CN110909947B - Rectangular part layout method and equipment based on wolf algorithm - Google Patents
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Abstract
The invention discloses a rectangular part stock layout method and equipment based on a wolf algorithm, and belongs to the field of structural part optimized blanking. The method comprises the following steps: setting an algorithm target function and a constraint condition; initializing a wolf group, decoding and positioning based on a lowest horizontal line method of fitness, solving the material utilization rate and sequencing the grades to determine alpha wolf; all the gray wolves wander, the material utilization rate and alpha wolves are obtained for updating; gray wolf attacks prey, and the material utilization rate and alpha wolf updating are obtained; the iteration is circulated until the end condition is reached to obtain the optimal solution, namely the position code X of the alpha wolf α And the concentration of prey odor Y it senses α Namely, the optimal layout scheme and the corresponding material utilization rate are obtained. The rectangular part layout method based on the gray wolf algorithm can improve the utilization rate of the plates and the solving speed, and has good practicability and applicability in solving the rectangular part layout problem.
Description
Technical Field
The invention belongs to the field of structural part optimized blanking, and particularly relates to a rectangular part layout method and equipment based on a gray wolf algorithm.
Background
With the upgrading and transformation of the manufacturing enterprise, the enterprise wants to obtain a larger market share in a fierce market competition and a revolutionary environment, and the realization of energy conservation, emission reduction, digitization and automatic intelligent manufacturing is very important. The requirements of enterprises on actual production cannot be met even though the stock layout is carried out through human experience and some low-efficiency algorithms, and the enterprises urgently need a stock layout method with high raw material utilization rate and high solving speed. The rectangular layout refers to the arrangement of rectangular pieces with different specifications on a specific rectangular plate according to an optimal layout scheme. The problem of layout of rectangular pieces is widely existed in the industries of panel furniture cutting, mechanical equipment manufacturing, clothing, glass, printing and the like. Because the part graphs except the rectangle can be converted into the rectangle through splicing or enveloping, the method for optimizing the layout of the rectangular part, which has the advantages of high solving speed and high material utilization rate, has important significance.
The essence of the rectangular piece layout problem is the sequencing and positioning of part graphs, and the prior art mainly adopts the meta-heuristic algorithm sequencing and the heuristic algorithm positioning mode to perform layout. The meta-heuristic algorithm mainly represents a genetic algorithm, an ant colony algorithm, a particle swarm algorithm, a simulated annealing algorithm, a tabu search algorithm and the like, and different algorithms can form a new algorithm through optimized combination. The heuristic algorithms mainly comprise a BL algorithm, a lower step algorithm, a minimum horizon method and the like, and the research on the aspects is also continuously improved and perfected. For the stock layout problem, the existing optimization algorithms can be used for solving a better stock layout scheme.
However, after examining and analyzing the published and published literature, the above prior art still has some defects or shortcomings:
firstly, the existing algorithm for solving the rectangular piece layout problem is complex in structure and multiple in steps, so that the solving time is long, and the production efficiency of an enterprise is influenced; secondly, the existing algorithms are not strong in adaptability, for example, when a rectangular part to be subjected to layout is determined by the lowest horizontal line algorithm, the width of the lowest horizontal line is mainly compared with the width of the rectangle, when a strip rectangle with small width exists in the part to be subjected to layout, a layout pattern has a local area which is higher and has more gaps, and the utilization rate of the plate is obviously reduced; finally, in the current intelligent optimization algorithms, solution time is shortened by sacrificing a certain utilization rate, so that the utilization rate of the plate is low, and a certain lifting space exists.
Based on the defects and shortcomings, the existing stock layout method is needed to be improved, a new rectangular optimized stock layout method is designed, and the utilization rate of the plate is further improved within an acceptable solving time range, so that the production efficiency of enterprises can be improved, the production cost is reduced, and the upgrading and transformation of the manufacturing industry are facilitated.
Disclosure of Invention
Aiming at the defects or the improvement requirements of the prior art, the invention provides a rectangular piece layout method and equipment based on a gray wolf algorithm, and aims to complete sequencing and positioning calculation of rectangular pieces to be laid by combining a decimal gray wolf algorithm and a lowest horizontal line algorithm based on fitness, so that a layout scheme with high utilization rate is obtained by adopting shorter solving time, the solving efficiency and the optimal solution quality are considered, the adaptability is strong, and the problem of optimizing layout of various rectangular pieces can be solved quickly and effectively.
