CN115099459A - Workshop multi-row layout method considering gaps and loading and unloading points - Google Patents
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Abstract
The invention discloses a workshop multi-row layout method considering gaps and loading and unloading points, which belongs to the technical field of facility layout and comprises the following steps: establishing a facility layout objective function based on the logistics cost and the land resource utilization rate and proposing constraint conditions to form a workshop multi-row layout model; the model is solved to obtain an optimal layout scheme, and the method comprehensively considers gaps and loading and unloading points to carry out multi-row layout of the workshop, so that the product processing is more orderly and the logistics are smoother. Meanwhile, the invention provides a two-stage algorithm for solving the problem aiming at the model, wherein the first stage and the second stage adopt an improved biogeography algorithm and a linear programming algorithm for solving, the improved biogeography algorithm improves the original algorithm through operations such as staged migration, a reverse learning mechanism, self-adaptive variation, local search and the like, and adopts a double-threshold stopping criterion to remove the redundant cycle number. The algorithm has the advantages of high solving quality and high stability.
Description
Technical Field
The invention relates to a layout mode and a layout method of facilities, belongs to the technical field of facility layout, and particularly relates to a workshop multi-row layout method considering gaps and loading and unloading points.
Background
The Multi-row facility layout problem (MRFLP) is a relatively important class of facility layout. MRFLP is widely used for its good layout configuration, such as shop floor layout, numerical analysis, semiconductor manufacturing, etc. The multi-row layout can improve the utilization rate of equipment, promote the production activities to be carried out orderly, is particularly suitable for flexible workshops, and plays a role of a booster in upgrading and transformation of the current manufacturing industry, so that the MRFLP is a topic which is relatively concerned in both the industrial and academic fields.
The gap in the MRFLP is a frequently discussed factor, and the proper gap can effectively prevent collision in the equipment carrying process, so that the equipment is convenient to dissipate heat and maintain, and meanwhile, the overlong carrying distance is avoided so as to save time and energy. The safety clearance provided by the invention refers to the safety distance between the equipment and other objects under the condition of avoiding any potential safety hazard. The safety clearance is considered in the layout activity, the space constraint between the same row, the adjacent row and the equipment and the wall can be simultaneously met, and the safety factor of enterprise operation can be effectively improved. The starting point and the end point of logistics interaction between production units in a manufacturing system are collectively called as Material Handling Points (MHP), and the position planning of the point directly influences the transportation distance of materials, thereby causing great fluctuation of logistics cost. The position separation of MHP can effectively avoid the crossing of transportation routes and the mixed accumulation of products and raw materials, so that the loading and unloading process is orderly and efficient. Optimization of MHP location in a facility layout is also an important research context.
In conclusion, the consideration of the facility safety clearance is further fit with the reality, unnecessary loss in enterprise operation can be reduced, and MHP separation arrangement also enables the product processing to be more orderly and the logistics to be smoother. Therefore, considering the influence of the above factors together, the present invention proposes for the first time an extended Multi-row layout problem (eMLLP) with safety clearance and material handling points
Disclosure of Invention
In view of the above problems, the present invention provides a method for arranging multiple rows of workshops in consideration of gaps and loading/unloading points, so as to reduce unnecessary loss in enterprise operation, and to make product processing more orderly and logistics smoother.
The technical scheme of the invention is as follows:
a method for multi-row layout of a workshop considering gaps and loading and unloading points, comprising the following steps:
s1, establishing a facility layout objective function based on the logistics cost and the land resource utilization rate;
the logistics cost is determined by the sum of the product of unit interactive object flow and carrying distance between facilities, and is a key index for evaluating the quality of the layout, and the expression of the objective function can be as follows:
i. j is a facility number, i, j belongs to Q; q is a set of facilities, {1,2, …, n }; n is the number of facilities; f. of ij Is the flow of the unidirectional object from facility i to facility j; dx (x) ij Is the distance in the x-direction between the loading point of facility i to the unloading point of facility j; dy ij Is the distance in the y-direction between the loading point of facility i to the unloading point of facility j.
The facility layout footprint is the area of the smallest rectangle that can envelop all facilities and their safety clearances after the layout solution is determined. The smaller the area is, the higher the land resource utilization rate of the facility scheme is, and the expression of the objective function can be as follows:
F 2 ＝length·width (2)
length is the length of the envelope surface of n facilities; width is the envelope width of n facilities.
