CN116050685A - Path planning method based on improved multi-factor optimization - Google Patents
Path planning method based on improved multi-factor optimization Download PDFInfo
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Abstract
The invention discloses a path planning method based on improved multi-factor optimization, which comprises the following steps: firstly, constructing a path planning map, then forming a parent population P in the constructed path planning map, randomly generating a T group task group, performing iterative optimization, and finally obtaining the shortest path distance of each task in the task group to complete path planning. According to the path planning method, the genetic algorithm is combined with the multi-factor evolution algorithm, the problem that the calculation speed of the genetic algorithm is reduced when the optimization operation is carried out on a plurality of path planning tasks with constraints is solved, the efficiency of the path planning tasks during the simultaneous optimization is improved, gaussian disturbance is added to part of individuals in the generated offspring population, the diversity of the algorithm is increased, and the situation that the partial optimization is involved is avoided.
Description
Technical Field
The invention belongs to the technical field of path planning, and relates to a path planning method based on improved multi-factor optimization.
Background
Genetic algorithm is a typical evolutionary method and is widely applied to path planning. The genetic algorithm utilizes the biological genetic viewpoint, and realizes the improvement of the adaptability of each individual through natural selection, crossover, mutation and other action mechanisms. However, when optimizing a plurality of path planning tasks at the same time, the genetic algorithm cannot solve the path planning tasks with high efficiency, so that the addition of the multi-factor evolution algorithm on the basis of the genetic algorithm is considered, and the efficiency is improved during iterative optimization.
Multi-factor evolutionary algorithm (MFEA) is inspired by a multi-factor genetic model, which utilizes a single population to simultaneously solve multiple optimization tasks across domains. In a multitasking environment, the MFEA algorithm simulates genetic processes of genes and cultural factors through a special knowledge migration mechanism, namely, recessive gene transfer through chromosome crossover. In the evolution process of a single population, each task provides a unique factor to influence the evolution direction of the whole population, the genetic characters of offspring individuals are influenced by genes and cultural factors from a plurality of tasks, and research shows that the MFEA algorithm can potentially promote the knowledge migration of the cross-tasks in the optimization process, so that a plurality of cross-domain tasks are simultaneously optimized.
Therefore, the genetic algorithm and the multi-factor evolution algorithm are combined in the method and the device for optimizing the path planning tasks.
Disclosure of Invention
The invention aims to provide a path planning method based on improved multi-factor optimization, which solves the problem of low efficiency when a path planning method adopted in the prior art optimizes a plurality of path planning tasks simultaneously.
The technical scheme adopted by the invention is that the path planning method based on improved multi-factor optimization comprises the following specific steps: firstly, constructing a path planning map, then randomly generating T groups of task groups in the constructed path planning map, performing iterative optimization in a population, and finally obtaining the shortest path distance of each task in the task groups to complete path planning.
The present invention is also characterized in that,
the specific steps of the path planning map construction are as follows:
step 1.1, selecting W cities in a national geographic library, wherein each city is given a number in a range of 1-W, and the numbers of the cities are different;
step 1.2, using a python crawler to climb the distance between any two cities with different numbers, setting a distance threshold, setting the distance to infinity if the distance is greater than M and no direct passage exists between the default cities, and storing the distance into an adjacent matrix if the distance is less than or equal to M, wherein the adjacent matrix is the distance between the two cities, so as to finally obtain the path planning map.
The iterative optimization method comprises the following steps:
individuals are defined as a set of 1-W numbered random sequences;
task ti is defined as: ti= [ si, ei ] (1)
In the formula (1), si is the starting city number of the task ti, and ei is the ending city number of the task ti;
step 2.1, randomly acquiring N individuals in a constructed path planning map to form a parent population P; simultaneously, randomly acquiring T task groups;
step 2.2, adding time constraint and cost constraint to each individual Pi in the parent population P;
step 2.3, evaluating all individuals Pi in the parent population P;
step 2.4, iteratively generating a child population C by utilizing a multi-factor evolution algorithm;
step 2.5, adding Gaussian disturbance to part of individuals Ci in the sub-generation population C;
step 2.6, merging the parent population P and the offspring population C to form a population R;
step 2.7, updating scalar fitness and factor cost of all individuals Ri in the population R;
step 2.8, selecting F elite individuals in the population R to construct a new parent population P1;
and 2.9, repeating the steps 2.3-2.8 until the current algebra GEN is more than or equal to MAXGEN, obtaining a population Pn, wherein the population Pn is the shortest path distance set, and completing the optimization of path planning, wherein MAXGEN is the maximum iteration algebra, and MAXGEN is 200.
