pbest, replacing the individual best Pbest with the particles which can govern the individual best Pbest to become a new individual best, otherwise, not updating the individual best Pbest;
(4) similarly, when there is a particle subGbest that can dominate the global optimum in the individual optimum Pbest, the particle that can dominate the global optimum subGbest is used to replace the global optimum subGbest to become a new global optimum, otherwise, the global optimum subGbest is not updated.
Preferably, the specific steps of S5 are:
(1) connecting the non-dominated solution sets of each population end to form a ring topology, and regarding each non-dominated solution set and two adjacent non-dominated solution sets as a neighborhood;
(2) putting all non-dominant particles in the neighborhood into a neighborhood file, and sorting the particles according to a non-dominant sorting method and a special crowding distance;
(3) regarding the first-order particle in the neighborhood file as the best Nbest neighborhood, and then updating the best global subGbest of each population, wherein the updating method comprises the following steps:
V′i＝wVi+c1r1(Pbesti-Xi)+c2r2(Nbesti-Xi)
X′i＝Xi+Vi
(4) and putting the updated global optimal subGbest of each population into a respective non-dominated solution set, sorting the particles in the non-dominated solution set again according to a non-dominated sorting method and a special congestion distance, deleting the dominated particles, and taking the first-ranked particles as new global optimal subGbest.
Preferably, the specific steps of S6 are:
and updating the speed and the position of the particles in the population according to the new population global optimum subGbest obtained in the step S5 and the rule in the step S4, then updating the population global optimum according to the rule in the step S5, and continuously iterating in a circulating mode until a termination condition is met.
It should be noted that:
the termination condition is typically that a specified number of iterations or resulting solution meets a certain error range.
Preferably, the specific steps of S6 are: after iteration is completed, the non-dominant particles in each non-dominant solution set are pareto optimal solutions in a decision space, and the pareto optimal solutions are substituted into an objective function to obtain the pareto frontier in the objective space.
Preferably, before dividing the particle swarm into a plurality of populations by using the bayesian adaptive resonance theory, the method further comprises the following steps: and determining related parameters of the particle swarm, randomly generating N particles in a decision space, and initializing the particle swarm.
Preferably, the relevant parameters include the total number of particles N, the particle dimension D, the inertial weight w, the velocity control parameter c1 and the velocity control parameter c 2; the velocity and position of each particle is initialized.
The technical scheme can show that the invention discloses and provides a multi-target multi-modal particle swarm optimization method based on Bayesian adaptive resonance, and compared with the prior art, the method has the advantages that:
firstly, the invention utilizes Bayesian self-adaptive resonance theory to divide the population of the particle swarm, which is different from the traditional clustering method based on Euclidean distance and k-means, the method does not need to preset the number of clusters, and utilizes the posterior probability of the particles relative to all existing clusters to perform unsupervised self-adaptive clustering;
secondly, the pareto optimal solution set of a decision space is simultaneously and independently tracked and stored by different sub-populations based on a multi-population mechanism, so that the solution of a multi-mode problem is facilitated; in addition, the invention also adopts non-dominated sorting and special crowding distance to sort the particles of each population, and utilizes the global optimal particle swarm algorithm to independently excavate each sub-population, thereby being beneficial to finding the distribution of non-dominated solution sets and pareto frontier, and being more beneficial to solving the multi-target multi-modal problem;
in addition, after the non-dominant solutions of the sub-populations are obtained, through the interaction among the found non-dominant solutions of the sub-populations, each population can obtain guiding information from adjacent populations, so that the inter-population communication is realized, the diversity of particles is kept, the search efficiency is further improved by utilizing the local search based on the ring topology, and the space exploration capability of the algorithm is improved;
and finally, the pareto optimal solution set of the decision space and the pareto optimal solution of the corresponding target space can be output simultaneously, and the solutions of multi-target and multi-modal problems can be presented more intuitively.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the provided drawings without creative efforts.
