CN112859761B - Distributed forging flow shop energy-saving scheduling method considering centralized heat treatment - Google Patents
Distributed forging flow shop energy-saving scheduling method considering centralized heat treatment Download PDFInfo
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Abstract
The invention discloses an energy-saving scheduling method for a distributed forging flow shop considering centralized heat treatment, which comprises the steps of providing a brand-new distributed scheduling problem in the scheduling field; an energy-saving scheduling model aiming at minimizing completion time and energy consumption is established, and the model comprises various constraints such as machine limitation, a hybrid production mode and the like; aiming at the problem of large consumption of idle machines, an energy-saving strategy for reducing production energy consumption at the cost of reducing production rate is provided; an intelligent optimization algorithm suitable for solving the problem of distributed scheduling is provided, and a coding and decoding rule, an elite mutual aid strategy, four evolution strategies and two local search strategies are designed; the real problem is solved by combining the proposed energy-saving scheduling model and the proposed intelligent optimization algorithm, the superiority of the algorithm is verified through comparison of algorithm performance, and the effectiveness of the energy-saving strategy is verified. The energy-saving scheduling method can effectively solve the energy-saving scheduling problem of distributed forging production.
Description
Technical Field
The invention relates to the field of energy-saving scheduling of forging production, in particular to a distributed forging flow shop energy-saving scheduling method considering centralized heat treatment.
Background
In the context of sustainable development, the problem of energy consumption is always a critical issue facing the manufacturing industry. Forging is an important production method in manufacturing industry, and energy consumption is huge due to the existence of processes such as heating and heat treatment. Energy-saving scheduling has become a research hotspot as an effective energy-saving method, and is concerned by more and more scholars. With the development of advanced manufacturing and smart manufacturing, the ever-shortening production cycle and the customized demands of user personalization, distributed production is gradually replacing the traditional production methods. Therefore, the research on energy-saving scheduling of distributed forging production becomes a research trend in the field of forging energy-saving scheduling.
At present, in the aspect of energy-saving scheduling of forging production, the targeted object is mainly furnace charging scheduling of a heating furnace. Only a few studies have considered energy efficient scheduling of the entire forging line. However, no intensive research has been conducted on an energy-saving scheduling method for a distributed forging line shop.
In a distributed forging flow shop, complex working conditions and multi-resource constraints are the difficulty of production scheduling, for example, factors such as different processing capacities of various flow lines, a mixed production mode combining continuous production and intermittent production, centralized heat treatment after distributed production and the like need to be considered. How to carry out the distribution of the production line and the sequencing of the workpieces becomes two targets of distributed forging scheduling, so that the research on the energy-saving scheduling method of the distributed forging production line workshop considering the centralized heat treatment is very important.
Disclosure of Invention
The distributed forging flow shop energy-saving scheduling method considering the centralized heat treatment, provided by the invention, establishes a multi-target scheduling model according to the characteristics of distributed production, and also provides an elite cooperative multi-target optimization algorithm suitable for solving the model.
The invention provides a distributed forging flow shop energy-saving scheduling method considering centralized heat treatment, which mainly comprises the following steps:
step 1: proposing a distributed forging flow shop scheduling problem considering centralized heat treatment and determining relevant parameters
In the distributed forging flow shop considering the centralized heat treatment, the parameter arrangement and definition of the forging stock to be processed are required before scheduling,
step 2: establishing a scheduling model of targets in a distributed forging flow shop considering centralized heat treatment
In the problem of scheduling the distributed forging flow shop considering the centralized heat treatment, the influence of various time factors is considered, including processing time, transportation time, waiting time and adjusting time, wherein the adjusting time is determined by the time consumed by adjusting machine parameters and dies due to the fact that the sizes of the adjacent processed forgings on the same machine are different. The calculation model targeting the maximum completion time is as follows:
Tmax＝nax(QI,1,QI,2…QI,N)#(1)#
wherein, the formula (1) is a mathematical model with the maximum completion time as the target; the formula (2) gives the completion time of the workpiece at the first position in any flow shop on the first process; formula (3) gives the completion time of the workpiece on the first processing position on the machine (m is more than or equal to 2) in any flow shop; the completion time of the forge piece at the position (l is more than or equal to 2) in any flow shop on the first machine is given by a formula (4); the completion time of the forge piece on the machine (m is more than or equal to 2) at the position (l is more than or equal to 2) in any flow shop is given by a formula (5); equation (6) gives the finish time for the first forging processed on any heat treatment machine; the completion time of the ith (i is more than or equal to 2) forged piece processed on any heat treatment machine is given by a formula (7); formula (8) is the adjustment time of any machine in any flow shop before processing the workpiece; equations (9) - (10) are the idle time between any adjacent tasks for any machine in any flow shop.
