CN101051361A - Class genetic method for logistic optmum - Google Patents

Abstract

The present invention discloses a quasi-genetic method for material flow optimization. Said method provides a chromosome model formed from two portions of head portion and truncus portion-chromosomoid, in which the gene of said head portion can be used for defining accessed top point of every group in current loop, and the gene of truncus portion can be used for defining a GTSP loop, so that can effective GTSP loop can be obtained, and has no need of making additional modification. At the same time of effectively raising calculation efficiency it can retain diversity of gene segments in the population. On the basis of chromosomoid and quasi-genetic operation said invention can adopt traditional genetic algorithm process to resolve the problem of material flow optimization.

Description

A kind of class genetic method that is used for logistic optmum

Technical field

The present invention relates to a kind of class genetic method, be particularly related to a kind of class genetic method that is used for logistic optmum, chromosome wherein is made of head and trunk two parts, define genetic manipulation and fitness such as its corresponding class intersection, class variation, class reverse according to this chromosome, thus can be enough it find the solution the broad sense traveling salesman problem, and can realize finding the solution simultaneously to conventional traveling salesman problem.

Background technology

General travelling salesman (traveling salesman problem, TSP) and broad sense travelling salesman (generalizedtraveling salesman problem, GTSP) problem is two class ranges of application combinatorial optimization problems very widely, and wherein GTSP is a class problem more more complicated than TSP.Broad sense travelling salesman is by Henry-Labordere the earliest, a kind of combinatorial optimization problem that people such as Saksena and Srivastava propose under the access order background of computer recording balance and welfare institution.GTSP can be described as: supposition exist complete weighted graph G=(V, E, W), V=(v wherein ₁, v ₂..., v _n) be the vertex set of v 〉=3; V is divided into and has the m group that partially overlaps, i.e. V ₁, V ₂..., V _m, wherein | V _j| 〉=1, j=(1,2 ..., m) and $V=\underset{j=1}{\overset{m}{\∪}}{V}_j;$ E={e _Ij| v _i, v _j∈ V} is the limit collection; W={w _Ij| w _Ij〉=0, w _Ij=0,  i, j ∈ N (n) } be the cost collection, the problem of seeking the Hamiltonian loop of all groups of process and cost minimum is called as GTSP.For the convenience of narrating, we claim also that sometimes W is the cost matrix, and W=(w is arranged this moment _Ij) _{N * n}The GTSP:(1 that two versions are arranged at present) every group only has a summit accessed in the loop, as shown in Figure 1, also claims E-GTSP, and (2) every group have at least a summit as shown in Figure 2 accessed in the loop.

The computational intelligence method that comprises neural network and genetic algorithm is a kind of effective tool of finding the solution combinatorial optimization problem, and has been widely used in finding the solution TSP.But up to the present, the theory and application research of relevant calculation intelligent method on GTSP finds the solution is still very rare.The GA of common integer coding has when finding the solution TSP intuitively, and is easy to operate, carries out the efficient advantages of higher, therefore makes it all obtain intensive research in the theory and the application of finding the solution on the TSP.But since among the GTSP general every group number of vertex all greater than 1, according to original thinking, can determine the visit order of each group based on the GA of normal dyeing body, but can't determine every group of accessed summit, therefore make existing GA algorithm lose original advantage when finding the solution GTSP, GA temporarily has been absorbed in predicament finding the solution on the GTSP.

Summary of the invention

The purpose of this invention is to provide a kind of class genetic method that is used for logistic optmum, this method is utilized chromosomal structure in the general genetic algorithm, and having proposed the class genetic algorithm based on this new chromosome is method, this method does not need the conversion of GTSP to TSP, do not need the cost matrix to satisfy triangle inequality, therefore greatly simplified solution procedure, improved and found the solution efficient.And it can find the solution TSP, GTSP and TSP-GTSP mixed problem with unified pattern.The proposition of this method makes based on the method for solving of GA some problem in the processing machine processing effectively, and the problem of logistic optmum, has greatly promoted the application of GA in GTSP finds the solution.