The specific steps of the step 2.1 are as follows:
step 2.1.1, randomly generating a population P containing N individuals in a constructed path planning map, wherein each individual Pi in the population P has W dimensions, each dimension stores the number of a city, and N individuals are random sequences of N numbers 1-W;
step 2.1.2, randomly generating T different task groups, and defining a skill factor tau for each task in each task group;
the definition of the skill factor τ is: τ= [1, 2..t ] (2)
In the formula (2), tau is a skill factor, and t is a task number;
the relationship of task group T to task T is defined as: ti= [ t1, t 2..ti ].
The specific steps of step 2.2 are as follows:
defining a time constraint two-dimensional matrix as:
in equation (3), each element t in the Time matrix ij ∈[a,b],t ij Defined as the time spent, t ij Is a real number; setting the time constraint range from a to b, a, b being the time spent;
defining a cost constraint two-dimensional matrix as:
in formula (4), each element p in the Price matrix ij ∈[a',b']，p ij Defined as cost, refers to the cost of oil and high speed required for the road distance between actual cities, p ij The range of spending constraints a 'to b', a 'and b' is set for integers, which is the cost.
The evaluation process for all individuals in the parent population P is as follows:
step 2.3.1, randomly assigning a skill factor τ to each individual Pi in the parent population P, wherein τ= [1, 2..t ], t being the task number;
step 2.3.2, calculating the skill factor tau ranking of each individual Pi in the population P and the ranking of each individual Pi on different tasks;
step 2.3.3, calculating a scalar fitness value ScalFit of each individual Pi in the population P, wherein a calculation formula of the scalar fitness value is as follows:
ScalFit＝len+cost time +cost price (5)
in equation (5), scalFit is a scalar fitness value, len is a path length, cost time Cost as a time factor cost price To cost a factor cost;
time factor cost time The formula is:
cost time ＝cost time +(time-maxtime)*M (6)
in the formula (6), M is a penalty factor, cost time For the time factor cost, the part of maxtime that is the maximum time will multiply the penalty factor to add to the time factor cost time In (a) and (b);
the cost factor cost is:
cost price ＝cost price +(price-maxprice)*M (7)
in the formula (7), M is a penalty factor, cost price Maxpace is the maximum cost to spend a factor cost;
step 2.3.4, updating the individual Pi factor ranking and scalar fitness value according to the factor cost;
the factor cost is defined as: cost pi ＝len(8)
In formula (8), cost pi At the cost of a factor, len is the path length.
The specific process of step 2.4 is as follows:
step 2.4.1, randomly selecting two individuals in the population P as parents, and generating a child population C by utilizing the mating probability rmp mating in a multi-factor evolution algorithm if the skill factors tau of the two parents are different or the probability is smaller than the random mating probability 1 The method comprises the steps of carrying out a first treatment on the surface of the If the skill factors tau of the parent and the parent are the same or the probability is larger than the random mating probability, generating a offspring population C by using a self mutation method 2 Offspring population c=c 1 +C 2 ；
And 2.4.2, carrying out vertical culture propagation operation of a multi-factor evolution algorithm on the individuals Ci in the child population C, and inheriting the skill factor tau of the parent.
Step 2.5, adding Gaussian disturbance to the position of the end point for child individuals generated by utilizing self variation, wherein the Gaussian distribution is centered on a certain random variable, and the specific steps are as follows:
the formula of the gaussian distribution is:
mu in equation (9) is all that is expected, σ 2 Is the variance, equation (9) can also be written as:
x～N(μ,σ 2 )(10)
in the formula (10), μ is mathematical expectation, σ 2 Is variance, where μ is the mean of the distribution, in this algorithm the standard deviation is the position of the endpoint, σ is the standard deviation, and the formula of the standard deviation is:
in the formula (11), leftlen is the length of the left side of the end point, right tlen is the length of the right side of the end point, r obeys normal distribution with the average value of 0 and the standard deviation of 1, a position meeting the formula (11) is found near the end point position e, and the position is exchanged with the end point position, so that Gaussian disturbance addition is completed.
