CN113537841B - Method for optimizing dispatching of yard crane by considering customer satisfaction - Google Patents

Method for optimizing dispatching of yard crane by considering customer satisfaction Download PDF

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CN113537841B
CN113537841B CN202111053151.XA CN202111053151A CN113537841B CN 113537841 B CN113537841 B CN 113537841B CN 202111053151 A CN202111053151 A CN 202111053151A CN 113537841 B CN113537841 B CN 113537841B
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杨文强
李勇峰
张素君
杨之乐
陈永刚
徐君鹏
杜留锋
聂福全
彭占磊
李然
苏金哲
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Abstract

The invention relates to a method for optimizing dispatching of a yard crane, which takes customer satisfaction into consideration. The method introduces the customer satisfaction index into the dispatching of the yard crane, establishes a yard crane dispatching optimization mathematical model fusing the customer satisfaction factor, and solves the model by adopting an Improved Dragonfly Algorithm (IDA). Aiming at the defects of low convergence efficiency and poor solving quality of the standard dragonfly algorithm, a multi-match strategy is introduced to increase the genetic probability of excellent genes, so that the quality of offspring individuals is improved; the neighborhood radius is updated based on the Gaussian operator, the local development and the global exploration capability of the algorithm are effectively balanced, and the opportunity of finding the optimal solution or the suboptimal solution is improved. The invention further improves the economic benefit of enterprises and the intelligent level of the yard crane, and has good popularization value and market prospect.

Description

Method for optimizing dispatching of yard crane by considering customer satisfaction
Technical Field
The invention belongs to the field of intelligent storage yards, and further relates to a method for optimizing the dispatching of a storage yard crane by considering customer satisfaction.
Background
The concept of 'customer to the top' is gradually deepened into the enterprise culture, and the customer is satisfied with the nature and becomes the target of the enterprise pursuit. In yard storage, the customer orders should be sorted out of the warehouse with the highest efficiency so as to meet the customer satisfaction, however, in most of the actual yard customer order sorting operations, the customer grades are ignored, that is, the sorting order of the yard orders is not determined according to the customer grades, so that the customer satisfaction is reduced, and further, the customer is lost to a certain extent. Therefore, the method for optimizing the dispatching of the storage yard crane considering the customer satisfaction is not only beneficial to improving the work efficiency, improving the customer experience, maintaining and attracting the customer resources, but also has a better demonstration effect on the improvement of the operation strategy of the enterprise.
So far, as for the scheduling optimization problem of the crane, the learner pays more attention to the picking path optimization, and factors such as customer grade and the like are less or not considered, so that the practical application scene is difficult to meet. Such as: (crop-operated cranes: Integrating location assignment and crop scheduling, Computers & Industrial Engineering,2019) to optimize the Crane scheduling from both the cargo space allocation and cargo picking order and solve with a hill climbing algorithm; li et al (intelligent crane cargo handling order optimization and automatic generation technology, proceedings of mechanical engineering, 2020) select a candidate set of cargo by a heuristic rule of shortest handling distance to optimize the cargo handling order.
The Dragonfly Algorithm (DA) is a novel bionic group intelligent optimization algorithm proposed by the australian scholari Seyedali mirjali in 2015 based on social behaviors of dragonflies, and global and local search is performed by simulating 5 behaviors of dragonfly group collision avoidance, companioning, aggregation, foraging and enemy avoidance. The method has the advantages of few parameters, easiness in implementation and the like, but still has the defects of low convergence efficiency and poor solving quality, and therefore, the method adopts the improved dragonfly algorithm to solve the scheduling optimization problem of the yard crane considering the customer satisfaction. Disclosure of Invention
In view of the above analysis, in order to overcome the disadvantages in the background art, the present invention aims to disclose a yard crane scheduling optimization method considering customer satisfaction, so as to improve the operation efficiency and economic benefits.