The relative importance degree between the two optimization targets is balanced, a new objective function is constructed by using a weighting method, so that the multi-objective optimization problem is converted into a single-objective optimization problem, and the expression of the implementation layout objective function can be as follows:
F＝α 1 β 1 F 1 +α 2 β 2 F 2 (3)
in the formula, alpha 1 、α 2 Is a weight factor, and alpha 1 +α 2 ＝1；β 1 、β 2 Is a normalization factor.
And S2, collecting workshop data and proposing constraint conditions of the objective function to form a workshop multi-row layout model.
And S3, solving the workshop multi-row layout model to obtain an optimal layout scheme.
The MRFLP needs to determine the mutual sequence and the accurate position of facilities, has the characteristics of combination optimization and continuous optimization, and the two-stage solving method can effectively integrate the solving requirements of the discreteness and the continuity and has the highest matching degree with the solving requirements. Therefore, the invention provides a two-stage algorithm for solving the problem, wherein the first stage adopts an Improved Biogeography-Based Optimizer with Linear Programming, IBBO _ LP, and the second stage adopts Linear Programming for solving, wherein the Improved Biogeography algorithm improves the original algorithm through operations such as staged migration, a reverse learning mechanism, adaptive variation, local search and the like, and adopts a dual-threshold stopping criterion to remove redundant cycle times.
The improved biophysical algorithm comprises the following steps:
step 1: setting initialization parameters such as maximum iteration number MaxIt, habitat number npop and initial temperature T 0 Termination temperature T f An external threshold value it _ max, an annealing threshold value T _ max, an annealing factor alpha, etc.;
step 2: initializing a population N, calculating the fitness index HSI of each habitat individual in the population N, and taking the habitat X with the highest HSI as an optimal solution;
and step 3: respectively feeding the population NCarrying out staged migration operation to obtain a population N _1, carrying out reverse learning operation to obtain a population N _2, and carrying out self-adaptive variation operation to obtain a population N _ 3; mixing N _1, N _2 and N _3, sorting the mixed materials from high to low according to HSI, and taking the first npop individuals to form a population N _ new; taking the first N of the population N according to a specified proportion 1 Individual and first N of N _ new 2 Updating the initial population N and the optimal individual X by the individual;
and 4, step 4: carrying out simulated annealing local search operation on the optimal individual X, and updating the X;
and 5: if the external file is updated, it is equal to 0, otherwise it is equal to it +1, if it is greater than it _ max, the current optimal solution X is output, otherwise step 6 is executed;
step 6: and (5) making t be t +1, if t is greater than MaxIt, outputting the current optimal solution X, and otherwise, repeating the steps 3-6.
The invention has the technical effects that:
1. the invention comprehensively considers the gaps and the loading and unloading points to carry out multi-row layout of the workshop, so that the product processing is more orderly and the logistics are smoother.
2. The invention provides a two-stage algorithm-an improved biophysical algorithm with linear programming fused, the algorithm optimizes the mutual positions of facilities through IBBO, and then determines the accurate positions of the facilities by utilizing the linear programming, and the algorithm has the advantages of excellent solving quality and strong stability.
Drawings
In order to more clearly illustrate the technical solution of the embodiments of the present invention, the drawings used in the embodiments will be briefly described below.
FIG. 1 is a schematic view of a multi-row facility layout with safety clearances and material handling points;
FIG. 2 is a flow chart of an improved biophysical algorithm according to an embodiment of the invention;
FIG. 3 is a schematic diagram of encoding and decoding of habitat individuals according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of a staged migration operation according to an embodiment of the present invention;
FIG. 5 is a diagram illustrating an adaptive mutation operation according to an embodiment of the present invention;
FIG. 6 is a schematic diagram of a simulated annealing local search according to an embodiment of the present invention;
FIG. 7 is a flow chart of a simulated annealing local search according to an embodiment of the present invention;
FIG. 8 is a block diagram of the result of IBBO _ LP and BBO _ LP in accordance with an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the following examples and the accompanying drawings.
In order to make the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings, which are attached to the drawings and are a part of the embodiments of the present invention, but not all of the embodiments of the present invention. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, are within the scope of the present invention.
