CN106169106A - A kind of one-dimensional cutting-stock problem optimized algorithm based on uniform ordered search - Google Patents

Abstract

The invention discloses a kind of one-dimensional cutting-stock problem optimized algorithm based on uniform ordered search, for solving the problem that in actual production, one-dimensional cutting-stock problem optimizes.The present invention includes: (1) calculates the average total number needing raw sheet material；(2) calculate lath and be evenly distributed in the quantity in every block of sheet material, the situation that prevention utilization rate is uneven；(3) structure lath demand pair, descending；(4) according to the lath demand constructed to arranging, one group of typesetting combination is obtained；(5) by progressively in order scalping method, current permutation and combination of recombinating on the basis of traversal principle, and preserve that utilization rate is more excellent one group.(6) repeat step (5), until meet set search element condition, obtain optimum combination.The present invention is by being evenly distributed typesetting so that global optimization utilization rate is high, and avoids the uneven phenomenon of utilization rate, and production efficiency is improved.

Description

A kind of one-dimensional cutting-stock problem optimized algorithm based on uniform ordered search

Technical field

The present invention relates to plate cutting optimized algorithm method, be specifically related to the one-dimensional stock-cutting method of sheet material.

Background technology

The one-dimensional cutting-stock problem of sheet material, refers to when raw material and material requested dimension are all one-dimensional, at known order requirements and How optimizing incision blanking under raw material data so that raw material is fully used as far as possible, cost obtains the planning saved as far as possible Problem.Traditional one-dimensional cutting-stock problem algorithm there is also a lot of deficiency, and waste is big, and algorithm performs unreasonable, and algorithm performs process efficiency Low.

Summary of the invention

The technical problem to be solved is for above-mentioned deficiency of the prior art, it is provided that a kind of based on uniform The one-dimensional cutting-stock problem optimized algorithm of ordered search, its algorithm is with the obvious advantage, it is possible to efficient and rational typesetting.

In order to achieve the above object, the present invention is achieved by the following technical solutions:

A kind of one-dimensional cutting-stock problem optimized algorithm based on uniform ordered search, it comprises the steps of:

(1) structure lath demand pair: according to width of sheet, descending lath demand is to (H_i,N_i,) queue, from queue Middle rejecting N_iIt is the demand pair of zero, recalculates quantity n of demand pair；If n=0, illustrate that this processing tasks is fully completed, knot Shu Benci processing tasks goes to step (7), otherwise turns next step (2)；

(2) judge that width is W_sIf sheet material only put wide lath H₁, if can just put down.

First sheet material W is calculated_sIn can put wide lath H₁Maximum typesetting quantity

$Q_s^1=W_s/H_1$

IfThen

Then sheet material surplus material width is sought

$E_s^1=W_s-H_1{Q}_s^1$

IfBetween 0-5mm, then the N of centering of upgrading demand₁,Front s block sheet material surplus material width sumPreserve current typesetting data, O [1] .H=H₁,

This width is W_sSheet material typesetting terminate, the 1st group of data of the Array for structural body O [k] deposited that goes bail for, generate processing G code program, take off a sheet material (s adds 1), go to step (1)；

IfMore than 5mm, that is this typesetting is invalid typesetting, turns next step (3)；

(3) the s time processing strip width are W_sSheet material time, according to lath demand to (H_i,N_i,) queue, computational theory On need average total number amount M of sheet material^s:

$M^s=\left(\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{H}_i{N}_i\right)/\stackrel{\‾}{W}$

Make sheet material W_sResidue widthInitial typesetting number of times k=1, takes first group of lath demand to i.e. i=1, under turning One step (4)；

(4) if i is more than n, then i=1.Calculate lath H_iAt sheet material W_sOn average typesetting quantity

$P_s^i=N_i/M^s$

IfThenUpdate i-th group of lath demand to (H_i,N_i,In)Turn next step (5)；

(5) s block sheet materials, when kth time typesetting, take i-th group of lath demand to (H_i,N_i,), calculate