To achieve the above object, according to an aspect of the present invention, there is provided a rectangular part layout method based on a graywolf algorithm, including the steps of:
step 1: setting a target function to enable the material utilization rate to be highest, wherein the constraint conditions are that all rectangular parts do not exceed the plate boundary after being discharged, the parts do not overlap with each other, the rectangular parts do not rotate, and no cutting process constraint exists;
step 2: initializing a wolf cluster in a random mode, namely randomly generating M decimal grays to represent M rectangular piece sequences, decoding to form corresponding layout patterns based on a lowest level line method of fitness, calculating the material utilization rate of each layout pattern, and setting the solution with the maximum current material utilization rate in the wolf cluster as alpha wolf according to the social level system of the wolf cluster to represent the current optimal rectangular piece sequence;
and step 3: the gray wolf walks step according to the preset wandering operator a Until all the grey wolves finish wandering,
n is the total number of the rectangular pieces;
and 4, step 4: comparing the gray wolf with the optimal material utilization rate in the wandering gray wolf group with the alpha wolf in the step (2.2), if the gray wolf is better than the alpha wolf, updating the alpha wolf into the gray wolf with the optimal material utilization rate after wandering, and completing one wandering;
and 5: after the wandering is finished, the distance between each gray wolf and the alpha wolf updated in the step (2.4) is judged, and when the distance of a certain gray wolf is smaller than or equal to the attack judgment distance d attack When the gray wolf is in place,at the moment, the gray wolf is not rushing, otherwise, the gray wolf takes the alpha wolf as a prey to carry out attack according to a rushing motion operator until the attack judgment of each gray wolf is finished; wherein the content of the first and second substances,
step 6: comparing the gray wolf with the optimal material utilization rate in the gray wolf group after the prey is attacked with the alpha wolf updated in the step (2.4), and if the gray wolf is better than the alpha wolf updated in the step (2.4), updating the alpha wolf into the gray wolf with the optimal material utilization rate after the prey is attacked, and finishing one-time prey;
and 7: judging whether the iteration number reaches k max If yes, the position code X of alpha wolf which is the optimal solution of the solving problem is output α And the prey odor concentration Y felt by it α I.e. the optimal layout scheme and the corresponding material utilization rate are obtained, otherwise, the step3 is carried out.
Further, decimal coding is carried out in step2, and the activity field of the wolf group is abstracted into an Mxn European space, X i ＝(x i1 ,x i2 ,x i3 ,…,x ij ,…,x in ) Indicating the location of the ith wolf in n-dimensional space.
Further, a maximum number of walks h is set max (ii) a In step3, the gray wolf i is paired with X every time the gray wolf i wanders i Execution h max Minor wandering operator T (X) i ,Q,step a ) And Q is {1,2,3, …, n }, recording the smell concentration of the prey every time the wandering walking operator is executed, and taking the position where the prey smell concentration sensed by the wolfsbane i is the maximum as the wandering position
Further, in step5, the position X of the alpha wolf is determined α Position X of Grey wolf i participating in hunting as the position of the prey i According to the running motion operator R (X) i ,L 1 ,L 2 ,step b ) Performing a position change, L 1 For coded bits requiring assignment, L 2 Is corresponding to the coded bit positionA value to be assigned;
when d is ip ＝d hm ≤d attack The time indicates that the wolf has killed the prey, and the sensed prey odor concentration is calculated; wherein d is ip Is the distance between grey wolf i and alpha wolf,
determining distance, θ, for hunting 2 Is a step size factor of attack; when d is ip ＝d hm >d attack In time, the grayish i follows the attack step length b ＝d hm -d attack Rapidly rushing, and calculating the odor concentration of the felt prey after the gray wolf i rushes at a very high speed.
Furthermore, in the processes of initialization, walking and attack, the lowest horizontal line method based on fitness is called to decode the position of the gray wolf to form a sample arrangement diagram, and then the corresponding material utilization rate is calculated according to the sample arrangement diagram.