Generating a offspring population C in step 2.4.1 by utilizing mating probability rmp in a multi-factor evolution algorithm 1 The specific steps of (1) selecting operation, cross operation and mutation operation are carried out on both parents;
the selection operation adopts a tournament selection method, and the specific steps of the selection operation are as follows: selecting the first 60% of individuals Pi from the population P with the replaced tournament selection method for subsequent crossover operations;
the crossing operation adopts partial matching crossing, and comprises the following specific steps: randomly selecting two crossing points in the individual gene sequences in the first 60% of individuals Pi selected by the selection operation to determine a crossing region, and executing matching crossing;
the mutation operation comprises the following specific steps: combining 60% of individuals generated by the crossover operation and 40% of individuals not subjected to the crossover operation into a new population Cn (P), and carrying out mutation operation on the new population Cn with the probability of 0.45 to obtain a child population C 1 ；
The self mutation operation comprises the following specific steps: and carrying out mutation operation on the individual, randomly selecting two points in the gene sequence of the individual, and randomly sequencing the sequence between the two points.
The specific process of step 2.4.2 is as follows:
the individuals Ci in the offspring population C are subjected to model selection mating by a genetic algorithm, if the skill factors tau of the parent and the parent are different, the individuals Ci inherit the skill factors of the parent with the probability of 0.5, and if the skill factors tau of the parent and the parent of the individuals Ci are the same, the skill factors are directly inherited; if the individual Ci is generated by direct variation to the parent Pi, the skills factors of the parent are directly inherited.
The beneficial effects of the invention are as follows:
(1) The method combines the genetic algorithm with the multi-factor evolution algorithm by utilizing the characteristic of high iterative optimization efficiency of the genetic algorithm on the discrete optimization problem, so that the problem that the calculation speed is reduced when the genetic algorithm performs optimization operation on a plurality of constrained path planning tasks is solved, and the efficiency of the simultaneous optimization of the plurality of path planning tasks is improved;
(2) According to the method, gaussian disturbance is added to part of individuals in the generated offspring population, so that the diversity of the algorithm is increased, and the situation that the offspring population falls into local optimum is avoided.
Drawings
FIG. 1 is a flow chart of a path planning method based on improved multi-factor optimization of the present invention;
FIG. 2 is a convergent comparison of the MFGA algorithm of the present invention with a genetic algorithm.
Detailed Description
The invention will be described in detail below with reference to the drawings and the detailed description.
The path planning method based on improved multi-factor optimization of the invention is characterized in that, as shown in figure 1,
the method comprises the following specific steps: firstly, constructing a path planning map, then randomly generating T groups of task groups in the constructed path planning map, performing iterative optimization in a population, and finally obtaining the shortest path distance of each task in the task groups to complete path planning.
The specific steps of the path planning map construction are as follows:
step 1.1, selecting W cities in a national geographic library, wherein each city is given a number in a range of 1-W, and the numbers of the cities are different;
step 1.2, using a python crawler to climb the distance between any two cities with different numbers, setting a distance threshold, setting the distance to infinity if the distance is greater than M and no direct passage exists between the default cities, and storing the distance into an adjacent matrix if the distance is less than or equal to M, wherein the adjacent matrix is the distance between the two cities, so as to finally obtain the path planning map.
The iterative optimization method comprises the following steps:
individuals are defined as a set of 1-W numbered random sequences;
task ti is defined as: ti= [ si, ei ] (1)
In the formula (1), si is the starting city number of the task ti, and ei is the ending city number of the task ti;
step 2.1, randomly acquiring N individuals in a constructed path planning map to form a parent population P; simultaneously, randomly acquiring T task groups;
the method comprises the following specific steps:
step 2.1.1, randomly generating a population P containing N individuals in a constructed path planning map, wherein each individual Pi in the population P has W dimensions, each dimension stores the number of a city, and N individuals are random sequences of N numbers 1-W;
step 2.1.2, randomly generating T different task groups, and defining a skill factor tau for each task in each task group;
the definition of the skill factor τ is: τ= [1, 2..t ] (2)
In the formula (2), tau is a skill factor, and t is a task number;
the relationship of task group T to task T is defined as: ti= [ t1, t 2..ti ].
