CN108921379A - A kind of Job-based class scheduling problem similarities and differences analysis method of fitness landform driving - Google Patents
A kind of Job-based class scheduling problem similarities and differences analysis method of fitness landform driving Download PDFInfo
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Abstract
The invention discloses a kind of Job-based class scheduling problem similarities and differences analysis methods of fitness landform driving, belong to Job-based class scheduling problem field.A problem-instance is selected according to actual needs, according to the corresponding relationship of solution and fitness in its solution space, draws fitness landform；Regard fitness landform as discrete series point, using discrete time Fourier transform, from the angle analysis fitness features of terrain of amplitude spectrum.Calculate the primary evaluation index and auxiliary evaluation index of fitness landform；The numerical values recited and changing rule for analyzing more each evaluation index, obtain the similitude and otherness of each problem-instance.Fitness features of terrain parameter proposed by the present invention has very strong adaptability and generality, both the different scales example of same problem had been can be used for, the characteristic of vertical analysis problem can be used for the same scale example of different problems, the similarities and differences between horizontal analysis difference problem.
Description
Technical field
The invention belongs to Job-based class scheduling problem fields, and in particular to a kind of Job- of fitness landform driving
Based class scheduling problem similarities and differences analysis method.
Background technique
In recent years, scheduling problem is widely applied in each field such as manufacturing industry, service trade, cloud computing and Internet of Things.Job-
Based class scheduling problem is a big branch of scheduling field, including Flexible workshop scheduling (FJSP), fluvial incision
(FSSP) and test assignment dispatches (TTSP) etc..A series of task that such scheduling problem is executed by sequences or parallel forms,
In the case where meeting various constraint conditions, reasonable execution sequence and efficient resource distribution mode are arranged for these tasks, is had
Obtain biggish economic benefit conducive to lesser time and resources costs, for promoted related fields task execution efficiency,
It optimizes allocation of resources and plays a significant role.
Job-based class scheduling problem can be abstracted as the combination of assignment problem and sequencing problem, i.e., several constraint conditions
Under combinatorial optimization problem, therefore have certain relevance.In terms of problem characteristic, there is " multiple shot array " effect, from meter
It is a NP problem from the point of view of evaluation time complexity.In terms of optimization aim, objective function is completion date, time of delaying work, cost
Or average load etc. is one of or several, can usually be converted into minimization problem.From the point of view of solution, such scheduling is asked
Topic experienced the evolution process of exact algorithm, heuritic approach, meta-heuristic algorithm, hybrid algorithm mostly.Wherein exact algorithm
It is only applicable to the small-scale problem of early stage, mostly uses the fusion of heuritic approach and meta-heuristic algorithm greatly at present, with comprehensively simultaneous
The ability of searching optimum and local search ability for caring for algorithm, improve the performance of solution.
Various Job-based class scheduling problems problem characteristic, regulation goal, method for solving and in terms of
There is very strong relevance, but at present to research both not utilizations to solution space priori knowledge of such scheduling problem,
Not to the analysis of problem characteristic and relevance, this research mode for isolating, not mutually using for reference relatively is unfavorable for such tune
The theoretical research and development of degree problem.
Fitness terrain analysis is to obtain the conventional means of solution space priori knowledge.Pass through fitness terrain analysis, research
Distribution of the fitness value in solution space facilitates the architectural characteristic for understanding solution space, and then problem analysis characteristic and variation are advised
Rule.Common fitness landform evaluation parameter includes rugged property, fitness apart from degree of correlation, evolution etc., for difference
Fitness features of terrain establish the Main way that corresponding parameter description system is fitness landform theoretical developments.
It is described in conjunction with the problem of scheduling problem, expands and embody certain characteristic evaluating parameters, dispatched for Job-based class
Similarities and differences analysis and algorithm design between problem provide foundation, may advantageously facilitate the mutual reference between such scheduling problem, and real
The close coupling of existing problem characteristic and algorithm design.