Further, the fitness-based minimum horizon method comprises the following sub-steps:
step 1: taking a first plate, namely i-1;
step 2: initializing a horizontal line sequence as the bottom edge of the plate i being 1;
step 3: selecting a lowest horizontal line section in the horizontal line sequence, and if a plurality of horizontal line sections exist, selecting a leftmost horizontal line section;
step 4: searching the first rectangular piece which does not exceed the plate boundary and has the maximum fitness value in all the rectangular piece sequences which are not subjected to layout;
step 5: judging whether a rectangular piece meeting the Step4 condition exists, if so, turning to Step7, and otherwise, turning to Step 6;
step 6: judging whether the horizontal line sequence only has one horizontal line with the length equal to the bottom edge of the plate i, if so, starting the next plate, namely, making i equal to i +1, then initializing the horizontal line sequence to be the bottom edge of the plate i +1, and turning to step 8; otherwise, after the lowest horizontal line is lifted, step8 is switched;
step 7: according to whether the rectangular piece is arranged or not, the horizontal line is operated, the horizontal line sequence is updated, and step8 is switched;
step 8: if all parts are discharged, turning to Step9 if yes, or turning to Step3 if not;
step 9: and outputting a stock layout result after finishing stock layout, and calculating the material utilization rate.
Further, in Step4, the method of determining the rectangular piece with the largest fitness value is as follows;
for the region to be arranged where the lowest horizontal line is located, when the region is completely filled with the rectangular pieces after the rectangular pieces are arranged, the fitness value is recorded as 3; when the rectangular piece is just matched with two boundaries of the area to be arranged after being arranged, the fitness value is recorded as 2; when the rectangular piece is just matched with one boundary of the region to be arranged after being arranged, the fitness value is recorded as 1; when the rectangular piece is discharged into a section of horizontal line which is adjacent to the lowest horizontal line and is higher than the lowest horizontal line, the adaptability value is marked as 0; when the rectangular piece is arranged into a section of horizontal line without boundary coincidence and the upper edge of the rectangular piece is lower than the adjacent and lower section of the lowest horizontal line, the adaptability value is marked as-1.
Further, the objective function in step1 is as follows:
the material utilization rate Y is highest:
wherein n is the total number of the rectangular pieces, m is the number of the plates for stock layout, and the width of the plate k is W k High is H k The width of the rectangular member i is w i High is h i The maximum height of the layout chart of the last plate is H m Maximum width of W m ；
The constraint that all rectangular parts do not exceed the boundary of the plate after being discharged and do not overlap with parts is as follows:
wherein x is i,k 、x j,k Respectively are the abscissa and y of the lower left corners of the rectangular pieces i and j on the kth plate i,k 、y j,k Respectively are the ordinate of the lower left corner of the rectangular piece i and the lower left corner of the rectangular piece j on the kth plate, and the width of the rectangular piece j is w j High is h j 。
In order to achieve the above object, the present invention also provides a computer-readable storage medium having stored thereon a computer program which, when executed by a processor, implements the rectangular piece layout method as set forth in any one of the preceding claims.
In order to achieve the above object, the present invention further provides a rectangular piece stock layout device based on the gray wolf algorithm, which includes the computer readable storage medium as described above and a processor for calling and processing the computer program stored in the computer readable storage medium.
In general, compared with the prior art, the above technical solution contemplated by the present invention can obtain the following beneficial effects:
1. the decimal wolf grey algorithm is adopted, two intelligent behaviors of wolf colony surrounding and hunting are integrated into a surrounding behavior, the structure and the flow of the traditional wolf grey algorithm are simplified, the parameters of the whole algorithm are reduced, the minimum horizontal line method decoding based on fitness is combined for layout, and in the layout process, along with the actions of the wolf colony, the rectangular pieces are sequenced and positioned interactively, are iterated continuously, and are updated and optimized in the direction of higher material utilization rate. Therefore, the solving speed is improved, and meanwhile, the quality of the optimal solution is not reduced, so that the plate utilization rate and the solving speed can be improved simultaneously, and the method has good practicability and applicability in solving the rectangular part layout problem.
2. The invention improves the intelligent behavior of wandering search of the wolf pack, and only updates the alpha wolf after all the wolf completes the wandering search operation, thereby enhancing the search capability of the wolf pack, avoiding the whole wolf pack from falling into local optimum and increasing the possibility of finding global optimum by the algorithm. And multidirectional exploration is carried out every time of walking, so that the possibility and efficiency of finding the global optimum are further improved.
3. The minimum horizontal line algorithm is improved, and a method based on the fitness criterion is provided, so that the most appropriate rectangular pieces in the rectangular pieces to be subjected to layout can be selected from multiple parts for arrangement, the flexibility of the algorithm is improved, and the utilization rate and the solving speed of the plate can be obviously improved.
4. The invention provides a novel rectangular piece layout method which is short in solving time, can further improve the utilization rate of plates, is generally superior to the traditional wolf algorithm and other existing layout algorithms in effect after verification, and can quickly and effectively solve the problem of optimizing layout of various rectangular pieces.
