CN110874697A

CN110874697A - Flexible workshop scheduling method and system with crane

Info

Publication number: CN110874697A
Application number: CN201911136677.7A
Authority: CN
Inventors: 李俊青; 杜宇
Original assignee: Shandong Normal University
Current assignee: Shandong Normal University
Priority date: 2019-11-19
Filing date: 2019-11-19
Publication date: 2020-03-10
Anticipated expiration: 2039-11-19
Also published as: CN110874697B

Abstract

The utility model discloses a flexible workshop scheduling method and system with a crane, comprising: constructing a flexible workshop scheduling optimization model with a crane by taking the minimized completion time and the energy consumption in the machining and crane transportation processes as optimization targets; solving a flexible workshop dispatching optimization model with a crane by combining a hybrid algorithm of iterative greedy and simulated annealing to obtain a dispatching optimization scheme; and scheduling the workpiece processing of each factory in the flexible workshop of the belt crane by using the obtained scheduling optimization scheme. Combining a hybrid algorithm of iterative greedy and simulated annealing, firstly considering the lifting condition of a crane in CFJSP, and expressing a processing sequence and a machine distribution sequence by using a simple and effective two-dimensional vector; the heuristic method for exploring the problem features is designed, and the exploration capability and the time complexity of the algorithm can be balanced; an improved construction heuristic is proposed, which can reduce the number of embedding positions by ignoring repeated positions, improving the efficiency of the model.

Description

Flexible workshop scheduling method and system with crane

Technical Field

The disclosure relates to the technical field of production scheduling, in particular to a flexible workshop scheduling method and system with a crane.

Background

The statements in this section merely provide background information related to the present disclosure and may not necessarily constitute prior art.

The flexible job shop scheduling problem (FJSP) has applications and developments in many practical industrial fields. FJSP can be considered an extension of the job-shop scheduling problem and therefore also proves to be an NP-hard problem. In a classic FJSP, n workpieces need to be machined on m machines, each workpiece needs to undergo a plurality of machining steps, each machining step corresponds to a set of machines capable of machining, each machining step needs to be completed by selecting one machine, each machine can only machine one workpiece at the same time, and each workpiece can only be machined by one machine at the same time, which is usually allowed to be preempted. However, classical FJSPs cannot be directly applied to actual industrial production processes because of the numerous practical constraints to be considered, such as crane transport and energy consumption factors.

In many practical production processes, the weight of the workpiece and therefore also the transport time and energy consumption of the crane between the machines should be taken into account. In order to meet the requirements of green production, the energy consumption of the machining process should also be considered. However, FJSP (i.e., CFJSP) related documents transported with cranes are less studied, especially if the cranes need to be considered to lift the work piece to a certain height.

Disclosure of Invention

In order to solve the problems, the disclosure provides a flexible workshop scheduling method and system with a crane, provides a hybrid algorithm combining Iterative Greedy (IG) and Simulated Annealing (SA), considers the lifting condition of the crane in CFJSP for the first time, and adopts a simple and effective two-dimensional vector to express a processing sequence and a machine allocation sequence; the heuristic method for exploring the problem features is designed, and the exploration capability and the time complexity of the algorithm can be balanced; an improved construction heuristic is proposed, which can reduce the number of embedding positions by ignoring repeated positions, improving the efficiency of the model.

In order to achieve the purpose, the following technical scheme is adopted in the disclosure:

in a first aspect, the present disclosure provides a flexible workshop scheduling method with a crane, including:

constructing a flexible workshop scheduling optimization model with a crane by taking the minimized completion time and the energy consumption in the machining and crane transportation processes as optimization targets;

solving a flexible workshop dispatching optimization model with a crane by combining a hybrid algorithm of iterative greedy and simulated annealing to obtain a dispatching optimization scheme;

and scheduling the workpiece processing of each factory in the flexible workshop of the belt crane by using the obtained scheduling optimization scheme.

As some possible implementations, the energy consumption of the machining process is,

each machine can only process one workpiece at the same time, and each workpiece can only be processed on one processing machine at the same time, and the energy consumption of the processing process of the machine is as follows:

the total energy consumption of the machining process is as follows:

wherein K is the number of machines; j is the number of workpieces; i is a process number; j is the workpiece number; o is_i,jI is 1,2, …, theta is the ith machining process of the workpiece j_j；θ_jIs a set of machining processes for workpiece J, J being 1,2, …, J; ep_kIs the operating power of machine k; t is_i,j,kIs a process O_i,jMachining time at machine k; decision variable x_i,j,kIs a process O _i,j1 when processed on machine k; otherwise it is 0.

As some possible implementations, the energy consumption of the crane transportation process includes the sum of the energy consumption of an empty load operation process, an empty load waiting process, a load waiting process and a load operation process;

in the energy consumption in the no-load operation process, calculating transverse transportation no-load starting time, transverse transportation no-load transportation time and transverse transportation no-load stopping time in the no-load operation process, so as to calculate the total energy consumption of all workpieces in the no-load operation process according to the transverse movement starting power of the crane, the transverse movement stopping power of the crane and the related power of the crane in the horizontal direction;

in the energy consumption of the no-load waiting process, the difference between the finishing time of the current process of a certain workpiece and the starting time of the current process and the time of the no-load operation of the crane is calculated to obtain the no-load waiting time, so that the energy consumption of the no-load waiting process of all the workpieces is calculated.