Summary of the invention
The method that the present invention uses fitness terrain analysis studies Job-based class scheduling problem, and then probes into such tune
Similitude and otherness between degree problem promote mutual reference and theoretical developments between scheduling field.Specifically a kind of fitness
The Job-based class scheduling problem similarities and differences analysis method of landform driving.
With steps are as follows：
Step 1: selecting a problem-instance according to actual needs in Job-based generic task scheduling problem；
Step 2: drawing fitness landform according to the corresponding relationship of solution and fitness in the solution space of the problem-instance；
Fitness landform by solution space all solutions or sampling solution be arranged in order as abscissa, and by each solution
Fitness is as ordinate, with the Distribution and change of this intuitive reflection solution space.
Step 3: regarding fitness landform as discrete series point, using discrete time Fourier transform, from the angle of amplitude spectrum
Degree analysis fitness features of terrain.
Regard each fitness landform as discrete-time series x (n)：
N is the discrete point number in sequence, and j is imaginary number, and ω is angular frequency.
Discrete-time series x (n) is substituted into the range value of different frequency ingredient in frequency spectrum | X (ejω) | in, when carrying out discrete
Between Fourier transformation, obtain corresponding frequency spectrum.
Step 4: calculating the primary evaluation index and auxiliary evaluation index of fitness landform；
Primary evaluation index is for two fitness landform, the similarity indices including comparing two fitness landform
With acuteness index；Auxiliary evaluation index includes the amplitude variations stability (SAC) and periodicity of each fitness landform；
Similarity indices refer to：Using dynamic time warping distance, two fitness landform are described in external structure
Similitude, and then reflect the similarity degree of solution space.
It is described as follows：
Firstly, by two fitness landform f1And f2Regard discrete series as respectively, it is standardized and eliminates amplitude influence
Obtain sequence F1And F2；
Then adjacency matrix is constructed, satisfaction is found by the way of Dynamic Programming
Most short crooked route；wkFor the bending consumption of k-th of lattice point in path.
Finally, the degree of similarity of landform is characterized as sim (f by dynamic time warping distance1,f2)=DTW (F1,F2).It should
Index value is smaller, and the degree of similarity of two fitness landform is higher.
Acuteness index reflects the catastrophe between solution space neighborhood solution, describes the acuteness degree of fitness landform；
It is described as follows：
Firstly, when for the two solution space scale differences compared, if extensive solution space is A, small-scale solution space
For B, the corresponding fitness landform of extensive solution space A is divided into several segments, the number of the solution in every section and small-scale solution space B
The number of middle solution is identical.
Then, it is A or small-scale solution space B for extensive solution space, it is suitable successively compares two adjacent solutions in solution space
The size of angle value is answered, a new data sequence is obtained.
Since extensive solution space is first solution fitness value of A or small-scale solution space B, if second solution is suitable
It answers angle value to be greater than first solution fitness value, replaces the two with 1, otherwise, replace the two with -1；If two neighboring solution fitness
Be worth it is equal, then with 0 replace both.And so on, obtain new integer sequence { 1, -1,0 }N-1。
Continue, traverse new data sequence from front to back, if 0 continuous appearance, the number that the company of calculating 0 occurs simultaneously are denoted as
ai, i represent the situation appearance number；If 1 or -1 continuous appearance, calculates 1 or -1 number continuously occurred, is denoted as respectively
ciAnd di；If 1 and -1 is alternately present, calculates the number that ± 1 is alternately present and be denoted as ei；If there is other situations, then b is usedi
Record.With bulk billing system scatter plot corresponding coordinate location position ai,bi,ci,di,ei, and according to generation sequential connection scatterplot
Obtain non-directed graph, and by ai,bi,ci,di,eiLast aggregate-value is denoted as asum,bsum,csum,dsum,esum。
Finally, the contribution according to each case to acuteness, distributes weight for aggregate-value and obtains acuteness：
keetd=asum×pa+bsum×pb+csum×pc+dsum×pd+esum×pe
paFor aggregate-value asumThe weight of distribution, pbFor aggregate-value bsumThe weight of distribution, pcFor aggregate-value csumThe power of distribution
Weight, pdFor aggregate-value dsumThe weight of distribution, peFor aggregate-value esumThe weight of distribution；The distribution of weight is to obtain based on experience value
's.Acuteness value is bigger, and the fitness landform is more sharp.