$E_s^k=E_s^{k-1}-H_i{P}_s^i$

IfAt 0-H_nBetween (can be by progressively in order scalping method and ergodic algorithm are searched optimum typesetting and combined), the most more New i-th group of lath demand is to (H_i,N_i,N in)_i,Front s block sheet material surplus material width sumProtect Deposit current typesetting data, O [k] .H=H_i,This width is W_sSheet material typesetting terminate, the structure deposited of going bail for The front k group data of array O [k], generate the G code program of processing, take off a sheet material (s adds 1), go to step (1)；

IfLess than 0 andMore than 1, thenSubtract 1, update i-th group of demand to (H_i,N_i,In)After go to step (5)；

IfLess than 0 andLess than or equal to 1, this time typesetting is invalid typesetting, then take off one group of lath i=i+1, go to step (4)；

IfMore than H_n, then i-th group of lath demand is updated to (H_i,N_i,N in)_i,Reject from queue N_iIt is the demand pair of zero, recalculates quantity n of demand pair.Preserve current typesetting data, O [k] .H=H_i,Turn Next step (6)；

(6) if n more than 0 andAt 0-H_nBetween, then this width is W_sSheet material typesetting terminate, front s block sheet material residue material Material width sumGo bail for the front k group data of the Array for structural body O [k] deposited, generate the G code program of processing, take off one Sheet material (s adds 1), goes to step (1)；

If n more than 0 andMore than H_n, then take off one group of lath i=i+1, k=k+1, go to step (4)；

If n is equal to 0, current width is W_sSheet material typesetting terminate, and all laths machine.Front s block sheet material remains Material width sumGo bail for the front k group data of the Array for structural body O [k] deposited, generate the G code program of processing, under turning One step (7)；

(7) terminate.

Further: described sheet material is workblank sheet material, it is known that workblank sheet material mean breadth isAnd

Further: described lath is to meet the sheet material of client's width requirement after processing, and lath thickness is the thickness of lath Degree is added with the thickness of cutting knife.

Further: lath demand is to (H_i,N_i) expression width is H_iLath quantity required be N_i(i=1,2 ..., n)；

During s block sheet material typesetting, theoretical demand sheet material average total number amount is M^s, its computing formula is:

$M^s=\left(\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{H}_i{N}_i\right)/\stackrel{\‾}{W}$

Process a width of W the s time_sSheet material time, a width of H of lath can be put_iPar be

$P_s^i=N_i/M^s$

Value principle be: if N_i/M^sThere is decimal, then add 1 after round numbers part, otherwise direct round numbers part；IfMore than N_i, thenEqual to N_i, otherwiseValue is carried out by above-mentioned value principle；

Process a width of W the s time_sSheet material when kth time typesetting, put intoThe a width of H of block_iLath after, sheet material W_sResidue material Material width is Being the process successively decreased of a circulation, k is the effective of current sheet material Typesetting number of times；Often add 1 through once effectively typesetting k value, until sheet material surplus material widthUndressed less than current residual Lath in minimum width of sheet；

Process a width of W the s time_sSheet material when kth time typesetting, the maximum quantity that can put into i-th group of lath is

$Q_s^i=E_s^{k-1}/H_i,(E_s^0=W_s,k=1)$

Value beInteger part, ifMore than N_i, thenEqual to N_i；OtherwiseConstant.

The medicine have the advantages that

Algorithm disclosed by the invention is the most efficient, it is possible to efficient and rational typesetting, greatly reduces waste, it is possible to contribute to automatically Change the realization of typesetting；Its typesetting scheme also more conforms to needs of production, and according to concrete practice, its effect saving material is non- Chang Hao.

Accompanying drawing explanation

Fig. 1 is that a kind of one-dimensional cutting-stock problem optimized algorithm based on uniform ordered search of the present invention obtains one group of fundamental optimum combination Flow chart.

Fig. 2 is the description of flow diagram that progressively rejecting is sent out in order used in the present invention.

Detailed description of the invention

Below in conjunction with embodiment, the present invention is further described, and following embodiment is illustrative, is not determinate, Protection scope of the present invention can not be limited with following embodiment.

A kind of one-dimensional cutting-stock problem optimized algorithm based on uniform ordered search disclosed by the invention following basic principle of employing:

1. start typesetting from the widest lath every time, ranked second successively, the 3rd wide lath, by that analogy.