This method has at first designed a kind of chromosomoid at the broad sense traveling salesman problem, and it is made up of head and trunk two parts, and wherein the gene of head is in order to determine that super vertex is on accessed summit in front loop; The gene of torso portion is used for determining a GTSP loop of generalized vertex.Like this when chromosomoid being decoded into actual loop, just can obtain legal GTSP loop easily, and not need the correction that adds, when having improved counting yield effectively, can keep the diversity of genetic fragment in the colony again, help the generation of defect individual.The singularity of the chromosomoid structure of the present invention's design makes conventional genetic manipulation no longer suitable, so this paper has proposed new genetic manipulation scheme---based on the genetic algorithm (class genetic method) of chromosomoid.Simulated experiment is the result show, it is the logistic optmum problem that the class genetic method that the present invention proposes can be found the solution the broad sense traveling salesman problem effectively, compare with existing method, class genetic method has the fast advantage of travelling speed, and can obtain optimum solution to the partial test problem, the result of most of test problem and the error of optimum solution are in 8%.

Description of drawings

Fig. 1 is for only there being a summit accessed GTSP synoptic diagram in the loop in every group.

Fig. 2 has a summit accessed GTSP synoptic diagram in the loop at least for every group.

Fig. 3 is a chromosomoid mode chart of the present invention.

Fig. 4 is the synoptic diagram of TSP of the present invention with GTSP mixing example.

Fig. 5 is chromosomoid example 1 synoptic diagram of the present invention.

Fig. 6 is chromosomoid example 2 synoptic diagram of the present invention.

Fig. 7 is the GTSP loop synoptic diagram of chromosomoid example 1 correspondence of the present invention.

Fig. 8 is the GTSP loop synoptic diagram of chromosomoid example 2 correspondences of the present invention.

Fig. 9 is a colony of the present invention initializer process flow diagram.

Figure 10 is a class crossover operator process flow diagram of the present invention.

Figure 11 is a class mutation operator process flow diagram of the present invention.

Figure 12 reverses the gene position synoptic diagram for the present invention.

Figure 13 reverses the operator process flow diagram for class of the present invention.

Embodiment

1, related definition

Definition 1: with v ₁, v ₂..., v _n(W) summit in is referred to as original vertices to the figure G=that mode is represented for V, E.

Definition 2: if | V _j|＞1 (j ∈ N (m)), then title group V _jBe super vertex.

Definition 3: if v _i∈ V _jAnd | V _j|=1 (j ∈ 1,2 ..., m}), then claim vertex v _i(i ∈ 1,2 ..., n}) be the point that looses.

Definition 4:, claim that then it is an element of this super vertex if original vertices belongs to a certain super vertex.

Definition 5: the super vertex and the point that looses are referred to as generalized vertex.

Definition 6: the Hamilton loop that comprises all generalized vertex is called the GTSP loop.

Definition 7:, then be referred to as legal GTSP loop if the GTSP loop is satisfied each original vertices and visited at the most once.

Definition 8: if comprise the Hamilton loop of all generalized vertex is not legal GTSP loop, then is referred to as illegal GTSP loop.

2, chromosomoid

According to the summit number to the group V after cutting apart ₁, V ₂..., V _mCarry out detailed differentiation,, can count m to original group and resolve into two parts, promptly by top definition 2,3

$m=\hat{m}+\tilde{m},---\left(1\right)$

Wherein

Be the number of super vertex,

Be the number of diffusing point, we claim $\hat{m}\≠0$ And $\tilde{m}\≠0$ And the GTSP problem be TSP-GTSP mixed problem, remember that all super vertexs are respectively:

$u_1,u_2,\·\·\·,u_{\hat{m}},---\left(N1\right)$

Wherein

u _i＝{u _i1，u _i2，…，u _ik}， (N2)

$k_i(i\∈N\left(\hat{m}\right))$ The number of representing i super vertex institute containing element, u _Il[l ∈ N (k _i)] represent l element in i the super vertex, claim that also l is u _IlAt super vertex u _iInterior sequence number, and remember that all points that loose are respectively:

${\tilde{u}}_1,{\tilde{u}}_2,\·\·\·,{\tilde{u}}_{\tilde{m}},---\left(N3\right)$

These super vertexs and loose point according to

$u_1,u_2,\·\·\·u_{\hat{m}},{\tilde{u}}_1,{\tilde{u}}_2,\·\·\·{\tilde{u}}_{\tilde{m}}---\left(N4\right)$

Series arrangement, simultaneously remember that according to the order of (N4) all generalized vertex are:

$w_1,w_2,\·\·\·,w_{\hat{m}+\tilde{m}}.---\left(N5\right)$

The pass of generalized vertex and super vertex and the point that looses is:

$w_k=\left\{\begin{array}{cc}{\mathrm{<figure-callout\; id="1"\; label="u\; k"\; filenames="A20071005565200181.png,A20071005565200183.png"\; state="\{\{state\}\}">u</figure-callout>}}_k& 1\&le;k\&le;\hat{m}\\ {\tilde{u}}_{k-\hat{m}}& \hat{m}+1\&le;k\&le;\hat{m}+\tilde{m}\end{array}\right.,k\&Element;N(\hat{m}+\tilde{m}).---\left(2\right)$

Therefore, also claim super vertex $u_i(i=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,\hat{m})$ Be i generalized vertex, claim the point that looses ${\tilde{u}}_i(i=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,\tilde{m})$ Be

Individual generalized vertex is easily known, the number of generalized vertex is

Promptly the number m of original group notices that same original vertices may belong to a plurality of super vertexs, and therefore inequality is arranged:

$n\&le;\tilde{m}+\underset{i=1}{\overset{\hat{m}}{\mathrm{\&Sigma;}}}{k}_i---\left(3\right)$

Set up.

The pattern of the chromosomoid of the present invention design as shown in Figure 3, this chromosome is divided into two parts: first is contained

Individual allele is called head; Second portion contains

Individual allele is called trunk; When $0<i\&le;\hat{m}$ The time, i gene is positioned at the head of chromosomoid.That this gene is deposited is the sequence number l[l ∈ N (k of accessed summit in super vertex in i the super vertex _i)] (seeing mark (N2)), when $\hat{m}<i\&le;\hat{m}+(\hat{m}+\tilde{m})$ The time, i gene is positioned at the trunk of chromosomoid, and what this gene was deposited is the sequence number of generalized vertex $k[k\&Element;N(\hat{m}+\tilde{m})],$ At this moment, as can be known: if k satisfies by (2) formula $k-\hat{m}\&le;\hat{m},$ Then the representative of this gene is the

Individual super vertex, promptly

If k satisfies $k-\hat{m}>\hat{m},$ Then the representative of this gene is the

Individual diffusing point, promptly

When carrying out the chromosomoid decoding, the gene of torso portion has been determined a GTSP loop of generalized vertex; The gene of head is in order to determine that super vertex is on accessed summit in front loop; If note

$H=\left\{h\right|h=[h\left(1\right),h\left(2\right),\&CenterDot;\&CenterDot;\&CenterDot;h\left(\hat{m}\right)],h\left(i\right)\&Element;N\left(k_i\right),i\&Element;N\left(\hat{m}\right)\},---\left(4\right)$

Wherein $h=[h\left(1\right),h\left(2\right),\&CenterDot;\&CenterDot;\&CenterDot;h\left(\hat{m}\right)]$ Be a finite sequence, the sequence number of the some elements in i super vertex of h (i) expression, then H is the set that all feasible genetic fragments of chromosomoid head constitute; If note

B＝{b|b＝∏(m)} (5)

B=∏ (m)=[b wherein ₁, b ₂..., b _m] be 1,2 ..., the full arrangement of m, then b represents a GTSP loop, so B is the set that all feasible genetic fragments of chromosomoid trunk constitute; If the set of all pairing chromosomoids in GTSP loop of note is D, then

D＝{x|x＝hb，h∈H，b∈B}， (6)

Wherein x=h  b represents by H, the chromosomoid that the genetic fragment among the B combines.

Having the vertex set V={1 of 20 elements, 2 ..., 20} is an example, establishes its part summit and is divided into following three groups

V ₁＝{1，2，3，4，12，13，15，17}， (7)

V ₂＝{3，4，6，7，16，19}， (8)

V ₃＝{8，9，10，11}， (9)

Diffusing point is respectively 5,14,18,20, as shown in Figure 4, at this moment, has

u ₁＝{u _1，1，u _1，2，u _1，3，u _1，4，u _1，5，u _1，6，u _1，7，u _1，8}

u ₂＝{u _2，1，u _2，2，u _2，3，u _2，4，u _2，5，u _2，6}， (10)