In the calculation of the total production energy consumption, the processing energy consumption and standby energy consumption of each machine and the transportation energy consumption between the processes need to be considered, and a calculation model taking the total production energy consumption as a target is as follows:
wherein, the formula (7) is a calculation model taking the maximum production energy consumption as a target; formula (8) is the total energy consumption of any machine of any plant during production; formula (9) is the total energy consumed for inter-process transport; equation (10) is the total energy consumed by any machine during the heat treatment phase;
and step 3: establishing an optimization objective and constraint model of a distributed forging flow shop considering centralized heat treatment
In the problem of scheduling the distributed forging flow shop considering the centralized heat treatment, in the optimization process, the calculation models of the two targets in the step 2 need to be constrained. The optimization objective and constraint model is as follows:
Minimize{Tmax,Etotal}#(15)
wherein, the formula (15) is the target of optimization; equations (16) - (18) are constraints in the forging line shop, and equation (16) ensures that each forging is arranged to a certain position in a certain line shop; formula (17) ensures that at most one forging is arranged at any position of any flow shop; equation (18) ensures that each forging is scheduled into its available flow shop; equations (19) - (20) are constraints in the heat treatment shop, and equation (19) ensures that each forging is arranged into a certain heat treatment furnace; the formula (20) ensures that at most one forging piece is arranged at any processing position of any heat treatment furnace; equation (21) is a constraint on the completion time between adjacent machines; formula (22) is the constraint of the completion time between adjacent forgings on any machine; equation (23) ensures zero-wait constraint for a particular process; the formulas (24) to (25) ensure the value ranges of the variable parameters.
And 4, step 4: proposing an energy-saving strategy and establishing a correlation calculation and constraint model
In the problem of scheduling the distributed forging flow shop considering the concentrated heat treatment, because the processing time is different among all the working procedures and the size of the forged piece is different, some machines have longer idle time in the processing process, and the energy consumption is increased. The method adopts an energy-saving strategy for reducing the production energy consumption of the machine at the cost of reducing the machining rate of the machine, and a relevant calculation and constraint model is as follows:
wherein, formula (26) gives the calculation method of the machine energy consumption after the energy-saving strategy is adopted; formula (27) gives the total energy consumption of the machine after the energy-saving strategy is adopted; formula (28) gives the total energy saved after the energy-saving strategy is adopted; equation (29) ensures the limitation of the machine deceleration; the value range of the variable parameters is ensured by the formula (30);
and 5: intelligent optimization algorithm suitable for distributed scheduling problem
Considering the scheduling problem of the distributed forging flow shop with centralized heat treatment, due to the influence of complex working conditions and multi-resource constraints, an elite cooperation non-dominated sorting genetic algorithm is provided to be combined with the mathematical model provided in the step 2-4 for scheduling optimization. The process of the elite cooperative non-dominated sorting genetic algorithm comprises the following steps:
s1: and (4) making a coding rule according to the distributed characteristics, wherein each code is a row matrix, elements in the matrix consist of integers and decimals, the integer part represents the number of the forging, and the decimal part represents the flow shop to which the forging is distributed.
S2: and (3) carrying out population initialization, wherein two populations are initialized because the algorithm is a coevolution algorithm, and individuals initialized by an LCT rule and an LEC rule are added into the two populations respectively. The LCT initialization rule is a minimum completion time rule, firstly, all forgings are arranged in an ascending order according to the processing time, then the forgings are sequentially distributed to available flow workshops, the current completion time is calculated through distribution each time, and the flow workshop with the minimum completion time is selected; and the LEC initialization rule is a lowest energy consumption rule, and similarly, the current total energy consumption is calculated by distribution each time and the flow shop with the minimum total energy consumption is selected.