As some possible implementations, in the energy consumption of the load waiting process, the starting time of the horizontal moving load transportation of the previous process of a certain workpiece, the stopping time of the horizontal moving load transportation of the current process and the time of the uniform-speed transportation process of the horizontal moving load are respectively calculated, and the starting time of the load transportation, the stopping time of the load transportation and the time of the transportation process in the vertical direction are respectively calculated; obtaining the time in the load waiting process according to the difference between the completion time of the process and the time of the load operation in the horizontal direction and the time of the load operation in the vertical direction, and calculating the energy consumption of the load waiting process of all the workpieces;

in the energy consumption of the load operation process, the energy consumption of the start time, the stop time and the transportation time of the load operation process in the horizontal direction and the energy consumption of the start time, the stop time and the lifting time of the load operation process in the vertical direction are respectively calculated, so that the energy consumption of the load operation process of all the workpieces is calculated.

As some possible implementation manners, two-dimensional vectors of the machining sequence and the machine allocation sequence are defined, and tasks of arranging proper machine machining for each procedure and arranging corresponding machined workpieces for each machine are completed through coding;

and distributing the processing procedures of the workpieces according to the idle time of the crane, the idle time of the preorder procedure of the same workpiece, the idle time of a processing machine and the key factors of the moving path of the crane.

In a second aspect, the present disclosure provides a flexible shop scheduling system with a crane, comprising,

the scheduling optimization model building module is used for building a flexible workshop scheduling optimization model with a crane by taking the minimized completion time and the energy consumption in the machining and crane transportation processes as optimization targets;

the scheduling optimization scheme solving module is used for solving a flexible workshop scheduling optimization model with the crane by combining a hybrid algorithm of iterative greedy and simulated annealing to obtain a scheduling optimization scheme;

and the scheduling module is used for scheduling the workpiece processing of each factory in the flexible workshop with the crane by using the obtained scheduling optimization scheme.

In a third aspect, the present disclosure provides a computer-readable storage medium having stored therein a plurality of instructions adapted to be loaded by a processor of a terminal device and to perform the steps of the method for flexible shop scheduling with crane.

In a fourth aspect, the present disclosure provides a terminal device comprising a processor and a computer-readable storage medium, the processor being configured to implement instructions; the computer readable storage medium is used for storing a plurality of instructions which are suitable for being loaded by a processor and executing the steps of the flexible workshop scheduling method with the crane.

Compared with the prior art, the beneficial effect of this disclosure is:

aiming at the problem of flexible operation scheduling of belt crane transportation, the disclosure provides a hybrid algorithm (IGSA) combining iterative greedy and simulated annealing, and simultaneously considers two targets, including minimizing the maximum completion time and the energy consumption in the machining and crane transportation processes, and considering the time and energy consumption in the crane lifting process for the first time;

an improved construction heuristic is provided, the number of embedding positions can be reduced by neglecting repeated positions, and the efficiency of the model is improved;

and the exploration heuristic method aiming at problem features is adopted to balance the exploration capability and the time complexity of the proposed algorithm.

Drawings

The accompanying drawings, which are included to provide a further understanding of the disclosure, illustrate embodiments of the disclosure and together with the description serve to explain the disclosure and are not to limit the disclosure.

FIG. 1 is a flow chart of the disclosed method;

FIGS. 2(a) and (b) are Gantt diagrams of encoding and encoding, respectively, of the solution in the present embodiment;

FIG. 3 is a diagram illustrating the TPR operation process in this embodiment;

FIG. 4 is a schematic diagram illustrating an inserting operation in the present embodiment;

FIG. 5 is a diagram illustrating analysis of variance of parameters in the present embodiment;

FIGS. 6(a) and (b) are graphs of fitness values for 95% confidence intervals for parameters T and d, respectively, after screening;

FIG. 7(a) is a diagram illustrating the mean value of fitness values and the confidence interval of 95% Least Significant Difference (LSD) in the heuristic comparison of the present embodiment;

FIG. 7(b) is a diagram illustrating the mean value of the fitness value and the 95% LSD confidence interval in the heuristic comparison constructed in the present embodiment;

FIG. 7(c) is a comparison of analysis of variance for the second class of examples of this embodiment.

The specific implementation mode is as follows:

the present disclosure is further described with reference to the following drawings and examples.

It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the disclosure. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure belongs.

It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present disclosure. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.

To address CFJSP, the present disclosure proposes a hybrid algorithm combining Iterative Greedy (IG) and Simulated Annealing (SA), referred to as IGSA algorithm. The method mainly comprises the steps that (1) the lifting condition of the crane is considered in CFJSP for the first time, and a mathematical model of the lifting condition is provided; (2) a simple and effective two-dimensional vector is adopted to express a processing sequence and a machine distribution sequence; (3) an exploration heuristic method aiming at problem characteristics is designed, and the exploration capability and the time complexity of an algorithm can be balanced; (4) an improved construction heuristic is presented that can improve the efficiency of the model by reducing the number of embedded locations by ignoring duplicate locations.

A. Symbols and description

(1) Suppose that: all workpieces are allowed to start machining at time 0 and must be machined on the machine in the order and schedule of the machining sequence;

all machines can process the workpiece at 0 moment and are in a usable state in the whole production process;

each workpiece can be processed on only one (and only one) of the selectable machines at the same time;

each machine can only process one workpiece at the same time; preemption is not allowed to occur;

for each workpiece, the first processing step does not require crane equipment to handle;

the crane can only carry one workpiece to operate at the same time, namely the condition of overlapping operation of the crane is not considered;

the initial position of the crane is on the machine on which the first pass of the first workpiece of the machining sequence is located;

the crane can work continuously without stopping working in midway;

enough space allowance is reserved for storing the workpieces waiting to be transported by the crane;

the arrival time of the next workpiece transportation cannot be earlier than the idle time of the target position machine, if the situation occurs, the crane should wait for the end of the machine processing, and then the next workpiece transportation is carried out after the machine enters the idle state;

if continuous working processes of the same workpiece are required on the same machine, crane transportation is not required.

