Multi-target single-machine scheduling algorithm with controllable production time in MTO mode

Abstract

The multi-target single-machine scheduling algorithm with controllable production time in the MTO mode is characterized by comprising the following steps: a) setting printing conditions; b) constructing a mathematical model; c) carrying out discrete coding and decoding; d) performing population initialization; e) constructing a solution algorithm; f) carrying out social grade layering; g) updating operation; h), a cost reduction strategy; firstly, order printing conditions are set, then a mathematical model is constructed, discrete coding and decoding are carried out, then population initialization is carried out, a solving algorithm is constructed, social grade layering and updating operation is carried out in the solving process, and finally, a low-cost strategy is executed. According to the multi-target single-machine scheduling algorithm, the processing sequence of the printing order is finally obtained, so that the management task of production operation becomes simpler, the production plan and production scheduling are very reasonable, and the production management level and the economic benefit of an enterprise are improved.

Description

Technical Field

[0001] The present invention relates to a scheduling algorithm, and more specifically, to a multi-objective single-machine scheduling algorithm with controllable production time in an MTO mode. Background Art

[0002] Packaging and printing is a typical discrete manufacturing industry, involving a large number of equipment and personnel, complex process flow, chaotic material management, rough and time-consuming production planning, insufficient workshop control capabilities, and other problems. Most small and medium-sized enterprises still have relatively backward workshop management. At present, packaging and printing enterprises mainly organize production in the form of orders (MTO mode), and the automation and digitization of workshop production are low. In addition, there are uncertain factors such as equipment failure, emergency orders, and material shortages in the production process. The production scheduling of the workshop mainly relies on the experience of workshop managers to arrange, and the management is relatively rough, making the management task of production operations complex and arduous. Enterprises cannot respond to order demands quickly, cannot effectively solve the problem of inventory material accumulation, and the production plan scheduling is not reasonable. It is impossible to coordinate the contradiction between user personalized needs and rapid response, which greatly restricts the production management level and economic benefits of enterprises. Summary of the invention

[0003] In order to overcome the disadvantages of the above technical problems, the present invention provides a multi-objective single-machine scheduling algorithm with controllable production time under the MTO mode.

[0004] The multi-objective single-machine scheduling algorithm with controllable production time under the MTO mode of the present invention is characterized by including: a). Setting of printing conditions; assuming that n independent packaging printing orders are available at time zero on a single printing machine, and the printing machine can only produce at most one order at each time; once an order starts to be produced, the processing operation is not allowed to be interrupted; each order has a normal production time, and the production time of the order can be compressed by allocating additional available resources, but additional compression costs will be incurred; b). Construction of mathematical model; c). Discrete encoding and decoding; d). Population initialization; e). Construction of solution algorithm; f). Social class stratification; g). Update operation; h). Cost reduction strategy.

[0005] The multi-objective single-machine scheduling algorithm with controllable production time under the MTO mode of the present invention, the construction of the mathematical model described in step b) is specifically implemented by the following steps:

[0006] b-1). Definition of processing variables; define the following order variables:

[0007] n: total number of orders;

[0008] j, k: order index number;

[0009] Jj , J k : Order j and order k;

[0010] π: Order processing sequence, that is, π=[J [1] ,J [2] ,...,J [n] ];

[0011] J [i] : The order at the i-th position in the processing sequence;

[0012] p j : Normal processing time of order j;

[0013] The minimum allowed processing time for order j;

[0014] m j : The maximum allowed compression amount for order j,

[0015] The actual processing time of order j;

[0016] c j : Unit compression cost of order j;

[0017] d j : Delivery date of order j;

[0018] T j : Delay time of order j;

[0019] S j : The start time of order j;

[0020] M: an infinite positive number;

[0021] b-2). Definition of decision variables; define the following decision variables:

[0022] x j : The amount of compression in processing time of order j;

[0023]

[0024] b-3). Establish the objective function and constraint conditions; establish the objective function as shown in formula (1) and formula (2):