S3: and performing iterative search on the two populations to generate a new generation of sub-population, wherein the iterative process comprises calculating an objective function, non-dominant sorting, selecting operation, and crossing and mutation operation. Wherein the crossover and mutation operations respectively adopt operation modes based on procedures and pipeline distribution rules to enhance searching capability.
S4: and performing mutual elite operation between the two populations. In the elite mutual-help operation, elite is the first-layer Pareto solution in each population, and the mutual-help mode is that the elite solution and random individuals in another population are crossed and varied to generate new filial generation which is added into the population.
S5: and merging the parent population and the child population, returning to S3 if the end condition is not reached, and performing neighborhood search if the end condition is reached. The neighborhood search operation includes a neighborhood search strategy based on workpiece ordering and based on shop floor allocation. Inserting each workpiece in each workshop into a new position in the current workshop by the neighborhood search strategy based on workpiece sorting; the neighborhood search strategy based on plant allocation reinserts each workpiece of each plant into each location of other available plants.
S6: and combining all the populations, carrying out non-dominant sorting and outputting results.
Step 6: problem solving and numerical analysis are carried out by combining scheduling model and intelligent algorithm
Firstly, setting algorithm parameters, and calculating the influence of each parameter on the performance of the algorithm by adopting a control variable method, wherein the main parameters of the algorithm comprise iteration times, population quantity, crossing rate and variation rate. Second, the solution of the actual problem is performed and a gantt chart is drawn to guide production.
The invention establishes a scheduling model and provides a multi-objective optimization algorithm suitable for solving the scheduling model by analyzing and considering the characteristics of the distributed forging flow shop with centralized heat treatment, and compared with the prior art, the invention has the following technical effects:
(1) according to the characteristics of the distributed forging line shop considering the concentrated heat treatment, a scheduling model is established to minimize energy consumption and completion time.
(2) An energy saving method is proposed to reduce the energy consumption of the machine at the expense of reducing the idle machine production rate.
(3) An elite cooperation non-dominated genetic algorithm is provided, and a coding and decoding rule, two population initialization rules, four evolution strategies, an elite mutual aid strategy and two neighborhood search strategies which are suitable for the scheduling problem are designed.
(4) The constructed multi-target scheduling model can be combined with the provided elite cooperation non-dominated genetic algorithm to solve the distributed production scheduling problem and draw a Gantt chart to guide production.
The associated symbols are defined as shown in the following table:
drawings
The invention is further described with reference to the accompanying drawings and specific embodiments.
FIG. 1 is a flow chart of a scheduling method;
FIG. 2 is a diagram illustrating a distributed forging line shop scheduling problem considering a concentrated heat treatment
FIG. 3 is a Gantt chart comparison with and without power-saving strategy;
FIG. 4 is a flow chart of an elite synergy nondominant genetic algorithm;
FIG. 5 is a parameter comparison graph;
FIG. 6 is a comparison of a solution set with and without an energy saving strategy;
Detailed Description
As shown in fig. 1, the distributed forging flow shop energy-saving scheduling method considering centralized heat treatment provided by the invention mainly comprises six steps, namely determining the distributed forging flow shop workflow considering centralized heat treatment, establishing a multi-target scheduling model of the distributed forging flow shop considering centralized heat treatment, establishing an optimization target and a constraint model of the distributed forging flow shop considering centralized heat treatment, providing an energy-saving strategy, establishing a related calculation and constraint model, designing an intelligent optimization algorithm suitable for a distributed scheduling problem, solving the problem by combining the scheduling model and the intelligent algorithm, and performing numerical analysis.
The following detailed description will be described in detail with reference to the accompanying drawings, and the method of the present invention is mainly divided into the following steps:
step 1: proposing a distributed forging flow shop scheduling problem considering centralized heat treatment
As shown in fig. 2, the distributed forging flow shop scheduling problem considering the centralized heat treatment can be described as: the forging stock is uniformly heated and then distributed to different forging production lines for forging, punching, ring rolling, expanding and other operations, the forging stock needs to be conveyed to a heat treatment workshop for heat treatment after the forging is finished, and a finished product forging is obtained after the heat treatment is finished. Some time-like parameters, such as the processing time of the forging stock on each machine, the transportation time of each stage, the machine adjustment time and the like, need to be collected and recorded. Similarly, some energy consumption parameters, such as the operation energy and standby energy consumption of each machine, transportation energy consumption, etc., also need to be collected.