Referring to FIG. 1, FIG. 1 is a schematic view of a multi-row facility layout with safety clearance and material handling points; the purpose of this embodiment is to obtain the optimal layout, and the method for obtaining the optimal layout includes the following steps:
s1, establishing a facility layout objective function based on the logistics cost and the land resource utilization rate;
the logistics cost is determined by the sum of products of unit interactive object flow and carrying distance between facilities, and is a key index for evaluating the quality of the layout, and the expression of the objective function can be as follows:
i. j is a facility number, i, j belongs to Q; q is a set of facilities, {1,2, …, n }; n is the number of facilities; f. of ij Is the flow of the unidirectional object from facility i to facility j; dx (x) ij Is the distance in the x-direction between the loading point of facility i to the unloading point of facility j; dy ij Is the distance in the y-direction between the loading point of facility i to the unloading point of facility j.
The facility layout footprint is the area of the smallest rectangle that can envelop all facilities and their safety clearances after the layout solution is determined. The smaller the area is, the higher the land resource utilization rate of the facility scheme is, and the expression of the objective function can be as follows:
F 2 ＝length·width (2)
length is the length of the envelope surface of n facilities; width is the envelope width of n facilities.
The relative importance degree between the two optimization targets is balanced, a new objective function is constructed by using a weighting method, so that the multi-objective optimization problem is converted into a single-objective optimization problem, and the expression of the implementation layout objective function can be as follows:
F＝α 1 β 1 F 1 +α 2 β 2 F 2 (3)
in the formula, alpha 1 、α 2 Is a weight factor, and alpha 1 +α 2 ＝1；β 1 、β 2 Is a normalization factor.
S2, collecting workshop data and proposing constraint conditions of an objective function to form a workshop multi-row layout model;
the constraint conditions include:
in the formula, x i As the central abscissa of the facility i；l i Is the length of facility i; s i A safety clearance for facility i; l is the total length of the factory layout area; x is the number of ip Is the central abscissa of the material loading point of the facility i; x is a radical of a fluorine atom id Is the central abscissa of the material unloading point of the facility i; gamma ray i A judging function of whether the material loading points and the material unloading points of the facility i are separately arranged, wherein when the material loading points and the material unloading points of the facility i are separately arranged, gamma is i 1, otherwise γ i ＝0；p i A function is judged for the position of the material loading point of the facility i, wherein p is the position of the material loading point of the facility i when the material loading point is positioned at the left side of the mass center i 1, otherwise p i ＝0；c i Rotating a judging function for the facility i, wherein c is when the facility i rotates i 1, otherwise c i ＝0。
Equations (4), (5) are used to constrain the center abscissa of facility i; equations (6) and (7) are used to calculate the abscissa of the material loading point and the material unloading point of the facility i.
In the formula, y t Is the ordinate of the t-th row; w is a i The width of facility i; r is it A decision function for the facility i on the t-th row, wherein r is the time when the facility i is on the t-th row it 1, otherwise r it 0; w is the total width of the factory layout area; t is the set of distribution rows, {1,2, …, n }; y is ip For the central ordinate of the material loading point of the installation i；y id Is the central vertical coordinate of the material unloading point of the facility i;
equations (8), (9) are used to limit the ordinate of the distribution row; equations (10) and (11) are used to calculate the ordinate of the material loading point and the material unloading point of facility i.
In the formula, x jp Is the central abscissa of the facility j material loading point; x is the number of jd Is the central abscissa of the facility j material unloading point; dy ij The distance between the material loading point of the facility i and the material unloading point of the facility j in the y-axis direction; y is jp Is the central ordinate of the material loading point of the facility j; y is jd Is the central ordinate of the material unloading point of the facility j.
Equations (12), (13) are used to calculate the distance of the facilities i to j in the x direction; equations (14), (15) are used to calculate the distance of the facilities i to j in the y direction.