Step 2.2, adding time constraint and cost constraint to each individual Pi in the parent population P;
the method comprises the following specific steps:
defining a time constraint two-dimensional matrix as:
in equation (3), each element t in the Time matrix ij ∈[a,b],t ij Defined as the time spent, t ij Is a real number; setting the time constraint range from a to b, a, b being the time spent;
defining a cost constraint two-dimensional matrix as:
in formula (4), each element p in the Price matrix ij ∈[a',b']，p ij Defined as cost, refers to the cost of oil and high speed required for the road distance between actual cities, p ij The range of spending constraints a 'to b', a 'and b' is set for integers, which is the cost.
Step 2.3, evaluating all individuals Pi in the parent population P;
the specific evaluation process is as follows:
the evaluation process for all individuals in the parent population P is as follows:
step 2.3.1, randomly assigning a skill factor τ to each individual Pi in the parent population P, wherein τ= [1, 2..t ], T being the task number;
step 2.3.2, calculating the skill factor tau ranking of each individual Pi in the population P and the ranking of each individual Pi on different tasks;
step 2.3.3, calculating a scalar fitness value ScalFit of each individual Pi in the population P, wherein a calculation formula of the scalar fitness value is as follows:
ScalFit＝len+cost time +cost price (5)
in equation (5), scalFit is a scalar fitness value, len is a path length, cost time Cost as a time factor cost price To cost a factor cost;
time factor cost time The formula is:
cost time ＝cost time +(time-maxtime)*M (6)
in the formula (6), M is a penalty factor, cost time For the time factor cost, the part of maxtime that is the maximum time will multiply the penalty factor to add to the time factor cost time In (a) and (b);
the cost factor cost is:
cost price ＝cost price +(price-maxprice)*M (7)
in the formula (7), M is a penalty factor, cost price Maxpace is the maximum cost to spend a factor cost;
step 2.3.4, updating the individual Pi factor ranking and the scalar fitness value according to the individual factor cost; factor cost of individual Pi: cost pi ＝len(8)
In formula (8), cost pi Cost of factor cost pi Len is the path length.
Step 2.4, iteratively generating a child population C by utilizing a multi-factor evolution algorithm;
the method comprises the following specific steps:
step 2.4.1, randomly selecting two individuals in the population P as parents, and generating a child population C by utilizing the mating probability rmp mating in a multi-factor evolution algorithm if the skill factors tau of the two parents are different or the probability is smaller than the random mating probability 1 The method comprises the steps of carrying out a first treatment on the surface of the If the skill factors tau of the parent and the parent are the same or the probability is larger than the random mating probability, generating a offspring population C by using a self mutation method 2 Offspring population c=c 1 +C 2 ；
Generation of offspring using mating probability rmp mating in a multi-factor evolutionary algorithmPopulation C 1 The specific steps of (1) selecting operation, cross operation and mutation operation are carried out on both parents;
the selection operation adopts a tournament selection method, which comprises the following specific steps: selecting the first 60% of individuals Pi from the population P with the replaced tournament selection method for subsequent crossover operations;
the crossing operation adopts partial matching crossing, and comprises the following specific steps: randomly selecting two crossing points in the individual gene sequences from the first 60% of individuals selected by the selection operation to determine a crossing region, and executing matching crossing;
the mutation operation comprises the following specific steps: combining 60% of individuals generated by the crossover operation and 40% of individuals not subjected to the crossover operation into a new population Cn (P), and carrying out mutation operation on the new population Cn with the probability of 0.45 to obtain a child population C 1 。
The self mutation operation comprises the following specific steps: the mutation operation is carried out on the individual, the individual randomly selects two points in the own gene sequence, and the sequence between the two points is randomly ordered.
2.4.2, carrying out vertical culture propagation operation of a multi-factor evolution algorithm on the individuals Ci in the child population C, and inheriting the skill factor tau of the parent;
considering that the individuals Ci in the offspring population C are subjected to model selection mating by a genetic algorithm, if the two parents of the individuals Ci come from different tasks, inheriting the skill factors of the parents with the probability of 0.5, and if the two parents of the individuals Ci come from the same task, directly inheriting the skill factors; if the individual Ci is generated by direct variation to the parent Pi, the skills factors of the parent are directly inherited.