Step 2: establishing a scheduling model of targets in a distributed forging flow shop considering centralized heat treatment
In the distributed forging flow shop scheduling problem considering the centralized heat treatment, the scheduling model taking the completion time as the target needs to consider the influence of various time factors, including the processing time, the transportation time, the waiting time and the adjusting time, wherein the adjusting time is determined by the time consumed by adjusting the machine parameters and the dies due to the fact that the sizes of the forged pieces processed adjacently on the same machine are different. The calculation model targeting the maximum completion time is as follows:
Tmax＝max(QI,1,QI,2…QI,N)#(31)#
wherein, formula (31) is a mathematical model targeting the maximum completion time; the formula (32) shows the completion time of the workpiece at the first position in any flow shop on the first process; the formula (33) shows the completion time of the workpiece on the first processing position in any flow shop on the machine (m is more than or equal to 2); the completion time of the forge piece at the position (l is more than or equal to 2) in any flow shop on the first machine is given by a formula (34); the completion time of the forge piece at the position (l is more than or equal to 2) in any flow shop on the machine (m is more than or equal to 2) is given by a formula (35); equation (36) gives the finish time for the first forging processed on any heat treatment machine; formula (37) gives the completion time of the ith (i is more than or equal to 2) forging processed on any heat treatment machine; formula (38) is the setup time of any machine before processing the workpiece in any flow shop; equations (39) - (40) are the idle time between any adjacent tasks for any machine in any flow shop.
In the calculation of the total production energy consumption, the processing energy consumption and standby energy consumption of each machine and the transportation energy consumption between the processes need to be considered, and a calculation model taking the total production energy consumption as a target is as follows:
wherein, the formula (41) is a calculation model with the maximum production energy consumption as a target; equation (42) is the total energy consumed by any machine of any plant during production; formula (43) is the total energy consumed for inter-process transport; equation (44) is the total energy consumed by any machine during the heat treatment phase;
and step 3: establishing an optimization objective and constraint model of a distributed forging flow shop considering centralized heat treatment
In the distributed forging flow shop scheduling problem considering the centralized heat treatment, the calculation models of the two targets in the step 2 need to be constrained due to the complex working condition of the scheduling problem and the existence of multiple resource constraints. The optimization objective and constraint model is as follows:
Minimize{Tmax,Etotal}#(45)
wherein equation (45) is the goal of optimization; equations (46) - (48) are constraints in the forging line shop, with equation (46) ensuring that each forging is arranged to a location in a certain line shop; formula (47) ensures that at most one forging is arranged at any position of any flow shop; equation (48) ensures that each forging is scheduled into its available flow shop; equations (49) - (50) are constraints in the heat treatment shop, and equation (49) ensures that each forging is arranged into a certain heat treatment furnace; the formula (50) ensures that at most one forging piece is arranged at any processing position of any heat treatment furnace; equation (51) is a constraint on the completion time between adjacent machines; equation (52) is a constraint on the completion time between adjacent forgings on any machine; equation (53) ensures zero-wait constraint for a particular process; the formulas (54) to (55) ensure the value ranges of the variable parameters.
