CN111985012A - Two-dimensional irregular part layout method based on optimal foraging algorithm - Google Patents

Abstract

The invention relates to a two-dimensional irregular parts layout method based on an optimal foraging algorithm. The method includes the following steps: step S1: mathematical description of the two-dimensional irregular parts layout problem; step S2: establishing constraints to be satisfied in the layout optimization process; step S3: determining the target to be optimized, and establishing the corresponding two-dimensional Irregular parts layout objective optimization function; Step S4: Based on the optimal foraging algorithm, perform a global optimization search on the parts layout order and rotation angle, determine the optimal layout order and rotation angle of the parts, and output the best layout result. The invention proposes a two-dimensional irregular parts layout method based on an optimal foraging algorithm, which is suitable for the layout of convex and concave polygonal parts and complex parts with holes; compared with the two-dimensional irregular layout problem based on traditional heuristic algorithms The solution has the advantages of high layout efficiency, good robustness and high material utilization rate.

Description

2D Irregular Parts Layout Method Based on Optimal Foraging Algorithm

technical field

The invention relates to the technical field of computer-aided layout, in particular to a layout method for two-dimensional irregular parts based on an optimal foraging algorithm.

Background technique

1. The layout problem refers to the reasonable layout of the parts to be involved in the layout according to the processing requirements on the given raw material plate space, so as to maximize the utilization rate of raw materials while ensuring the production demand of the product. At present, layout problems are involved in many processing and manufacturing industries. With the rapid development of society, human demand for resources is also increasing, saving resources and minimizing waste of resources have become an important pillar of sustainable development in today's society.

2. For the layout of two-dimensional irregular parts, the manual method was mainly used in the early stage. This method not only fails to save raw materials, but also has high time cost. Later, with the continuous development of information technology, computer-aided layout technology began to be applied. Compared with the manual layout method, the layout efficiency is high and the layout effect is good, and it has gradually become the mainstream of industrial production. In the application of heuristic algorithm for the layout of two-dimensional irregular parts, the currently widely used intelligent algorithms include genetic genetic algorithm, particle swarm algorithm and simulated annealing algorithm, but they are basically used in small-scale layout. In actual production, due to the large scale of production, these methods are prone to produce bad layout results even if they take a long search time, and have poor robustness, making it difficult to be widely used.

3. The optimal foraging algorithm is a meta-heuristic algorithm based on the modern optimal foraging theory. The algorithm has better global search ability as a whole and better local search ability in detail, and requires less parameters, so it does not need to adjust the parameters too much to balance the global search and local search ability of the algorithm. This advantage ensures that it still has strong applicability when applied to the layout of two-dimensional irregular parts including convex, concave parts and complex parts with holes, and has high layout efficiency, good robustness and excellent layout results. .

SUMMARY OF THE INVENTION

The purpose of the invention is to solve the shortcomings of low layout efficiency and poor robustness when the existing heuristic layout algorithm is applied to the layout problem of two-dimensional irregular parts, so as to propose a two-dimensional algorithm based on the optimal foraging algorithm. Irregular parts layout method.

In order to achieve the above purpose, the technical scheme of the present invention is: a two-dimensional irregular parts layout method based on an optimal foraging algorithm, comprising the following steps:

Step S1, mathematically describe the two-dimensional irregular parts layout problem;

Step S2: establishing the constraints that need to be satisfied in the layout optimization process;

Step S3: determine the target to be optimized, and establish a corresponding two-dimensional irregular part layout target optimization function;

Step S4: Based on the optimal foraging algorithm, perform a global optimization search on the arrangement order and rotation angle of the parts, determine the optimal arrangement order and rotation angle of the parts, and output the best arrangement result.