In order to achieve the purpose, the invention adopts the following technical scheme:
a method for optimizing the dispatching of a storage yard crane considering customer satisfaction comprises the following steps:
(1) under the condition of considering the customer satisfaction, analyzing the constraints existing in the yard and the target to be optimized, and establishing a yard crane scheduling optimization mathematical model considering the customer satisfaction with the constraints;
(2) initializing parameters: the method comprises the following steps of initializing a dragonfly population individual, wherein the dragonfly population scale N, the maximum evolution algebra G _ max, an evolution algebra counter t, a dragonfly number counter N and a step length delta X are used for initializing the dragonfly population individual;
(3) making t equal to t +1, and carrying out global search;
(3-1) decoding the individual dragonflies into a feasible yard goods picking order;
(3-2) calculating the individual fitness of each mosquito hawk based on the mathematical model established in the step (1);
(3-3) updating the food and the natural enemy position;
(3-4) performing a local search by setting n to n + 1;
(3-4-1) updating 5 behavior factors S, A, C, F and E of collision avoidance, accompaniment, aggregation, foraging and enemy avoidance and corresponding weights and inertial weights S, a, C, F, E and omega;
(3-4-2) updating the neighborhood radius r by adopting a Gaussian operator;
(3-4-3) if an individual dragonfly exists in the current dragonfly neighborhood radius, updating the step length delta X and executing a multi-marriage strategy; otherwise, executing a Levy flight strategy;
(3-4-4) updating the food and the natural enemy position;
(3-4-5) if N is less than N, returning to the step (3-4); otherwise, turning to the step (3-5);
(3-5) if t < G _ max, returning to the step (3); otherwise, outputting the optimal solution.
Preferably, in the step (1), the picking customer satisfaction aiming at completing all customer orders is the highest, the constraint conditions are that the number of hooks of the yard crane is limited and the picking order of the goods on the goods space is limited, and meanwhile, the customer satisfaction factor is associated with the customer grade, namely the customer satisfaction factor is in a direct relation with the customer grade, and the mathematical model of the customer satisfaction factor is defined as follows:
min∑r∈R∑i∈o(ti·Bir·Di·Tir) (1)
s.t.
Figure GDA0003368887990000021
Figure GDA0003368887990000022
∑r∈R∑i∈oBir＝M (4)
Figure GDA0003368887990000023
Figure GDA0003368887990000024
Figure GDA0003368887990000025
wherein, the formula (1) is an objective function, namely a disappointment level; the expressions (2) to (6) are various constraints, and specifically: the formula (2) shows that the ith cargo can be picked only by one crane; the formula (3) limits that the number of cargos hoisted by the crane cannot exceed the number of hooks per se; the formula (4) requires the crane to complete all picking tasks; the formula (5) limits the goods picked by the crane to be positioned at the topmost layer of the goods position; equations (6) and (7) are binary value domain constraints for the decision variables.
O represents a set of customer orders to be picked; r represents a path set of all customer order picking tasks completed by the crane; r represents a sub-path; t is tiRepresents the time taken for the crane to pick the ith cargo, and is represented by equation (8); b isirIndicates whether the item i belongs to sub-path R, where i belongs to O, R belongs to R, if the ith item is completed in the R picking, then B ir1, otherwise Bir＝0；TirRepresenting whether goods i in the sub-path R are positioned at the top layer of the goods position, wherein i belongs to O, and R belongs to R; diAnd the customer satisfaction factor corresponding to the customer order level to which the goods i belong is represented.
Figure GDA0003368887990000031
In the formula vx、vyAnd vzRespectively representing the average speed of the crane trolley, the average speed of the crane trolley and the average speed of lifting of the lifting hook, pxi、pyiAnd pziIs the spatial coordinate of the ith cargo in the yard, and H is the maximum height of the yard.