u ₃＝{u _3，1，u _3，2，u _3，3，u _3，4}

${\tilde{u}}_1=5,{\tilde{u}}_2=14,{\tilde{u}}_3=18,{\tilde{u}}_4=20$

Wherein

u _1，1＝1，u _1，2＝2，u _1，3＝3，u _1，4＝4，u _1，5＝12，u _1，6＝13，u _1，7＝15，u _1，8＝17

u ₂，1＝3，u _2，2＝4，u _2，3＝5，u _2，4＝6，u _2，5＝16，u _2，6＝19，

u _3，1＝8，u _3，2＝9，u _3，3＝10，u _3，4＝11

${\tilde{u}}_1=5,{\tilde{u}}_2=14,{\tilde{u}}_3=18,{\tilde{u}}_4=20$

Original vertices can be arranged in any order in the super vertex, but recommends to arrange according to the mode of descending; Same arrangement of loosing point is also recommended to carry out according to the mode of descending, at this moment, has $\hat{m}=3,\tilde{m}=4,$ The head that is chromosomoid has $3(\hat{m}=3)$ Individual gene, trunk has $7(\hat{m}+\tilde{m}=7)$ Individual gene; In order more clearly chromosomoid to be explained, designed the embodiment of two chromosomoids here especially, order

h ₁＝h ₂＝[3，1，2]， (11)

b ₁＝[3，5，6，1，4，2，7]， (12)

b ₂＝[3，5，6，4，1，2，7]， (13)

Can obtain two chromosomoids thus, be respectively:

x ₁＝h ₁b ₁， (14)

x ₂＝h ₂b ₂. (15)

Its structure can represent with Fig. 5 and Fig. 6 visually that corresponding GTSP loop respectively as shown in Figure 7 and Figure 8.Below with x ₁Introduce the decode procedure of chromosomoid for example.The gene of this chromosomoid head is 3,1,2, and they represent super vertex u respectively ₁In accessed be u _1,3, u ₂In accessed be u _2,1, u ₃In accessed be u _3,2The gene of trunk is 3,5,6,1,4,2,7, and they have represented a loop of 7 generalized vertex:

a1：w ₃→w ₅→w ₆→w ₁→w ₄→w ₂→w ₇→w ₃，

$a2:{\mathrm{<figure-callout\; id="3"\; label="u"\; filenames="A20071005565200181.png,A20071005565200182.png"\; state="\{\{state\}\}">u</figure-callout>}}_3\&RightArrow;{\tilde{u}}_2\&RightArrow;{\tilde{u}}_3\&RightArrow;{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="A20071005565200181.png,A20071005565200183.png"\; state="\{\{state\}\}">u</figure-callout>}}_1\&RightArrow;{\tilde{u}}_1\&RightArrow;{\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="A20071005565200183.png,A20071005565200212.png"\; state="\{\{state\}\}">u</figure-callout>}}_2\&RightArrow;{\tilde{u}}_4\&RightArrow;{\mathrm{<figure-callout\; id="3"\; label="u"\; filenames="A20071005565200181.png,A20071005565200182.png"\; state="\{\{state\}\}">u</figure-callout>}}_3,$

When genic value is not more than

The time, corresponding generalized vertex is a super vertex; When genic value greater than

The time, corresponding generalized vertex is the point that looses, therefore according to top decoding rule, the loop that this chromosome is represented should be:

$a3:{\mathrm{<figure-callout\; id="3"\; label="u"\; filenames="A20071005565200181.png,A20071005565200182.png"\; state="\{\{state\}\}">\; <figure-callout\; id="2"\; label="u"\; filenames="A20071005565200183.png,A20071005565200212.png"\; state="\{\{state\}\}">u</figure-callout>\; </figure-callout>}}_{\mathrm{3,2}}\&RightArrow;{\tilde{u}}_2\&RightArrow;{\tilde{u}}_3\&RightArrow;{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="A20071005565200181.png,A20071005565200183.png"\; state="\{\{state\}\}">\; <figure-callout\; id="3"\; label="u"\; filenames="A20071005565200181.png,A20071005565200182.png"\; state="\{\{state\}\}">u</figure-callout>\; </figure-callout>}}_{\mathrm{1,3}}\&RightArrow;{\tilde{u}}_1\&RightArrow;{\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="A20071005565200183.png,A20071005565200212.png"\; state="\{\{state\}\}">\; <figure-callout\; id="3"\; label="u"\; filenames="A20071005565200181.png,A20071005565200182.png"\; state="\{\{state\}\}">u</figure-callout>\; </figure-callout>}}_{\mathrm{2,3}}\&RightArrow;{\tilde{u}}_4\&RightArrow;{\mathrm{<figure-callout\; id="3"\; label="u"\; filenames="A20071005565200181.png,A20071005565200182.png"\; state="\{\{state\}\}">\; <figure-callout\; id="2"\; label="u"\; filenames="A20071005565200183.png,A20071005565200212.png"\; state="\{\{state\}\}">u</figure-callout>\; </figure-callout>}}_{\mathrm{3,2}},$

Be expressed as with original vertices:

a4：v ₉→v ₁₄→v ₁₈→v ₃→v ₅→v ₃→v ₂₀→v ₉

Be that last GTSP loop is:

a5：9→14→18→3→5→3→20→9.