In an embodiment of the present invention, in step S1, the specific method of mathematically describing the two-dimensional irregular parts layout problem is as follows:

对应的排样方案为{(x₁,y₁),…,(x_i,y_i),…,(x_n,y_n)}；First, define variables: given that the number of parts participating in the layout is n, and the number of allowed rotation angles of each part is m, a layout order of parts is randomly generated {x ₁ ,…,x _i ,…,x _n } , x _i ∈{1,2,…,n}, the rotation angle number of each part {y ₁ ,y ₂ ,…,y _n },y _i ∈{1,2,…,m}, y _i corresponds to The rotation angle of is

The corresponding layout plan is {(x ₁ ,y ₁ ),…,(x _i ,y _i ),…,(x _n ,y _n )};

Then, the problem of two-dimensional irregular parts layout is defined: on a given raw material sheet, according to the processing requirements, the parts are reasonably discharged, and the utilization rate of raw materials is maximized while meeting the production demand.

In an embodiment of the present invention, in step S2, the constraints that need to be satisfied in the layout optimization process are: (1) the layout positions of the parts participating in the layout do not overlap each other; (2) the parts participating in the layout are placed inside the raw material sheet.

In an embodiment of the present invention, in step S3, the target to be optimized is to maximize the utilization rate of raw materials; the area of the i-th part participating in the layout is defined as s(i), i∈{1,2,...,n }, then the raw material utilization δ is as follows:

In the formula, w is the width of the plate in the horizontal direction, and h is the height of the plate in the vertical direction;

Then the two-dimensional irregular parts layout objective optimization function is described as follows:

In an embodiment of the present invention, in step S4, the optimal foraging algorithm includes the following steps:

Step S41, initialize algorithm parameters and population;

Step S42, population fitness evaluation; calculate the fitness values of all individuals in the initial population, arrange them in descending order, and save the optimal individual as the global optimal individual;

Step S43, update the population, calculate the fitness values of all individuals in the new population, arrange in descending order, and save the optimal individual;

Step S44, update the global optimal individual;

Step S45, iterative update, if the termination condition is satisfied, output the optimal layout result, otherwise, go to step S43.

In an embodiment of the present invention, the step S41 is specifically:

Initialization algorithm parameters: population size popsize, maximum iteration number maxIter, current iteration number t;

的种群个体采用随机生成方式生成，剩余

的种群个体则采用按面积大小降序排列的方式生成。The method of initializing the population is as follows: according to the initialized population size popsize, the integer encoding is used, where

The population of individuals is generated by random generation, and the remaining

The populations of individuals are generated in descending order of area size.

In an embodiment of the present invention, the population fitness evaluation function in step S42 is:

The smaller the value of F(x), that is, the higher the material utilization rate, the better the results of the arrangement of individuals in the population.

In an embodiment of the present invention, the method of updating the population in the step S43 is:

为迭代次数为t时的全局最优个体，

为种群中的第j的个体，j∈{1,2,…,n}；种群个体位置更新方式如下所示：defines the range factor k, and

is the global optimal individual when the number of iterations is t,

is the jth individual in the population, j∈{1,2,…,n}; the update method of the individual position of the population is as follows:

为个体

的第i维元素，r_1ji、r_2ji是0～1之间服从均匀分布的随机数，b∈{1,2,…,n}；

为种群中最差个体

的第i维元素，N＝n；In the formula,

for the individual

The i-th dimension element of , r _1ji and r _2ji are random numbers between 0 and 1 subject to uniform distribution, b∈{1,2,…,n};

the worst individual in the population

The i-th dimension element of , N=n;

是否被接受的模型为：The optimal foraging algorithm has a small probability of accepting some poor individuals in the iterative process, thus helping the algorithm to escape the constraints of the local optimal solution; for the minimization problem, judge the next generation of individuals

The accepted models are:

为0～1之间服从均匀分布的随机数，

和

分别表示迭代次数为t和t櫸1时，种群中个体j的适应度值。In the formula,

is a random number between 0 and 1 that obeys a uniform distribution,

and

Represents the fitness value of individual j in the population when the number of iterations is t and t and 1, respectively.

In an embodiment of the present invention, the method of updating the global optimal individual in the step S44 is an elite retention strategy.

In an embodiment of the present invention, the termination condition in step S45 is a preset maximum number of iterations maxIter.