[0025]

[0026] minf 1 is to minimize the total delay time, minf 2 is to minimize the total compression cost;

[0027] Establish the constraints shown in formula (3) to formula (7):

[0028] M.y jk +S j -(p k -x k )≥S k ;j,k=1,2,...,n;j<k (3)

[0029] M·(1-y jk )+S j -(p j -x j )≥S j ;j,k=1,2,...,n;j<k (4)

[0030] S j +p j -x j -d j ≥T j j=1,2,...,n (5)

[0031] m j ≥x j ; j = 1, 2, ..., n (6)

[0032] T j ≥0,x j ≥0,S j ≥0,y jk ={0,1};j,k=1,2,...,n;j<k (7)

[0033] Formula (3) and Formula (4) determine the priority relationship between orders and define that an order can be produced at any time; Formula (5) ensures the constraints of the delay time of each order in the processing sequence; Formula (6) limits the compression of the processing time of all orders; Formula (7) limits the non-negativity of the order variable.

[0034] The multi-objective single-machine scheduling algorithm with controllable production time under the MTO mode of the present invention, the discrete encoding and decoding described in step c), specifically comprises the following methods: two layers of information are used for encoding, the first layer represents the order sequence, denoted as π; the second layer represents the order processing time compression, denoted as x; there is a corresponding mapping relationship between the first layer and the second layer, that is, each order has a corresponding processing time compression; the order at position i in the order sequence π is denoted as J k , the corresponding order time compression is x k .

[0035] The multi-objective single-machine scheduling algorithm with controllable production time under the MTO mode of the present invention, the population initialization described in step d), the specific method is: since each solution is composed of an order sorting vector and a compressed time vector, in order to ensure the quality and diversity of the solution, the order sorting of one of the solutions is based on the non-descending order of the delivery date, and has the following characteristic attributes: if order l and order m satisfy p l <p m And d l <d m (l,m=1,2,…,n), there exists an optimal processing arrangement so that order l is processed before order m; the processing time of another solution in the population is the normal processing time, that is, the compression of the processing time is zero; the remaining population is generated randomly, and its expression is as follows:

[0036]

[0037] Where: π(i,k) represents the order at the kth position on the i-th solution in the j-th iteration, x(i,k) represents the processing time compression of the order at the kth position on the i-th solution in the j-th iteration;

[0038] Generate an initialized population P and construct a temporary set P′. At the beginning of the iterative search, put the first individual into the set P′, and then put the individuals in the set P into the constructed set P′ in turn; then compare the current solution P with each element in the set P′ in turn, and eliminate the individuals in P′ that are dominated by P. If any individual in P′ dominates P, P will be eliminated from P′.

[0039] The multi-objective single-machine scheduling algorithm with controllable production time in the MTO mode of the present invention, the construction and solution algorithm described in step e), the specific method is:

[0040] e). Construct a solution algorithm; follow the following steps to construct a hybrid multi-objective evolutionary algorithm MTOGG based on the genetic algorithm GA and the grey wolf optimization algorithm GWO:

[0041] e-1). Population initialization: Generate an initial population, i.e., a wolf pack, based on the encoding mechanism and population initialization strategy; Evaluate individual wolves based on the maximum completion time and additional resource consumption indicators, and use a fast non-dominated method to hierarchically sort the individual wolves;

[0042] e-2) Update operation; perform social level stratification operation and position update operation according to step e-2-1) and step e-2-2) respectively;

[0043] e-2-1). Social hierarchy operation: According to the Pareto dominance relationship, the population is divided into multiple non-dominated levels. If there are more than three non-dominated levels in the population, the solution in the first non-dominated level is called α, the solution in the second non-dominated level is called β, and the solution in the third non-dominated level is called δ;

[0044] e-2-2). Position update operation: According to the characteristics of multi-objective optimization problems, the crossover and mutation operators in the genetic algorithm are used to update the population;

[0045] e-3). Elite retention strategy; merge the parent population Pt of population size N and the offspring population Qt of the same size into a population Rt of size 2N; then evaluate the merged population Rt, and select the top N best individuals as the parents of the next generation based on non-dominated sorting and crowding distance;

[0046] e-4). Termination; if the stopping condition is met, stop searching and return the non-dominated solution, otherwise continue searching.