In like manner, according to top decode procedure, chromosomoid x ₂The loop of pairing above-mentioned 5 kinds of forms is respectively:

b1：w ₃→w ₅→w ₆→w ₄→w ₁→w ₂→w ₇→w ₃，

$b2:{\mathrm{<figure-callout\; id="3"\; label="u"\; filenames="A20071005565200181.png,A20071005565200182.png"\; state="\{\{state\}\}">u</figure-callout>}}_3\&RightArrow;{\tilde{u}}_2\&RightArrow;{\tilde{u}}_3\&RightArrow;{\tilde{u}}_1\&RightArrow;{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="A20071005565200181.png,A20071005565200183.png"\; state="\{\{state\}\}">u</figure-callout>}}_1\&RightArrow;{\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="A20071005565200183.png,A20071005565200212.png"\; state="\{\{state\}\}">u</figure-callout>}}_2\&RightArrow;{\tilde{u}}_4{\&RightArrow;\mathrm{<figure-callout\; id="3"\; label="u"\; filenames="A20071005565200181.png,A20071005565200182.png"\; state="\{\{state\}\}">u</figure-callout>}}_3,$

$b3:{\mathrm{<figure-callout\; id="3"\; label="u"\; filenames="A20071005565200181.png,A20071005565200182.png"\; state="\{\{state\}\}">\; <figure-callout\; id="2"\; label="u"\; filenames="A20071005565200183.png,A20071005565200212.png"\; state="\{\{state\}\}">u</figure-callout>\; </figure-callout>}}_{\mathrm{3,2}}\&RightArrow;{\tilde{u}}_2\&RightArrow;{\tilde{u}}_3\&RightArrow;{\tilde{u}}_1\&RightArrow;{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="A20071005565200181.png,A20071005565200183.png"\; state="\{\{state\}\}">\; <figure-callout\; id="3"\; label="u"\; filenames="A20071005565200181.png,A20071005565200182.png"\; state="\{\{state\}\}">u</figure-callout>\; </figure-callout>}}_{\mathrm{1,3}}\&RightArrow;{\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="A20071005565200183.png,A20071005565200212.png"\; state="\{\{state\}\}">\; <figure-callout\; id="1"\; label="u"\; filenames="A20071005565200181.png,A20071005565200183.png"\; state="\{\{state\}\}">u</figure-callout>\; </figure-callout>}}_{2,1}\&RightArrow;{\tilde{u}}_4\&RightArrow;{\mathrm{<figure-callout\; id="3"\; label="u"\; filenames="A20071005565200181.png,A20071005565200182.png"\; state="\{\{state\}\}">\; <figure-callout\; id="2"\; label="u"\; filenames="A20071005565200183.png,A20071005565200212.png"\; state="\{\{state\}\}">u</figure-callout>\; </figure-callout>}}_{\mathrm{3,2}},$

b4：v ₉→v ₁₄→v ₁₈→v ₅→v ₃→v ₃→v ₂₀→v ₉，

b5：9→14→18→5→3→3→20→9.

Loop a4, v among the a5 ₃And v ₅Between have the loop of a closure, wherein a part is represented with dotted line in the drawings, loop b4, v among the b5 ₃The last path that has a visit self, v under the both of these case ₃All accessed twice.The limit that Origin And Destination is identical is called as ring in the drawings, and that dot in Fig. 8 is exactly a v ₃On ring, the appearance of both of these case all is because super vertex u ₁And u ₂Between exist due to the lap; The cost that is encircled as can be known by the definition of cost matrix is 0, so x ₁Cost inevitable greater than x ₂Cost, when chromosomoid being decoded into actual loop, remove the ring that all produce owing to super vertex is overlapping, just can obtain legal GTSP loop.

Genetic algorithm-class genetic method based on chromosomoid

In order to make this method be accepted by the researcher who uses GA easily, in the design of class genetic method, the present invention's continue to follow conventional lines basic framework of genetic algorithm, but in the realization of genetic manipulation, the singularity of chromosome structure makes class genetic method and conventional GA have tangible difference, provides the performing step of this method below:

A. colony's initializer P:

Initializer P is used for producing the initial population of given scale, and it is a binary random operator, and two arguments of effect are respectively H, B, the consequently subclass of chromosomoid set D.If note P is a colony, the initialization of P can be expressed as:

P＝P _N(H，B)， (16)

P wherein _NBe that scale is the initializer of the colony of N, its effect flow process as shown in Figure 9.