Drawings
FIG. 1 is a block diagram of a rectangular layout problem solving framework of the present invention;
FIG. 2 is a flow chart of the decimal graying algorithm of the preferred embodiment of the present invention;
FIG. 3 is a diagram illustrating a code shift operation according to a preferred embodiment of the present invention;
FIG. 4 is a flow chart of a fitness based minimum horizon algorithm in accordance with a preferred embodiment of the present invention;
FIG. 5 is a layout chart corresponding to fitness values of a preferred embodiment of the present invention;
FIG. 6 is a diagram of a fit-based minimum horizon algorithm layout process in accordance with a preferred embodiment of the present invention;
FIG. 7 is a graph comparing the convergence curves of the layout results of the present invention and the prior art;
fig. 8 is a diagram illustrating the layout effect obtained by the layout method according to the preferred embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
For convenience of explanation, the following symbols introduced in this embodiment are explained in the following table:
TABLE 1 symbol comparison Table
As shown in fig. 1, the main idea of the framework for solving the rectangular piece layout problem provided by the present invention is as follows:
(1) selecting a group of parts to be subjected to stock layout from a part library, and extracting relevant information of the parts;
(2) selecting a plate which can be used for discharging the parts from a plate library, and extracting relevant information of the plate;
(3) determining the layout sequence of the rectangular pieces to be laid by utilizing a decimal grayish wolf algorithm;
(4) determining the discharge position of the rectangular piece to be subjected to stock layout by using a lowest horizontal line algorithm based on fitness evaluation;
(5) calculating the utilization rate of the plate as a standard for evaluating the quality of the stock layout scheme;
(6) and (4) circularly executing the step (3) and the step (4) until an optimal stock layout scheme is obtained.
Specifically, the framework for solving the rectangular layout problem can be summarized into two major modules: sequencing algorithms and positioning algorithms. The decimal wolf algorithm principle is simple, the parameters are few, the algorithm is easy to realize, the algorithm has good capability of balancing global optimization and local search, the wolf colony is encoded, the intelligent behaviors of wolf colony wandering search and prey are simulated by using a formula and a motion operator, and the key points are the design of an encoding and decoding method and the discretization design of the wolf intelligent behaviors. The invention provides a fitness-based minimum horizontal line algorithm which has no complex calculation formula, evaluates the rectangular pieces to be subjected to layout by the fitness to find the rectangular piece which is most suitable for being discharged at present, and can maximize the utilization rate of the plate as far as possible. In the stock layout process, sequencing and a positioning algorithm are interactively carried out, iteration is continuously carried out, and updating and optimization are carried out towards the direction that the material utilization rate is higher.
Based on the above concept, as shown in fig. 2, the preferred rectangular piece layout method based on the gray wolf algorithm of the present invention comprises the following steps:
step 1: setting the scale of the wolf colony as M and the iteration number of the algorithm as k max Maximum number of wandering times h max Step size factor of wandering theta 1 The attack step factor theta 2 (ii) a Setting an objective function and constraint conditions;
an objective function:
the material utilization rate is highest:
discharging n rectangular pieces to width W k High is H k In a plurality of rectangular plates of (2), H m The rectangular optimized layout aims to maximize the ratio of the sum of the areas of all rectangular parts to be laid to the sum of the areas of the plates for layout, namely the utilization rate, for the maximum height of the layout of the last plate.
Constraint conditions are as follows:
the constraint condition (2) ensures that all rectangular parts do not exceed the plate boundary after being arranged and parts do not overlap with each other. In addition, the rectangular piece is not allowed to rotate, and no 'one-cutting' process constraint exists.
Step 2: initializing gray wolf group
Initializing a wolf pack in a random mode, namely randomly generating M rectangular piece sequences, then calling a fitness-based minimum horizontal line algorithm to decode to form a layout, calculating the material utilization rate, and setting the solution with the maximum current material utilization rate in the wolf pack as alpha wolf according to the social grade system of the wolf pack;
and step 3: wandering gray wolf
The gray wolf searches for 'prey' in a wandering way according to the proposed wandering movement operator until all the gray wolf wanders completely;
and 4, step 4: comparing the wolf with the best result in the wandering gray wolf group with the alpha wolf, and if the wolf is better than the alpha wolf, updating the alpha wolf;
and 5: bingke prey
After the wandering is finished, the distance between the gray wolf and the alpha wolf is judged, and when the distance is smaller than or equal to the attack judgment distance
When the automobile warns are in place, the warns are not rushed any more, otherwise, the warns attack the prey (namely alpha wolfs) according to the rushing motion operator;
step 6: comparing the best-result wolf in the attacking gray wolf group with the alpha wolf, and if the best result wolf is better than the alpha wolf, updating the alpha wolf;
and 7: judging whether the algorithm reaches the termination condition, if so, outputting the optimal solution of the solving problem, namely the position code X of the alpha wolf α And the concentration of prey odor Y it senses α If not, the step3 is executed.