Preferably, the step (3-1) decodes the individual dragonfly into a feasible goods picking order in the yard, the invention adopts real number coding to the individual dragonfly, and the individual dragonfly coded by the real number has to be decoded for calculating the fitness of the individual dragonfly and providing a feasible scheduling solution considering that the numbers of goods to be picked are all discrete values. The specific decoding process is described as follows:
the 3 customer orders are noted A, B and C, where: order A contains 4 goods (goods numbers: 1, 2, 3 and 4) whose position coordinates in the yard are P1(3, 2, 9), P2(1, 15, 4), P3(3, 3, 6), P4(2, 1, 1), respectively; order B contains 2 goods (goods numbers: 5 and 6) whose position coordinates in the yard are P5(2, 1, 2), P6(2, 9, 9), respectively; the order C contains 4 goods (goods numbers: 7, 8, 9, and 10) whose position coordinates in the yard are P7(3, 3, 5), P8(3, 12, 6), P9(2, 9, 10), and P10(1, 15, 3), respectively. Here, the 3 coordinates in each position correspond to the row number, column number and layer height of the cargo at the yard, respectively, from front to back. Fig. 2 shows a particular individual dragonfly encoded with real numbers and decoded in ascending order. Considering that the goods on the same cargo space of the yard must be sorted from high to low, the decoding in ascending order of fig. 2 may result in an infeasible solution, and a constraint process must be performed to make it a feasible solution. The specific constraint processing process comprises the following steps: and sorting the goods on the same goods position from high to low, and correcting the infeasible solution into a feasible solution after constraint processing.
Preferably, in the step (3-3), the food and the natural enemy position respectively correspond to an optimal solution and a worst solution of the current generation.
Preferably, the step (3-4-1) updates the 5 behavior factors S, a, C, F, E and their corresponding weights and inertial weights S, a, C, F, E, ω for collision avoidance, accompaniment, aggregation, foraging and deterrence. The specific updating method is as follows:
1a) collision avoidance:
Figure GDA0003368887990000041
1b) and (3) accompanying behavior:
Figure GDA0003368887990000042
1c) aggregation behavior:
Figure GDA0003368887990000043
1d) foraging behavior:
Fi＝X+-Xi (12)
1e) and (4) avoiding behaviors:
Ei＝X-+Xi (13)
wherein, XiIndicating the current individual position of dragonfly, Xj、VjRespectively representing the position and velocity, X, of the j-th adjacent individual+、X-Respectively representing the positions of the food source and the natural enemies, and N representing the number of adjacent mosquito hawk individuals.
2a) Collision avoidance weight:
Figure GDA0003368887990000044
2b) association weight:
Figure GDA0003368887990000045
2c) aggregation weight:
Figure GDA0003368887990000046
2d) foraging weight:
f＝2·rand (17)
2e) avoidance of weight:
Figure GDA0003368887990000047
2f) inertial weight:
Figure GDA0003368887990000051
wherein rand is a random number between [0, 1], t is the current evolution algebra, and G _ max is the maximum evolution algebra.
Preferably, the step (3-4-2) updates the neighborhood radius r by using a gaussian operator. In the standard dragonfly algorithm, the neighborhood radius r is updated linearly, and considering that the group intelligent algorithm has certain randomness and nonlinear characteristics in the evolution process, the neighborhood radius r updated in a linear mode can cause the algorithm to miss the optimal solution or suboptimal solution in the evolution process, so that the solving quality and convergence speed of the algorithm are reduced. Therefore, the method adopts the Gaussian operator to disturb the neighborhood radius r in the standard dragonfly algorithm, so that the neighborhood radius r generates certain oscillation while being updated linearly, the chance of finding the optimal solution or suboptimal solution in the neighborhood is increased, and the solving efficiency of the algorithm is accelerated. The improved neighborhood radius r update formula is:
Figure GDA0003368887990000052
UB and LB are the upper and lower limits of each dimension variable respectively, N (mu, sigma) is a random number obeying Gaussian distribution [0, 1], mu and sigma are 0.5 and 0.2 respectively, t is the current evolution algebra, and G _ max is the maximum evolution algebra.