B. class crossover operator C:

In order to finish interlace operation, produce new chromosome, this paper has defined the class crossover operator

It is a binary random operator, and the argument of effect is the element among the chromosomoid set D, if x, and y ∈ D, x then, y can produce dyad under the effect of C:

(x′，y′)＝C(x，y)， (18)

X ' wherein, y ' be C with (genetic fragment of promptly intersecting is identical) under the direct action respectively with x, y be two words producing of parent for chromosome because C is a random operator, therefore generally speaking, if

(x ₁′，y ₁′)＝C(x，y)， (19)

(x ₂′，y ₂′)＝C(x，y)， (20)

Can not guarantee

x ₁′＝x ₂′， (21)

y ₁'=y ₂Set up ' (22).And if only if crossover operator C selects at random two intersect gene position when identical, (21), the establishment of (22) two formulas are just arranged.

Suppose x=h _x b _x, y=h _y b _y, the effect flow process of operator C as shown in figure 10, the effect of such crossover operator is similar to typical 2 interlace operations among the common GA, promptly selects two to intersect gene position on chromosome at random, is designated as i ₁, i ₂(might as well establish i ₁＜i ₂),

$i_1=\mathrm{random}(\hat{m}+(\hat{m}+\tilde{m})),$

$i_2=\mathrm{random}(\hat{m}+(\hat{m}+\tilde{m})),$

So, if $i_1>\hat{m},$ Then interlace operation occurs in trunk, because trunk is equivalent to a length is Autosome, therefore the effect of operator C is equivalent at autosome b in this case _x, b _yOn interlace operation, this moment has been owing to removed the chromosomal head genetic fragment of parent, needs translation to intersect the sequence number of gene position, that is:

$i_1\&DoubleLeftArrow;i_1-\hat{m},---\left(N6\right)$

$i_2\&DoubleLeftArrow;i_2-\hat{m}.---\left(N7\right)$

On the fragment that new intersection gene position is determined, carry out conventional interlace operation, be designated as

b _xb _y→(b _x′，b _y′)， (N8)

B wherein _x', b _y' ∈ B.Then with b _x', b _y' respectively with x, the combination of the head genetic fragment of y promptly obtains representing the child chromosome in corresponding GTSP loop, is designated as:

x′＝h _xb _x′. (23)

y′＝h _yb _y′. (24)

If $i_2\&le;\hat{m},$ Then the class interlace operation occurs in head fully, and at this moment the class crossover operator just exchanges the gene on the intersection fragment, is designated as:

h _xh _y→(h _x′，h _y′)， (N9)

H wherein _x', h _y' ∈ H.Then h _x', h _y' respectively with x, the combination of the head genetic fragment of y promptly obtains representing the child chromosome in corresponding GTSP loop, is designated as:

x′＝h _x′b _x. (25)

y′＝h _y′b _y. (26)

If $i_1\&le;\hat{m}$ And $i_2>\hat{m},$ Then can regard the combination of top two class interlace operations as, one occur in by And i ₂On the genetic fragment of determining, another occurs in by i ₁And

On the genetic fragment of determining; Carry out this two interlace operations respectively according to top mode, then corresponding new head that produces and trunk genetic fragment are made up the child chromosome that just obtains representing the GTSP loop, therefore, two broad sense child chromosome can be designated as respectively:

x′＝h _x′b _x′， (27)

y′＝h _y′b _y′. (28)

C. class mutation operator M:

In order to increase the diversity of chromogene fragment, the present invention with the genetic manipulation mode-definition of inserting variation the class mutation operator

It is the monobasic random operator, and the argument of effect is the element among the chromosomoid set D.If x ∈ D, then x can produce a new chromosome under the effect of M:

x′＝M(x). (30)

Be similar to class crossover operator C, because M is a random operator, so generally speaking, if the variation individuality that x produces under two secondary actions of class mutation operator M is respectively:

x ₁′＝M(x)， (31)

x ₂′＝M(x). (32)

Can not guarantee

x ₁′＝x ₂′. (33)

And if only if preparation gene that mutation operator M selects at random and insert gene position when all identical just has the establishment of (33) formula, and this probability for random operator M is very little.