[0047] The multi-objective single-machine scheduling algorithm with controllable production time under the MTO mode of the present invention, the social level stratification described in step f), the specific method is:

[0048] f). Social hierarchy: The three best individuals in the current population are used to guide other individuals to search for potential optimal solutions. According to the Pareto dominance relationship, the individual solutions in the first, second and third non-dominated levels are recorded as α, β and δ respectively, and the remaining individuals are recorded as ω;

[0049] If the current population is all in the non-dominated layer, that is, the first non-dominated horizontal layer, three individuals are randomly selected from the population as α, β and δ; if the current population has only non-dominated horizontal layers, α comes from the individuals in the first non-dominated horizontal layer, and β and δ come from the individuals in the second non-dominated horizontal layer; if the current population has three or more non-dominated horizontal layers, α, β, and δ come from the individuals in the first, second, and third non-dominated horizontal layers, respectively.

[0050] The multi-objective single-machine scheduling algorithm with controllable production time in the MTO mode of the present invention, the updating operation described in step g), specifically comprises the following steps:

[0051] g) Update operation: For the first non-dominated level layer of the solution, the partial matching crossover operator is used to update the order sorting part. For the second non-dominated level layer of the solution, the double-point crossover operator is used to update the order processing time compression part. The specific crossover steps are as follows:

[0052] g-1). For the first non-dominated horizontal layer of the solution, perform the following operations:

[0053] g-1-1). Select a substring; generate two points and define the area between the two points as the matching area;

[0054] g-1-2). Exchange substrings; exchange the matching area on the parent to generate temporary offspring;

[0055] g-1-3). Mapping relationship; determine the mapping relationship of contradictory elements, that is, if an order has elements that appear multiple times in the sequence, define the mapping relationship of the cross-sequence;

[0056] g-1-4). Legalize children; legalize the order sequence through the information of mapping relationship;

[0057] g-2). For the second non-dominated level of the solution, perform the following operations:

[0058] g-2-1). Select a substring; randomly generate two points and define the area between the two points as the intersection area;

[0059] g-2-2). Exchange substrings; exchange matching regions on the parent to generate offspring;

[0060] The mutation operator helps the algorithm escape from the local optimal solution. Two mutation operators are used, both of which are selected for operation with a probability of 0.5.

[0061] The beneficial effects of the present invention are as follows: the multi-objective single-machine scheduling algorithm with controllable production time under the MTO mode of the present invention first sets the order printing conditions, then constructs the mathematical model and performs discrete encoding and decoding, then initializes the population and constructs the solution algorithm, performs social level stratification and update operations in the solution process, and finally executes the low-cost strategy to solve the solution with minimizing the total delay time and minimizing the total compression cost as the objective function, and finally obtains the processing sorting of the printing order, while the scheduling work mainly relies on the experience of the workshop management personnel to arrange, and the management is relatively rough, which makes the management task of the production operation simpler, and the enterprise can respond quickly to the order demand, and the production plan scheduling is very reasonable, which is conducive to coordinating the contradiction between the personalized needs of users and the rapid response, and improves the production management level and economic benefits of the enterprise. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 It is a flow chart of the hybrid multi-objective evolutionary algorithm MTOGG in the present invention;

[0063] Figure 2 This is an example diagram of encoding and decoding in the present invention;

[0064] Figure 3 A schematic diagram of partial matching crossover mutation in the update operation of the present invention;

[0065] Figure 4 A schematic diagram of a double-point crossover mutation in an update operation of the present invention; DETAILED DESCRIPTION

[0066] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0067] The multi-objective single-machine scheduling algorithm with controllable production time under the MTO mode of the present invention is implemented by the following steps:

[0068] a). Setting of printing conditions. Assume that n independent packaging printing orders are available on a single printing machine at zero time, and the printing machine can only produce one order at most at each time; once an order starts to be produced, the processing operation is not allowed to be interrupted; each order has a normal production time, and the production time of the order can be compressed by allocating additional available resources, but it will incur additional compression costs.