FIG. 1 is a flowchart illustrating the general steps of a multi-objective multi-modal particle swarm optimization method based on Bayesian adaptive resonance provided by the present invention;
FIG. 2 is a flow chart of an algorithm of a multi-objective multi-modal particle swarm optimization method based on Bayesian adaptive resonance provided by the invention;
FIG. 3 is a schematic diagram of a decision space and a target space in the multi-target multi-modal particle swarm optimization method based on Bayesian adaptive resonance provided by the invention;
FIG. 4 is a clustering flow chart based on Bayesian adaptive resonance in the multi-objective multi-modal particle swarm optimization method based on Bayesian adaptive resonance provided by the invention;
FIG. 5 is a schematic diagram of a ring topology formed by non-dominated solution sets in the multi-objective multi-modal particle swarm optimization method based on Bayesian adaptive resonance provided by the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The embodiment of the invention discloses a multi-target multi-modal particle swarm optimization method based on Bayesian adaptive resonance, which comprises the following steps of shown in figure 1, and the specific flow of the algorithm is shown in figure 2:
determining relevant parameters of a particle swarm and initializing the particle swarm.
The relevant parameters here mainly include: the total number of particles N, the particle dimension D, the inertial weight w, the learning factors c1 and c 2. The total number of particles N is crucial to the performance of the algorithm, and if the number of particles is too small, the diversity of the population is insufficient, which is not enough to fully cover the decision space, resulting in poor decision performance. Conversely, if the population size is too large, too much computational resources are consumed, and therefore a suitable total number of particles needs to be selected. This parameter needs to be set according to the actual problem requirements, previous experience and some preliminary experiments.
The particle dimension D is determined by the number of variables, which is generally equal to the number of decision variables. The inertia weight w is the ability of the particle to maintain the motion state at the previous moment, and the learning factors c1 and c2 are mainly used for controlling the degree of influence of the particle on individual cognition and social understanding, and generally, the value of w is 0.7298, and the values of c1 and c2 are both 2.05.
The stability and maneuverability of an aircraft are two very important characteristics of an aircraft, the stability is good, the force and moment of the aircraft resisting the change of the flight state can be large, the response of the aircraft to the operation of a pilot can be slow, and the aircraft can be used for the control of the pilotThe handling property is deteriorated accordingly. How to coordinate the relationship between the stability and maneuverability of an aircraft is a very trade-off problem for modern aircraft design. In order to balance the longitudinal stability and maneuverability of an aircraft, it is necessary to determine the position of the focal point and the center of gravity of the aircraft, which are two important factors affecting the stability and maneuverability of the aircraft, during the design phase of the aircraft. When designing an airplane, the maneuverability needs to be ensured under the condition that the stability meets the requirement, and the problem is a multi-objective problem; there are also multiple solutions to the aircraft focus and center of gravity location that meet the same stability and maneuverability requirements, and therefore this is a multi-objective multi-modal problem, so the technology proposed by the present invention can be used to solve the aircraft design problem. In one embodiment, the stability and maneuverability of the aircraft is considered to be the objective function f1、f2Considering the focal point and the center of gravity position of the aircraft as decision variables x1、x2There are 2 decision variables, so the particle dimension N determined in this step is 2.
The decision space for a particle is shown on the left side of FIG. 3, where "x1，x2"is a decision variable; is a space consisting of the value ranges of each dimension variable of the particle; the target space is a space formed by the value ranges of the objective function determined by the decision space, as shown on the right side of fig. 3, where "y" is1，y2"is the objective function.
And randomly generating N particles in the decision space, and initializing the speed and the position of each particle.
In one embodiment, N particles (x) are randomly generated within the focal point and center of gravity positions of the aircraft according to the value ranges of the focal point and the center of gravity positions1，x2) Abscissa x of the particle1Representing the focal position of the aircraft, the ordinate x of the particle2Representing the position of the center of gravity of the particle.
Step two: and dividing the particle swarm into a plurality of groups by using a Bayesian adaptive resonance theory.
Bayesian adaptive resonance is considered as a clustering method here, and the flow is shown in fig. 4, and the specific method is as follows:
(1) and (3) population selection: in order to divide different particles into proper populations, the maximum posterior probability of each particle relative to all existing clusters is calculated, and the population corresponding to the maximum posterior probability is used as a winning population.