Step 2.5, adding Gaussian disturbance to part of individuals Ci in the sub-generation population C;
considering the problem of reduced post diversity of an algorithm, in order to increase the diversity of the population and prevent the post population from converging to local optimum, gaussian disturbance on the position of a terminal point is added to child individuals generated by utilizing self variation, wherein the Gaussian disturbance is random disturbance of Gaussian distribution;
the gaussian distribution is centered on a certain random variable, and comprises the following specific steps:
the formula of the gaussian distribution is:
mu in equation (9) is all that is expected, σ 2 Is the variance, equation (9) can also be written as:
x～N(μ,σ 2 )(10)
in the formula (10), μ is mathematical expectation, σ 2 Is variance, where μ is the mean of the distribution, in this algorithm the standard deviation is the position of the endpoint, σ is the standard deviation, and the formula of the standard deviation is:
in the formula (11), leftlen is the length of the left side of the end point, right tlen is the length of the right side of the end point, r obeys normal distribution with the average value of 0 and the standard deviation of 1, a position meeting the formula (11) is found near the end point position e, and the position is exchanged with the end point position, so that Gaussian disturbance addition is completed.
Step 2.6, merging the parent population P and the offspring population C to form a population R;
step 2.7, updating scalar fitness and factor cost of all individuals Ri in the population R;
the specific steps are carried out according to the step 2.3;
step 2.8, selecting F elite individuals in the population R to construct a new parent population P1;
and 2.9, repeating the steps 2.3-2.8 until the current algebra GEN is more than or equal to MAXGEN, obtaining a population Pn, wherein the population Pn is the shortest path distance set, and completing the optimization of path planning, wherein MAXGEN is the maximum iteration algebra, and MAXGEN is 200.
The process according to the invention is illustrated by the following examples:
example 1
Step 1.1, firstly, selecting 300 cities in a national geographic library, wherein each city is provided with a number, the range of the number is 1-300, and the numbers of the cities are different;
step 1.2, using a python crawler to climb the distance between 300 cities, storing the distance between 300 cities into an adjacent matrix, setting a distance threshold value to be 2000 in the process of constructing the matrix, setting the distance to be infinity if no direct passage exists between the default cities with the distance being more than 2000, storing the distance into the adjacent matrix if the distance is less than or equal to 2000, and finally obtaining a path planning map by the adjacent matrix. The method comprises the steps of carrying out a first treatment on the surface of the
Step 2.1, randomly acquiring N individuals in a constructed path planning map to form a parent population P; simultaneously, randomly acquiring T task groups;
step 2.1.1, randomly generating a population P containing N individuals in a constructed path planning map, wherein each individual Pi in the population P has 300 dimensions; each dimension stores the number of the city, and the N individuals are randomly ordered from 1 to 300 numbers;
step 2.1.2, randomly generating T different task groups, defining a skill factor tau for each task, wherein the definition formula of the task is as follows:
task ti is defined as: ti= [ si, ei ] (1)
The definition of the skill factor τ is: τ= [1, 2..t ] (2)
Where si is the starting city number of task ti and ei is the ending city number of task ti.
Step 2.2 adding a time constraint and a cost constraint to each individual Pi in the parent population P
Defining a time constraint two-dimensional matrix as:
in equation (3), each element t in the Time matrix ij ∈[0,6],t ij Defined as the time spent, t ij Is a real number; the time constraint is set here in the range of 0 to 6 because the time expenditure required is about so much in consideration of the road situation between actual cities;
defining a cost constraint two-dimensional matrix as:
in formula (4), each element p in the Price matrix ij ∈[50,900]，p ij Defined as the oil cost and the high-speed cost required for the road distance between actual cities, p ij The range of spending constraints 50 to 900 is set here for integers because of the oil costs required and the high speed costs that are considered for the road distance between actual cities.
Step 2.3, evaluating all individuals Pi in the parent population P;
step 2.3.1, randomly assigning a skill factor τ to each individual Pi in the parent population P, wherein τ= [1, 2..t ], t being the task number;
step 2.3.2, calculating the skill factor tau ranking of each individual Pi in the population P and the ranking of each individual Pi on different tasks;
step 2.3.3, calculating a scalar fitness value ScalFit of each individual Pi in the population P, wherein a calculation formula of the scalar fitness value is as follows:
ScalFit＝len+cost time +cost price (5)
in equation (5), scalFit is a scalar fitness value, len is a path length, cost time Cost as a time factor cost price To cost a factor cost;
time factor cost time The formula is:
cost time ＝cost time +(time-maxtime)*M (6)
in the formula (6), M is penalty factorPenalty factor value is set to 50, cost time As a time factor cost, maxtime is the maximum time;
the cost factor cost is:
cost price ＝cost price +(price-maxprice)*M (7)
in the formula (7), M is a penalty factor, the penalty factor value is set to be 50, and the cost price Maxpace is the maximum cost to spend a factor cost;
step 2.3.4, updating the individual Pi factor rank and scalar fitness value according to the factor cost.