Amplitude variations stability (SAC) reflects in fitness landform frequency spectrum, secondary lobe relative to main lobe (frequency be 0 when
Amplitude) variation degree, to a certain extent reflect fitness landform shape.
Calculation formula is：
Wherein, Aside(i)Represent i-th of secondary lobe amplitude in amplitude spectrum；AmainRepresent the main lobe amplitude in amplitude spectrum.N is
The number of all secondary lobes.The difference of main lobe and secondary lobe is bigger, and secondary lobe is more violent relative to the variation of main lobe, and the numerical value of sta is also
It is bigger.
The periodicity of fitness landform is characterized by the distance between main lobe in frequency spectrum and the first secondary lobe.
Calculation formula is：
fHIt is the frequency at the first secondary lobe, i.e. the frequency with 0 frequency at nearest lobe.fCIt is the frequency at main lobe.
One landform approximation is divided into several parts of shape and similar length, each section is a cycle.The value of per
For reflecting the length in period.
Step 5: the numerical values recited and changing rule of more each evaluation index of analysis, obtain the similitude of each problem-instance
With otherness.
The advantage of the invention is that：
(1) a kind of Job-based class scheduling problem similarities and differences analysis method of fitness landform driving, the fitness of proposition
Features of terrain parameter has very strong adaptability and generality, needs not rely on specific priori knowledge, empty to coding mode, solution
Between distribution, algorithms selection etc. there is no particular/special requirement.
(2) a kind of Job-based class scheduling problem similarities and differences analysis method of fitness landform driving, provides acquisition solution
The effective means of spatial prior knowledge facilitates understanding problem characteristic, provides guidance for algorithm design and parameter adjustment.
(3) a kind of Job-based class scheduling problem similarities and differences analysis method of fitness landform driving, can analyze difference
Similitude and otherness between Job-based class scheduling problem may advantageously facilitate the mutual reference between different scheduling fields, for this
The Unified Solution Frame Design of class scheduling problem provides theories integration.
(4) a kind of Job-based class scheduling problem similarities and differences analysis method of fitness landform driving, this method application
Flexibly, the different scales example of same problem had both been can be used for, the characteristic of vertical analysis problem can be used for different problems
Same scale example, the similarities and differences between horizontal analysis difference problem.
Detailed description of the invention
Fig. 1 is a kind of fitness landform driving Job-based class scheduling problem similarities and differences analysis method frame diagram of the present invention.
Fig. 2 is a kind of fitness landform appraisement system of the present invention.
Fig. 3 is a kind of similarity evaluation Indicators ' Principle figure of the present invention.
Fig. 4 is a kind of acuteness evaluation index schematic diagram of the present invention.
Fig. 5 is the fitness topographic map in the embodiment of the present invention comprising 3 kinds of Job-based scheduling problem examples.
Fig. 6 is the fitness topographic map in the embodiment of the present invention comprising 2 solution spaces.
Fig. 7 is the non-directed graph for calculating acuteness index in the embodiment of the present invention and obtaining.
Specific embodiment
Below in conjunction with attached drawing and case study on implementation, the present invention is described in further detail.
The present invention is a kind of Job-based class scheduling problem similarities and differences point of fitness landform time-frequency domain evaluation index driving
Analysis method proposes a series of fitness featuress of terrain by the Time-Frequency Analysis means such as non-directed graph, discrete time Fourier transform
Parameter, including acuteness, similitude, periodicity, stability and average characteristics etc..Then features of terrain is reflected according to each index
Ability and significance level are classified as two class of main indicator and auxiliary characteristics, for probing into asking for Job-based class scheduling problem
Inscribe characteristic and the similarities and differences.
