CN104866903B - The most U.S. path navigation algorithm of based on genetic algorithm - Google Patents

Abstract

The invention discloses a kind of the most U.S. path navigation algorithm of based on genetic algorithm, it uses the form of SEQ.XFER, each sight spot is numbered, route represents with the numbering through sight spot, being easy to coding and decoding, and use linear polymerization priority method to process multi-objective genetic algorithm (MOGA), insertion, deletion and mutation operator that design is controlled by adaptive probability process Varible-length chromsome genetic algorithm (Clv GA), add sequence operator and reduce search volume, add rapid convergence.The present invention can reach original design requirement, obtains corresponding efficient solution, and good solves the problem obtaining U.S. path.And user may specify calculating parameter, it is selected from, in the concentration that solves obtained, the path that body is liked.

Description

The most U.S. path navigation algorithm of based on genetic algorithm

Technical field

The present invention relates to intelligent optimization algorithm field, a kind of the most U.S. path navigation algorithm of based on genetic algorithm, answer U.S. path is obtained in digital map navigation.

Background technology

Using digital map navigation to become more popular, common navigation generally chooses the shortest between two places or the circuit of most convenient, But road is dry as dust.Can the route that navigation be allowed to obtain become excellent and be increasingly becoming study hotspot.Yahoo's laboratory in In ACM meeting, propose the problem of the most U.S. route in August, 2014, i.e. during journey, not only pay close attention to minimal path, with Time also to pay close attention to the local landscape of route process the most graceful.Traditional GPS map program, user have only to input starting point and Terminal, it is possible to obtain a travel path the shortest.But this is generally suitable only for the user that makes up for lost time rather than visitor.Visitor is usual Wish from the road of origin-to-destination, the scenery of beauty can be seen on the way.But problems is at present also in theoretical research stage, Experimental data mostly also is little scope map, does not the most put in actual application.Big owing to gathering scene data amount, formulate mark Accurate complicated, therefore develop full-automatic high performance algorithm tool and acquire a certain degree of difficulty.

Genetic algorithm is the random global search that grows up of natural imitation circle biological evolution mechanism and optimized algorithm, and it has been used for reference and has reached The theory of evolution of your literary composition and Mendelian theory of heredity.It can automatically obtain in search procedure and accumulate the knowledge about search volume, And adaptive command deployment process is in the hope of optimal solution.Operatings of genetic algorithm uses the principle of survival of the fittest, in potential solution Scheme population gradually produces the scheme of an approximate optimal solution.In every generation of genetic algorithm, according to individuality in Problem Areas Fitness value and the reconstruction method used for reference from natural genetics carry out individual selection, produce a new approximate solution.This Process causes evolution individual in population, and the new individuality obtained is suitable for environment than original individuality, just as the transformation in nature Equally.

Genetic algorithm is for solving optimized a kind of search heuritic approach in computer science artificial intelligence field, is to evolve The one of algorithm.Evolution algorithm is initially some phenomenons used for reference in Evolutionary Biology and grows up, and these phenomenons include Heredity, variation, natural selection and hybridization etc..

Genetic algorithm is typically implemented mode for a kind of computer simulation.In the algorithm, the solution of optimization problem is referred to as individuality, its table It is shown as a Variables Sequence, is called chromosome or gene string.Chromosome is typically expressed as simple character string or numeric string, The most also the method for expressing depending on specific question having other is suitable for, and this process is referred to as coding.First, algorithm stochastic generation A number of individuality, sometimes this random generation process can also be intervened by operator, to improve the matter of initial population Amount.In each generation, each individuality is evaluated, and obtains a fitness numerical value by calculating fitness function.Population In individuality by according to ranking fitness, fitness high above.

Next step is to produce of future generation individual and form population.This process, by selecting and having bred, wherein breeds bag Include intersection (crossover) and variation (mutation).

Select to be then to carry out according to new individual fitness, but be not meant to completely using fitness height as guiding simultaneously, Because selecting merely the individuality that fitness is high to would potentially result in algorithm rapidly converge to locally optimal solution rather than globally optimal solution, it is referred to as For precocity.As compromise, genetic algorithm basis principle: fitness is the highest, selected chance is the highest, and fitness is low, Selected chance is the lowest.Initial data can be by the colony of such selection course one relative optimization of composition.

Afterwards, selected individual entrance crossover process.General genetic algorithm has a crossover probability, and scope is usually 0.6～1, the probability that this crossover probability two selected individualities of reflection carry out intersecting.Each two produces two individual by intersecting New individual, replace original " always " individual, Uncrossed individuality then keeps constant.The chromosome of intersection father and mother is exchanged with each other, Thus produce two new chromosomes.