Suppose x=h _x b _x, and

$h_x=[h\left(1\right),h\left(2\right),\&CenterDot;\&CenterDot;\&CenterDot;h\left(\hat{m}\right)],---\left(34\right)$

$b_x=[b\left(1\right),b\left(2\right),\&CenterDot;\&CenterDot;\&CenterDot;b(\hat{m}+\tilde{m})],---\left(35\right)$

Then the effect flow process of operator M as shown in figure 11, such mutation operator executable operations is similar among the common GA genetic manipulation that inserts variation, promptly at first selects a preparation gene as the gene that is inserted on chromosomoid, supposes that the gene position of this preparation gene is:

$i=\mathrm{random}(\hat{m}+(\hat{m}+\tilde{m}))$

Different with common mutation genetic operation is:

If $i>\hat{m},$ Then should prepare the trunk of gene, and can determine it is b at chromosomoid _x

Individual component is b _xThe gene of middle preparation gene back moves forward a gene position successively, generates interim genetic fragment

$b_x^{\&prime;\&prime;}=[b\left(1\right),b\left(2\right),\&CenterDot;\&CenterDot;\&CenterDot;b(i-\hat{m}-1),b(i-\hat{m}+1),\&CenterDot;\&CenterDot;\&CenterDot;,b(\hat{m}+\tilde{m})].---\left(36\right)$

Next in length be

Interim genetic fragment b _x" on select one to insert gene position at random

$s=\mathrm{random}(\hat{m}+\tilde{m}-1),---\left(37\right)$

This is similar with conventional insertion mutation operation, the selectional restriction of just inserting gene position is on the interim genetic fragment that is generated by trunk, obtain preparing gene and insert after the gene position, mutation operator moves a gene position to the gene that inserts gene position b (s) back after successively earlier, and

Be inserted on the follow-up gene position of b (s), the new chromosomoid that note mutation operator M effect back produces is:

x′＝h _xb _x′， (38)

Wherein

$b_x^{\&prime;}=[b\left(1\right),b\left(2\right),\&CenterDot;\&CenterDot;\&CenterDot;,b(i-\hat{m}-1),$

$b(i-\hat{m}+1),\&CenterDot;\&CenterDot;\&CenterDot;,b\left(s\right),b(i-\hat{m}),b(s+1),\&CenterDot;\&CenterDot;\&CenterDot;,b(\hat{m}+\tilde{m})]---\left(39\right)$

If $i\&le;\hat{m},$ Then should prepare the head of gene, and can determine it is h at chromosomoid _xI component h (i).At this moment, need not to continue to select to insert gene position, be used in 1,2 ..., k _iIn the integer selected at random replace the preparation gene and get final product, the new chromosomoid that produces after the mutation operator effect is:

x′＝h _x′b _x， (40)

Wherein

$h_x=[h\left(1\right),h\left(2\right),\&CenterDot;\&CenterDot;\&CenterDot;,h(i-1),\mathrm{random}\left(k_i\right),h(i+1),\&CenterDot;\&CenterDot;\&CenterDot;h\left(\hat{m}\right)].---\left(41\right)$

D. class mutation operator R:

In order to improve the speed of convergence of class genetic method, this paper has designed class and has reversed operator

It is the monobasic random operator, and the argument of effect also is the element among the chromosomoid set D.If x ∈ D, then x produces a new chromosome under the effect of R:

x′＝R(x). (43)

Be similar to class mutation operator M equally, generally speaking, be respectively x if x reverses the variation individuality that produces under two secondary actions of operator R in class ₁'=R (x), x ₂'=R (x) can not guarantee

x ₁′＝x ₂′. (44)

When two reverse gene position that class that and if only if reverse operator R selects at random are identical, just there is (44) formula to set up.Different with class mutation operator M is that R only implements the torso portion of chromosomoid and reverses operation.Suppose that two reverse gene position selecting at random are respectively i ₁, i ₂(might as well establish i ₁＜i ₂), as shown in figure 12, then the effect flow process of operator R is as shown in figure 13.