In the formula I j Is the length of facility j; beta is a ij To determine the function, when s i ≥s j Time beta ij 1, otherwise β ij ＝0；s j A safety clearance for facility j; alpha (alpha) ("alpha") jit To judge the function, α is when the facilities i, j are arranged on the t-th row and the facility j is to the right of the facility i jit 1, otherwise α jit ＝0；w j The width of facility j; r is jt A decision function for the facility j on the t-th row, where r is the time when the facility j is on the t-th row jt 1, otherwise r jt ＝0。
The formula (16) is used for limiting adjacent facilities in the same row to meet the safety clearance constraint, and preventing the facilities from overlapping to cause unnecessary loss; equations (17), (18) are used to limit adjacent row facilities from meeting the safety clearance constraint.
length is the length of the envelope surface of n facilities; the width is the width of an enveloping surface of n facilities; u. u t Is a function for determining whether the t-th row is on or off, when the t-th row is on t 1, otherwise u t ＝0。
Equations (19) and (20) are used to calculate the length and width of the layout area occupied by the laid-out facilities.
The formula (21) indicates that each facility can be arranged only in one row; equation (22) represents the row on sequence; the formula (23) represents the upper and lower limits of the number of facilities arranged on the opening row; the limiting variables α of the formulae (24), (25) ijt Taking the value of (A); equations (26) and (27) limit the value ranges of the decision variables.
And S3, solving the workshop multi-row layout model to obtain an optimal layout scheme.
This embodiment solves the problem by using a two-stage algorithm, wherein the first stage uses an Improved Biogeography-Based optimizer with Linear Programming (IBBO _ LP) and the second stage uses a Linear Programming algorithm.
The improved biophysical algorithm in the first stage improves the original algorithm through operations such as staged migration, a reverse learning mechanism, self-adaptive variation, local search and the like, and removes redundant cycle times by adopting a double-threshold stopping criterion. As shown in fig. 2, the algorithm includes the following steps:
step 1: setting initialization parameters such as maximum iteration number MaxIt, habitat number npop and initial temperature T 0 Termination temperature T f An external threshold value it _ max, an annealing threshold value T _ max, an annealing factor alpha, etc.;
step 2: initializing a population N, calculating the fitness index HSI of each habitat individual in the population N, and taking the habitat X with the highest HSI as an optimal solution;
and step 3: respectively carrying out staged migration operation on the population N to obtain a population N _1, carrying out reverse learning operation to obtain a population N _2, and carrying out self-adaptive variation operation to obtain a population N _ 3; mixing N _1, N _2 and N _3, sorting the mixed materials from high to low according to HSI, and taking the first npop individuals to form a population N _ new; taking the first N of the population N according to a specified proportion 1 Individual and first N of N _ new 2 Updating the initial population N and the optimal individual X by the individual;
and 4, step 4: carrying out simulated annealing local search operation on the optimal individual X, and updating the X;
and 5: if the external file is updated, it is equal to 0, otherwise it is equal to it +1, if it is greater than it _ max, the current optimal solution X is output, otherwise step 6 is executed; the external profile refers to a population profile in which no local search is performed in the algorithm.
Step 6: and (5) making t be t +1, if t is greater than MaxIt, outputting the current optimal solution X, and otherwise, repeating the steps 3-6.
The encoding and decoding method of the habitat individuals in this embodiment is shown in fig. 3, and the habitat individuals are decoded by using an automatic line feed strategy, that is, facilities are arranged from the first line according to a solution sequence, when the total length of the facilities and the gaps exceeds the boundary, the facilities are automatically changed to the second line to be arranged, and so on until all the facilities are arranged. In addition, a penalty function is introduced in the decoding process to eliminate infeasible solutions of facility layout areas exceeding the original factory limited areas, and in order to ensure the population diversity of the algorithm in the early search process and improve the elimination rate of the infeasible solutions in the later period of the algorithm, a penalty factor is designed to be an exponential function with iterative increment.
The penalty function is as follows:
δ＝δ 0 θ t (29)
in the formula (I), the compound is shown in the specification,δ is a penalty factor, δ 0 And (4) setting an initial value of the penalty factor, wherein t is the current iteration number, and theta is a constant larger than 1.