Compared with the traditional heuristic two-dimensional irregular parts layout technology, the present invention has the following beneficial effects:

1. The present invention adopts an integer coding method for the arrangement order of the parts and the corresponding rotation angle, which reduces the complexity of the solution. The initial population is constructed in two ways: random generation and orderly arranging according to the size of the area. The population diversity is good, and The quality of the individuals in the initial population is guaranteed, the convergence speed is fast, and the solution efficiency of the algorithm is high.

2. Compared with the two-dimensional irregular problem layout method based on the traditional intelligent heuristic algorithm, the layout method requires less adjustment parameters and has a wide range of applications. For the layout of irregular parts, this method has good applicability. And the layout effect is good, the plate utilization rate is high, and the robustness is good.

Description of drawings

Fig. 1 is the schematic flow chart of the method of the present invention.

FIG. 2 is a layout effect diagram of an example part of the present invention based on the method of the present invention.

Detailed ways

The technical solutions of the present invention will be described in detail below with reference to the accompanying drawings.

As shown in Figure 1, the present invention provides a two-dimensional irregular parts layout method based on an optimal foraging algorithm, comprising the following steps:

Step S1, mathematically describe the two-dimensional irregular parts layout problem;

Step S2: establishing the constraints that need to be satisfied in the layout optimization process;

Step S3: determine the target to be optimized, and establish a corresponding two-dimensional irregular part layout target optimization function;

Step S4: Based on the optimal foraging algorithm, perform a global optimization search on the arrangement order and rotation angle of the parts, determine the optimal arrangement order and rotation angle of the parts, and output the best arrangement result.

Further, in step S1, the specific method of mathematically describing the two-dimensional irregular parts layout problem is as follows:

对应的排样方案为{(x₁,y₁),…,(x_i,y_i),…,(x_n,y_n)}；First, define variables: given that the number of parts participating in the layout is n, and the number of allowed rotation angles of each part is m, a layout order of parts is randomly generated {x ₁ ,…,x _i ,…,x _n } , x _i ∈{1,2,…,n}, the rotation angle number of each part {y ₁ ,y ₂ ,…,y _n },y _i ∈{1,2,…,m}, y _i corresponds to The rotation angle of is

The corresponding layout plan is {(x ₁ ,y ₁ ),…,(x _i ,y _i ),…,(x _n ,y _n )};

Then, the problem of two-dimensional irregular parts layout is defined: on a given raw material sheet, according to the processing requirements, the parts are reasonably discharged, and the utilization rate of raw materials is maximized while meeting the production demand.

Further, in step S2, the constraints that need to be satisfied in the layout optimization process are: (1) the layout positions of the parts participating in the layout do not overlap each other; (2) the parts participating in the layout are placed inside the raw material sheet.

Further, in step S3, the goal to be optimized is to maximize the utilization rate of raw materials; define the area of the i-th part participating in the layout as s(i), i∈{1,2,...,n}, then the utilization of raw materials The rate δ is as follows:

In the formula, w is the width of the plate in the horizontal direction, and h is the height of the plate in the vertical direction;

Then the two-dimensional irregular parts layout objective optimization function is described as follows:

Further, in step S4, the optimal foraging algorithm includes the following steps:

Step S41, initialize algorithm parameters and population;

Step S42, population fitness evaluation; calculate the fitness values of all individuals in the initial population, arrange them in descending order, and save the optimal individual as the global optimal individual;

Step S43, update the population, calculate the fitness values of all individuals in the new population, arrange in descending order, and save the optimal individual;

Step S44, update the global optimal individual;

Step S45, iterative update, if the termination condition is satisfied, output the optimal layout result, otherwise, go to step S43.

Further, the step S41 is specifically:

Initialization algorithm parameters: population size popsize, maximum iteration number maxIter, current iteration number t;

The population initialization method is generally: (1) randomly generated; (2) generated in descending order of area size; when the size of the layout is large, the randomly generated initial population has good diversity, but the quality of the population is not high, and the convergence speed of the algorithm is slow. , the layout efficiency is low; usually, parts with a larger area will generate more voids after they are discharged, which can be used by parts with a smaller area without occupying more space. Therefore, the initial population quality generated is arranged in descending order of area size. Better, the algorithm has fast convergence speed and high nesting efficiency.