2. during typesetting, (the sheet material surplus material width that first considers that wide lath is just arranged downBetween 0～5mm) Typesetting.

3. secondly, the lath of various different in width is evenly distributed in M as far as possible^sIn block sheet material.

Illustrate that the present invention's is embodied as step below in conjunction with the accompanying drawings.

As it is shown in figure 1, for obtaining the step that one group of fundamental optimum combines, idiographic flow is as follows:

(1) structure lath demand pair: according to width of sheet, descending lath demand is to (H_i,N_i,) queue, from queue Middle rejecting N_iIt is the demand pair of zero, recalculates quantity n of demand pair；If n=0, illustrate that this processing tasks is fully completed, knot Shu Benci processing tasks goes to step (7), otherwise turns next step (2)；

(2) judge that width is W_sIf sheet material only put wide lath H₁, if can just put down.

First sheet material W is calculated_sIn can put wide lath H₁Maximum typesetting quantity

$Q_s^1=W_s/H_1$

IfThen

Then sheet material surplus material width is sought

$E_s^1=W_s-H_1{Q}_s^1$

IfBetween 0-5mm, then the N of centering of upgrading demand₁,Front s block sheet material surplus material width sumPreserve current typesetting data, O [1] .H=H₁,

This width is W_sSheet material typesetting terminate, the 1st group of data of the Array for structural body O [k] deposited that goes bail for, generate processing G code program, take off a sheet material (s adds 1), go to step (1)；

IfMore than 5mm, that is this typesetting is invalid typesetting, turns next step (3)；

(3) the s time processing strip width are W_sSheet material time, according to lath demand to (H_i,N_i,) queue, computational theory On need average total number amount M of sheet material^s:

$M^s=\left(\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{H}_i{N}_i\right)/\stackrel{\‾}{W}$

Make sheet material W_sResidue widthInitial typesetting number of times k=1, takes first group of lath demand to i.e. i=1, under turning One step (4)；

(4) if i is more than n, then i=1.Calculate lath H_iAt sheet material W_sOn average typesetting quantity

$P_s^i=N_i/M^s$

IfThenUpdate i-th group of lath demand to (H_i,N_i,In)Turn next step (5)；

(5) s block sheet materials, when kth time typesetting, take i-th group of lath demand to (H_i,N_i,), calculate

$E_s^k=E_s^{k-1}-H_i{P}_s^i$

IfAt 0-H_nBetween (can on the basis of traversal principle by progressively in order scalping method search optimum typesetting group Close), then update i-th group of lath demand to (H_i,N_i,N in)_i,Front s block sheet material surplus material width sumPreserve current typesetting data, O [k] .H=H_i,This width is W_sSheet material typesetting terminate, go bail for and deposit The front k group data of Array for structural body O [k], generate the G code program of processing, take off a sheet material (s adds 1), go to step (1)；

IfLess than 0 andMore than 1, thenSubtract 1, update i-th group of demand to (H_i,N_i,In)After go to step (5)；

IfLess than 0 andLess than or equal to 1, that is this time typesetting is invalid typesetting, then take off one group of lath i=i+1, turns Step (4)；

IfMore than H_n, then i-th group of lath demand is updated to (H_i,N_i,N in)_i,Reject from queue N_iIt is the demand pair of zero, recalculates quantity n of demand pair.Preserve current typesetting data, O [k] .H=H_i,Turn Next step (6)；

(6) if n more than 0 andAt 0-H_nBetween, then this width is W_sSheet material typesetting terminate, front s block sheet material residue material Material width sumGo bail for the front k group data of the Array for structural body O [k] deposited, generate the G code program of processing, take off one Sheet material (s adds 1), goes to step (1)；

If n more than 0 andMore than H_n, then take off one group of lath i=i+1, k=k+1, go to step (4)；

If n is equal to 0, current width is W_sSheet material typesetting terminate, and all laths machine.Front s block sheet material remains Material width sumGo bail for the front k group data of the Array for structural body O [k] deposited, generate the G code program of processing, under turning One step (7)；

(7) terminate.