In conventional biophysical algorithms (BBO), the high HSI habitat is not prone to change, leading to a fall into local optima. To make up for this deficiency, this embodiment adds a habitat information exchange and self-regulation mechanism to enrich population diversity, that is, a staged migration operation is adopted, which specifically includes the following steps: generating a (0,1) random number in the algorithm process, if the random number is not greater than the immigration rate, performing migration operation, otherwise, performing staged optimization operation: if the iteration times do not exceed 1/3 of the total iteration times, performing information exchange between habitats by adopting partial mapping and crossing operation; if the iteration number does not exceed 2/3 of the total iteration number, the habitat adopts segment reversing operation; otherwise, the habitat adopts single point mutation operation to improve itself. The migration operation, the partial mapping crossover operation, the segment reversal operation, and the single-point mutation operation in this step all belong to the prior art, and refer to fig. 4, where fig. a is a schematic diagram of the migration operation, and fig. b is a schematic diagram of the partial mapping crossover operation; FIG. c is a schematic illustration of the segment reversal operation; FIG. d is a schematic diagram of a single point mutation operation.
In the migration mechanism of this embodiment, a hyperbolic tangent migration model is used to calculate the migration rate, as shown in equation (30).
In the formula, λ i For migration rate, mu i For the migration rate, a is a hyperbolic tangent model parameter, 1.1 is taken, npop is the population number, I, E is the maximum migration rate and the migration rate respectively, and 1 is taken.
Reverse learning is a novel interactive self-learning strategy, and a reverse learning strategy based on positions is provided aiming at the problem characteristics provided by the invention, so that the population diversity is further expanded, and the situation that the local optimum is trapped is effectively prevented. The location-based reverse learning strategy solves the following:
in the formula (I), the compound is shown in the specification,
a facility number of a jth position in an ith habitat for the tth iteration;
a rotation vector for a jth position in an ith habitat for the tth iteration;
are respectively as
The corresponding value after reverse learning.
Adaptive mutation operation this operation allows the rate and accuracy of convergence to be greatly improved by adaptive adjustment of the probability of mutation. The adaptive mutation probability formula is as follows:
in the formula, pm max 、pm min The upper limit and the lower limit of the mutation probability, newobj is the target value of the solution after the mutation operation, avabj is the target average value of the new population, newobj max The target value obj is the maximum target value of the individuals in the population, and the target value obj is the reciprocal of the HSI. Mutation operation adopts a single-point reverse insertion method, wherein the single-point reverse insertion is a prior art method, as shown in fig. 5.
And aiming at the habitat with the highest suitable housing index in the current population, a neighborhood solution is constructed by adopting double-layer variation operation, the structure of the solution is continuously optimized through an annealing mechanism, and finally, a greedy strategy is used as a judgment basis for updating the optimal individual. Simulated annealing local search is also prior art, see in particular fig. 6 and 7.
And in the second stage, the accurate position of the facility is solved by utilizing linear programming, and the method specifically comprises the following steps:
the first step is as follows: determining variable alpha by using feasible solution X obtained by first-stage operation ijt 、r it 、u t 、y t 。
The second step is that: linearizing the workshop multi-row layout model, bringing a feasible solution X and a decision variable thereof into a linear programming model, and finally solving the accurate position and the target value of the facility on each row; the objective function of the linearized model is equation (3), since y has been obtained t Thus y is t Corresponding constraints are not needed, and the constraints of the linear programming model are equations (4) to (7), (10) to (16), (19) and (20).
In specific implementation, all experiments in this embodiment are run on a desktop computer equipped with an intel (r) core (tm) i5-9500 processor, with a host frequency of 3GHZ, a Windows10 os, and a memory of 8.00 GB. Since the operation result of the eMRLP does not exist in the current research, in order to verify the accuracy of the model provided by the invention, a Matlab R2016b is applied to call a precision solver Gurobi to solve the model, and the calculation result is used as the basis of the algorithm. In order to verify the solving performance of the two-stage algorithm (IBBO _ LP), the IBBO _ LP is applied to solve a plurality of examples with the eMLP scale of 5-49. The algorithm has good superiority through calculation of a large number of examples.
In order to further verify the performance of the algorithm for solving the eMRLP, 10 examples with the scale of 5-30 are selected, BBO _ LP and IBBO _ LP are used for solving the eMRLP respectively, the algorithm of each example is operated for 10 times, and the solving result is stored as initial data. And performing hundred-differentiation treatment on the obtained data by using a formula, wherein the treated value is a solving deviation gap, and the solving formula is that the gap is (G-G)/G multiplied by 100 percent, wherein G is the current target value, and G is the optimal target value in the group of data. The box plot was plotted with 10 sets of gap values as statistical data, as shown in FIG. 8.