[0069] b). Construction of mathematical model. This is achieved through the following steps:

[0070] b-1). Definition of processing variables; define the following order variables:

[0071] n: total number of orders;

[0072] j, k: order index number;

[0073] J j , J k : Order j and order k;

[0074] π: Order processing sequence, that is, π=[J [1] ,J [2] ,...,J [n] ];

[0075] J [i] : The order at the i-th position in the processing sequence;

[0076] p j : Normal processing time of order j;

[0077] The minimum allowed processing time for order j;

[0078] m j : The maximum allowed compression amount for order j,

[0079] The actual processing time of order j;

[0080] c j : Unit compression cost of order j;

[0081] d j : Delivery date of order j;

[0082] T j : Delay time of order j;

[0083] S j : The start time of order j;

[0084] M: an infinite positive number;

[0085] b-2). Definition of decision variables; define the following decision variables:

[0086] x j : The amount of compression in processing time of order j;

[0087]

[0088] b-3). Establish the objective function and constraint conditions; establish the objective function as shown in formula (1) and formula (2):

[0089]

[0090] minf 1 is to minimize the total delay time, minf 2 is to minimize the total compression cost;

[0091] Establish the constraints shown in formula (3) to formula (7):

[0092] M.y jk +S j -(p k -x k )≥S k ;j,k=1,2,...,n;j<k (3)

[0093] M·(1-y jk )+S j -(p j -x j )≥S j ;j,k=1,2,...,n;j<k (4)

[0094] S j +p j -x j -d j ≤T j j=1,2,...,n (5)

[0095] m j ≥x j ; j = 1, 2, ..., n (6)

[0096] T j ≥0,x j ≥0,S j ≥0,y jk ={0,1};j,k=1,2,...,n;j<k (7)

[0097] Formula (3) and Formula (4) determine the priority relationship between orders and define that an order can be produced at any time; Formula (5) ensures the constraints of the delay time of each order in the processing sequence; Formula (6) limits the compression of the processing time of all orders; Formula (7) limits the non-negativity of the order variable.

[0098] c). Discrete encoding and decoding. The specific method is: use two layers of information for encoding, the first layer represents the order sequence, denoted as π; the second layer represents the order processing time compression, denoted as x; there is a corresponding mapping relationship between the first layer and the second layer, that is, each order has a corresponding processing time compression; the order at position i in the order sequence π is denoted as J k , the corresponding order time compression is x k .

[0099] The first problem in solving the scheduling problem is encoding and decoding. Unlike the traditional scheduling problem where the processing time is fixed, it needs to handle two subtasks, order sorting and order processing time compression, at the same time. Therefore, the present invention proposes a discrete encoding mechanism to adapt to the characteristics of the problem.

[0100] like Figure 2 As shown in the figure, an example diagram of encoding and decoding in the present invention is given, which gives an example of single-machine encoding and decoding of 5 orders. This solution contains two layers of information: the first layer is the order sorting, that is, π = (2, 1, 3, 4, 5); the second layer is the order processing time compression, that is, x = (1, 2, 1, 3, 0). There is a corresponding mapping relationship between these two layers, and each order has a corresponding processing time compression. i The order at the position is denoted by J k , which corresponds to a processing time compression of x k For example, the first station π(1) in the sequence corresponds to order J 2 , order J 2 The processing time compression χ 2 =2. Similarly, the second station π(2) in the sequence corresponds to order J 1 , the processing time compression of this order is χ 1=1. Therefore, for the order sequence π=(2,1,3,4,5), the corresponding compressed time vector is (1,2,1,3,0). This encoding method is easy to generate feasible solutions. In addition, this encoding mechanism has the following two advantages:

[0101] (1) The coding structure is simple and contains two layers of information, namely, order sorting and order processing time compression.