Process is as shown in Figure 1, include the following steps：
Step 1: selecting a problem-instance according to actual needs in Job-based generic task scheduling problem；
It is asked in every one kind Job-based generic task scheduling such as Flexible workshop scheduling, parallel machine scheduling or automatic test assignment
In topic, there is the problem of many different scales example.Their number of tasks, number of resources, processing time are different, lead to their solution
Space can have certain differences, but identical problem describes and constraint condition, and determines that their solution space is likely to have
There are certain consistent features.In addition, Job-based class scheduling problem belongs to sequencing problem and the Combinatorial Optimization of assignment problem is asked
Topic certainly exists some common ground between them, is embodied in the similitude of solution space external structure, simultaneously as different
The description of the problem of Job-based class scheduling problem and constraint condition are different, and every kind of problem has its characteristic, is especially reflected in
On the variation degree of neighbour structure.The problem of in order to probe into a certain particular problem characteristic or several scheduling problems between the similarities and differences,
Suitable problem-instance can be selected according to actual needs.
Step 2: drawing fitness landform according to the corresponding relationship of solution and fitness in the solution space of the problem-instance；
Fitness landform is the reflection of solution space and is abstracted that it has vividly described feasible solution and fitness in solution space
The corresponding relationship of value.It by solution space all solutions or sampling solution in a manner sequentially arrangement be used as abscissa, and will
The fitness of each solution is as ordinate, with the Distribution and change of this intuitive reflection solution space.
For example, the traversal that can be combined by the fully intermeshing and scheme of task sequence carries out enumerating for solution space, then press
Fitness landform is sequentially generated according to what solution generated.The fully intermeshing method of task sequence there are many selection, such as lexcographical order method, be incremented by into
The traversal of position preparation method, carry of successively decreasing preparation method, ortho position exchange process, recurrent class algorithm etc., scheme combination can be added using arbitrary carry system
Method counter successively increases the Protocol Numbers of each task.With the increase of number of tasks, solution space scale increases severely, can use
Reasonable sample mode, as drawn fitness landform after equal interval sampling again.
Step 3: regarding fitness landform as discrete series point, using discrete time Fourier transform, from the angle of amplitude spectrum
Degree analysis fitness features of terrain.
Discrete time Fourier transform and its inverse transformation are shown below：
Regard each fitness landform as discrete-time series x (n), n is the discrete point number in sequence, and j is imaginary number, ω
For angular frequency.
Sequence x (n) is resolved into a series of different complex indexes sequence of angular frequencies by DTFT.|X(ejω) | it indicates in frequency spectrum
The range value of different frequency ingredient；It can reflect sequence signature from the angle of frequency domain.It is used for the fitness of scheduling problem
Fitness landform is regarded as discrete series point, and is converted using DTFT by terrain analysis, from the angle analysis fitness of amplitude spectrum
Shape feature.
Step 4: calculating the primary evaluation index and auxiliary evaluation index of fitness landform；
As shown in Fig. 2, angle of the fitness landform appraisement system from time domain and frequency domain, quantitatively evaluating fitness landform certain
A little features.Time domain index includes similitude and acuteness etc., reflects the degree of similarity and neighborhood solution of landform external structure respectively
Between mutation content.Frequency-domain index includes amplitude variations periodicity and stability etc., reflects that the period of fitness landform is long respectively
Degree and degree of fluctuation.
The ability and significance level for reflecting problem characteristic according to these evaluation indexes can be classified as main indicator and auxiliary
Index is helped, for carrying out similarities and differences analysis；Primary evaluation index is for two fitness landform, including compares two adaptations
Spend the similarity indices and acuteness index of landform；Auxiliary evaluation index includes the amplitude variations stability of each fitness landform
(SAC) and periodically；
Similarity indices refer to：Using dynamic time warping distance, two fitness landform are described in external structure
Similitude, and then reflect the similarity degree of solution space.