(2) Symbol

Numbering: k is the number of machines; j, the number of workpieces; j is the workpiece number; i, process numbering; and k is the machine number.

Parameters are as follows: theta_jA set of machining processes for workpiece J, J being 1,2, …, J; o is_i,jI-th machining step of workpiece j, i being 1,2, …, θ_j；

M_j,l:O_i,jA set of machines available for processing; t is_i,j,kProcess O_i,jMachining time at machine k; ep_kThe working power of the machine k; k¹A processing machine of a first process;

P_ithe initial position of the crane; p_nl(O_i,j) Process O_i,jThe crane no-load position; p_l(O_i,j) Process O_i,jThe crane load position of;

Ts_i,jprocess O_i,jThe machining start time of (1); tc_i,jProcess O_i,jThe machining end time of (1);

wj is the weight of workpiece j; ws is the weight of the lifting device; wh: weight of the lateral movement device; wv is the weight of the longitudinal movement device; qn is the lifting quality of the crane;

Lx_kx, the abscissa value of machine k; ly_kThe ordinate value y of machine k; lz_kVertical coordinate value z of machine k;

vh is the horizontal moving speed of the crane; vv is the vertical moving speed of the crane;

a_hsmoving in the horizontal direction to start acceleration; a is_hbMoving in the horizontal direction to stop deceleration; a is_vsMoving the starting acceleration in the vertical direction; a is_vbMoving in the vertical direction to stop deceleration;

P_ohthe related power of the crane in the horizontal direction; p_ovThe relative power of the crane in the vertical direction; p_ohsStarting power when the crane moves transversely; p_ohbStopping power when the crane moves transversely; p_ovsStarting power for longitudinal movement of the crane; p_ovbStopping power when the crane moves longitudinally; ps is the waiting state power of the crane;

E_mptotal energy consumption in the machining process; e_ctTotal energy consumption in the transportation process of the crane; e_noTotal energy consumption of the crane in the no-load transportation process; e_nsThe total energy consumption of the no-load waiting process of the crane; e_lsThe total energy consumption of the crane in the process of load waiting; e_loTotal energy consumption in the process of carrying and transporting the load of the crane; e_no(O_i,j) Process O_i,jEnergy consumption in the no-load transportation process; e_ns(O_i,j) Process O_i,jEnergy consumption of the no-load waiting process; e_ls(O_i,j) Process O_i,jEnergy consumption in the loading waiting process; e_lo(O_i,j) Process O_i,jEnergy consumption in the process of carrying and transporting;

T_no(O_i,j) Process O_i,jThe time of the empty-load transportation process; t is_ns(O_i,j) Process O_i,jTime of idle waiting process of (a); t is_ls(O_i,j) Process O_i,jTime of the load waiting process; t is_lo(O_i,j) Process O_i,jThe time of the payload transport process; t is_lf(O_i,j) Process O_i,jTime of the load lifting process; t is_hnos(O_i,j) Process O_i,jThe start duration of the horizontal movement no-load transportation process; t is_hnob(O_i,j) Process O_i,jThe stopping duration of the horizontal movement no-load transportation process; t is_hnod(O_i,j) Process O_i,jThe process of horizontal movement no-load uniform-speed transportation is long; t is_hlds(O_i,j) Process O_i,jThe start-up duration of the horizontal movement load transport; t is_hldb(O_i,j) Process O_i,jThe stop duration of the horizontal movement load transportation; t is_hldd(O_i,j) Process O_i,jThe length of the process of transporting the horizontally moved load at a constant speed; t is_vlds(O_i,j) Process O_i,jFor vertical load-carrying transportThe length of the operation time; t is_vldb(O_i,j) Process O_i,jThe stopping duration of the vertical load transportation process; t is_vldd(O_i,j) Process O_i,jThe length of the vertical load uniform speed transportation process;

Ψ<O_i1,j1,O_i,j>a crane carrying process O_i1,j1After the end of the work, the conveying step O follows_i,jA relation parameter of the workpiece;

Φ<O_i-1,j,O_i,j,k,k2>the crane completes the preceding procedure O on the machine k_i-1,jThen, the step O on the transfer machine k2_i,jThe relation parameter of the workpiece;

Θ<O_i2,j2,O_i,j>process O_i2,j2Subsequent step O of_i,jProcessing the relation parameters on the same machine; l very large number

Decision variables:

x_i,j,kwhen working procedure O _i,j1 when processed on machine k; otherwise, the value is 0;

y_i1,j1,i2,j2if the<O_i1,j1,O_i2,j2>E psi is 1; otherwise, the value is 0;

z_{i-1,j,k,i,j,k2}if the<O_i-1,j,O_i,j,k,k2>E is phi is 1; otherwise, the value is 0;

u_i2,j2,i,jif the<O_i2,j2,O_i,j>E.g. theta is 1; otherwise, the value is 0;

B. energy consumption of machine processes

Each machine can only process one workpiece at the same time, and each workpiece can only be processed on one processing machine at the same time. The energy consumption of the machining process is calculated by equation (1), and therefore, the total energy consumption of the machining process of the entire system can be obtained by equation (2).