Next step is variation, produces new " sub " by variation individual.General genetic algorithm has a fixing mutation probability, Being typically 0.1 or less, this represents the probability that variation occurs.According to this probability, the variation that new individual chromosome is random, Generally change a byte (0 changes to 1, or 1 changes to 0) of chromosome exactly.

Through this series of process (select, intersect and make a variation), the individuality of new generation of generation is different from an initial generation, and changes In generation, develops to the direction increasing overall fitness, because best individuality is the most more chosen to produce the next generation, and adapts to Spend low individuality to be gradually eliminated.Such process constantly repeats: each individuality is evaluated, and calculates fitness, two Individual intersection, then suddenlys change, and produces the third generation.Go round and begin again, until end condition meets.

Biological evolutionary process is mainly by the intersection between chromosome with made a variation.Lose based on to biological in nature Passing the imitation with evolution mechanism, for different problems, a lot of scholars devise many different coded methods and carry out problem of representation Feasible solution, have developed the different genetic operator of many kinds to the biological heredity characteristic imitating under varying environment.So, by difference Coded method and different genetic operators just constitute various different genetic algorithm.

For the analysis of the most U.S. path navigation problem, genetic algorithm is used to carry out solving problem both ways of depositing:

Problem 1: the process problem of Varible-length chromsome.Being different from fixed length chromosome sequence in traditional genetic algorithm, path navigation is tied Really route should be elongated sequence.

Problem 2: by way of path length and on the way sight spot choose both Balancing selection problems.It is different from traditional genetic algorithm single Objective optimisation problems, path navigation relates to multi-objective optimization question.

Use the chromosome of fixed length compared to traditional genetic algorithm, obtaining path node in the most U.S. routing problem is change, i.e. Chromosome is elongated.In order to keep during evolution, the length of chromosome is variable, and traditional intersection and mutation operator will The most applicable.Secondly, it is not that a random sequence node just can be expressed as a useful path, in addition it is also necessary in view of being No have the problems such as node repeats.It addition, describe and encoding and decoding for simplification problem, use SEQ.XFER compared to binary coding more Have superiority.

Fitness function effect in genetic algorithm holds the balance.Fitness function designs and should meet following condition: standardization, Reasonability, monodrome, continuously, amount of calculation is little, versatility.It addition, design fitness function is it should be noted that the taking advantage of of two genetic algorithms Deceive problem: at the algorithm initial stage, the cognition that in population, the minority fitness of appearance is higher is full of whole population, makes generation newly individuality Operating ineffective, algorithm converges to rapidly a locally optimal solution；In the algorithm later stage, in population, interindividual variation reduces, and calculates Method loses competitiveness, is degenerated to random selection process.During design fitness function, need functional expression is optimized.Optimize mesh It is designated as ensureing that fitness value is not limited to a subinterval the least；The closer to optimal solution, fitness value change is the sensitiveest；Flat All individualities below fitness value, fitness value declines faster.

Summary of the invention

It is an object of the invention to provide a kind of the most U.S. path navigation algorithm of based on genetic algorithm, this algorithm can reach original design Requirement, obtains corresponding efficient solution, and good solves the problem obtaining U.S. path.

The object of the present invention is achieved like this:

A kind of the most U.S. path navigation algorithm of based on genetic algorithm, this algorithm is for digital map navigation, wherein: sight spot sum is n, In algorithm, fitness function is:

$\mathrm{fit}=\frac{1}{2}\left(\frac{1}{\mathrm{\π}}\right[\frac{\mathrm{\π}}{2}+\arctan ((\underset{i=0}{\overset{n}{\mathrm{\Σ}}}{p}_i-c\×p_{\min })\×q+(-1))\left]\right)+\frac{1}{2}(1-\sin (\frac{\mathrm{\π}}{2}\×\frac{\underset{i=0}{\overset{n}{\mathrm{\Σ}}}{\mathrm{rank}}_i}{5\×n}))$

Distance total length and overall score, p for n sight spot_minFor the short line of origin-to-destination, c For user's distance nominal parameter；Q is hash parameter；Use the form of SEQ.XFER, each sight spot is numbered, then one Route represents with origin number 0, numbering by way of sight spot and terminal numbering n, and each gene all represents a corresponding road Footpath；Concretely comprise the following steps:

1) the initial path of design is as initial gene, including starting point v₀, terminal v_n, and random several random node；Mei Tiao road Footpath should not have the node of repetition；

2) initial U.S. path is set as (v₀, v_n), this path does not comprise any sight spot, only beginning and end；Set often for population For pop；

3) set algorithm greatest iteration number is maxGen, as long as not up to this number, then repeats step 4-7；

4) fitness function is used to calculate the fitness value of each genetic entities g in pop；

5) calculate the fitness value of each genetic entities and the ratio of the fitness value summation when all genetic entities of former generation, produce one at random Number, finds out fitness ratio and is inferior to the genetic entities of this random number, and this genetic entities is selected addition candidate gene collection；

6) concentrate from candidate gene successively and select individual g ', carry out following a-d operation:

If a) meeting insertion probability, all sight spots collection that setting g ' comprises outside sight spot is combined into Candidate Set；Randomly select from Candidate Set Random several node city is to the random site in g ', but on position does not include saving with last before first node After Dian；

If b) meeting probability of erasure, the random several sight spots of random site deletion in g ', but in the filial generation after deletion action at least Beginning and end should be comprised；

If c) meeting mutation probability, all sight spots collection that setting g ' comprises outside sight spot is combined into Candidate Set；Select not wrap from Candidate Set Include random several nodes of beginning and end, equal number of node in random replacement g '；

D) being ranked up the sight spot sequence in g ', ordering rule is the distance according to each sight spot to terminal, draws near and carries out；

7) by the gene g of fitness value maximum_maxSave as U.S. path；

8) output U.S. path.

The present invention proposes multiple target Varible-length chromsome genetic algorithm and is applied to solve the most U.S. route, uses the form of SEQ.XFER, right Each sight spot is numbered, and route represents with the numbering through sight spot, it is simple to encodes and decodes, and also makes the simpler side of calculating Just.And gene is limited by design function, each gene order is enable to represent an effective route.Employing linear polymerization is excellent First power method processes multi-objective genetic algorithm (MOGA), and insertion, deletion and mutation operator that design is controlled by adaptive probability process and become Long chromosomal inheritance algorithm (Clv GA), adds sequence operator and reduces search volume, add rapid convergence.This algorithm can reach original Design requirement, obtains corresponding efficient solution, and good solves the problem obtaining U.S. path.And user may specify calculating ginseng Number, is selected from, in the concentration that solves obtained, the path that body is liked.

Accompanying drawing explanation

Fig. 1 is the insertion operator schematic diagram in the present invention；

Fig. 2 is the deletion operator schematic diagram in the present invention；

Fig. 3 is the mutation operator schematic diagram in the present invention；

Fig. 4 is the sequence operator schematic diagram in the present invention；

Fig. 5 is the flow chart of the present invention；

Fig. 6 is counted ten result schematic diagrams of the embodiment of the present invention；

Fig. 7 is the path of embodiment of the present invention schematic diagram on map.

Detailed description of the invention

Describe the present invention below in conjunction with accompanying drawing.

The present invention is a kind of the most U.S. path navigation algorithm of based on genetic algorithm, and this algorithm is used for digital map navigation.

Assume have a non-directed graph M=(V, R, E), wherein set of node V={v_i(i=1,2 ... N) represent each node, scoring collection R={r_i(i=1,2 ... N) represent that the graceful degree of each node is marked, and limit collection E ∈ V*V represents the limit of connection node.Two Expense between node and the scoring of grace degree are all the integers of non-negative.Path representation is a sequence node (v_i,v_k,v_l,…,v_m,v_j), and node identical in path can not occur twice.The graceful degree general comment in this path is divided into U.S. path is then that the minimum and graceful degree overall score of total path length is the highest.

Sight spot sum is n, and in algorithm, fitness function is:

$\mathrm{fit}=\frac{1}{2}\left(\frac{1}{\mathrm{\π}}\right[\frac{\mathrm{\π}}{2}+\arctan ((\underset{i=0}{\overset{n}{\mathrm{\Σ}}}{p}_i-c\×p_{\min })\×q+(-1))\left]\right)+\frac{1}{2}(1-\sin (\frac{\mathrm{\π}}{2}\×\frac{\underset{i=0}{\overset{n}{\mathrm{\Σ}}}{\mathrm{rank}}_i}{5\×n}))$

Distance total length and overall score, p for n sight spot_minFor the short line of origin-to-destination, c For user's distance nominal parameter；Q is hash parameter.