的种群个体采用随机生成方式生成，剩余

的种群个体则采用按面积大小降序排列的方式生成。Therefore, the method for initializing the population of the present invention is: according to the initialized population size popsize, an integer encoding form is adopted, wherein

The population of individuals is generated by random generation, and the remaining

The populations of individuals are generated in descending order of area size.

Further, the population fitness evaluation function in the step S42 is:

The smaller the value of F(x), that is, the higher the material utilization rate, the better the results of the arrangement of individuals in the population. Parts are placed based on the critical polygon positioning strategy of the lower left center of gravity. After all the parts have been placed, the F(x) values of all individuals in the population are calculated and arranged in descending order. The better the individual is, the higher its position is. That is, when selecting the feasible nesting position of the parts to be arranged, always select the feasible point with the lowest center of gravity position. If there are multiple nesting positions with the lowest feasible center of gravity, the leftmost feasible minimum center of gravity nesting position is selected.

Further, the method of updating the population in the step S43 is:

为迭代次数为t时的全局最优个体，

为种群中的第j的个体，j∈{1,2,…,n}；种群个体位置更新方式如下所示：defines the range factor k, and

is the global optimal individual when the number of iterations is t,

is the jth individual in the population, j∈{1,2,…,n}; the update method of the individual position of the population is as follows:

为个体

的第i维元素，r_1ji、r_2ji是0～1之间服从均匀分布的随机数，b∈{1,2,…,n}；

为种群中最差个体

的第i维元素，N＝n；In the formula,

for the individual

The i-th dimension element of , r _1ji and r _2ji are random numbers between 0 and 1 subject to uniform distribution, b∈{1,2,…,n};

the worst individual in the population

The i-th dimension element of , N=n;

是否被接受的模型为：The optimal foraging algorithm has a small probability of accepting some poor individuals in the iterative process, thus helping the algorithm to escape the constraints of the local optimal solution; for the minimization problem, judge the next generation of individuals

The accepted models are:

为0～1之间服从均匀分布的随机数，

和

分别表示迭代次数为t和t櫸1时，种群中个体j的适应度值。In the formula,

is a random number between 0 and 1 that obeys a uniform distribution,

and

Represents the fitness value of individual j in the population when the number of iterations is t and t and 1, respectively.

Further, the method of updating the global optimal individual in the step S44 is an elite retention strategy.

Further, the termination condition in the step S45 is the preset maximum number of iterations maxIter, and it is judged whether the number of evolution iterations t reaches the maximum number of iterations; if so, output the optimal solution, otherwise, go to step S43.

Referring to Fig. 2, the layout effect diagram of some irregular parts of the present invention (material height: 1000mm, number of samples: 28, layout width H: 5200mm, material utilization rate: 78.6%), the initial algorithm parameters are set as: population Scale popsize=20, maximum number of iterations maxIter=500.

The above are the preferred embodiments of the present invention, all changes made according to the technical solutions of the present invention, when the resulting functional effects do not exceed the scope of the technical solutions of the present invention, belong to the protection scope of the present invention.

Claims (10)

1. a two-dimensional irregular parts layout method based on optimal foraging algorithm, is characterized in that, comprises the steps: Step S1, mathematically describe the two-dimensional irregular parts layout problem; Step S2: establishing the constraints that need to be satisfied in the layout optimization process; Step S3: determine the target to be optimized, and establish a corresponding two-dimensional irregular part layout target optimization function; Step S4: Based on the optimal foraging algorithm, perform a global optimization search on the arrangement order and rotation angle of the parts, determine the optimal arrangement order and rotation angle of the parts, and output the best arrangement result. 2. the two-dimensional irregular parts layout method based on optimal foraging algorithm according to claim 1, is characterized in that, in step S1, the concrete way that two-dimensional irregular parts layout problem is mathematically described is as follows: First, define variables: given that the number of parts participating in the layout is n, and the number of allowed rotation angles of each part is m, a layout order of parts is randomly generated {x ₁ ,…,x _i ,…,x _n } , x _i ∈{1,2,…,n}, the rotation angle number of each part {y ₁ ,y ₂ ,…,y _n },y _i ∈{1,2,…,m}, y _i corresponds to The rotation angle of is