The method for calculating the posterior probability of the particle to the existing cluster is as follows:
wherein,
representing particle x for yjPosterior probability of population, K represents the number of already existing populations, ylRepresents the j-th population of the plant,
representing the estimated prior probability of the jth population,
representing the probability of a population j being a particle x;
wherein,
sum-sigmajAn estimated mean vector and a covariance matrix representing the j population;
and (3) selecting a winning population j according to the population with the maximum posterior probability:
(2) matching test: if the sample point capacity of the winning population is less than the warning threshold SMAXThen execution proceeds to S13; otherwise, the next winning population is found according to S11; if the sample point capacity of all the populations is larger than the warning threshold value SMAXIf so, establishing a new population, wherein the mean vector of the new population is the particle per se, and the covariance matrix is a minimum value;
population sample capacity usage hypervolume SJThe representation is a determinant of a gaussian covariance matrix, for a diagonal covariance matrix, the hyper-volume is the product of the variances per dimension:
wherein d represents the dimension of the particle,
represents the variance;
(3) and (3) learning and updating: and adjusting the mean vector and the covariance matrix of the winning population according to the new particles:
wherein,
and
respectively representing the population mean vector and covariance after the addition of new particles, MJDenotes the number of particles in the J population, and I denotes the identity matrix.
Using this method, N particles can be divided into k populations.
Step three: and sorting the particles of each population according to a non-dominated sorting method and a special crowding distance.
1. The non-dominated ranking method is explained as follows:
in a multi-objective problem, a solution a dominates a solution B if one solution a outperforms another solution B on all objectives. If one solution A is not dominated by other solutions, then solution A is referred to as a non-dominated solution.
In one embodiment, it is considered better to have greater stability and maneuverability of the aircraft, and solution A dominates solution B if the position of the aircraft's focal point and center of gravity of one solution A determines greater stability and maneuverability of the aircraft than the other solution B.
And (4) bringing the particles into a plurality of objective functions to obtain an objective solution represented by the particles.
If the particles in the population are not dominated by other particles, the target solution for these particles is partitioned in the target space into a first layer of non-dominated layers.
If the particles in the population are not dominated by other particles except the particles of the first non-dominated layer, the target solution of these particles is divided into a second non-dominated layer in the target space.
And sequentially carrying out layering sequencing on all the particles in the population according to the method.
2. The interpretation of the special crowding distance is as follows:
the crowding distance is an index of crowding degree between a target solution of a particle and a target solution of an adjacent particle in a target space, and the larger the crowding distance is, the more distributed the target solution distribution of the particle is, the more diversity of the solution can be ensured. Calculating a target space crowding distance CDi，obj：
Where M represents the number of all objective functions, CDim，objRepresenting the particle i at the objective function fm(x) The calculation method of the congestion distance of the dimension comprises the following steps:
wherein f ism(xi+1) And fm(xi-1) Solution f of an objective function representing a particle im(xi) Of the neighboring target solution, fm(xmax) And fm(xmin) Representing an objective function fm(x) Maximum and minimum values of.
The multi-target multi-modal problem needs to consider not only the diversity of the target space but also the diversity of the decision space, so that the congestion distance of the target space is extended into the decision space, and the congestion distance CD of the decision space can be obtained by the same methodi，dec(ii) a Namely, the objective function in the method is replaced by the decision function to obtain the decision space congestion distance CDi，dec；
In order to compare the crowding distances of the decision space and the target space, normalization processing needs to be performed on the crowding distances of the decision space and the target space;
wherein, CDi，obj' represents the target space crowding distance, CD, of the particle i after normalizationi，obj' represents the decision space congestion distance of the particle i after normalization, wherein M represents a target space dimension, and N represents a decision space dimension;
(7) calculating the special crowding distance of the particle i:
wherein, CDavg，obj' and CDavg，dec' represents normalized target space average congestion distance and decision space, respectivelyAverage congestion distance of.
And finally, sorting the non-dominant particles in the first non-dominant layer in a descending order according to the size of the special congestion distance, wherein the first non-dominant particle has the largest special congestion distance.