C. Energy consumption during crane transportation

The crane transportation process can be divided into four steps: the method comprises an idle load operation process, an idle load waiting process, a load waiting process and a load operation process. Suppose the crane has completed process O on machine k1_i1,j1In process O_i,jRequiring crane transport, a preceding process O of this process_i-1,jProcessed on machine k. Machine k2 is responsible for machining process O_i,jAnd in process O_i,jPreceded by a process step O_i2,j2。

(1) Energy consumption during idling operation

During transport, the crane should first move from the current machine k1 position to a position on machine k, and if the two machines are different, pass through O_i-1,jThe carrying process of (1). This process is called an empty operation process, in which the crane should first be transported laterally and then longitudinally to the position of the machine k. The time of the empty transportation process is divided into three parts, namely the transverse transportation empty start time, the transverse transportation empty transportation time and the transverse transportation empty stop time, and the process is calculated by the formulas (4) to (6). The total time of no-load operation is calculated from equation (7), and process O is calculated from equation (8)_i,jTotal energy consumption for medium to no load operation. The total energy consumption of all workpieces during no-load operation is calculated from equation (9).

T_no(O_i,j)＝T_hnos(O_i,j)+T_hnob(O_i,j)+T_hnod(O_i,j) (7)

(2) Energy consumption of idle waiting process

If the process O is carried out_i-1,jWithout completion on machine k, the crane should be in an idle waiting process. Wait for preamble procedure O_i-1,jThe time to completion is calculated by equation (10), where the wait time is process O_i-1,jCompletion time of (3) and Process O_i1,j1And empty transit time. Calculating Process O from formula (11)_i,jThe energy consumption of the no-load waiting process of all the workpieces is calculated by the formula (12).

T_ns(O_i,j)＝max(Tc_i-1,j-Ts_i1,j1-T_no(O_i,j),0) (10)

E_ns(O_i,j)＝T_ns(O_i,j)·Ps (11)

(3) Energy consumption of load waiting process

For safety reasons, the crane should not be able to transport the workpiece to the target machine k2 earlier than the machining completion time of the preceding process on machine k 2. Therefore, the crane should be loaded with process O_i-1,jUntil the process of the target machine position is finished. The start time of the horizontal direction load process is calculated by equation (14). Equation (15) calculates the stop time of the horizontal load, and thus from the process O_i-1,jTo O_i,jThe time of the horizontal loading process is calculated by (16)And (4) obtaining. The total time of the load operation is calculated by equation (17). Accordingly, the load start time, the load stop time, and the load transportation time in the vertical direction are obtained by equations (19) to (21), respectively. Equation (22) calculates the total time to lift the workpiece. Equation (23) gives the time length for the calculation of the idle waiting process, which is the procedure O_i2,j2And the difference between the time of completion of the horizontal direction load operation and the time of the vertical direction load operation. Process O_i,jAnd the energy consumption of the load waiting process of all the workpieces are calculated by (24) and (25), respectively.

T_lo(O_i,j)＝T_hlds(O_i,j)+T_hldb(O_i,j)+T_hldd(O_i,j) (17)

T_lf(O_i,j)＝T_vlds(O_i,j)+T_vldb(O_i,j)+T_vldd(O_i,j) (22)

T_ls(O_i,j)＝max(Tc_i2,j2-T_lf(O_i,j)-T_lo(O_i,j),0) (23)

E_ls(O_i,j)＝T_ls(O_i,j)·Ps (24)

(4) Energy consumption during load handling

The formula (26) represents the step O_i,jThe energy consumption of the load handling process of (2), which includes two parts. The first part is the energy consumption of the start time, stop time and transport time of the horizontal direction load-carrying operation process. The second part is the energy consumption of the start time, stop time and lifting time of the vertical direction load-carrying operation process. The energy consumption of the load handling process of all the workpieces is calculated by equation (27).

(5) Total energy consumption of crane during transportation

The total energy consumption of the transportation process can be obtained from equation (28) by considering the energy consumption of the above four transports together.

E_ct＝E_no+E_ns+E_ls+E_ld(28)

Formula of CFJSP

minf＝ω₁·f₁+ω₂·f₂(29)

minf₁＝max(O_i,j),i＝1,2,...,θ_j；j＝1,2,...,J (30)

minf₂＝E_mp+E_ct(31)

Ts_i,j≥Tf_i-1,j(32)

(Ts_i,j-Tf_i2,j2)·u_i2,j2,i,j≥0 (33)

P_i＝K¹(35)

Tf_i-1,j+T_ls(O_i,j)-Ts_i2,j2≥0 (36)

Constraint (29) describes the overall objective of the problem, minimizing the sum of the weighted values of the two objectives, i.e. the maximum completion time in (30) and the total energy consumption in (31). The constraint (32) ensures the processing sequence relation of the continuous working procedures of the same workpiece, namely the starting time of the subsequent working procedure must not be earlier than the ending time of the previous working procedure. Constraints (34) ensure that each process can only be completed on one machine. The constraint (35) calculates the initial position of the crane. Constraints (36) indicate that a process on a machine is only allowed to have other processes processed on the machine after the process is complete. Constraint (37) describes that the first pass of each workpiece does not require crane transport. Constraints (38) indicate that the same workpiece does not require crane transport if both successive processes are performed on the same machine. Constraints (39) - (42) give the value ranges of the four decision variables.

The model method comprises the following steps: and the hybrid IGSA algorithm solves the CFJSP problem. Coding, decoding, a damage heuristic aiming at problems and an establishment heuristic; and building a main frame of the IGSA.