[0102] (2) Compared with random key encoding, discrete encoding can usually effectively reduce information redundancy.

[0103] d). Population initialization. The specific method is as follows: Since each solution consists of an order sorting vector and a compressed time vector, in order to ensure the quality and diversity of the solution, the order sorting of one of the solutions is based on the non-descending order of the delivery date and has the following characteristic properties: if order l and order m satisfy p l <p m And d l <d m (l,m=1,2,…,n), there exists an optimal processing arrangement so that order l is processed before order m; the processing time of another solution in the population is the normal processing time, that is, the compression of the processing time is zero; the remaining population is generated randomly, and its expression is as follows:

[0104]

[0105] Where: π(i,k) represents the order at the kth position on the i-th solution in the j-th iteration, x(i,k) represents the processing time compression of the order at the kth position on the i-th solution in the j-th iteration;

[0106] Generate an initialized population P and construct a temporary set P′. At the beginning of the iterative search, put the first individual into the set P′, and then put the individuals in the set P into the constructed set P′ in turn; then compare the current solution P with each element in the set P′ in turn, and eliminate the individuals in P′ that are dominated by P. If any individual in P′ dominates P, P will be eliminated from P′.

[0107] When constructing a non-dominated solution set, the second individual in set P only needs to be compared once, the third individual in P needs at most two comparison operations, and so on, the Nth individual in P needs at most N-1 comparisons. In the worst case, the total number of comparison operations is N 2 / 2. In addition, considering that there are m targets in each comparison, the time complexity of this method is O(mZ 2 ).

[0108] e). Construct a solution algorithm. Figure 1As shown, a flow chart of the hybrid multi-objective evolutionary algorithm MTOGG in the present invention is given. The specific method is: construct a hybrid multi-objective evolutionary algorithm MTOGG based on the genetic algorithm GA and the grey wolf optimization algorithm GWO according to the following steps:

[0109] e-1). Population initialization: Generate an initial population, i.e., a wolf pack, based on the encoding mechanism and population initialization strategy; Evaluate individual wolves based on the maximum completion time and additional resource consumption indicators, and use a fast non-dominated method to hierarchically sort the individual wolves;

[0110] e-2) Update operation; perform social level stratification operation and position update operation according to step e-2-1) and step e-2-2) respectively;

[0111] e-2-1). Social hierarchy operation: According to the Pareto dominance relationship, the population is divided into multiple non-dominated levels. If there are more than three non-dominated levels in the population, the solution in the first non-dominated level is called α, the solution in the second non-dominated level is called β, and the solution in the third non-dominated level is called δ;

[0112] e-2-2). Position update operation: According to the characteristics of multi-objective optimization problems, the crossover and mutation operators in the genetic algorithm are used to update the population;

[0113] e-3). Elite retention strategy; merge the parent population Pt of population size N and the offspring population Qt of the same size into a population Rt of size 2N; then evaluate the merged population Rt, and select the top N best individuals as the parents of the next generation based on non-dominated sorting and crowding distance;

[0114] e-4). Termination; if the stopping condition is met, stop searching and return the non-dominated solution, otherwise continue searching.

[0115] It can be seen that multi-objective optimization problems are different from single-objective optimization problems. In multi-objective optimization problems, the improvement of one objective will lead to the deterioration of another objective. Therefore, special methods are needed to improve the overall performance. Although the introduction of controllable processing time increases the difficulty of problem solving, the controllable attribute of processing time also brings flexibility to obtain high-quality solutions to the problem, thereby providing convenience for improving the overall performance of the production system. Therefore, the present invention utilizes this attribute to strengthen the exploration and optimization mechanism. Because the mining optimization mechanism usually occurs in the later stage of the search, the search mechanism is implemented when the number of function evaluations reaches a certain value.