As in figure 2 it is shown, be the algorithm flow of the progressively orderly scalping method arrived used herein, specific implementation process is as follows Shown in:

A () obtains the permutation and combination that current one-dimensional cutting-stock problem optimizes；

B () current permutation and combination is the most only made up of the widest of lath demand centering and strap, if it is optimize Terminate, obtain optimum combination, otherwise turn next step；

C () judges whether the minimum lath in current permutation and combination is equal to the minimum lath of lath demand centering, if Then the minimum lath of current permutation and combination is therefrom rejected, after then the second little lath arrangement quantity being reduced one piece, take lath Next group lath of demand centering arranges, and turns next step；Otherwise the minimum lath of current permutation and combination is therefrom rejected, so After take lath demand centering next group lath carry out arrangement turn next step；

D () is according to basic principle, re-optimization typesetting, it is thus achieved that one group of new optimum organization, goes to step (a).

Concrete denotational description in above-mentioned detailed description of the invention and in description such as table 1:

Table 1

Makeup Optimization data variation process of the algorithm of the present invention is as shown in table 2:

Table 2 typesetting data change procedure

The most just to algorithm proposed by the invention, the superiority of the present invention is described for an application example.

Assume sheet material mean breadth:Specifically every piece of former strip width only just knows when feeding that it is concrete Value, cutting knife thickness is 10mm.Existing lath needs processing, and occurrence is as shown in table 3:

Table 3 lath demand pair

Theory demands sheet material average total number amount is:

$\begin{array}{c}{M}^1=\left(\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{H}_i{N}_i\right)/\stackrel{\‾}{W}\\ =19073/1500\\ \≈13\end{array}$

According to the average total number amount of required raw sheet material, calculate the average typesetting quantity of lath demand pair, take raw sheet successively Material is optimized typesetting, obtains final cutting data, as shown in table 4 below:

The final process data of table 4 principle of the invention

By examples detailed above, can verify that the Optimum utilization rate of inventive algorithm is the highest, it is possible to be prevented effectively from excellent Changing the situation that utilization rate is uneven, above example, after the time getting rid of data input, obtains the deficiency of time 1 second of optimum results, It is quickly that visible its optimizes efficiency.

Above the preferred embodiment for the present invention is explained in detail, but the invention is not restricted to above-mentioned embodiment, In the ken that those of ordinary skill in the art are possessed, it is also possible to make various on the premise of without departing from present inventive concept Change, these changes relate to correlation technique well-known to those skilled in the art, and these both fall within the protection model of patent of the present invention Enclose.

Many other can be made without departing from the spirit and scope of the present invention to change and remodeling.Should be appreciated that the present invention is not Being limited to specific embodiment, the scope of the present invention is defined by the following claims.

Claims (6)

1. an one-dimensional cutting-stock problem optimized algorithm based on uniform ordered search, it is characterised in that comprise the steps of:

(1) structure lath demand pair: according to width of sheet, descending lath demand is to (H_i, N_i,) queue, from queue Reject N_iIt is the demand pair of zero, recalculates quantity n of demand pair；If n=0, illustrate that this processing tasks is fully completed, terminate This processing tasks goes to step (7), otherwise turns next step (2)；

(2) judge that width is W_sIf sheet material only put wide lath H₁, if can just put down:

First sheet material W is calculated_sIn can put wide lath H₁Maximum typesetting quantity:

=W_s/H₁

If>N₁, then= N₁;

Then sheet material surplus material width is sought:

=W_s-H₁

IfBetween 0-5mm, then the N of centering of upgrading demand₁, N₁=N₁-, front s block sheet material surplus material width sum=+, preserve current typesetting data, O [1] .H=H₁, O [1] .N=;

This width is W_sSheet material typesetting terminate, the 1st group of data of the Array for structural body O [k] deposited that goes bail for, generate processing G generation Coded program, takes off a sheet material (s adds 1), goes to step (1)；

IfMore than 5mm, that is this typesetting is invalid typesetting, turns next step (3)；

(3) the s time processing strip width are W_sSheet material time, according to lath demand to (H_i, N_i, ) queue, in computational theory Need average total number amount M of sheet material^s:

Make sheet material W_sResidue width=W_s, initial typesetting number of times k=1, take first group of lath demand to i.e. i=1, turn next step (4)；

(4) if i is more than n, then i=1, lath H is calculated_iAt sheet material W_sOn average typesetting quantity:

=N_i/M^s

If>N_i, then=N_i, update i-th group of lath demand to (H_i, N_i, In), turn next step (5)；

(5) s block sheet materials, when kth time typesetting, take i-th group of lath demand to (H_i, N_i, ), calculate:

IfAt 0-H_nBetween (can on the basis of traversal principle by progressively in order scalping method search optimum typesetting and combine), Then update i-th group of lath demand to (H_i, N_i, N in)_i, N_i=N_i-, front s block sheet material surplus material width sum=+, preserve current typesetting data, O [k] .H=H_i, O [k] .N=, this width is W_sSheet material typesetting terminate, the knot deposited of going bail for The front k group data of structure body array O [k], generate the G code program of processing, take off a sheet material (s adds 1), go to step (1)；

IfLess than 0 andMore than 1, thenSubtract 1, update i-th group of demand to (H_i, N_i, In)After go to step (5)；

IfLess than 0 andLess than or equal to 1, this time typesetting is invalid typesetting, then take off one group of lath i=i+1, go to step (4)；

IfMore than H_n, then i-th group of lath demand is updated to (H_i, N_i, N in)_i, N_i=N_i-, from queue, reject N_iFor The demand pair of zero, recalculates quantity n of demand pair, preserves current typesetting data, O [k] .H=H_i, O [k] .N=, turn next step Suddenly (6)；

(6) if n more than 0 andAt 0-H_nBetween, then this width is W_sSheet material typesetting terminate, front s block sheet material surplus material width Degree sum=+, the front k group data of the Array for structural body O [k] deposited that goes bail for, generate the G code program of processing, take off a sheet material (s adds 1), go to step (1)；

If n more than 0 andMore than H_n, then take off one group of lath i=i+1, k=k+1, go to step (4)；

If n is equal to 0, current width is W_sSheet material typesetting terminate, and all laths machine, front s block sheet material surplus material width Degree sum=+, the front k group data of the Array for structural body O [k] deposited that goes bail for, generate the G code program of processing, turn next step (7)；

(7) terminate.

A kind of one-dimensional cutting-stock problem optimized algorithm based on uniform ordered search, it is characterised in that: it is used for Optimizing the width of sheet calculated is that actual demand width of sheet adds upper cutter thickness.

A kind of one-dimensional cutting-stock problem optimized algorithm based on uniform ordered search, it is characterised in that: lath Demand is to (H_i, N_i) expression width is H_iLath quantity required be N_i(i=1,2 ..., n)；

During s block sheet material typesetting, theoretical demand sheet material average total number amount is M^s, its computing formula is:

Process a width of W the s time_sSheet material time, a width of H of lath can be put_iPar be:

=N_i/M^s

Value principle be: if N_i/M^sThere is decimal, then add 1 after round numbers part, otherwise direct round numbers part；IfGreatly In N_i, thenEqual to N_i, otherwiseValue is carried out by above-mentioned value principle.

A kind of one-dimensional cutting-stock problem optimized algorithm based on uniform ordered search, it is characterised in that: can put The a width of H of lath_iPar be, lath is evenly distributed in every block of raw sheet material and cuts, prevention utilization rate distribution Uneven.

A kind of one-dimensional cutting-stock problem optimized algorithm based on uniform ordered search, it is characterised in that: time Combined by the typesetting that progressively scalping method lookup is optimum in order on the basis of going through principle.

A kind of one-dimensional cutting-stock problem optimized algorithm based on uniform ordered search, it is characterised in that: progressively In order in scalping method, if the minimum width of sheet in current optimum organization is equal to the minimum lath H in lath demand queue_n, then Last two groups of laths of this permutation and combination are rejected, takes next group of lath demand centering and carry out new one and take turns optimization；Otherwise will Last 1 group of lath of this permutation and combination is rejected, and takes next group of lath demand centering and carries out new one and take turns optimization.