Step four: and storing the sorted non-dominant solutions of the various populations in the non-dominant solution sets of the various populations.
And establishing a non-dominant solution set of each population, and storing the non-dominant particles of various populations in the non-dominant solution set according to descending order of the special congestion distance. And subsequently, if a new non-dominant solution is generated, adding the new non-dominant solution into the non-dominant solution set, and deleting the particles dominated by the new non-dominant solution.
Step five: the particles of each population are evolved by utilizing a global optimal particle swarm optimization algorithm, and the method comprises the following steps:
(1) creating an archive of each particle for storing historical information of each particle, regarding the first-ranked particle in the non-dominant solution set of each population as a population global optimal subGbest, and then updating the speed and position of each particle in the population according to the following formula:
V′i＝wVi+c1r1(Pbesti-Xi)+c2r2(Gbest-Xi)
X′i＝Xi+Vi
wherein, XiIs the position of the current particle, Xi' is the updated position of the particle, ViIs the velocity, V, of the current particlei' is the updated particle speed, Pbest is the individual best for each particle, and Gbest is the global best for the population, subGbest;
(2) storing the updated particles into a particle file, and deleting the particles dominated by the updated particles in the file;
(3) when the particle file contains particles which can govern the individual best Pbest, replacing the individual best Pbest with the particles which can govern the individual best Pbest to become a new individual best, otherwise, not updating the individual best Pbest;
(4) similarly, when there is a particle subGbest that can dominate the global optimum in the individual optimum Pbest, the particle that can dominate the global optimum subGbest is used to replace the global optimum subGbest to become a new global optimum, otherwise, the global optimum subGbest is not updated.
Step six: local search is carried out by utilizing a particle swarm optimization algorithm based on ring topology, and the method comprises the following steps:
(1) the non-dominated solution sets of each population are connected end to form a ring topology, as shown in fig. 5, each solid line circle represents a non-dominated solution set of one population, where "Nset" is a non-dominated solution set, and three non-dominated solution sets contained in each dotted line are a neighborhood.
(2) And putting all non-dominant particles in the neighborhood into a neighborhood file, and sorting the particles according to a non-dominant sorting method and a special crowding distance.
(3) Regarding the first-ranked particle in the neighborhood file as the best Nbest neighborhood, and then updating the best global subGbest of each population according to the following formula:
V′i＝wVi+c1r1(Pbesti-Xi)+c2r2(Nbesti-Xi)
X′i＝Xi+Vi
(4) and then putting the updated global optimal subGbest of each population into a respective non-dominant solution set, sorting the particles in the non-dominant solution set again according to a non-dominant sorting method and a special congestion distance, deleting the dominant particles, and taking the first-ranked particles as new global optimal subGbest.
Step seven: and repeating the evolution of each population and the local search process based on the ring topology until a termination condition is met.
And updating the particle speed and position in the population according to the new global optimum subGbest obtained in the step six and the rule in the step five, then updating the global optimum according to the rule in the step 6, and continuously and circularly iterating until a termination condition is met, wherein the termination condition is generally a specified iteration number or an obtained solution meets a certain error range.
Step eight: and outputting the non-dominant particles in each non-dominant solution set and the corresponding pareto fronts thereof.
After iteration is completed, the non-dominant particles in each population non-dominant solution set are the pareto optimal solutions in the decision space, and the pareto front edges in the target space can be obtained by bringing the non-dominant particles into the objective function.
In one embodiment, the final output pareto front is an optimal combination of stability and maneuverability of the aircraft, and the non-dominant particles in the non-dominant solution set are optimal positions of a focal point and a center of gravity of the aircraft corresponding to the optimal combination of stability and maneuverability of the aircraft.
The multi-target multi-modal particle swarm method based on the Bayesian adaptive resonance can be constructed, firstly, a clustering method based on the Bayesian adaptive theory is utilized to divide a particle swarm into a plurality of sub-populations in a decision space, then, each particle in each population is sorted according to a non-dominated sorting method and a special crowding distance, a non-dominated solution is stored in a non-dominated solution set, and the first-ranked particle is used as the global optimum of the population; then, updating the particles in the population by utilizing the individual optimization of the particles and the global optimization of the population; then connecting the non-dominated solution sets end to form a closed ring topology, and performing local exploration by using a particle swarm optimization algorithm based on the ring topology; and repeating the two updating and exploring processes until a termination condition is met, and outputting all the non-dominated solution sets and the pareto frontier.