And 8: and outputting the optimal stock layout scheme.
As a preference of the present embodiment:
in step2, the initialization phase of the wolf set carries out decimal coding, and abstracts the activity field of the wolf set into an M multiplied by n European space, X i ＝(x i1 ,x i2 ,x i3 ,…,x ij ,…,x in ) The position of the ith grey wolf in the n-dimensional space is shown, namely the sequence of the rectangular elements corresponding to the grey wolf i.
Secondly, in step3, only after all the gray wolves in the wolves finish the wandering search operation, the alpha wolves are updated. First, the wolf heuristically moves to h max Investigation in one direction, i.e. Hui wolf X i Execution h max Minor wandering operator T (X) i ,Q,step a )，Q＝{1,2,3，…，n}，step a Is the step size of the walk,
θ 1 recording the smell concentration of prey for the walking step-size factor by executing an operator once, and taking the position where the prey smell concentration sensed by the wolfsbane i is the maximum as the walking position
And thirdly, in the step5, integrating the surrounding and hunting intelligent behaviors into a surrounding attack behavior, and updating the alpha wolf after the surrounding attack behavior is finished. Abstracting the intelligent behavior of the attack, and taking the position X of the alpha wolf α Position X of Grey wolf i participating in hunting as the position of the prey i According to the running motion operator R (X) i ,L 1 ,L 2 ,step b ) Performing position conversion when d ip ＝d hm ≤d attack Indicating that the wolf has killed the prey, calculating the concentration of the smell of the prey as Y i Wherein d is ip Is the distance between grey wolf i and alpha wolf,
determining distance, θ, for hunting 2 Is a step size factor of attack; when d is ip ＝d hm >d attack The gray wolf is according to the attack step b ＝d hm -d attack Rushing rapidly. After the gray wolf i is rushed at a very high speed, the odor concentration Y of the sensed prey is calculated i And comparing the smell concentrations of the prey before and after the attack, and performing greedy decision.
In step5, as shown in FIG. 3, the running motion operator R (X) is executed i ,L 1 ,L 2 And s), encoding the shift operation diagram. L is 1 Indicating the coded bit to be assigned, L 2 Representing the value to which the corresponding coded bit needs to be assigned, and s represents the number of coded bits to which the assignment is made. Suppose X i ＝(2,1,3,4,6,5,8,7,10,9)，L 1 ＝(3,5,6,7)，L 2 (5,8,4,10), s is 2, and L is selected 1 First and second of (a), performing a running motion operator R (X) i ,L 1 ,L 2 S) is first to X i The 3 rd bit in the sequence carries out assignment operation, and L is firstly used 2 In this case, there are two numbers with equal absolute values as in fig. 3 (b), and then the original 5 of the sequence is replaced with 3 as in fig. 3 (c), as is the fifth bit in the sequence.
In the initialization, walking and surrounding attack process of the wolf group, a lowest horizontal line algorithm based on fitness is called to decode the position of the wolf to form a layout, namely, in the positioning stage of the layout of the rectangular piece, the lowest horizontal line method based on the fitness is utilized to determine the discharge position of the rectangular piece to be subjected to the layout, and then the material utilization rate of the wolf in the corresponding step is calculated according to the layout. And determining a fitness evaluation criterion, and selecting a rectangular piece with the highest fitness value from the sequence of rectangular pieces to be subjected to stock layout to be discharged, so that the rectangular pieces discharged each time are the most suitable. The flowchart is shown in fig. 4, and specifically includes the following sub-steps:
step 1: taking a first plate, namely i-1;
step 2: initializing a horizontal line sequence as the bottom edge of the plate i being 1;
step 3: selecting a lowest horizontal line section in the horizontal line sequence, and if a plurality of horizontal line sections exist, selecting a leftmost horizontal line section; because the horizontal line sequence in the first iteration step only has the bottom edge of the first plate, the lowest horizontal line is the bottom edge of the first plate; in the subsequent iteration step, as the parts are discharged, the heights and the number of the horizontal lines contained in the horizontal line sequence are correspondingly changed according to the different heights of the discharged parts, and the lowest section of the horizontal line is selected according to the actual condition of the discharged parts.