A. Representation and coding of solutions

To solve the CFJSP problem, each solution in the algorithm is represented by a two-dimensional vector. The first vector is named as a machining sequence, and the length of the sequence is pi ═ pi total of all machining processes₁,π₂,...,π_n}. Each element pi in the working procedure_iIndicated by the work piece number, the order of each work piece represents the work piece's corresponding machining process. The second vector is named machine assignment sequence xi ═ δ₁,δ₂,...,δ_nWhere each element in the sequence is δ_iIndicated by the machine number. The length of the machine dispense sequence is also equal to the overview of all processing steps. Fig. 2(a) shows an example of a solution in which there are three

workpieces

1,2 and 3. The number of steps for these three workpieces is 3, 2 and 3, respectively. The machine allocation sequence specifies the processing machine arrangement for the respective positional sequence. For example: workpiece J₁Is arranged in the machine M₂Upper working, work J₃Is arranged in the machine M₁Upper working, J₂Is arranged in the machine M₁And (6) processing.

From the representation of the solution, the present disclosure can find that two tasks of the problem have been accomplished, namely, arranging an appropriate machine for each process and arranging a corresponding machined workpiece for each machine. Fig. 2(b) shows a Gantt chart in the above example.

B. Decoding heuristic

After completing two tasks of the encoding process, two additional tasks need to be completed in the decoding heuristic: how to determine the start time and finish time of each process and how to determine the path of the crane movement. The specific steps of decoding the heuristic are as follows:

in order to determine the start time and the completion time of each process, each process is allocated one by one from left to right. Four key factors should be considered in scheduling each process: idle time of the crane, idle time of the same workpiece preorder procedure, idle time of the processing machine and moving path of the crane.

The moving path of the crane is divided into several categories. The first category includes the processes of no-load operation, no-load waiting, load operation and load waiting. During no-load operation, the crane is moved from the current position to the preceding operating machine position of the same workpiece. And in the idle waiting process, the crane waits for the completion of the preorder process. In the process of waiting for loading, the target machine in the preceding process needs to wait for finishing processing. During the loading operation, the workpiece needs to be moved from the preceding machining position to the subsequent machining position.

At the same time, the present disclosure also contemplates crane lifting action that occurs due to the height of the machine. The present disclosure therefore proposes for the first time a lifting operation of the crane, which moves the crane to a determined height.

An example of the solution of fig. 2(a) is shown in fig. 2(b) with the corresponding Gantt chart. It can be found that in order to complete the process O_3,2The crane first of all shall be M₂Move to M₁To load the preamble procedure O_3,1Then the workpiece is moved from M₁Move to M₃Upper completion step O_3,1. The crane should then be M₃Move to M₂Then from M₂To M₁To complete the process O_1,2The operation of (2). The complete crane travel path is thus as follows: {<2-1>,<1-3>,<3-2>,<2-1>,<1-3>,<3-2>,<2-1>,<1-3>,<3-2>,<2-1>}. In addition to this, different colors are usedIndicating the kind of movement of the crane. For example, green represents empty load movement and yellow represents load movement.

C. Mutation heuristic for problem features

Mutation operations are commonly used in heuristics to achieve local search for a given solution. Considering the CFJSP problem in this disclosure, where there are two vectors in a given solution, we should solve the problem of how to generate adjacent solutions for the process sequence and the machine allocation sequence, and propose five compact random variation operation methods.

(1) Two-point reverse rotation (TPR) operation: the adjacent solution is generated by reversing the selected sector elements. Fig. 3 illustrates a TPR operation process, which includes the following specific steps:

step 1: randomly selecting two positions in the processing sequence, each position being p₁And p₂。

Step 2: assign p in sequence to machine₁And p₂The machine schedule between locations is recorded into the MS.

And 3, step 3: will process p in the sequence₁And p₂The process steps between the positions are reversed.

And 4, step 4: in the machine assignment sequence, p is assigned according to the machine schedule recorded in the MS₁And p₂The corresponding processes are compared again.

(2) Two point exchange (TPS) operation: adjacent solutions are generated by swapping two selected artifacts. The major difference between TPS and TPR is the 3 rd step of the above process, where TPS is p in the exchange processing sequence₁And p₂And (5) the process between the positions.

(3) Two-point switching (TPSM) operation of random machines: except that p in the machine allocation sequence₁And p₂In place, the TPSM operation is similar to the TPS operation, which selects a randomly available machine for each corresponding process.

(4) Two Point Insertion (TPI) operation: the adjacent solution is generated by an operation that inserts one process before another selected process. TPI differs from TPR mainly in step 3 of the above process, where TPI is p to be later in the processing sequence₂Operation of position insertion into p₁Before the position.

(5) Random and two-point interpolation (TPIM) operations: except that p in the machine allocation sequence₁And p₂In some embodiments, the TPIM operation is similar to the TPI operation, which selects a randomly available machine for each corresponding process.

Failure heuristic of IGSA

The destruction step is an operation of deleting several artifacts from the sequence mountain of the solution. The general method of deleting workpieces is to randomly select a certain number of workpieces and then delete them from both sequences. However, the method of random selection does not take into account any information that the workpiece is different. It is clear that the pieces with the largest end time of machining are usually the critical steps and in turn influence the maximum completion time of the solution, so that it should be considered first to delete these pieces from the current solution. The present disclosure presents a novel damage heuristic in Algorithm 1.

Construction heuristic of IGSA

In the classical IG algorithm, the purpose of the build process is to test the best insertion location for each deleted workpiece. In order to solve the CFJSP problem, the main difficulties of inserting heuristics are: (1) how to select the optimal insertion position without any repeated experiments; (2) how to preserve machine allocation after insertion.

(1) To solve the first difficulty, i.e., how to select the optimal insertion position without any repetitive experiments, the following reasoning is proposed.

Introduction 1: given a solution, the addition sequence is pi ═ pi₁,π₂,...,π_i,...,π_nXi, the machine sequence is xi ═ delta₁,δ₂,...,δ_i,...,δ_n}. To be pi_iInserted into all possible positions in pi, pi not being considered by this disclosure_j＝π_iJ in the position of (g), and when pi_iIs |_πiThe total number of repeat locations should beNeglect of, wherein | II_πiI is that all elements are pi_iA collection of (a).