The technology is beneficial to solving the optimization problem of the multi-objective multi-modal function, can help people to plan a plurality of selectable schemes in reality so as to realize a plurality of objectives, provides a redundant backup method and improves the reliability of engineering practice activities.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. The device disclosed by the embodiment corresponds to the method disclosed by the embodiment, so that the description is simple, and the relevant points can be referred to the method part for description.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims (10)
1. The multi-target multi-modal particle swarm optimization method based on Bayesian adaptive resonance is characterized by comprising the following steps of:
s1, dividing a particle swarm into a plurality of populations through a Bayes self-adaptive resonance theory;
s2, sorting the particles of each population according to a non-dominated sorting method and a special crowding distance: according to a non-dominant sorting method, all particles in various groups are sorted in a layered mode in a target space, and the particles which are located in a first non-dominant layer after sorting are sorted in a descending mode according to the size of a special crowding distance;
s3, storing the sorted non-dominant solutions of the various populations in a non-dominant solution set of the various populations;
s4, evolving the particles of each population by using a global optimal particle swarm optimization algorithm;
s5, local search is carried out by utilizing a particle swarm optimization algorithm based on ring topology;
s6, repeating the evolution of each population and the local search process based on the ring topology until a termination condition is met;
and S7, outputting the non-dominant particles in each non-dominant solution set and corresponding pareto fronts.
2. The Bayesian adaptive resonance-based multi-objective multi-modal particle swarm optimization method according to claim 1, wherein the specific contents of S1 include:
s11, selecting a population: in order to divide different particles into proper populations, the maximum posterior probability of each particle relative to all existing populations is calculated, and the population corresponding to the maximum posterior probability is used as a winning population; the posterior probability of the particles to the existing population is calculated by the following method:
wherein,
representing particle x for yjPosterior probability of population, K represents the number of already existing populations, ylRepresents the j-th population of the plant,
representing the estimated prior probability of the jth population,
representing the probability of a population j being a particle x;
wherein,
sum ΣjAn estimated mean vector and a covariance matrix representing the j population;
and (3) selecting a winning population j according to the population with the maximum posterior probability:
s12, matching test: if the sample point capacity of the winning population is less than the warning threshold SMAXThen execution proceeds to S13; otherwise, the next winning population is found according to S11; if the sample point capacity of all the populations is larger than the warning threshold value SMAXThen establishing a new population, wherein the mean vector of the new population is the particle itself;
population sample capacity usage hypervolume SJThe representation is a determinant of a gaussian covariance matrix, for a diagonal covariance matrix, the hyper-volume is the product of the variances per dimension:
wherein d represents the dimension of the particle,
represents the variance;
s13, learning and updating: and adjusting the mean vector and the covariance matrix of the winning population according to the new particles:
wherein,
and
respectively representing the population mean vector and covariance after the addition of new particles, MJIn the group of JI represents an identity matrix.
3. The Bayesian adaptive resonance-based multi-objective multi-modal particle swarm optimization method according to claim 1, wherein the non-dominated sorting method comprises the following steps:
(1) substituting the particles into a plurality of objective functions to obtain a target solution represented by the particles;
(2) if the particles in the population are not dominated by other particles, dividing the target solution of the particles into a first layer of non-dominated layer in a target space;
if the particles in the population are not dominated by other particles except the particles of the first non-dominated layer, dividing the target solution of the particles into a second non-dominated layer in the target space;
and (3) sequentially carrying out layering sequencing on all particles in the population according to the method in the step (2).