And 4, step 4: proposing an energy-saving strategy and establishing a correlation calculation and constraint model
In the scheduling problem of the distributed forging flow shop considering the centralized heat treatment, because the processing time is different among all the working procedures and the size of the forged piece is different, some machines have longer idle time in the processing process, and the energy consumption is increased. To minimize these idle times, each machine is used with maximum utility, an energy-saving strategy is employed to reduce the energy consumption of the machine production at the expense of reducing the machine processing rate, with a model of the associated calculations and constraints:
wherein, the formula (56) gives the calculation method of the machine energy consumption after the energy-saving strategy is adopted; formula (57) gives the total energy consumption of the machine after the energy-saving strategy is adopted; formula (58) gives the total energy saved after the energy-saving strategy is adopted; equation (59) ensures a limit on machine deceleration; the formula (60) ensures the value range of the variable parameter;
and 5: intelligent optimization algorithm suitable for distributed scheduling problem
Considering the scheduling problem of the distributed forging flow shop with centralized heat treatment, due to the influence of complex working conditions and multi-resource constraints, an elite cooperation non-dominated sorting genetic algorithm is provided to be combined with the scheduling model provided in the step 2-4 for scheduling optimization. The flow of the elite cooperative non-dominated sorting genetic algorithm is shown in fig. 4, and the specific steps are described as follows:
s1: and (4) making a coding rule according to the distributed characteristics, wherein each code is a row matrix, elements in the matrix consist of integers and decimals, the integer part represents the number of the forging, and the decimal part represents the flow shop to which the forging is distributed.
S2: and (3) carrying out population initialization, wherein two populations are initialized because the algorithm is a coevolution algorithm, and individuals initialized by an LCT rule and an LEC rule are added into the two populations respectively. The LCT initialization rule is a minimum completion time rule, firstly, all forgings are arranged in an ascending order according to the processing time, then the forgings are sequentially distributed to available flow workshops, the current completion time is calculated through distribution each time, and the flow workshop with the minimum completion time is selected; and the LEC initialization rule is a lowest energy consumption rule, and similarly, the current total energy consumption is calculated by distribution each time and the flow shop with the minimum total energy consumption is selected.
Pseudo code for two initialization rules is:
s3: and performing iterative search on the two populations to generate a new generation of sub-population, wherein the iterative process comprises calculating an objective function, non-dominant sorting, selecting operation, and crossing and mutation operation. The crossing and mutation operations respectively adopt a process-based rule (SC sequencing crossing rule: randomly selecting n forgings, keeping the positions of the forgings in two parents, crossing the rest parts of the two parents to generate two filial generations; SM sequencing mutation rule: randomly selecting m flow shop, and reordering the position of one of the forgings to generate one filial generation) and an operation mode based on a flow line distribution rule (DC distribution crossing rule: randomly selecting n forgings, exchanging the flow shop selected by the forgings in the two parents and generating two filial generations; DM distribution mutation rule: randomly selecting n forgings, replacing the selected flow shop with other available flow shop to generate one filial generation) to strengthen the search capability.
S4: and performing mutual elite operation between the two populations. In the elite mutual-help operation, elite is the first-layer Pareto solution in each population, and the mutual-help mode is that the elite solution and random individuals in another population are crossed and varied to generate new filial generation which is added into the population.
Pseudo code for elite interoperability is as follows:
s5: and merging the parent population and the child population, returning to S3 if the end condition is not reached, and performing neighborhood search if the end condition is reached. The neighborhood search operation includes a neighborhood search strategy based on workpiece ordering and based on shop floor allocation. Inserting each workpiece in each workshop into a new position in the current workshop by the neighborhood search strategy based on workpiece sorting; the neighborhood search strategy based on plant allocation reinserts each workpiece of each plant into each location of other available plants.
The pseudo-code for both neighborhood searches is as follows:
procedure 6: allocation-based neighborhood search
S6: and combining all the populations, carrying out non-dominant sorting and outputting results.
Step 6: problem solving and numerical analysis are carried out by combining scheduling model and intelligent algorithm
Firstly, setting algorithm parameters, and calculating the influence of each parameter on algorithm performance by adopting a control variable method, wherein the main parameters of the algorithm comprise iteration times, population quantity, crossing rate and variation rate, the iteration times belong to a set {50, 100, 150 and 200}, the population quantity belongs to a set {20, 50, 100 and 150}, the crossing rate belongs to a set {0.3, 0.5, 0.7 and 0.9}, the variation rate belongs to a set {0.2, 0.4, 0.6 and 0.8}, and all combinations are operated for 10 times and the optimal solution set is recorded. The average contribution of different values of the parameters to the optimal solution is shown in fig. 5, the population number and the iteration number are in direct proportion to the performance of the optimal solution, but the population number can be selected to be 100 and the iteration number is 100 in consideration of the calculation time, and according to the statistical result, the cross rate can be 0.7 and the variation rate can be 0.6. Next, the actual problem is solved and a gantt chart is drawn.