Calculating process is as shown in figure 3, be directed to two fitness landform to be compared, respectively by landform normalization and foundation
Adjacency matrix obtains similitude matching and carries out Dynamic Programming, calculates most short crooked route and dynamic bending distance DTW, obtain this
The similitude of two fitness landform.It is described as follows：
Firstly, by two fitness landform f1And f2Regard discrete series as respectively, it is standardized and eliminates amplitude influence
Obtain sequence F1And F2；
According to formulaFitness landform is normalized,
Wherein f (xi) it is that x is solved in landformiFitness value, f'(xi) it is solution xiNormalization fitness value, N be solution number.By two
Fitness landform after a problem-instance normalization regards two sequences as, and is expressed as：
F1=f1'(x1),f1'(x2),...,f1'(xn)
F2=f2'(x1),f2'(x2),...,f2'(xm)
Then the construction adjacency matrix of n × m, the element (i, j) in matrix represent point qiWith point cjBetween local distance d
(qi,cj), its calculation formula is：d(qi,cj)=(qi-cj)2；Most short crooked route is calculated by the way of Dynamic Programming：
γ (i, j)=d (qi,cj)+min{γ(i-1,j-1),γ(i-1,j),γ(i,j-1)}
γ (i, j) indicates cumulative distance, it consists of two parts：First part is the local distance d (q of current lattice pointi,
cj), second part is the minimum Cumulative Distance that can reach the adjoining lattice point of current lattice point.
Dynamic time warping distance can be expressed as DTW (F1,F2)=γ (n, m), and then obtain two fitness landform
Similitude sim (f1,f2)=DTW (F1,F2)；The index value is smaller, and the degree of similarity of two fitness landform is higher.
Acuteness index reflects the catastrophe between solution space neighborhood solution, describes the acuteness degree of fitness landform；
Its committed step is as shown in figure 4, first carry out fitness value adjacent in the solution space of two fitness landform
Compare, classify by sequence conversion and trend, by counting classification, calibration coordinate points and in sequence connecting line segment are drawn undirected
Figure, to calculate the acuteness index of fitness landform.
It is described as follows：
Firstly, when for the two solution space scale differences compared, if extensive solution space is A, small-scale solution space
For B, the corresponding fitness landform of extensive solution space A is divided into several segments, the number of the solution in every section and small-scale solution space B
The number of middle solution is identical.
Then, it is A or small-scale solution space B for extensive solution space, it is suitable successively compares two adjacent solutions in solution space
The size of angle value is answered, a new data sequence is obtained.
Since extensive solution space is first solution fitness value of A or small-scale solution space B, if adjacent second
A solution fitness value is greater than first solution fitness value, replaces the two with 1, otherwise, replaces the two with -1；If two neighboring solution
Fitness value is equal, then replaces the two with 0.And so on, obtain new integer sequence { 1, -1,0 }N-1Instead of former fitness
Shape.
Continue, traverse new data sequence from front to back, if 0 continuous appearance, the number that the company of calculating 0 occurs simultaneously are denoted as
ai, i represent the situation appearance number；If 1 or -1 continuous appearance, calculates 1 or -1 number continuously occurred, is denoted as respectively
ciAnd di；If 1 and -1 is alternately present, calculates the number that ± 1 is alternately present and be denoted as ei；If there is other situations, then b is usedi
Record.With bulk billing system scatter plot corresponding coordinate location position ai,bi,ci,di,ei, and according to generation sequential connection scatterplot
Obtain non-directed graph, and by ai,bi,ci,di,eiLast aggregate-value is denoted as asum,bsum,csum,dsum,esum。
Finally, the contribution according to each case to acuteness, distributes weight for aggregate-value and obtains acuteness keetd：
keetd=asum×pa+bsum×pb+csum×pc+dsum×pd+esum×pe
paFor aggregate-value asumThe weight of distribution, pbFor aggregate-value bsumThe weight of distribution, pcFor aggregate-value csumThe power of distribution
Weight, pdFor aggregate-value dsumThe weight of distribution, peFor aggregate-value esumThe weight of distribution；The distribution of weight is to obtain based on experience value
, it can slightly adjust to reach better effect.Acuteness value is bigger, and the fitness landform is more sharp.