4. The Bayesian adaptive resonance-based multi-objective multi-modal particle swarm optimization method according to claim 1, wherein the calculation method of the special crowding distance is as follows:
(1) calculating a target space crowding distance CDi，obj：
Where M represents the number of all objective functions, CDim，objRepresenting the particle i at the objective function fm(x) The calculation method of the congestion distance of the dimension comprises the following steps:
wherein f ism(xi+1) And fm(xi-1) Solution f of an objective function representing a particle im(xi) Of the neighboring target solution, fm(xmax) And fm(xmin) Representing objectsFunction fm(x) Maximum and minimum values of;
the similar method is used for obtaining the decision space congestion distance CDi，dec；
(2) Carrying out normalization processing on the crowding distance of the target space and the decision space;
wherein, CDi，obj' represents the target space crowding distance, CD, of the particle i after normalizationi，obj' represents the decision space congestion distance of the particle i after normalization, wherein M represents a target space dimension, and N represents a decision space dimension;
(3) calculating the special crowding distance of the particle i:
wherein, CDavg，obj' and CDavg，dec' represents the normalized average congestion distance of the target space and the average congestion distance of the decision space, respectively.
5. The method of claim 1, wherein the specific steps of S4 are as follows:
(1) creating an archive of each particle for storing historical information of each particle, regarding the first-ranked particle in the non-dominant solution set of each population as a population global optimal subGbest, and then updating the speed and position of each particle in the population by the following method:
V′i＝wVi+c1r1(Pbesti-Xi)+c2r2(Gbest-Xi)
X′i＝Xi+Vi
wherein, XiIs the position of the current particle, Xi' is the updated position of the particle, ViIs the velocity, V, of the current particlei' is the updated particle speed, Pbest is the individual best for each particle, and Gbest is the global best for the population, subGbest;
(2) storing the updated particles into a particle file, and deleting the particles dominated by the updated particles in the file;
(3) when the particle file contains particles which can govern the individual best Pbest, replacing the individual best Pbest with the particles which can govern the individual best Pbest to become a new individual best, otherwise, not updating the individual best Pbest;
(4) similarly, when there is a particle subGbest that can dominate the global optimum in the individual optimum Pbest, the particle that can dominate the global optimum subGbest is used to replace the global optimum subGbest to become a new global optimum, otherwise, the global optimum subGbest is not updated.
6. The method of claim 1, wherein the specific steps of S5 are as follows:
(1) connecting the non-dominated solution sets of each population end to form a ring topology, and regarding each non-dominated solution set and two adjacent non-dominated solution sets as a neighborhood;
(2) putting all non-dominant particles in the neighborhood into a neighborhood file, and sorting the particles according to a non-dominant sorting method and a special crowding distance;
(3) regarding the first-order particle in the neighborhood file as the best Nbest neighborhood, and then updating the best global subGbest of each population, wherein the updating method comprises the following steps:
V′i＝wVi+c1r1(Pbesti-Xi)+c2r2(Nbesti-Xi)
X′i＝Xi+Vi
(4) and putting the updated global optimal subGbest of each population into a respective non-dominated solution set, sorting the particles in the non-dominated solution set again according to a non-dominated sorting method and a special congestion distance, deleting the dominated particles, and taking the first-ranked particles as new global optimal subGbest.
7. The method of claim 1, wherein the specific steps of S6 are as follows:
and updating the speed and the position of the particles in the population according to the new population global optimum subGbest obtained in the step S5 and the rule in the step S4, then updating the population global optimum according to the rule in the step S5, and continuously iterating in a circulating mode until a termination condition is met.
8. The method of claim 1, wherein the specific steps of S6 are as follows: after iteration is completed, the non-dominant particles in each non-dominant solution set are pareto optimal solutions in a decision space, and the pareto optimal solutions are substituted into an objective function to obtain the pareto frontier in the objective space.
9. The multi-objective multi-modal ion swarm optimization method according to claim 1, wherein before dividing the population of particles into a plurality of populations using Bayesian adaptive resonance theory, the method further comprises the following steps: and determining related parameters of the particle swarm, randomly generating N particles in a decision space, and initializing the particle swarm.
10. The multi-objective multi-modal ion swarm optimization method according to claim 9, wherein the relevant parameters comprise total number of particles N, particle dimension D, inertial weight w, velocity control parameter c1 and velocity control parameter c 2; the velocity and position of each particle is initialized.