[0116] f). Social hierarchy. The specific method is: use the three best individuals in the current population to guide other individuals to search in the direction of potential optimal solutions. According to the Pareto dominance relationship, the individual solutions in the first, second and third non-dominated levels are recorded as α, β and δ respectively, and the remaining individuals are recorded as ω;

[0117] If the current population is all in the non-dominated layer, that is, the first non-dominated horizontal layer, three individuals are randomly selected from the population as α, β and δ; if the current population has only non-dominated horizontal layers, α comes from the individuals in the first non-dominated horizontal layer, and β and δ come from the individuals in the second non-dominated horizontal layer; if the current population has three or more non-dominated horizontal layers, α, β, and δ come from the individuals in the first, second, and third non-dominated horizontal layers, respectively.

[0118] Since the three best individuals in the population are used to guide other individuals to search in the direction of potential optimal solutions, however, due to the inherent conflicting characteristics of each sub-objective in the multi-objective optimization problem, the solution is usually not a solution but a set of compromise solutions called non-dominated solutions. In other words, for a compromise solution, the improvement of one objective performance may lead to the deterioration of other objective performance. Therefore, combined with the characteristics of multi-objective optimization problems, each individual is assigned a rank (i.e., non-dominated level).

[0119] g). Update operation. The specific method is:

[0120] For the first non-dominated level of the solution, the partial matching crossover operator is used to update the order sorting part. For the second non-dominated level of the solution, the double-point crossover operator is used to update the order processing time compression part. The specific crossover steps are as follows:

[0121] g-1). For the first non-dominated horizontal layer of the solution, perform the following operations:

[0122] g-1-1). Select a substring; generate two points and define the area between the two points as the matching area;

[0123] g-1-2). Exchange substrings; exchange the matching area on the parent to generate temporary offspring;

[0124] g-1-3). Mapping relationship; determine the mapping relationship of contradictory elements, that is, if an order has elements that appear multiple times in the sequence, define the mapping relationship of the cross-sequence;

[0125] g-1-4). Legalize children; legalize the order sequence through the information of mapping relationship;

[0126] g-2). For the second non-dominated level of the solution, perform the following operations:

[0127] g-2-1). Select a substring; randomly generate two points and define the area between the two points as the intersection area;

[0128] g-2-2). Exchange substrings; exchange matching regions on the parent to generate offspring;

[0129] The mutation operator helps the algorithm escape from the local optimal solution. Two mutation operators are used, both of which are selected for operation with a probability of 0.5.

[0130] like Figure 3 As shown in FIG. 1 , a schematic diagram of partial matching crossover mutation in the update operation of the present invention is given. The initial order sequence π = (2, 1, 4, 3, 5). If two randomly selected crossover points (i.e., the points at the 2nd and 4th positions) are exchanged for the corresponding order 1 and order 3, the order sequence after the exchange becomes π = (2, 3, 4, 1, 5). Figure 4 As shown, a schematic diagram of double-point crossover mutation in the update operation of the present invention is given. First, two crossover points (such as the points at the 2nd position and the 4th position) are randomly selected, and then feasible integers are randomly generated to replace the original values. It can be seen that the processing time compression amount of order 2 at the 2nd position of the order arrangement is replaced by a new value of 1. The processing time compression amount corresponding to order 4 at the 4th position is updated to a value of 2. These values ​​all vary within their respective ranges, so the updated offspring is still feasible.

[0131] h) Cost reduction strategy: In this invention, the local search strategy is introduced into the improved algorithm, and a cost release strategy is proposed to improve the quality of the solution. This strategy can reduce the total compression cost and keep the total delay time unchanged without changing the order processing sequence. According to the characteristics of the problem, by adjusting the compression amount of the order processing time, the total compression cost can be further reduced without affecting the total delay time. Therefore, for a given order sequence, this strategy can improve the quality of the solution to a certain extent.