Assuming that solution space 1 has 32 feasible solutions, the fitness value of these solutions forms fitness vector [6 34685
5 5 6 4 7 7 6 4 3 5 2 6 3 9 5 6 10 10 10 10 5 7 4 9 12 12].The fitness of the solution space
Shape is shown as shown in Figure 6 (a), calculates acuteness index according to above-mentioned steps：
1) due to only one solution space and scale is smaller, the first step is skipped.
2) the ergodic solutions space since first solution, 3 less than 6, so they are replaced by -1, and then 4 are greater than 3, so
They are replaced by 1, and so on replace remaining solving and obtaining new sequence [- 111 1-1 00 1-1 1 0-1-1-1
1 -1 1 -1 1 -1 1 1 0 0 0 -1 1 -1 1 1 0]。
3) the case where the first two number in new sequence belongs to 1 and -1 and is alternately present, therefore e1=2-1+1=2.2nd to the 4th
Number belonged to for 1 continuous the case where occurring, with this c1=4-2+1=3.The case where 4th 5th number belongs to 1 and -1 again and is alternately present,
Therefore e2=5-4+1=2.New sequence has been traversed in such a manner and obtains other value b1=2, a1=2, b2=2, e3=3, b3=
3,d1=3, e4=8, c2=2, b4=2, a2=3, b5=2, e5=4, c3=2, b6=2.With bulk billing system in the corresponding of Fig. 7 (a)
It draws these points and obtains scatter plot in position.According to generating sequential connection scatterplot, and the accumulated value at available each abscissa,
asum=a1+a2=5, bsum=b1+b2+b3+b4+b5+b6=13, csum=c1+c2+c3=7, dsum=d1=3, esum=e1+e2+e3
+e4+e5=19.Shown in connection procedure such as Fig. 7 (a).
4) finally, calculating acuteness value, p according to formulaa, pb, pc, pd, peBe respectively set to -1, -0.6, -0.2, -0.2,
1：
kee1=5* (- 1)+13* (- 0.6)+7* (- 0.2)+3* (- 0.2)+19*1=4.2
Assuming that solution space 2 also has 32 feasible solutions, fitness value vector is [6 66685556477
6 4 5 5 5 5 5 5 5 6 10 10 10 10 5 7 4 9 9 9].The fitness of the solution space shaped like Fig. 6 (b) institute
Show, draws non-directed graph after the same method and obtain Fig. 7 (b) and calculate acuteness value, obtain kee2=-17.2.Due to kee1>
kee2, therefore the acuteness degree of solution space 1 is greater than solution space 2, is consistent with actual conditions.
Amplitude variations stability (SAC) reflects in fitness landform frequency spectrum, secondary lobe relative to main lobe (frequency be 0 when
Amplitude) variation degree, to a certain extent reflect fitness landform shape.
Calculation formula is：
Wherein, Aside(i)Represent i-th of secondary lobe amplitude in amplitude spectrum；AmainRepresent the main lobe amplitude in amplitude spectrum.N is
The number of all secondary lobes.The difference of main lobe and secondary lobe is bigger, and secondary lobe is more violent relative to the variation of main lobe, and the numerical value of sta is also
It is bigger.
The periodicity of fitness landform is characterized by the distance between main lobe in frequency spectrum and the first secondary lobe.
Calculation formula is：
fHIt is the frequency at the first secondary lobe, i.e. the frequency with 0 frequency at nearest lobe.fCIt is the frequency at main lobe.
If a landform approximation to be divided into several parts of shape and similar length, each section is a cycle.per
Value be used to reflect the length in period.
Step 5: the numerical values recited and changing rule of more each evaluation index of analysis, obtain the solution space of each problem-instance
Characteristic and the similarities and differences.
It, can be to the characteristic that searches problem of the same problem of different scales, and not by index analysis and regularity summarization
With the similarities and differences between problem.
The present invention chooses the small-scale problem-instance in three fields respectively to illustrate specific implementation process.