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Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101763528A (en) * | 2009-12-25 | 2010-06-30 | 深圳大学 | Gene regulation and control network constructing method based on Bayesian network |
| CN106203689A (en) * | 2016-07-04 | 2016-12-07 | 大连理工大学 | A kind of Hydropower Stations cooperation Multiobjective Optimal Operation method |
| CN108846411A (en) * | 2018-05-03 | 2018-11-20 | 武汉理工大学 | Main reducing gear method for diagnosing faults based on pairing sparse Bayesian extreme learning machine |
| CN111144581A (en) * | 2019-12-31 | 2020-05-12 | 杭州雅拓信息技术有限公司 | Machine learning hyper-parameter adjusting method and system |
| US20200184131A1 (en) * | 2018-06-27 | 2020-06-11 | Dalian University Of Technology | A method for prediction of key performance parameter of an aero-engine transition state acceleration process based on space reconstruction |
Family Cites Families (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108268979B (en) * | 2018-02-01 | 2021-11-19 | 北京科技大学 | Medium plate quality prediction method based on evolutionary fuzzy association rule |
| CN111077896B (en) * | 2019-12-27 | 2022-07-19 | 南京理工大学 | Liquid-filled flexible spacecraft parameter optimization method based on improved layering algorithm |
| CN111814251B (en) * | 2020-07-08 | 2021-03-26 | 北京航空航天大学 | Multi-target multi-modal particle swarm optimization method based on Bayesian adaptive resonance |
-
2020
- 2020-07-08 CN CN202010652340.8A patent/CN111814251B/en active Active
-
2021
- 2021-01-04 WO PCT/CN2021/070103 patent/WO2022007376A1/en active Application Filing
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101763528A (en) * | 2009-12-25 | 2010-06-30 | 深圳大学 | Gene regulation and control network constructing method based on Bayesian network |
| CN106203689A (en) * | 2016-07-04 | 2016-12-07 | 大连理工大学 | A kind of Hydropower Stations cooperation Multiobjective Optimal Operation method |
| CN108846411A (en) * | 2018-05-03 | 2018-11-20 | 武汉理工大学 | Main reducing gear method for diagnosing faults based on pairing sparse Bayesian extreme learning machine |
| US20200184131A1 (en) * | 2018-06-27 | 2020-06-11 | Dalian University Of Technology | A method for prediction of key performance parameter of an aero-engine transition state acceleration process based on space reconstruction |
| CN111144581A (en) * | 2019-12-31 | 2020-05-12 | 杭州雅拓信息技术有限公司 | Machine learning hyper-parameter adjusting method and system |
Non-Patent Citations (3)
| Title |
|---|
| YANG SHUNKUN等: "Embedded Software Test Model Based on Hierarchical State Machine", 《RECENT ADVANCES IN COMPUTER SCIENCE AND INFORMATION ENGINEERING》 * |
| 杨顺昆等: "结合贝叶斯网与SFMEA技术的软件故障诊断框架", 《计算机科学》 * |
| 王玲等: "基于局部分布的贝叶斯自适应共振理论增量聚类算法", 《控制与决策》 * |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2022007376A1 (en) * | 2020-07-08 | 2022-01-13 | 北京航空航天大学 | Multi-objective multimodal particle swarm optimization method based on bayesian adaptive resonance |
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| CN113343380B (en) * | 2021-05-31 | 2022-09-09 | 温州大学 | Forced air cooling radiator optimization method and system based on multi-objective particle swarm algorithm |
| CN113848970A (en) * | 2021-08-31 | 2021-12-28 | 中南大学 | Multi-target collaborative path planning method for vehicle and unmanned aerial vehicle |
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| CN114553489A (en) * | 2022-01-24 | 2022-05-27 | 北京北卡星科技有限公司 | Industrial control system safety protection method and device based on multi-objective optimization algorithm |
| CN118012004A (en) * | 2024-01-26 | 2024-05-10 | 北京航空航天大学 | Multi-target test data generation method based on self-adaptive resonance topological network |
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