Finally, to prove the superiority of the proposed algorithm, the algorithm was compared with the original algorithm and other algorithms, the comparison method used the average coverage C (a, B) (coverage of a versus B) of the solutions between two algorithms, the test included four scales of orders, each group was calculated 10 times and the comparison results were examined non-parametrically, the comparison results are shown in tables 1-3, where ECNSGA is the proposed elite cooperative non-dominated genetic algorithm, OA1 is the classical non-dominated genetic algorithm (NSGA ii), OA2 is ECNSGA without population initialization, OA3 is ECNSGA without elite mutual assistance strategy, OA4 is ECNSGA without local search strategy, OA5 is ECNSGA without energy saving strategy. And the performance of the algorithm is better than that of other comparison algorithms.
TABLE 1
In order to prove the effectiveness of the proposed energy-saving strategy, the optimal solution sets with or without the energy-saving strategy running for 10 times are compared, and the comparison result is shown in fig. 6, so that the effectiveness of the energy-saving strategy is verified.
The associated symbols are defined as shown in the following table:
Claims (2)
1. a distributed forging flow shop energy-saving scheduling method considering centralized heat treatment is characterized by comprising the following steps:
step 1: proposing a distributed forging flow shop scheduling problem considering centralized heat treatment
The scheduling problem of the distributed forging flow line workshop considering the centralized heat treatment is described as that a forging stock is uniformly heated and then distributed into different forging flow lines for forging, punching, ring rolling and expanding operations, the forging stock needs to be conveyed to a heat treatment workshop for heat treatment after the forging is finished, and a finished product forging is obtained after the heat treatment is finished; time and energy consumption parameters related to scheduling problems need to be collected and recorded;
step 2: establishing a computational model of targets in a distributed forging line shop taking into account centralized heat treatment
In the scheduling problem of the distributed forging flow shop considering the centralized heat treatment, the influence of various time factors, including processing time, transportation time, waiting time and adjusting time, needs to be considered in the calculation of the completion time, wherein the adjusting time is determined according to the time consumed by adjusting machine parameters and dies caused by different sizes of adjacent processed forgings on the same machine; the calculation model targeting the maximum completion time is as follows:
Tmax＝max(QI,1,QI,2…QI,N) (1)
wherein, the formula (1) is a mathematical model with the maximum completion time as the target; the formula (2) gives the completion time of the workpiece at the first position in any flow shop on the first process; formula (3) gives the completion time of the workpiece on the machine at the first processing position in any flow shop; the completion time of the forge piece at any position in the flow shop on the first machine is given by a formula (4); the completion time of the forge piece on the machine at any position in the flow shop is given by a formula (5); equation (6) gives the finish time for the first forging processed on any heat treatment machine; equation (7) gives the finish time for the ith forging processed on any heat treatment machine; formula (8) is the adjustment time of any machine in any flow shop before processing the workpiece; formulas (9) to (10) represent idle time of any machine in any flow shop between any adjacent tasks;
in the calculation of the total production energy consumption, the processing energy consumption and standby energy consumption of each machine and the transportation energy consumption between the processes need to be considered, and a calculation model taking the total production energy consumption as a target is as follows:
wherein, the formula (11) is a calculation model taking the maximum production energy consumption as a target; equation (12) is the total energy consumption of any machine in any plant during production; formula (13) is the total energy consumed for inter-process transport; equation (14) is the total energy consumed by any machine during the heat treatment phase;
and step 3: establishing an optimization objective and constraint model of a distributed forging flow shop considering centralized heat treatment
In the scheduling problem of the distributed forging flow shop considering the centralized heat treatment, in the optimization process, the calculation models of the two targets in the step 2 need to be constrained; the optimization objective and constraint model is as follows:
Minimize{Tmax,Etotal} (15)
wherein, the formula (15) is the target of optimization; equations (16) - (18) are constraints in the forging line shop, and equation (16) ensures that each forging is arranged to a certain position in a certain line shop; the formula (17) ensures that at most one forging is arranged at any position of any flow shop; equation (18) ensures that each forging is scheduled into its available flow shop; equations (19) - (20) are constraints in the heat treatment shop, and equation (19) ensures that each forging is arranged into a certain heat treatment furnace; the formula (20) ensures that at most one forging piece is arranged at any processing position of any heat treatment furnace; equation (21) is a constraint on the completion time between adjacent machines; formula (22) is the constraint of the completion time between adjacent forgings on any machine; equation (23) ensures zero-wait constraint for a particular process; the formulas (24) to (25) ensure the value range of the variable parameters;