Step 4: searching the first rectangular piece which does not exceed the plate boundary and has the maximum fitness value in all the rectangular piece sequences which are not subjected to layout;
step 5: judging whether a rectangular piece meeting the Step4 condition exists, if so, turning to Step7, and otherwise, turning to Step 6;
step 6: judging whether the horizontal line sequence only has one horizontal line with the length equal to the bottom edge of the plate i, if so, starting the next plate, namely, making i equal to i +1, then initializing the horizontal line sequence to be the bottom edge of the plate i +1, and turning to step 8; otherwise, after raising the lowest level (i.e., reselecting the lowest level upward for use after the next round of stock placement when stock placement is not over), step 8;
step 7: according to whether the rectangular piece is arranged or not, the horizontal line is operated, the horizontal line sequence is updated, and step8 is switched;
step 8: if all parts are discharged, turning to Step9 if yes, or turning to Step3 if not;
step 9: and outputting a stock layout result after finishing stock layout, and calculating the material utilization rate.
As a preference of the present embodiment:
firstly, in Step4, a method for determining a rectangular piece with the largest fitness value is as follows;
as shown in fig. 5, the profile condition and the corresponding fitness value. In the proposed fitness system, for the region to be arranged where the lowest horizontal line is located, the region is completely filled with rectangular pieces after the rectangular pieces are arranged, that is, the region is marked as the highest fitness 3 as shown in fig. 5 (a); when the situation is as shown in fig. 5 (b) and (c), that is, the two boundaries of the region to be lined just coincide, the fitness value is recorded as 2; when the situation is shown in (d) to (f) of fig. 5, that is, when a boundary of the region to be lined is just matched, the fitness value is recorded as 1; when the situation is shown in (g) of fig. 5, namely, no boundary coincidence exists and the upper edge of the rectangular member exceeds a section of the horizontal line adjacent to and higher than the lowest horizontal line, the fitness value is marked as 0; when in the situation shown in fig. 5 (h), i.e. no border-fit and the upper edge of the rectangular member is lower than the adjacent and lower horizontal line of the lowest horizontal line, the fitness value is the smallest and is marked as-1.
Secondly, finding out the rectangular pieces with the maximum current fitness value in Step5, and sequentially arranging the rectangular pieces into the area to be arranged of the current plate, wherein FIG. 6 shows the layout process of the lowest horizontal line positioning algorithm based on the fitness evaluation criterion. The initial layout diagram is shown in fig. 6 (a), where rectangles 5, 6, 7 are to be arranged, the lowest horizontal line is selected, and the fitness of the three rectangles at this time is found to be-1, 0, and 1 through calculation, as shown in fig. 6 (b), (c), and (d), and the rectangle 7 is arranged according to the principle of selecting the first rectangle with the largest fitness value, as shown in fig. 6 (e). Rectangles 6 and 5 are sequentially lined in according to the same principle, and the final layout is shown in fig. 6 (i).
Under the condition that various data are sufficiently prepared, the rectangular piece stock layout method based on the gray wolf algorithm provided by the invention is adopted to complete the stock layout task. In this example, the classical C example is used as the test example, and the C example is proposed by Hopper et al, and a total of 21 sub-examples are divided into seven groups. Setting relevant parameters of the algorithm: the scale M of the wolf colony is 40, and the maximum wandering times h max 20 times, walk step factor theta 1 1/10, the attack step factor theta 2 To 2/5, the algorithm runtime is set to 60 s.
IDGWO is an improved decimal graywolf algorithm, DGWO is a general graywolf algorithm, and the layout method provided by the invention is compared with the layout results of other excellent algorithms, wherein the excellent algorithms comprise GA + BLF, SA + BLF, HACO, HAS, SRA, GRASP and ISA.
The method for optimizing stock layout of the rectangular part comprises the following steps:
(1) extracting relevant information of the rectangular piece and the plate, and creating a layout task;
(2) initializing relevant parameters, solving a stock layout task by using the rectangular piece stock layout method based on the gray wolf algorithm, and outputting an optimal stock layout scheme;
(3) using best solution height h and optimal solution height h opt Relative distance of (g ═ h opt )/h opt X 100 as an evaluation index, compared with other excellent algorithms, and the results are shown in table 2 below;
TABLE 2 calculation results of the algorithms in the example C
(4) And obtaining a convergence curve of the stock layout height relative to the distance gap of each algorithm, as shown in fig. 7, and outputting a stock layout effect diagram generated by the rectangular piece stock layout method provided by the invention, as shown in fig. 8.