The corresponding layout plan is {(x ₁ ,y ₁ ),…,(x _i ,y _i ),…,(x _n ,y _n )}; Then, the problem of two-dimensional irregular parts layout is defined: on a given raw material sheet, according to the processing requirements, the parts are reasonably discharged, and the utilization rate of raw materials is maximized while meeting the production demand. 3. the two-dimensional irregular parts layout method based on optimal foraging algorithm according to claim 1, is characterized in that, in step S2, the constraint condition that needs to be satisfied in the layout optimization process is: (1) participate in The placement positions of the parts to be laid out do not overlap each other; (2) the parts involved in the layout are placed inside the raw material sheet. 4. The two-dimensional irregular parts layout method based on the optimal foraging algorithm according to claim 1, is characterized in that, in step S3, the target to be optimized is that the utilization rate of raw materials is maximized; The area of i parts is s(i), i∈{1,2,…,n}, then the raw material utilization δ is as follows:

In the formula, w is the width of the plate in the horizontal direction, and h is the height of the plate in the vertical direction; Then the two-dimensional irregular parts layout objective optimization function is described as follows:

5. The two-dimensional irregular parts layout method based on the optimal foraging algorithm according to claim 1, is characterized in that, in step S4, the optimal foraging algorithm comprises the following steps: Step S41, initialize algorithm parameters and population; Step S42, population fitness evaluation; calculate the fitness values of all individuals in the initial population, arrange them in descending order, and save the optimal individual as the global optimal individual; Step S43, update the population, calculate the fitness values of all individuals in the new population, arrange in descending order, and save the optimal individual; Step S44, update the global optimal individual; Step S45, iterative update, if the termination condition is satisfied, output the optimal layout result, otherwise, go to step S43. 6. the two-dimensional irregular parts layout method based on optimal foraging algorithm according to claim 4, is characterized in that, described step S41 is specifically: Initialization algorithm parameters: population size popsize, maximum iteration number maxIter, current iteration number t; The method of initializing the population is as follows: according to the initialized population size popsize, the integer encoding is used, where

The population of individuals is generated by random generation, and the remaining

The populations of individuals are generated in descending order of area size. 7. The two-dimensional irregular parts layout method based on optimal foraging algorithm according to claim 4, is characterized in that, in described step S42, population fitness evaluation function is:

The smaller the value of F(x), that is, the higher the material utilization rate, the better the results of the arrangement of individuals in the population. 8. the two-dimensional irregular parts layout method based on optimal foraging algorithm according to claim 4, is characterized in that, the mode of updating population in described step S43 is: defines the range factor k, and

is the global optimal individual when the number of iterations is t,

is the jth individual in the population, j∈{1,2,…,n}; the update method of the individual position of the population is as follows:

In the formula,

for the individual

The i-th dimension element of , r _1ji and r _2ji are random numbers between 0 and 1 subject to uniform distribution, b∈{1,2,…,n};

the worst individual in the population

The i-th dimension element of , N=n; The optimal foraging algorithm has a small probability of accepting some poor individuals in the iterative process, thus helping the algorithm to escape the constraints of the local optimal solution; for the minimization problem, judge the next generation of individuals

The accepted models are:

In the formula,

is a random number between 0 and 1 that obeys a uniform distribution,

and

Represents the fitness value of individual j in the population when the number of iterations is t and t+1, respectively. 9 . The two-dimensional irregular parts layout method based on the optimal foraging algorithm according to claim 4 , wherein the method of updating the global optimal individual in the step S44 is an elite retention strategy. 10 . 10 . The two-dimensional irregular parts layout method based on the optimal foraging algorithm according to claim 4 , wherein the termination condition in the step S45 is the preset maximum number of iterations maxIter . 11 .

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