Be similar to the conventional operation that reverses, operator R is at first at b _xTwo of last selections reverse gene position i ₁, i ₂

$i_1=\mathrm{random}(\hat{m}+\tilde{m}),---\left(45\right)$

$i_2=\mathrm{random}(\hat{m}+\tilde{m})---\left(46\right)$

If b is (i ₁), b (i ₂) in have super vertex, relate to b (i in the pricing below then ₁), b (i ₂) the place, all be in accessed original vertices in the front loop for this super vertex.Note

g ₁＝d(b(i ₁)，b(i ₂))+d(b(i ₁+1)，b(i ₂+1))， (47)

g ₂＝d(b(i ₁)，b(i ₂+1))+d(b(i ₁+1)，b(i ₂))， (48)

If g ₂＜g ₁, then b (i ₁+ 1) to b (i ₂) order of gene reverses on the fragment, obtain

$b_x^{\&prime;}=[b\left(1\right),\&CenterDot;\&CenterDot;\&CenterDot;,b\left(i_1\right)b\left(i_2\right),b(i_2-1),$

$\&CenterDot;\&CenterDot;\&CenterDot;,b({\mathrm{<figure-callout\; id="1"\; label="i"\; filenames="A20071005565200181.png,A20071005565200183.png"\; state="\{\{state\}\}">i</figure-callout>}}_1+2),b({\mathrm{<figure-callout\; id="1"\; label="i"\; filenames="A20071005565200181.png,A20071005565200183.png"\; state="\{\{state\}\}">i</figure-callout>}}_1+1),b({\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="A20071005565200183.png,A20071005565200212.png"\; state="\{\{state\}\}">i</figure-callout>}}_2+1),\&CenterDot;\&CenterDot;\&CenterDot;,b(\hat{m}+\tilde{m}){]}^{,}---\left(49\right)$

Produce new chromosomoid then

x′＝h _xb _x′. (50)

Otherwise, do not do any operation.

E. fitness:

Fitness function adopts the form that is similar to common GA used fitness function when finding the solution the TSP problem among the present invention, still line taking calibration, and its form is:

$f\left(x\right)=\mathrm{\&alpha;}\sqrt{\hat{m}+\tilde{m}}A/T\left(x\right),---\left(51\right)$

X ∈ D wherein, α is predefined constant,

With

Be respectively the number of the super vertex and the point that looses, A is the length of side that comprises the minimum regular polygon of vertex set V, when V is point set under the two-dimentional euclidean geometry meaning, A is exactly the length of side that comprises the smallest square on all summits, T (x) is an objective function, the access cost in promptly actual GTSP loop, and its form is;

$T\left(x\right)T(h_x\&CirclePlus;b_x)=d(b\left(1\right),b(\hat{m}+\tilde{m}))+\underset{i=2}{\overset{\hat{m}+\tilde{m}}{\mathrm{\&Sigma;}}}d(b\left(i\right),b(i-1)).---\left(52\right)$

Here it should be noted that not every original vertices all is comprised in the current loop in GTSP, the calculating of super vertex cost refers to that it is at original vertices accessed in front loop and the access cost between other summit.

Claims (6)

1, a kind of class genetic method that is used for logistic optmum is characterized in that: comprise the steps: at least

Step (1): the structure chromosomoid, chromosomoid is to grouping information and accessed vertex information coding;

Step (2): the intersection task of chromosomoid is finished in definition class crossover operator/operation;

Step (3): the variation task of chromosomoid is finished in definition class mutation operator/operation;

Step (4): class reverses the reverse task that chromosomoid is finished in operator/operation;

Step (5): the class fitness function is finished the evaluation task of chromosomoid.

2, a kind of class genetic method that is used for logistic optmum according to claim 1 is characterized in that: by chromosomoid grouping information in the broad sense traveling salesman problem and accessed vertex information are encoded simultaneously.

3, a kind of class genetic method that is used for logistic optmum according to claim 2, it is characterized in that: described chromosomoid is made up of two parts coded strings, wherein:

Part coded strings has and the relevant figure place of grouping book;

Another part coded strings has the coding figure place relevant with two accessed class summits.

4, a kind of class genetic method that is used for logistic optmum according to claim 1, it is characterized in that: the process of described class interlace operation comprises at least:

Transposition section is carried out a class interleaved scheme when head;

Transposition section is carried out a class interleaved scheme when trunk;

When transposition section comprises head and trunk bits of coded, carry out a class interleaved scheme.

5, a kind of class genetic method that is used for logistic optmum according to claim 1, it is characterized in that: the process of described class mutation operation comprises at least:

Class variation scheme is carried out in the variation position when head;

Class variation scheme is carried out in the variation position when trunk.

6, a kind of class genetic method that is used for logistic optmum according to claim 1 is characterized in that: the process that described class reverses operation comprises at least:

Reverse the interval when trunk, carry out a class and reverse scheme;

Reverse the interval when head, carry out a class and reverse scheme.

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