Preferably, the step (3-4-3) specifically includes:
a) update step size Δ X:
ΔXt+1＝(sSi+aAi+cCi+fFi+eEi)+ωΔXt (21)
wherein t is the current evolution algebra.
b) Multi-marriage strategy:
marriage is an effective way for the next generation with excellent biological reproduction, however, in the standard dragonfly algorithm, the marriage behavior of the dragonfly is not considered, which has a certain influence on the evolution effect of the algorithm. Therefore, the invention introduces the marriage behavior into the standard dragonfly algorithm, and adopts multiple marriage operators to guide the marriage process to breed excellent individuals in order to increase the chance of excellent genetic inheritance. The principle can be described as follows: and (4) a plurality of mating operators all participate in mating, the optimal filial generation individuals are selected through comparison, if the optimal filial generation individuals are better than the worst individuals of the whole population, the optimal filial generation individuals are replaced, and if not, the optimal filial generation individuals are kept unchanged. It follows that the polygenic operator will increase the probability of breeding good individuals. Current individual dragonflyIs recorded as: xm＝[X1m，x2m，…，xqm]Q is the dimension of the problem to be solved, and a dragonfly is randomly selected as a mating individual X in the neighborhood radius rg＝[x1g，x2g，…，xqg]Then, the multi-match strategy is described as follows:
first neighborhood marriage operator
Figure GDA0003368887990000053
Second operator marriage operator
Figure GDA0003368887990000061
③ average marriage operator
Figure GDA0003368887990000062
Fourthly, extreme value marriage operator
Figure GDA0003368887990000063
Fifth edge marriage operator
Figure GDA0003368887990000064
Wherein rand is a random number between [0, 1], i is an arbitrary integer between [1, q ], and UB and LB are respectively the upper limit and the lower limit of each dimension variable.
c) Levy flight strategy:
Xt+1＝Xt+Levy(q)·Xt (27)
Figure GDA0003368887990000065
Figure GDA0003368887990000066
Figure GDA0003368887990000067
where randn is a random number that follows a normal distribution, and β is a control factor constant.
Due to the adoption of the technical scheme, the invention has the following beneficial effects:
(1) the customer satisfaction is introduced into the dispatching model of the yard crane, so that the customer orders with high grades can be better guaranteed to be sorted preferentially, and the customer service accuracy is improved.
(2) The Gaussian operator and the multi-marriage strategy are introduced into the standard dragonfly algorithm, the depth and the breadth of searching in the algorithm evolution process are considered, and the solving precision and the convergence speed of the algorithm are improved.
The invention can effectively ensure that important customer orders are selected in time, improves the satisfaction degree of customers, further consolidates the customer relationship, avoids customer loss, and has better demonstration driving effect on the implementation of the 'people-oriented and customer-up' operating concept of related logistics enterprises such as yards and the like.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic diagram of the present invention for decoding in ascending order and performing constraint processing;
FIG. 3 is a schematic illustration of the yard layout of the present invention;
FIG. 4 is a comparison of the solving effects of the algorithms of the present invention for the preferred embodiment;
fig. 5 is a comparison of the results of 30 runs of each algorithm for the preferred embodiment of the present invention.
Detailed Description
The method of the invention will be further described with reference to the accompanying drawings and preferred embodiments. It is to be understood that the described embodiments are merely some embodiments of the invention and not all embodiments. All other embodiments that can be obtained by a person skilled in the art based on the embodiments of the present invention without any creative effort belong to the protection scope of the present invention.
As shown in fig. 1, the invention discloses a method for optimizing dispatching of a yard crane considering customer satisfaction, which specifically comprises the following steps:
(1) under the condition of considering the customer satisfaction, the constraint existing in the storage yard and the target to be optimized are analyzed, and a storage yard crane scheduling optimization mathematical model with the constraint considering the customer satisfaction is established.
The invention aims to be optimized to finish the picking of all customer orders with the highest customer satisfaction, the constraint conditions are that the quantity of hooks of a yard crane is limited and the picking order of goods on the same goods position is limited, and simultaneously, a customer satisfaction factor is associated with the customer grade, namely the customer satisfaction factor is in a direct proportion relation with the customer grade, and the mathematical model of the invention is defined as follows:
f(t)＝min∑r∈R∑i∈O(ti·Bir·Di·Tir) (1)
s.t.