And (3) proving that: FIG. 4 gives an example of an insert operation, where π will be_i2 are inserted into all possible positions. When pi_iAfter insertion into the second position, i.e. j-2, then pi_iBecome J₂The first operation of (1). However, considering the insertion position J-3, where J-2 after insertion becomes J₂And the second operation, the solution after the operation is consistent with the operation result of the second position insertion. Thus, pi at the insertion position_iThe results obtained after the intervening years are the same and one should be ignored.

In addition, let | Π_πiI is that all elements are pi_iAnd | Π_πiAnd | is the length of this set. It is clear that the total number of positions that should be ignored is | Π_πiL. Therefore, the above citations are warranted.

(2) To address the second problem of how to preserve machine assignments after insertion, a machine assignment preservation construct heuristic is proposed. The main idea of this heuristic is to assign a suitable machine for the insert operation and to record other operations of the assigned machine, since the insert of a workpiece may cause a change in the processing sequence of subsequent processes. Algorithm 2 is a structured heuristic.

IGSA heuristic development

To accomplish the development task of the proposed algorithm, the present disclosure incorporates a simple local search heuristic, given by: (1) for the best individuals found at present, mutation heuristic N is carried out on the IV-C part_loWherein N is_loAccording to the document [24 ]]Setting J/4, wherein J is the number of workpieces; and (2) evaluating each newly generated solution and updating the optimal solution if it is more optimal than the historical solutions.

Heuristic method of g.igsa exploration

Applying the development heuristics discussed above, it is easy to get into local optimality. If the solution cannot be improved through a certain number of iterations, more optimization space should be obtained by using a more efficient heuristic development. In order to improve the exploration capability and reduce the time complexity of the algorithm, a simple and efficient exploration heuristic is provided, and the specific steps are as follows.

Step 1: recording the updated times U after the optimal solution is obtained at present_t。

Step 2: each time the optimal individual is updated, U_tSet to 0, otherwise, U_tAnd increased by 1.

And 3, step 3: if U is present_t>U_limitWherein U is_limitIs the maximum limit value of the iterative update times, and then the optimal solution is destroyed and a heuristic is constructed to generate an adjacent solution.

And 4, step 4: if the neighboring solution is better than the current optimal solution, the former is used to update the latter.

IGSA acceptance index

After the heuristic steps are destroyed and built, a newly generated solution is selected to replace the current solution. In the IGSA algorithm, SA-based heuristics are also used in the acceptance criteria, thus enhancing the ability of the algorithm to jump out of local optima. The present disclosure employs a more compact constant temperature acceptance criterion, wherein

T is a parameter that needs to be calibrated.

IGSA framework, algorithm 3 gives the framework part of IGSA.

In order to evaluate the performance of the proposed algorithm, the algorithm disclosed by the disclosure is realized by C + + and is operated on an IntelCore i73.4-GHz computer with a 16GB memory. Algorithms to which this comparison is made include the empire competition algorithm (ICA) proposed by Karimi et al, the integrated algorithm of the genetic algorithm and the firefly population algorithm (GA-GSO) proposed by Liu et al, the GA proposed by Sangsawang et al, the SA proposed by Batur et al, the IG algorithm proposed by Ruiz et al, and the ABC algorithm proposed by Li et al. All comparison algorithms go through a re-encoding process to fit the problem to be considered, wherein the parameters are set according to the corresponding documents. To demonstrate the efficiency and effectiveness of the disclosed algorithms, all algorithms were run independently 30 times, resulting in an optimal solution for algorithm comparison. The performance index of the algorithm is measured by Relative Percent Increase (RPI), and the calculation formula is as follows:

wherein f is_bIs the optimal fitness value among all algorithms participating in the comparison, f_cIs the minimum fitness value for a given algorithm.

A. Experimental example

To test the performance of the disclosed algorithm, three types of examples were chosen. The first example has four products, where the number of workpieces is n ═ {7,9,10,10} in this order, and the number of machines for the four products is 6. The present disclosure generates a second class of algorithms, including 30 algorithms for different workpieces and machines, where the number of workpieces is J ═ {20,30,40,50,80,100} and the number of machines is K ═ 6,7,8,9,10 }. In addition, the number of operational processes per workpiece is distributed uniformly over the interval [ K/2, K ], and a third category of calculations considers the lifting operation of the crane.

B. Experimental parameters

The stop criteria for each example varied depending on the size of the example, and was set to 0.6 x J seconds, where J is the total number of workpieces. It should be noted that the time constraint allows more computation time as the number of workpieces increases. Two important parameters include the destruction length (d) and the acceptance criterion temperature parameter (T). The present disclosure employs a design of experiments (DOE) to adjust the parameters of the algorithm. Further, the present disclosure performs full parameter design using two parameters, and the levels of the parameters are as follows:

t, level 6: 0.0,0.1,0.2,0.3,0.4, 0.5; d, grade 5: 2,3,4,5,6

A total of 30 different parameter combinations were calibrated, each combination being a pair of parameters consisting of a certain value of two factors. For parameter calibration, a series of examples were randomly generated, where the number of workpieces is {20,30,40,50,80}, the number of machines is {5,8,10}, and the processing time is evenly distributed in intervals [5,30 ]. In addition, the total number of processing procedures of each workpiece is uniformly distributed according to the interval [ K/2, K ]. Each set of calibration parameter combinations was run independently 30 times.