It is 1:1 according to realistic meaning, set path distance and grace degree scoring weight proportion in fitness function；Use three The graphic characteristics of angle function evades two deceptive problems of genetic algorithm；Interpolation parameter is by data normalization, and uniform hashing In function sphere of action.So meaning of design is: 1. the algorithm initial stage can eliminate the individuality that fitness value is relatively low as early as possible； 2. the algorithm later stage can effectively pull open the fitness value of point near optimal solution, encourages means to be easy to make sensitive selection as one, Avoid being absorbed in suboptimal solution.

Use the form of SEQ.XFER, be numbered each sight spot, then route is with origin number 0, volume by way of sight spot Number and terminal numbering n represent, each gene all represents a corresponding path；Concretely comprise the following steps:

1) the initial path of design is as initial gene, including starting point v₀, terminal v_n, and random several random node；Often Paths should not have the node of repetition；

2) initial U.S. path is set as (v₀, v_n), this path does not comprise any sight spot, only beginning and end；Set per generation Population is pop；

3) set algorithm greatest iteration number is maxGen, as long as not up to this number, then repeats step 4-7；

4) fitness function is used to calculate the fitness value of each genetic entities g in pop；

5) calculate fitness value and the ratio of the fitness value summation when all genetic entities of former generation of each genetic entities, produce one Random number, finds out fitness ratio and is inferior to the genetic entities of this random number, and this genetic entities is selected addition candidate gene collection；

6) concentrate from candidate gene successively and select individual g ', carry out following a-d operation:

If a) meeting insertion probability, all sight spots collection that setting g ' comprises outside sight spot is combined into Candidate Set；From Candidate Set at random Choose random several node city to the random site in g ', but on position does not include before first node and last After individual node；

If b) meeting probability of erasure, the random site in g ' deletes random several sight spots, but in the filial generation after deletion action At least should comprise beginning and end；

If c) meeting mutation probability, all sight spots collection that setting g ' comprises outside sight spot is combined into Candidate Set；Select from Candidate Set Do not include random several nodes of beginning and end, equal number of node in random replacement g '；

D) being ranked up the sight spot sequence in g ', ordering rule is the distance according to each sight spot to terminal, draws near and carries out；

7) by the gene g of fitness value maximum_maxSave as U.S. path；

8) output U.S. path.

Embodiment

With Shanghai as starting point, Chengdu is terminal.Use the route between Yahoo's digital map navigation two places, choose 48 cities at route periphery The each city comprising terminal, as sight spot, is numbered by city, and wherein starting point is 0, and terminal is 49.

Sight spot scoring is given a mark according to Baidupedia information, and fraction levels is that 1-5 divides, and five grades, the scoring of beginning and end is equal Being 0, fraction levels 5 is optimum.

Concrete steps:

1) initial path is set, including starting point Shanghai, terminal Chengdu, and random several random sight spot.By initial path As initial gene；

2) setting initial U.S. path as (Shanghai, Chengdu), this path does not comprise any sight spot, only beginning and end；If Fixed is the most often 50000 for population quantity；

3) set algorithm greatest iteration number is 100000, as long as not up to this number, then repeats step 4)-7)；

4) fitness function:

$\mathrm{fit}=\frac{1}{2}\left(\frac{1}{\mathrm{\π}}\right[\frac{\mathrm{\π}}{2}+\arctan ((\underset{i=0}{\overset{n}{\mathrm{\Σ}}}{p}_i-c\×p_{\min })\×q+(-1))\left]\right)+\frac{1}{2}(1-\sin (\frac{\mathrm{\π}}{2}\×\frac{\underset{i=0}{\overset{n}{\mathrm{\Σ}}}{\mathrm{rank}}_i}{5\×n}))$

Wherein p_minFor the path 1963.2 in Shanghai to Chengdu, c is set as 1.5；

Fitness function is used to calculate often for the fitness value of genetic entities g each in population；

5) calculate fitness value and the ratio of the fitness value summation when all genetic entities of former generation of each genetic entities, produce one Random number, finds out fitness ratio and is inferior to the genetic entities of this random number, and this genetic entities is selected addition candidate gene collection；

6) select individual g ' from candidate gene concentration successively, carry out following a)-d) operation:

If a) meeting insertion probability, all sight spots collection that setting g ' comprises outside sight spot is combined into Candidate Set；From Candidate Set at random Choose random several node city to the random site in g ', but on position does not include before first node and last After individual node；In accompanying drawing 1, if parent chromosome is (0,5,2,49), possible through insertion operator operation latter Result is (0,3,5,2,7,49)；