Step 2.4, iteratively generating a child population C by utilizing a multi-factor evolution algorithm;
step 2.4.1, randomly selecting two individuals in the population P as parents, and generating a child population C by utilizing the mating probability rmp mating in a multi-factor evolution algorithm if the skill factors tau of the two parents are different or the probability is smaller than the random mating probability 1 The method comprises the steps of carrying out a first treatment on the surface of the If the skill factors tau of the parent and the parent are the same or the probability is larger than the random mating probability, generating a offspring population C by using a self mutation method 2 Offspring population c=c 1 +C 2 ；
Generation of offspring population C by mating probability rmp in multi-factor evolutionary algorithm 1 The specific steps of (1) selecting operation, cross operation and mutation operation are carried out on both parents;
the selection operation adopts a tournament selection method, and the specific steps of the selection operation are as follows: selecting the first 60% of individuals from the population P by using a replaced tournament selection method to perform subsequent crossing operations;
the crossing operation adopts partial matching crossing, and comprises the following specific steps: randomly selecting two crossing points in the individual gene sequences from the first 60% of individuals selected by the selection operation to determine a crossing region, and executing matching crossing; partial matched crossover (PMX) is used, ensuring that genes in each chromosome occur only once, and by this crossover strategy, no repeated genes occur in one chromosome, PMX is similar to two-point crossover, and two crossover points in individual gene sequences are randomly selected to determine crossover regions. After crossing is performed, two invalid chromosomes are generally obtained, the situation that individual genes are repeated is generally obtained, in order to repair the chromosomes, a matching relation of each chromosome is established in a crossing area, then the matching relation is applied to the repeated genes outside the crossing area, so that the conflict can be eliminated, and in the process of crossing operation, invisible knowledge transfer of individuals among different tasks is realized to accelerate convergence.
The mutation operation comprises the following specific steps: combining 60% of individuals generated by the crossover operation and 40% of individuals without crossover operation into a new population Pn, and carrying out mutation operation on the new population Pn with the probability of 0.45 to obtain a child population C 1 。
And 2.4.2, carrying out vertical culture propagation operation of a multi-factor evolution algorithm on the individuals Ci in the child population C, and inheriting the skill factor tau of the parent.
Considering that the individuals Ci in the offspring population C are subjected to model selection mating by a genetic algorithm, if the two parents of the individuals Ci come from different tasks, inheriting the skill factors of the parents with the probability of 0.5, and if the two parents of the individuals Ci come from the same task, directly inheriting the skill factors; if the individual Ci is generated by direct variation to the parent Pi, the skills factors of the parent are directly inherited.
Step 2.5, adding Gaussian disturbance to part of individuals Ci in the sub-generation population C;
step 2.6, merging the parent population P and the offspring population C to form a population R;
step 2.7, updating scalar fitness and factor cost of all individuals Ri in the population R;
step 2.8, selecting F elite individuals in the population R to construct a new parent population P1;
and 2.9, repeating the steps 2.3-2.8 until the current algebra GEN is more than or equal to MAXGEN, obtaining a population Pn, wherein the population Pn is the shortest path distance set, and completing the optimization of path planning, wherein MAXGEN is the maximum iteration algebra, and MAXGEN is 200.
The effects of the present invention are further illustrated by the following simulation experiments.
First, the city is given, along with the city number, as shown in table 1.
TABLE 1 City numbering information
Then, given a discrete task group, as shown in table 2, the performance of the proposed algorithm is tested in 10 discrete task groups, and in this simulation, the population size of the discrete task group is 100, and the maximum function iteration algebra MAXGEN is 200.
TABLE 2 discrete task group information
And performing simulation experiments on the discrete task groups according to the specific flow of the MFGA, so as to obtain test results corresponding to the discrete task groups. To better illustrate the effect of the present invention, a genetic algorithm proposed by John h.holland in 1975 was chosen to also perform simulation experiments on discrete task groups, the performance of which was compared to that of the MFGA of the present invention, and the best values in the comparison algorithm and MFGA for each task group are marked in bold as shown in fig. 2, table 3.