Firstly, three problem-instances of selection：It is derived from Flexible workshop scheduling, parallel machine scheduling and automatic test assignment scheduling neck
Domain, the conditions such as the task number of each example, Scheme Choice, processing time are as shown in table 1.
Table 1
Then, when obtaining fitness landform, the traversal combined by the fully intermeshing and scheme of task sequence is to solution sky
Between enumerated.Here, it selects to be incremented by fully intermeshing algorithm of the carry preparation method as task sequence, betweenness is as the row of calculating in
The intermediate link of column.The task sequence determining for one, then arbitrary carry system up counter is used, it is incremented by the side of each task
Case serial number is until traversed all possibility of scheme combination.All solutions are arranged successively according to generation sequence as abscissa, and
Using the fitness value of each solution as ordinate, fitness landform is obtained.The fitness landform of each example is as shown in Figure 5 in table 1.
Continue discrete time Fourier transform, regard each fitness landform as discrete-time series x (n), substitutes into
FormulaDiscrete time Fourier transform is carried out, corresponding frequency spectrum is obtained.
Finally, calculating landform evaluation index：Similitude in computational chart 1 between three problem-instances two-by-two, and according to small rule
The calculation of mould solution space calculates acuteness in 3 fitness landform in Fig. 5, refers mainly between different scheduling problems
Mark calculated result is recorded in table 2.
Table 2
0 frequency amplitude A is calculated separately in the frequency spectrum of 3 fitness landformmainWith secondary lobe amplitude Aside(i), substitute into formulaAmplitude variations stability is obtained, and average characteristics are calculated by 0 frequency amplitude.
Find main lobe frequency spectrum f respectively in the frequency spectrum of 3 fitness landformCWith the frequency f at the first secondary lobeH, substitute into formulaObtain the periodicity of three landform.
The above auxiliary characteristics calculated result between different scheduling problems is recorded in table 3.
Table 3
Finally, in analytical table each index numerical values recited and changing rule, obtain each problem external structure, fluctuation journey
The similitude and otherness of degree, periodicity, acuteness etc..
Claims (6)
1. a kind of Job-based class scheduling problem similarities and differences analysis method of fitness landform driving, which is characterized in that have step
It is rapid as follows：
Step 1: selecting a problem-instance according to actual needs in Job-based generic task scheduling problem；
Step 2: drawing fitness landform according to the corresponding relationship of solution and fitness in the solution space of the problem-instance；
Step 3: regarding fitness landform as discrete series point, using discrete time Fourier transform, from the angle of amplitude spectrum point
Analyse fitness features of terrain；
Regard each fitness landform as discrete-time series x (n)：
N is the discrete point number in sequence, and j is imaginary number, and ω is angular frequency；
Discrete-time series x (n) is substituted into the range value of different frequency ingredient in frequency spectrum | X (ejω) | in, carry out discrete time Fu
In leaf transformation, obtain corresponding frequency spectrum；
Step 4: calculating the primary evaluation index and auxiliary evaluation index of fitness landform；
Primary evaluation index is for two fitness landform, similarity indices and point including comparing two fitness landform
Sharp property index；Auxiliary evaluation index includes the amplitude variations stability and periodicity of each fitness landform；
Step 5: the numerical values recited and changing rule of more each evaluation index of analysis, the similitude of each problem-instance and poor is obtained
It is anisotropic.
2. a kind of Job-based class scheduling problem similarities and differences analysis method of fitness landform driving as described in claim 1,
It is characterized in that, fitness landform described in step 2 be by solution space all solutions or sampling solution be arranged in order as cross
Coordinate, and using the fitness of each solution as ordinate, with the Distribution and change of this intuitive reflection solution space.