As can be seen from fig. 7 and table 2, in 21 sub-examples, the IDGWO algorithm obtains a layout plan with 100% utilization of 11 sub-examples, which is five more than the DGWO algorithm, the average optimal relative distance of the whole C-example is 0.50, which is 57.2% lower than the DGWO algorithm before improvement, which is one tenth of the GA + BLF and SA + BLF algorithms, which is one sixth of the HACO and HSA algorithms, and the better SRA algorithm is also reduced by nearly 20%. Compared with the DGWO algorithm, the IDGWO algorithm obtains the solution of 100% material utilization rate of C3, C43 and C52, and the optimal relative distance is better on the basis of C61 and C62, so that the material utilization rate is improved. Therefore, as can be seen from the C calculation, the IDGWO algorithm proposed by the present invention is effective, and can improve the material utilization rate.
The layout effect of the IDGWO algorithm proposed by the present invention in several sub-examples of the C-example is shown in fig. 8, where the gray area surrounded by a rectangle represents an unused area. It can be seen that in the sub-examples, the utilization rate of the plate in the stock layout result reaches 100%, no gap exists in the plate, and the utilization rate of the plate is improved to the maximum, so that the effectiveness of the rectangular piece stock layout method provided by the invention is proved.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (6)
1. A rectangular part stock layout method based on a wolf algorithm is characterized by comprising the following steps:
step 1: setting a target function to enable the material utilization rate to be highest, wherein the constraint conditions are that all rectangular parts do not exceed the plate boundary after being discharged, the parts do not overlap with each other, the rectangular parts do not rotate, and no cutting process constraint exists;
the objective function in step1 is as follows:
the material utilization rate Y is highest:
wherein n is the total number of the rectangular pieces, m is the number of the plates for stock layout, and the width of the plate k is W k High is H k The width of the rectangular member i is w i High is h i The maximum height of the layout chart of the last plate is H m Maximum width of W m ；
The constraint that all rectangular parts do not exceed the boundary of the plate after being discharged and do not overlap with parts is as follows:
wherein x is i,k 、x j,k Respectively are the abscissa and y of the lower left corners of the rectangular pieces i and j on the kth plate i,k 、y j,k Respectively are the ordinate of the lower left corner of the rectangular piece i and the lower left corner of the rectangular piece j on the kth plate, and the width of the rectangular piece j is w j High is h j ；
Step 2: initializing a wolf cluster in a random mode, namely randomly generating M decimal grays to represent M rectangular piece sequences, decoding to form corresponding layout patterns based on a lowest level line method of fitness, calculating the material utilization rate of each layout pattern, and setting the solution with the maximum current material utilization rate in the wolf cluster as alpha wolf according to the social level system of the wolf cluster to represent the current optimal rectangular piece sequence;
and step 3: the gray wolf walks step according to the preset wandering operator a Until all the gray wolves finish wandering,
n is the total number of the rectangular pieces;
and 4, step 4: comparing the gray wolf with the optimal material utilization rate in the wandering gray wolf group with the alpha wolf in the step2, if the gray wolf is better than the alpha wolf, updating the alpha wolf into the gray wolf with the optimal material utilization rate after wandering, and completing one wandering;
and 5: after the wandering is finished, the distance between each gray wolf and the alpha wolf updated in the step4 is judged, and when the distance of a certain gray wolf is smaller than or equal to the attack judgment distance d attack If so, indicating that the gray wolf is in place, wherein the gray wolf does not rush any more, otherwise, the gray wolf attacks the alpha wolf as a prey according to a rush motion operator until the attack judgment of each gray wolf is finished; wherein the content of the first and second substances,
step 6: comparing the gray wolf with the optimal material utilization rate in the gray wolf group after the prey is attacked with the alpha wolf updated in the step4, if the gray wolf is better than the alpha wolf updated in the step4, updating the alpha wolf into the gray wolf with the optimal material utilization rate after the prey is attacked, and finishing one-time prey;
and 7: judging whether the iteration number reaches k max If yes, the position code X of alpha wolf which is the optimal solution of the solving problem is output α And the concentration of prey odor Y it senses α If the optimal layout scheme and the corresponding material utilization rate are obtained, otherwise, turning to the step 3;