As can be seen from fig. 2, the MFGA performs better than the genetic algorithm alone in optimizing multiple discrete path planning tasks simultaneously;
TABLE 3 comparison of GA and MFGA algorithms
From the data in table 3, it can be seen that: over these ten discrete task groups, the performance of the MFGA was better than the GA algorithm over tasks 1,2, 3, 8, 10, worse than the GA algorithm over tasks 4, 5, 9, and similar to GA over tasks 6, 7, as seen from the average ranking.
From fig. 2, it can be seen that the convergence algebra of MFGA is in most cases smaller than that of GA algorithm.
Claims (10)
1. The path planning method based on improved multi-factor optimization is characterized by comprising the following specific steps: firstly, constructing a path planning map, then randomly generating T groups of task groups in the constructed path planning map, performing iterative optimization in a population, and finally obtaining the shortest path distance of each task in the task groups to complete path planning.
2. The path planning method based on improved multi-factor optimization according to claim 1, wherein the specific steps of the path planning map construction are as follows:
step 1.1, selecting W cities in a national geographic library, wherein each city is given a number in a range of 1-W, and the numbers of the cities are different;
step 1.2, using a python crawler to climb the distance between any two cities with different numbers, setting a distance threshold, setting the distance to infinity if the distance is greater than M and no direct passage exists between the default cities, and storing the distance into an adjacent matrix if the distance is less than or equal to M, wherein the adjacent matrix is the distance between the two cities, so as to finally obtain the path planning map.
3. The path planning method based on improved multi-factor optimization of claim 1, wherein the iterative optimization comprises the following steps:
individuals are defined as a set of 1-W numbered random sequences;
task ti is defined as: ti= [ si, ei ] (1) in formula (1), si is the starting city number of the task ti, ei is the ending city number of the task ti;
step 2.1, randomly acquiring N individuals in a constructed path planning map to form a parent population P; simultaneously, randomly acquiring T task groups;
step 2.2, adding time constraint and cost constraint to each individual Pi in the parent population P;
step 2.3, evaluating all individuals Pi in the parent population P;
step 2.4, iteratively generating a child population C by utilizing a multi-factor evolution algorithm;
step 2.5, adding Gaussian disturbance to part of individuals Ci in the sub-generation population C;
step 2.6, merging the parent population P and the offspring population C to form a population R;
step 2.7, updating scalar fitness and factor cost of all individuals Ri in the population R;
step 2.8, selecting F elite individuals in the population R to construct a new parent population P1;
and 2.9, repeating the steps 2.3-2.8 until the current algebra GEN is more than or equal to MAXGEN, obtaining a population Pn, wherein the population Pn is the shortest path distance set, and completing the optimization of path planning, wherein MAXGEN is the maximum iteration algebra, and MAXGEN is 200.
4. A path planning method based on improved multi-factor optimization according to claim 3, wherein the specific steps of step 2.1 are as follows:
step 2.1.1, randomly generating a population P containing N individuals in a constructed path planning map, wherein each individual Pi in the population P has W dimensions, each dimension stores the number of a city, and N individuals are random sequences of N numbers 1-W;
step 2.1.2, randomly generating T different task groups, and defining a skill factor tau for each task in each task group;
the definition of the skill factor τ is: τ= [1, 2..t ] (2) in formula (2), τ is a skill factor, t is a task number;
the relationship of task group T to task T is defined as: ti= [ t ] 1 ,t 2 ...t i ]。
5. A path planning method based on improved multi-factor optimization according to claim 3, characterized in that the specific steps of step 2.2 are as follows:
defining a time constraint two-dimensional matrix as:
in equation (3), each element t in the Time matrix ij ∈[a,b],t ij Defined as the time spent, t ij Is a real number; setting the time constraint range from a to b, a, b being the time spent;
defining a cost constraint two-dimensional matrix as:
in formula (4), each element p in the Price matrix ij ∈[a',b']，p ij Defined as cost, refers to the cost of oil and high speed required for the road distance between actual cities, p ij The range of spending constraints a 'to b', a 'and b' is set for integers, which is the cost.