3. a kind of Job-based class scheduling problem similarities and differences analysis method of fitness landform driving as described in claim 1,
It is characterized in that, similarity indices described in step 4 refer to：Using dynamic time warping distance, two fitness landform are described
Similitude in external structure, and then reflect the similarity degree of solution space；It is described as follows：
Firstly, by two fitness landform f1And f2Regard discrete series as respectively, elimination amplitude is standardized on it to be influenced to obtain
Sequence F1And F2；
Then adjacency matrix is constructed, satisfaction is found by the way of Dynamic Programming's
Most short crooked route；wkFor the bending consumption of k-th of lattice point in path；
Finally, the degree of similarity of landform is characterized as sim (f by dynamic time warping distance1,f2)=DTW (F1,F2)；The index
It is worth smaller, the degree of similarity of two fitness landform is higher.
4. a kind of Job-based class scheduling problem similarities and differences analysis method of fitness landform driving as described in claim 1,
It is characterized in that, the catastrophe between the reflection solution space neighborhood solution of acuteness index described in step 4, describes fitness landform
Acuteness degree；It is described as follows：
Firstly, if extensive solution space is A, small-scale solution space is B when for the two solution space scale differences compared,
The corresponding fitness landform of extensive solution space A is divided into several segments, is solved in the number of the solution in every section and small-scale solution space B
Number it is identical；
Then, it is A or small-scale solution space B for extensive solution space, successively compares two adjacent solution fitness in solution space
The size of value obtains a new data sequence；
Since extensive solution space is first solution fitness value of A or small-scale solution space B, if second solution fitness
Value is greater than first solution fitness value, replaces the two with 1, otherwise, with both -1 replacements；If two neighboring solution fitness value phase
Deng then with both 0 replacements；And so on, obtain new integer sequence { 1, -1,0 }N-1；
Continue, traverse new data sequence from front to back, if 0 continuous appearance, the number that the company of calculating 0 occurs simultaneously are denoted as ai, i generation
The number that the table situation occurs；If 1 or -1 continuous appearance, calculates 1 or -1 number continuously occurred, is denoted as c respectivelyiAnd di；
If 1 and -1 is alternately present, calculates the number that ± 1 is alternately present and be denoted as ei；If there is other situations, then b is usediRecord；With
Corresponding coordinate location position a of the bulk billing system in scatter ploti,bi,ci,di,ei, and according to generate sequential connection scatterplot obtain it is undirected
Figure, and by ai,bi,ci,di,eiLast aggregate-value is denoted as asum,bsum,csum,dsum,esum；
Finally, the contribution according to each case to acuteness, distributes weight for aggregate-value and obtains acuteness：
keetd=asum×pa+bsum×pb+csum×pc+dsum×pd+esum×pe
paFor aggregate-value asumThe weight of distribution, pbFor aggregate-value bsumThe weight of distribution, pcFor aggregate-value csumThe weight of distribution, pd
For aggregate-value dsumThe weight of distribution, peFor aggregate-value esumThe weight of distribution；The distribution of weight obtains based on experience value；Point
Sharp property value is bigger, and the fitness landform is more sharp.
5. a kind of Job-based class scheduling problem similarities and differences analysis method of fitness landform driving as described in claim 1,
It is characterized in that, amplitude variations stability described in step 4 reflects in fitness landform frequency spectrum, secondary lobe is relative to main lobe
Variation degree reflects the shape of fitness landform to a certain extent；
Calculation formula is：
Wherein, Aside(i)Represent i-th of secondary lobe amplitude in amplitude spectrum；AmainRepresent the main lobe amplitude in amplitude spectrum；N is all
The number of secondary lobe；The difference of main lobe and secondary lobe is bigger, and secondary lobe is more violent relative to the variation of main lobe, and the numerical value of sta is also bigger.
6. a kind of Job-based class scheduling problem similarities and differences analysis method of fitness landform driving as described in claim 1,
It is characterized in that, fitness landform described in step 4 periodically carries out table by the distance between main lobe in frequency spectrum and the first secondary lobe
Sign；
Calculation formula is：
fHIt is the frequency at the first secondary lobe, i.e. the frequency with 0 frequency at nearest lobe；fCIt is the frequency at main lobe；
One landform approximation is divided into several parts of shape and similar length, each section is a cycle；The value of per is used to
Reflect the length in period.
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