Analysis of the experiments reference the variable multi-factor analysis of variance (ANOVA) technique. Figure 5 lists the results of the analysis. The results show that both variables are significant factors (p-value < 0.05). The parameter d, F value is 90.11, which has a significant impact on the algorithm. The parameter T, F value is 20.78, which has a smaller effect than d. At the same time, the interplay between the two parameters was insignificant, with p values greater than 0.05.

Fig. 6(a) and (b) are fitness values at 95% confidence intervals for the parameters T and d, respectively, after screening. According to fig. 6(a), a better fitness value can be obtained when T is 0.3 than other values. According to fig. 6(b), when d is 2, a better fitness value can be obtained. According to the test results, the parameters T and d are set to 0.3 and 2, respectively. The present disclosure determines a maximum iteration limit number U_limit＝200。

C. Comparison of first class of examples

The first type of example production process is from a large cement plant company, Tianjin, China. The company mainly produces large complex cement equipment, so that the specific data good parameters of the machine and the workpiece should be found by simultaneously considering the weight of the equipment and the energy consumption factor of a crane. The first column of the table is the example number and the next two columns list the optimal results for the two comparison algorithms. Then, the next two columns give the results of the IGSA algorithm calculations proposed by the present disclosure, and the next two columns give the results of the GA-GSO algorithm. The last four columns give the deviation values or RPI values of the two targets of the two comparison algorithms, respectively.

Table I shows the results of the IGSA algorithm and the calculation of GA-GSO, which consists of two main components, the GA and the GSO process. From table I it can be concluded: (1) to solve the problem of four examples of different scales, all optimization results are calculated by using the IGSA algorithm, for example, for the first example, IGSA obtains the optimal solution of two targets, f₁63.03 and f₂434.56, with significant advantages over the two results 75.49 and 482.10 calculated for GA-GSO; (2) from the last four columns, it can be found that the algorithm provided by the present disclosure has better RPI values in all four examples, which is obviously better than the GA-GSO algorithm, and particularly for the first target, the algorithm provided by the present disclosure obtains better maximum completion time.

D. Exploring heuristic efficiency

To evaluate the effect of the heuristic approach, the present disclosure proposes two different IGSA algorithms, i.e., IGSA-NE algorithm and IGSA algorithm without heuristic approach. It should be noted that in IGSA-NE, the IG-based destruction and construction steps are run once per iteration, whereas for IGSA algorithms, the destruction and construction steps are run in the solution referred to above. The other part settings of the above two algorithms are the same.

To evaluate whether the difference between the two methods is significant, the present disclosure employs a multi-factor analysis of variance (ANOVA), in which the method of comparison is considered a factor. Fig. 7(a) shows the mean and 95% Least Significant Difference (LSD) confidence intervals for the fitness values of the two methods. The p value is close to 0, and therefore, the two methods of comparison are considered to have significant differences. It can be obtained that the exploration strategy improves the performance of the algorithms proposed by the present disclosure.

E. Efficiency of building heuristics

In order to evaluate the effect of constructing the heuristic, the present disclosure writes two different IGSA algorithms, i.e., IGSA-NR without constructing the heuristic, wherein the position replication link and the IGSA algorithm of lemma 1 are not considered. FIG. 7(b) shows the mean and 95% LSD confidence intervals for the fitness values of the two methods. It can be obtained that the construction strategy improves the performance of the algorithm proposed by the present disclosure.

F. Comparison of algorithm efficiencies

To further demonstrate the performance of the disclosed algorithms, as compared to other highly efficient algorithms, the present disclosure selected algorithms including ABC, GA, ICA, IG, GA-GSO and SA, and the results of all comparison algorithms run independently 30 times are shown in tables II and III, where the RPI values of all algorithms are given in turn.

Table II gives the results of the calculation for the seven algorithms of the second class of examples. The second column gives the optimal fitness value for each example, given in turn by the RPI values obtained by seven algorithms including GA, SA, ABC, GA-GSO, IG, ICA and IGSA. Table III gives the results of the calculations to solve the third class of examples, i.e. the CFJSP problem considering crane lifting operations. The running CPU of all the examples of each algorithm is 30 s.

From the two tables above it can be observed that: (1) considering that the CPU is 30s, to solve the second algorithm, the IGSA obtains 29 optimal values in the given 30 algorithms compared to the other six algorithms, for example, the second best algorithm ICA can only obtain one optimal value in the second algorithm; (2) regarding the third kind of algorithm, namely the algorithm considering the lifting operation of the crane, the algorithm of the present disclosure also obtains 29 optimal values, which is obviously superior to other comparison algorithms; (3) from the RPI values given by the two tables, the IGSA has stronger robustness; and (4) can conclude that the IGSA algorithm has significantly superior performance compared to the other six algorithms.

Results of four examples of calculation obtained by GA-GSO algorithm in Table I

To further prove that the present disclosure proposes the performance of the algorithm with respect to the iteration duration, the present disclosure also sets the CPU to 50s and observes the operation results after independently operating 30 times for each of the examples. Table IV gives the running results of the third category of the examples. It can be found from the table that: (1) for the problem of smaller scale, from the calculation example 20-6 to the calculation example 50-10, compared with other six algorithms, the IGSA algorithm shows obvious superiority; (2) for larger scale problems, from examples 80-6 to 100-10, IGSA is less favorable than ICA algorithm; (3) in the column of the RPI mean value of the last row, the IGSA can be found to obtain the minimum value of 1.18, and the method has obvious superiority compared with the second-best ICA algorithm; and (4) to evaluate whether the difference between the two theories is significant, fig. 7(c) shows that the seven algorithms solve the mean and 95% LSD intervals of the third class of algorithms when CPU is 50 s. As can be seen from the figure, the IGSA algorithm of the present disclosure performs best compared to the comparative algorithm.