As can be seen from FIG. 8, when solving the small-scale calculation example, the gap values solved by IBBO _ LP are all 0, which indicates that the 10-time operation results of the algorithm are the same and the algorithm stability is strong. When a medium-scale and large-scale calculation example is solved, the longitudinal length of a rectangular box of the IBBO _ LP is smaller than that of the BBO _ LP, and the data obtained by the IBBO _ LP are more concentrated; in addition, the positions of black dashed lines in the rectangular boxes solved by IBBO _ LP are lower than BBO _ LP, which indicates that the data deviation value obtained by IBBO _ LP is small and the dispersion is low.
The above description is only a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the embodiment of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.
Claims (7)
1. A workshop multi-row layout method considering gaps and loading and unloading points, which is characterized by comprising the following steps:
s1, establishing a facility layout objective function based on the logistics cost and the land resource utilization rate;
s2, collecting workshop data and proposing constraint conditions of the objective function to form a workshop multi-row layout model;
s3, solving the workshop multi-row layout model to obtain an optimal layout scheme;
the objective function is as follows:
F＝α 1 β 1 F 1 +α 2 β 2 F 2
wherein the content of the first and second substances,
F 2 ＝length·width
in the formula, alpha 1 、α 2 Is a weight factor, and α 1 +α 2 ＝1；β 1 、β 2 Is a normalization factor; i. j is a facility number, i, j belongs to Q; q is a set of facilities, {1,2, …, n }; n is the number of facilities; f. of ij Is the flow of the unidirectional object from facility i to facility j; dx (x) ij Is the distance in the x-direction between the loading point of facility i to the unloading point of facility j; dy ij Is the distance in the y-direction between the loading point of facility i to the unloading point of facility j; length is the length of the envelope surface of n facilities; width is n facilitiesThe envelope width of (d);
the constraint conditions include:
in the formula, x i 、x j Respectively the central abscissa of the facility i and the facility j; l i 、l j The lengths of facilities i, j, respectively; s i 、s j Safety clearances for facilities i, j, respectively; l is the total length of the factory layout area; x is the number of ip 、x jp The center horizontal coordinate of the material loading points of the facilities i and j is shown; x is the number of id 、x jd The center horizontal coordinate of the material unloading points of the facilities i and j is set; gamma ray i For material loading and unloading of facilities iA function for judging whether the loading points are separately arranged, wherein when the material loading point and the material unloading point of the facility i are separately arranged, gamma is i 1, otherwise γ i ＝0；p i Determining a function for a material loading point location for facility i, wherein p is the center of mass of the plant i when the material loading point is located to the left of the center of mass i 1, otherwise p i ＝0；c i Determining a function for rotation of the facility i, wherein c is the time when the facility i rotates i 1, otherwise c i ＝0；y t Is the ordinate of the t-th row; w is a i 、w j The width of the facilities i, j, respectively; r is it A decision function for the facility i on the t-th row, wherein r is the time when the facility i is on the t-th row it 1, otherwise r it 0; w is the total width of the factory layout area; t is the set of distribution rows, {1,2, …, n }; y is ip 、y jp Respectively are central vertical coordinates of material loading points of facilities i and j; y is id 、y jd Respectively are central vertical coordinates of material unloading points of facilities i and j; dy ij The distance between the material loading point of the facility i and the material unloading point of the facility j in the y-axis direction; beta is a ij To determine the function, when s i ≥s j Time beta ij 1, otherwise β ij ＝0；s j A safety clearance for facility j; alpha is alpha jit To judge the function, α is when the facilities i, j are arranged on the t-th row and the facility j is to the right of the facility i jit 1, otherwise α jit ＝0；r jt Is a decision function for a facility j on the t-th row, where r is the time when the facility j is on the t-th row jt 1, otherwise r jt ＝0；u t Is a function for determining whether the t-th row is on, when the t-th row is on t 1, otherwise u t ＝0。
2. The method for the multi-row layout of the workshop considering the gaps and the loading and unloading points as claimed in claim 1, wherein the multi-row layout model of the workshop is solved by a two-stage algorithm in step S3, wherein the feasible solution X is obtained by a modified biophysical algorithm in the first stage, and the accurate position and the target value of the facility on each row are obtained by a linear programming algorithm in the second stage; the improved biophysical algorithm improves the biophysical algorithm through operations such as staged migration, a reverse learning mechanism, self-adaptive variation, local search and the like, and removes redundant cycle times by adopting a double-threshold stopping criterion;
the second stage comprises the following steps:
the first step is as follows: determining variable alpha by using feasible solution X obtained by first-stage operation ijt 、r it 、u t 、y t ；
The second step: and linearizing the workshop multi-row layout model, and substituting the feasible solution X and decision variables thereof into a linear programming model to obtain the accurate position and the target value of the facility on each row.