6. A path planning method based on improved multi-factor optimization according to claim 3, characterized in that the evaluation procedure of all individuals in the parent population P is as follows:
step 2.3.1, randomly assigning a skill factor τ to each individual Pi in the parent population P, wherein τ= [1, 2..t ], t being the task number;
step 2.3.2, calculating the skill factor tau ranking of each individual Pi in the population P and the ranking of each individual Pi on different tasks;
step 2.3.3, calculating a scalar fitness value ScalFit of each individual Pi in the population P, wherein a calculation formula of the scalar fitness value is as follows:
ScalFit＝len+cost time +cost price (5)
in equation (5), scalFit is a scalar fitness value, len is a path length, cost time Cost as a time factor cost price To cost a factor cost;
time factor cost time The formula is:
cost time ＝cost time +(time-maxtime)*M (6)
in the formula (6), M is a penalty factor, cost time For the time factor cost, the part of maxtime that is the maximum time will multiply the penalty factor to add to the time factor cost time In (a) and (b);
the cost factor cost is:
cost price ＝cost price +(price-maxprice)*M (7)
in the formula (7), M is a penalty factor, cost price Maxpace is the maximum cost to spend a factor cost;
step 2.3.4, updating the individual Pi factor ranking and scalar fitness value according to the factor cost;
the factor cost is defined as: cost pi In expression (8) =len (8), cost pi At the cost of a factor, len is the path length.
7. A path planning method based on improved multi-factor optimization according to claim 3, wherein the specific procedure of step 2.4 is as follows:
step 2.4.1, randomly selecting two individuals in the population P as parents, and generating a child population C by utilizing the mating probability rmp mating in a multi-factor evolution algorithm if the skill factors tau of the two parents are different or the probability is smaller than the random mating probability 1 The method comprises the steps of carrying out a first treatment on the surface of the If the skill factor tau of both parents is the same or the probability is larger than the random mating probability, the self mutation method is utilizedGeneration of offspring population C 2 Offspring population c=c 1 +C 2 ；
And 2.4.2, carrying out vertical culture propagation operation of a multi-factor evolution algorithm on the individuals Ci in the child population C, and inheriting the skill factor tau of the parent.
8. A path planning method based on improved multi-factor optimization according to claim 3, wherein said step 2.5 of adding gaussian disturbances adds gaussian disturbances to the position of the end point to child individuals generated by self variation, wherein the gaussian distribution is centered on a random variable, and comprises the following specific steps:
the formula of the gaussian distribution is:
mu in equation (9) is all that is expected, σ 2 Is the variance, equation (9) can also be written as:
x～N(μ,σ 2 ) (10) in equation (10), μ is mathematical expectation, σ 2 Is variance, where μ is the mean of the distribution, in this algorithm the standard deviation is the position of the endpoint, σ is the standard deviation, and the formula of the standard deviation is:
in the formula (11), leftlen is the length of the left side of the end point, right tlen is the length of the right side of the end point, r obeys normal distribution with the average value of 0 and the standard deviation of 1, a position meeting the formula (11) is found near the end point position e, and the position is exchanged with the end point position, so that Gaussian disturbance addition is completed.
9. The path planning method according to claim 7, wherein the generating offspring seed in step 2.4.1 uses the mating probability rmp mating in the multi-factor evolutionary algorithmGroup C 1 The specific steps of (1) selecting operation, cross operation and mutation operation are carried out on both parents;
the selection operation adopts a tournament selection method, and the specific steps of the selection operation are as follows: selecting the first 60% of individuals Pi from the population P with the replaced tournament selection method for subsequent crossover operations;
the crossing operation adopts partial matching crossing, and comprises the following specific steps: randomly selecting two crossing points in the individual gene sequences in the first 60% of individuals Pi selected by the selection operation to determine a crossing region, and executing matching crossing;
the mutation operation comprises the following specific steps: combining 60% of individuals generated by the crossover operation and 40% of individuals not subjected to the crossover operation into a new population Cn (P), and carrying out mutation operation on the new population Cn with the probability of 0.45 to obtain a child population C 1 ；
The self mutation operation specifically comprises the following steps: and carrying out mutation operation on the individual, randomly selecting two points in the gene sequence of the individual, and randomly sequencing the sequence between the two points.
10. The path planning method based on improved multi-factor optimization according to claim 7, wherein the specific process of step 2.4.2 is as follows:
the individuals Ci in the offspring population C are obtained by carrying out type selection mating through a genetic algorithm, if the skill factors tau of the parent and the parent are different, the individuals Ci inherit the skill factors of the parent with the probability of 0.5, and if the skill factors tau of the parent and the parent of the individuals Ci are the same, the skill factors are directly inherited; if the individual Ci is generated by direct variation to the parent Pi, the skills factors of the parent are directly inherited.
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