in the process, in the processes of initialization, walking and attack, the lowest horizontal line method based on fitness is called to decode the position of the grey wolf to form a sample arrangement diagram, and then the corresponding material utilization rate is calculated according to the sample arrangement diagram;
the lowest horizontal line method based on the fitness comprises the following sub-steps:
step 1: taking a first plate, namely i-1;
step 2: initializing a horizontal line sequence as the bottom edge of the plate i being 1;
step 3: selecting a lowest horizontal line section in the horizontal line sequence, and if a plurality of horizontal line sections exist, selecting a leftmost horizontal line section;
step 4: searching the first rectangular piece which does not exceed the plate boundary and has the maximum fitness value in all the rectangular piece sequences which are not subjected to layout;
step 5: judging whether a rectangular piece meeting the Step4 condition exists, if so, turning to Step7, and otherwise, turning to Step 6;
step 6: judging whether the horizontal line sequence only has one horizontal line with the length equal to the bottom edge of the plate i, if so, starting the next plate, namely, making i equal to i +1, then initializing the horizontal line sequence to be the bottom edge of the plate i +1, and turning to step 8; otherwise, after the lowest horizontal line is lifted, step8 is switched;
step 7: according to whether the rectangular piece is arranged or not, the horizontal line is operated, the horizontal line sequence is updated, and step8 is switched;
step 8: if all parts are discharged, turning to Step9 if yes, or turning to Step3 if not;
step 9: after the stock layout is finished, outputting a stock layout result, and calculating the material utilization rate;
in Step4, the method of determining the rectangular piece having the largest fitness value is as follows;
for the region to be arranged where the lowest horizontal line is located, when the region is completely filled with the rectangular pieces after the rectangular pieces are arranged, the fitness value is recorded as 3; when the rectangular piece is just matched with two boundaries of the area to be arranged after being arranged, the fitness value is recorded as 2; when the rectangular piece is just fit with one boundary of the region to be arranged after being arranged, the fitness value is recorded as 1; when the rectangular piece is discharged into a section of horizontal line which is adjacent to the lowest horizontal line and is higher than the lowest horizontal line, the adaptability value is marked as 0; when the rectangular piece is arranged into a section of horizontal line without boundary coincidence and the upper edge of the rectangular piece is lower than the adjacent and lower section of the lowest horizontal line, the adaptability value is marked as-1.
2. The method as claimed in claim 1, wherein the decimal coding is performed in step2 to abstract the activity field of wolf group into mxn Euclidean space, X i ＝(x i1 ,x i2 ,x i3 ,…,x ij ,…,x in ) Indicating the location of the ith wolf in n-dimensional space.
3. The method for stock layout of rectangular parts based on the grayling algorithm as claimed in claim 2, wherein the maximum number of wandering times h is set max (ii) a In step3, the gray wolf i is paired with X every time the gray wolf i wanders i Execution h max Minor wandering operator T (X) i ,Q,step a ) And Q is {1,2,3, …, n }, recording the smell concentration of the prey every time the wandering walking operator is executed, and taking the position where the prey smell concentration sensed by the wolfsbane i is the maximum as the wandering position
4. The method for stock layout of rectangular parts based on wolf's algorithm as claimed in claim 2, wherein in step5, the position X of alpha wolf is determined α Position X of Grey wolf i participating in hunting as the position of the prey i According to the running motion operator R (X) i ,L 1 ,L 2 ,step b ) Performing a position change, L 1 For coded bits requiring assignment, L 2 A value to be assigned to the corresponding coded bit;
when d is ip ＝d hm ≤d attack The time indicates that the wolf has killed the prey, and the sensed prey odor concentration is calculated; wherein d is ip Is the distance between grey wolf i and alpha wolf,
determining distance, θ, for hunting 2 Is a step size factor of attack; when d is ip ＝d hm >d attack In time, the gray wolf i follows the attack step size step b ＝d hm -d attack Rapidly rushing, and calculating the odor concentration of the felt prey after the gray wolf i rushes at a very high speed.
5. A computer-readable storage medium, wherein a computer program is stored on the computer-readable storage medium, and when the computer program is executed by a processor, the computer program implements the method for laying out a rectangular piece according to any one of claims 1 to 4.
6. A grey wolf algorithm based rectangular piece stock layout apparatus comprising the computer-readable storage medium of claim 5 and a processor for invoking and processing a computer program stored in the computer-readable storage medium.
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