Claims

1. A multi-objective single-machine scheduling algorithm with controllable production time under MTO mode, characterized in that: include: a). Setting of printing conditions; Assume that n independent packaging printing orders are available on a single printing machine at time zero, and the printing machine can only produce one order at most at each moment; Once an order starts to be produced, the processing operation must not be interrupted; Each order has a normal production time, and the production time of the order can be compressed by allocating additional available resources, but additional compression costs will be incurred; b). Construction of mathematical model; c). Discrete encoding and decoding; d). Population initialization; e). Construction of solution algorithm; f). Social class stratification; g). Update operation; h). Cost reduction strategy.

2. The multi-objective single-machine scheduling algorithm with controllable production time under the MTO mode according to claim 1 is characterized by: The construction of the mathematical model described in step b) is specifically achieved through the following steps: b-1). Definition of processing variables; define the following order variables: n: total number of orders; j, k: order index number; J j , J k : Order j and order k; π: Order processing sequence, that is, π=[J [1] ,J [2] ,...,J [n] ]; J [i] : The order at the i-th position in the processing sequence; p j : Normal processing time of order j; The minimum allowed processing time for order j; m j : The maximum allowed compression amount for order j, The actual processing time of order j; c j : Unit compression cost of order j; d j : Delivery date of order j; T j : Delay time of order j; S j : The start time of order j; M: an infinite positive number; b-2). Definition of decision variables; define the following decision variables: x j : The amount of compression in processing time of order j; b-3). Establish the objective function and constraint conditions; establish the objective function as shown in formula (1) and formula (2): minf1 is to minimize the total delay time, minf2 is to minimize the total compression cost; Establish the constraints shown in formula (3) to formula (7): M·y jk +S j -(p k -x k )≥S k ;j,k=1,2,...,n;j<k (3) M·(1-y jk )+S j -(p j -x j )≥S j ;j,k=1,2,...,n;j<k (4) S j +p j -x j -d j ≤T j j=1,2,...,n (5) m j ≥x j ;j=1,2,...,n (6) T j ≥0,x j ≥0,S j ≥0,y jk ={0,1};j,k=1,2,...,n;j<k (7) Formula (3) and Formula (4) determine the priority relationship between orders and define that an order can be produced at any time; Formula (5) ensures the constraints of the delay time of each order in the processing sequence; Formula (6) limits the compression of the processing time of all orders; Formula (7) limits the non-negativity of the order variable.

3. The multi-objective single-machine scheduling algorithm with controllable production time under the MTO mode according to claim 2 is characterized by: The discrete encoding and decoding described in step c) is specifically performed as follows: two layers of information are used for encoding, the first layer represents the order sequence, denoted as π; the second layer represents the order processing time compression, denoted as x; there is a corresponding mapping relationship between the first layer and the second layer, that is, each order has a corresponding processing time compression; The order at position i in the order sequence π is recorded as J k , the corresponding order time compression is x k .

4. The multi-objective single-machine scheduling algorithm with controllable production time under the MTO mode according to claim 3 is characterized by: The population initialization described in step d) is specifically as follows: Since each solution is composed of an order sorting vector and a compressed time vector, in order to ensure the quality and diversity of the solutions, the order sorting of one of the solutions is based on the non-descending order of the delivery date and has the following characteristic attributes: If orders l and m satisfy p l <p m And d l <d m (l,m=1,2,…,n), there exists an optimal processing arrangement so that order l is processed before order m; the processing time of another solution in the population is the normal processing time, that is, the compression of the processing time is zero; the remaining population is generated randomly, and its expression is as follows: Where: π(i,k) represents the order at the kth position on the i-th solution in the j-th iteration, x(i,k) represents the processing time compression of the order at the kth position on the i-th solution in the j-th iteration; Generate an initialized population P and construct a temporary set P′. At the beginning of the iterative search, put the first individual into the set P′, and then put the individuals in the set P into the constructed set P′ in turn; then compare the current solution P with each element in the set P′ in turn, and eliminate the individuals in P′ that are dominated by P. If any individual in P′ dominates P, P will be eliminated from P′.