3. A method for multi-line layout of a workshop taking into account gaps and handling points according to claim 3, characterized in that said improved biophysical algorithm comprises the following steps:
step 1: setting initialization parameters such as maximum iteration number MaxIt, habitat number npop and initial temperature T 0 Termination temperature T f An external threshold value it _ max, an annealing threshold value T _ max, an annealing factor alpha, etc.;
step 2: initializing a population N, calculating the fitness index HSI of each habitat individual in the population N, and taking the habitat X with the highest HSI as an optimal solution;
and step 3: respectively carrying out staged migration operation on the population N to obtain a population N _1, carrying out reverse learning operation to obtain a population N _2, and carrying out self-adaptive variation operation to obtain a population N _ 3; mixing N _1, N _2 and N _3, sorting the mixed materials from high to low according to HSI, and taking the first npop individuals to form a population N _ new; taking the first N of the population N according to a specified proportion 1 Individual and first N of N _ new 2 Updating the initial population N and the optimal individual X by the individual;
and 4, step 4: carrying out simulated annealing local search operation on the optimal individual X, and updating the X;
and 5: if the external file is updated, it is equal to 0, otherwise it is equal to it +1, if it is greater than it _ max, the current optimal solution X is output, otherwise step 6 is executed;
step 6: and (5) making t be t +1, if t is greater than MaxIt, outputting the current optimal solution X, and otherwise, repeating the steps 3-6.
4. The method for the multi-row layout of the workshop considering gaps and loading and unloading points as claimed in claim 4, wherein a penalty function is introduced in the decoding process of the habitat individuals to eliminate infeasible solutions that the facility layout area exceeds the original factory defined area; the penalty function is as follows:
δ＝δ 0 θ t
where δ is a penalty factor, δ 0 And (4) setting an initial value of the penalty factor, wherein t is the current iteration number, and theta is a constant larger than 1.
5. The method for the multi-row layout of the workshop considering gaps and loading and unloading points as claimed in claim 4, wherein a hyperbolic tangent migration model is adopted to calculate the migration rate in the staged migration operation; if the random number is not greater than the migration rate, performing migration operation, otherwise performing staged optimization operation;
the staged optimization operation is as follows: if the iteration times do not exceed 1/3 of the total iteration times, performing information exchange between habitats by adopting partial mapping and crossing operation; if the iteration number does not exceed 2/3 of the total iteration number, the habitat adopts segment reversing operation, otherwise the habitat adopts single-point variation operation to improve itself;
the hyperbolic tangent migration model is as follows:
in the formula of lambda i For migration rate, mu i For the migration rate, a is a hyperbolic tangent model parameter, npop is the population number, and I, E is the maximum migration rate and the migration rate, respectively.
6. The method for the multi-row layout of the workshop in consideration of gaps and loading and unloading points as claimed in claim 4, wherein the reverse learning operation adopts a position-based reverse learning strategy;
the reverse learning strategy based on position is solved as follows:
in the formula (I), the compound is shown in the specification,
a facility number of a jth position in an ith habitat for the tth iteration;
a rotation vector for a jth position in an ith habitat for the tth iteration;
are respectively as
The corresponding value after reverse learning.
7. The method as claimed in claim 4, wherein the adaptive mutation probability formula in the adaptive mutation operation is as follows:
in the formula, pm max 、pm min Respectively an upper limit and a lower limit of the variation probability; newobj is the target value of the solution after mutation operation; avobj is the target average value of the new population; newobj j max The maximum target value of an individual in the population; target valueobj is the reciprocal of HSI; the mutation operation adopts a single-point reverse insertion mode.
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