and 4, step 4: proposing an energy-saving strategy and establishing a correlation calculation and constraint model
In the scheduling problem of the distributed forging flow shop considering the centralized heat treatment, because the processing time is different among all the working procedures and the size of the forged piece is different, some machines have longer idle time in the processing process, so that the energy consumption is increased; an energy-saving strategy for reducing the energy consumption of machine production at the cost of reducing the machining rate of the machine is adopted, and a relevant calculation and constraint model is as follows:
wherein, formula (26) gives the calculation method of the machine energy consumption after the energy-saving strategy is adopted; formula (27) gives the total energy consumption of the machine after the energy-saving strategy is adopted; formula (28) gives the total energy saved after the energy-saving strategy is adopted; equation (29) ensures the limitation of the machine deceleration; the value range of the variable parameters is ensured by the formula (30);
and 5: intelligent optimization algorithm suitable for distributed scheduling problem
Due to the influence of complex working conditions and multi-resource constraints, the scheduling optimization is carried out by combining an elite cooperative non-dominated sorting genetic algorithm with the mathematical model in the step 2-4 in the consideration of the scheduling problem of the distributed forging flow shop with centralized heat treatment;
step 6: problem solving and numerical analysis are carried out by combining scheduling model and intelligent algorithm
Firstly, setting algorithm parameters, and calculating the influence of each parameter on the performance of the algorithm by adopting a control variable method, wherein the main parameters of the algorithm comprise iteration times, population quantity, crossing rate and variation rate; secondly, solving an actual problem and drawing a Gantt chart;
the associated symbols are defined as shown in the following table:
2. the distributed forging flow shop energy-saving scheduling method considering centralized heat treatment according to claim 1, wherein the flow of the elite collaborative non-dominated sorting genetic algorithm is as follows:
s1: making coding rules according to the distributed characteristics, wherein each code is a row matrix, elements in the matrix consist of integers and decimals, the integer part represents a forging number, and the decimal part represents a flow shop to which the forging number is distributed;
s2: performing population initialization, wherein two populations are initialized because the algorithm is a coevolution algorithm, and individuals initialized by an LCT rule and an LEC rule are added into the two populations respectively; the LCT initialization rule is a minimum completion time rule, firstly, all forgings are arranged in an ascending order according to the processing time, then the forgings are sequentially distributed to available flow workshops, the current completion time is calculated through distribution each time, and the flow workshop with the minimum completion time is selected; the LEC initialization rule is a lowest energy consumption rule, and the current total energy consumption is calculated and the flow shop with the minimum total energy consumption is selected in each distribution in the same manner;
s3: performing iterative search on the two populations to generate a new generation of sub-population, wherein the iterative process comprises calculating an objective function, non-dominant sorting, selecting operation, crossing and mutation operation; wherein, the cross operation and the mutation operation respectively adopt operation modes based on the process and the assembly line distribution rule to strengthen the searching capability;
s4: performing mutual elite operation between the two populations; in the elite mutual-help operation, elite is a first-layer Pareto solution in each population, and the mutual-help mode is that the elite solution and random individuals in another population are crossed and varied to generate new filial generations and the new filial generations are added into the population;
s5: merging parent population and child population, if the end condition is not reached, returning to S3, and if the end condition is reached, performing neighborhood search; the neighborhood search operation comprises a neighborhood search strategy based on workpiece sorting and based on workshop allocation; inserting each workpiece in each workshop into a new position in the current workshop by the neighborhood search strategy based on workpiece sorting; the neighborhood searching strategy based on workshop allocation reinserts each workpiece of each workshop into each position of other available workshops;
s6: and combining all the populations, carrying out non-dominant sorting and outputting results.
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