5. The multi-objective single-machine scheduling algorithm with controllable production time under the MTO mode according to claim 4 is characterized by: The specific method of constructing the solution algorithm described in step e) is as follows: e). Construct a solution algorithm; follow the following steps to construct a hybrid multi-objective evolutionary algorithm MTOGG based on the genetic algorithm GA and the grey wolf optimization algorithm GWO: e-1). Population initialization: Generate an initial population, i.e., a wolf pack, based on the encoding mechanism and population initialization strategy; Evaluate individual wolves based on the maximum completion time and additional resource consumption indicators, and use a fast non-dominated method to hierarchically sort the individual wolves; e-2) Update operation; perform social level stratification operation and position update operation according to step e-2-1) and step e-2-2) respectively; e-2-1). Social hierarchy operation: According to the Pareto dominance relationship, the population is divided into multiple non-dominated levels. If there are more than three non-dominated levels in the population, the solution in the first non-dominated level is called α, the solution in the second non-dominated level is called β, and the solution in the third non-dominated level is called δ; e-2-2). Position update operation: According to the characteristics of multi-objective optimization problems, the crossover and mutation operators in the genetic algorithm are used to update the population; e-3). Elite retention strategy; merge the parent population Pt of population size N and the offspring population Qt of the same size into a population Rt of size 2N; then evaluate the merged population Rt, and select the top N best individuals as the parents of the next generation based on non-dominated sorting and crowding distance; e-4). Termination; if the stopping condition is met, stop searching and return the non-dominated solution, otherwise continue searching.

6. The multi-objective single-machine scheduling algorithm with controllable production time under the MTO mode according to claim 5 is characterized by: The social class stratification described in step f) is specifically carried out as follows: f). Social hierarchy: The three best individuals in the current population are used to guide other individuals to search for potential optimal solutions. According to the Pareto dominance relationship, the individual solutions in the first, second and third non-dominated levels are recorded as α, β and δ respectively, and the remaining individuals are recorded as ω; If the current population is all in the non-dominated layer, that is, the first non-dominated horizontal layer, three individuals are randomly selected from the population as α, β and δ; if the current population has only non-dominated horizontal layers, α comes from the individuals in the first non-dominated horizontal layer, and β and δ come from the individuals in the second non-dominated horizontal layer; if the current population has three or more non-dominated horizontal layers, α, β, and δ come from the individuals in the first, second, and third non-dominated horizontal layers, respectively.

7. The multi-objective single-machine scheduling algorithm with controllable production time under the MTO mode according to claim 6 is characterized by: The update operation described in step g) is specifically performed as follows: g) Update operation: For the first non-dominated level layer of the solution, the partial matching crossover operator is used to update the order sorting part. For the second non-dominated level layer of the solution, the double-point crossover operator is used to update the order processing time compression part. The specific crossover steps are as follows: g-1). For the first non-dominated horizontal layer of the solution, perform the following operations: g-1-1). Select a substring; generate two points and define the area between the two points as the matching area; g-1-2). Exchange substrings; exchange the matching area on the parent to generate temporary offspring; g-1-3). Mapping relationship; Determine the mapping relationship of contradictory elements, that is, elements that appear multiple times in a certain order in the sequence, and define the mapping relationship of the intersecting part of the sequence; g-1-4). Legalize children; legalize the order sequence through the information of mapping relationship; g-2). For the second non-dominated level of the solution, perform the following operations: g-2-1). Select a substring; randomly generate two points and define the area between the two points as the intersection area; g-2-2). Exchange substrings; exchange matching regions on the parent to generate offspring; The mutation operator helps the algorithm escape from the local optimal solution. Two mutation operators are used, both of which are selected for operation with a probability of 0.5.

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