Table II calculation results of the second type of arithmetic example (CPU ═ 30S)

Table III calculation results of the third type of arithmetic example (CPU ═ 30S)

Table IV calculation results of the third type of arithmetic example (CPU 50S)

The present disclosure addresses the more typical flexible job shop scheduling problem with crane transport in industrial production optimization. The goal is to minimize the maximum completion time and energy consumption. A mathematical model considering the transportation scheduling problem of the crane is established for the first time; an effective algorithm combining an iterative greedy algorithm and a simulated annealing algorithm is provided; heuristics for problems are presented to balance the exploration and development capabilities of the model.

The utility model provides a take flexible workshop dispatch system of hoist includes:

The present disclosure provides a computer readable storage medium having stored therein a plurality of instructions adapted to be loaded by a processor of a terminal device and to perform the steps of a method for flexible shop scheduling with crane.

The present disclosure provides a terminal device comprising a processor and a computer-readable storage medium, the processor configured to implement instructions; the computer readable storage medium is for storing a plurality of instructions adapted to be loaded by a processor and for performing the steps of a method for flexible shop scheduling with crane.

The above is merely a preferred embodiment of the present disclosure and is not intended to limit the present disclosure, which may be variously modified and varied by those skilled in the art. Any modification, equivalent replacement, improvement and the like made within the spirit and principle of the present disclosure should be included in the protection scope of the present disclosure.

Although the present disclosure has been described with reference to specific embodiments, it should be understood that the scope of the present disclosure is not limited thereto, and those skilled in the art will appreciate that various modifications and changes can be made without departing from the spirit and scope of the present disclosure.

Claims

1. A flexible workshop scheduling method with a crane is characterized by comprising the following steps:

2. The flexible workshop scheduling method with crane according to claim 1,

the energy consumption of the machining process is such that,

the total energy consumption of the machining process is as follows:

wherein K is the number of machines; j is the number of workpieces; i is a process number; j is the workpiece number; o is_i,jI is 1,2, …, theta is the ith machining process of the workpiece j_j；θ_jIs a set of machining processes for workpiece J, J being 1,2, …, J; ep_kIs the operating power of machine k; t is_i,j,kIs a process O_i,jMachining time at machine k; decision variable x_i,j,kIs a process O_i,j1 when processed on machine k; otherwise it is 0.

3. The flexible workshop scheduling method with crane according to claim 1,

the energy consumption of the crane in the transportation process comprises the sum of the energy consumption of an idle load operation process, an idle load waiting process, a load waiting process and a load operation process;

4. The flexible workshop scheduling method with crane according to claim 3,

in the energy consumption of the load waiting process, respectively calculating the starting time of horizontal moving load transportation of a previous process of a certain workpiece, the stopping time of the horizontal moving load transportation of a current process, the time of the uniform-speed transportation process of the horizontal moving load, and the starting time of the load transportation, the stopping time of the load transportation and the time of the transportation process in the vertical direction; obtaining the time in the load waiting process according to the difference between the completion time of the process and the time of the load operation in the horizontal direction and the time of the load operation in the vertical direction, and calculating the energy consumption of the load waiting process of all the workpieces;

5. The flexible workshop scheduling method with crane according to claim 1,

in the iterative greedy and simulated annealing mixed algorithm, two-dimensional vectors of a processing sequence and a machine distribution sequence are defined, and tasks of arranging proper machine processing for each procedure and arranging corresponding processing workpieces for each machine are completed through coding;

6. The flexible workshop scheduling method with the crane according to claim 1, wherein the hybrid iterative greedy and simulated annealing algorithm pair is used for constructing a heuristic construction process:

inputting the sequence S after deleting the workpiece_dAnd the sequence S remaining after deletion_rRecording the distribution machine of all the operations of the initial solution;

when the sequence after deleting the workpieces is larger than 0, selecting the first workpiece in the sequence as an insertion workpiece and deleting the first workpiece from the sequence;

selecting all operations equal to inserting the workpiece to form a processing sequence;

testing all positions of the inserted workpiece in the sequence left after deletion;

for each inserted position, finding an optimal machine for the inserted workpiece by utilizing minimum local optimization, and adjusting a machine distribution sequence for subsequent operation;

and finding the optimal insertion position for inserting the workpiece, and updating the machining sequence and the machine distribution sequence after inserting the workpiece.

7. The flexible workshop scheduling method with crane according to claim 1,

the iterative greedy and simulated annealing mixed algorithm is used for exploring a heuristic construction process:

recording the updating times after the optimal solution is obtained currently;

judging whether the optimal individual is updated, if so, setting the updating frequency to be 0, otherwise, increasing the updating frequency by 1;

presetting a maximum limit value of iterative update times, comparing the update times with the maximum limit value of the iterative update times, and if the update times are larger than the maximum limit value of the iterative update times, destroying the optimal solution and constructing a heuristic method to generate an adjacent solution;

and judging whether the adjacent solution is superior to the current optimal solution, and if so, updating the current optimal solution by using the adjacent solution.

8. A flexible workshop scheduling system with a crane is characterized by comprising:

9. A computer readable storage medium having stored therein a plurality of instructions adapted to be loaded by a processor of a terminal device and to carry out the steps of a method for flexible plant scheduling with crane according to any one of claims 1-7.

10. A terminal device comprising a processor and a computer readable storage medium, the processor being configured to implement instructions; a computer readable storage medium for storing a plurality of instructions adapted to be loaded by a processor and for performing the steps of a method for flexible plant scheduling with crane according to any of claims 1-7.