If b) meeting probability of erasure, the random site in g ' deletes random several sight spots, but in the filial generation after deletion action At least should comprise beginning and end；In accompanying drawing 2, if parent chromosome is (0,3,5,2,7,49), through deleting operator operation The result that latter is possible is (0,5,2,49)；

If c) meeting mutation probability, all sight spots collection that setting g ' comprises outside sight spot is combined into Candidate Set；Select from Candidate Set Random several node (does not include beginning and end), equal number of node in random replacement chromosome；In accompanying drawing 3, if father It is (0,3,5,2,7,49) for chromosome, is (0,8,5,2,4,49) through the result that mutation operation latter is possible；

D) being ranked up the sight spot sequence in g ', ordering rule is the distance according to each sight spot to terminal, draws near and carries out； In accompanying drawing 4, if parent chromosome is (0,6,4,3,49), after sequence operator operation, obtain (0,4,3,6,49), warp The path crossing sequence to be significantly better than unsorted path；

7) by the gene g of fitness value maximum_maxSave as U.S. path；

8) output U.S. path.

Algorithm runs the ten groups of results obtained as shown in Figure 6.From in figure, in the many groups solution obtained, the long sight spot of distance The less route of many routes and the slightly shorter sight spot of distance, along with distance number increases, corresponding scoring also can increase, and user is permissible According to self liking choosing the path having a preference for most.

Fig. 7 shows the route in Fig. 6 (0,3,5,2,15,17,33,37,49) true path on map: Shanghai, good Emerging, Suzhou, Hangzhou, Mount Huang, Wuhan, Chongqing, Leshan, Chengdu.Can be seen that the city on path is domestic famous Tourist city, meet reality, also reach design requirement.

Claims (1)

1. the most U.S. path navigation algorithm of based on genetic algorithm, it is characterised in that this algorithm is used for digital map navigation, wherein: sight spot is total Number is n, and in algorithm, fitness function is:

$fit=\frac{1}{2}(\frac{1}{\mathrm{\π}}\[\frac{\mathrm{\π}}{2}+\arctan (\left(\underset{i=0}{\overset{n}{\mathrm{\Σ}}}{p}_i-c\×p_{min}\right)\×q+\left(-1\right))\])+\frac{1}{2}(1-sin(\frac{\mathrm{\π}}{2}\×\frac{\underset{i=0}{\overset{n}{\Σ}}{\mathrm{rank}}_i}{5\×n}\left)\right),$

Distance total length and overall score, p for n sight spot_minFor the short line of origin-to-destination, c is for using Family distance nominal parameter；Q is hash parameter；Use the form of SEQ.XFER, each sight spot is numbered, then a route Representing with origin number 0, numbering by way of sight spot and terminal numbering n, each gene all represents a corresponding path； Concretely comprise the following steps:

1) the initial path of design is as initial gene, including starting point v0, terminal vn, and random several random node；Often Paths should not have the node of repetition；

2) set initial U.S. path and do not comprise any sight spot, only beginning and end as (v0, vn), this path；Set per generation Population is pop；

3) set algorithm greatest iteration number is maxGen, as long as not up to this number, then repeats step 4-7；

4) fitness function is used to calculate the fitness value of each genetic entities g in pop；

5) calculate fitness value and the ratio of the fitness value summation when all genetic entities of former generation of each genetic entities, produce one Random number, finds out the fitness ratio genetic entities less than this random number, and this genetic entities is selected addition candidate gene collection；

6) concentrate from candidate gene successively and select individual g ', sets and insert probability: span as 0.6～1, probability of erasure: Span is 0.6～1 and mutation probability: span is 0～0.1, carries out following a-d operation:

If a) meeting insertion probability, all sight spots collection that setting g ' comprises outside sight spot is combined into Candidate Set；From Candidate Set at random Choose random several node city to the random site in g ', but on position does not include before first node and last After individual node；

If b) meeting probability of erasure, the random site in g ' deletes random several sight spots, but in the filial generation after deletion action At least should comprise beginning and end；

If c) meeting mutation probability, all sight spots collection that setting g ' comprises outside sight spot is combined into Candidate Set；Select from Candidate Set Do not include random several nodes of beginning and end, equal number of node in random replacement g '；

D) being ranked up the sight spot sequence in g ', ordering rule is the distance according to each sight spot to terminal, draws near and carries out；

7) the gene gmax that fitness value is maximum is saved as U.S. path；

8) output U.S. path.