Figure GDA0003368887990000071
Figure GDA0003368887990000072
∑r∈R∑i∈OBir＝M (4)
Figure GDA0003368887990000073
Figure GDA0003368887990000074
Figure GDA0003368887990000075
wherein, the formula (1) is an objective function, namely a disappointment level; the expressions (2) to (6) are various constraints, and specifically: the formula (2) shows that the ith cargo can be picked only by one crane; the formula (3) limits that the number of cargos hoisted by the crane cannot exceed the number of hooks per se; the formula (4) requires the crane to complete all picking tasks; the formula (5) limits the goods picked by the crane to be positioned at the topmost layer of the goods position; equations (6) and (7) are binary value domain constraints for the decision variables.
O represents a set of customer orders to be picked; r represents a path set of all customer order picking tasks completed by the crane; r represents a sub-path; t is tiRepresents the time taken for the crane to pick the ith cargo, and is represented by equation (8); b isirIndicates whether the item i belongs to sub-path R, where i belongs to O, R belongs to R, if the ith item is completed in the R picking, then B ir1, otherwise Bir＝0；TirRepresenting whether goods i in the sub-path R are positioned at the top layer of the goods position, wherein i belongs to O, and R belongs to R; diAnd the customer satisfaction factor corresponding to the customer order level to which the goods i belong is represented.
Figure GDA0003368887990000081
In the formula vx、vyAnd vzRespectively representing the average speed of the crane trolley, the average speed of the crane trolley and the average speed of lifting of the lifting hook, pxi、pyiAnd pziIs the spatial coordinate of the ith cargo in the yard, and H is the maximum height of the yard.
(2) Initializing parameters: the method comprises the following steps of initializing a dragonfly population individual, wherein the dragonfly population scale N, the maximum evolution algebra G _ max, an evolution algebra counter t, a dragonfly number counter N and a step length delta X are used for initializing the dragonfly population individual;
(3) making t equal to t +1, and carrying out global search;
the method specifically comprises the following steps:
(3-1) decoding the individual dragonflies into a feasible yard goods picking order;
the method adopts real number coding for the individual dragonfly, and the individual dragonfly with the real number coding must be decoded for calculating the fitness of the individual dragonfly and providing a feasible scheduling solution in consideration of the fact that the serial numbers of the goods to be picked are discrete values. The specific decoding process is described as follows:
there are 3 customer orders noted A, B and C, where: order A contains 4 goods (goods numbers: 1, 2, 3 and 4) whose position coordinates in the yard are P1(3, 2, 9), P2(1, 15, 4), P3(3, 3, 6), P4(2, 1, 1), respectively; order B contains 2 goods (goods numbers: 5 and 6) whose position coordinates in the yard are P5(2, 1, 2), P6(2, 9, 9), respectively; the order C contains 4 goods (goods numbers: 7, 8, 9, and 10) whose position coordinates in the yard are P7(3, 3, 5), P8(3, 12, 6), P9(2, 9, 10), and P10(1, 15, 3), respectively. Here, the 3 coordinates in each position correspond to the row number, column number and layer height of the cargo at the yard, respectively, from front to back. Fig. 2 shows a particular individual dragonfly encoded with real numbers and decoded in ascending order. Considering that the goods on the same cargo space of the yard must be sorted from high to low, the decoding in ascending order of fig. 2 may result in an infeasible solution, and a constraint process must be performed to make it a feasible solution. The specific constraint processing process comprises the following steps: and sorting the goods on the same goods position from high to low, and correcting the infeasible solution into a feasible solution after constraint processing.
(3-3) updating the food and the natural enemy position;
this step is prior art and will not be described further.
(3-4) performing a local search by setting n to n + 1;
(3-4-1) updating 5 behavior factors S, A, C, F and E of collision avoidance, accompaniment, aggregation, foraging and enemy avoidance and corresponding weights and inertial weights S, a, C, F, E and omega. The specific updating mode and the corresponding weight are specifically expressed as follows:
1a) collision avoidance:
Figure GDA0003368887990000091
1b) and (3) accompanying behavior:
Figure GDA0003368887990000092
1c) aggregation behavior:
Figure GDA0003368887990000093
1d) foraging behavior:
Fi＝X+-Xi (12)
1e) and (4) avoiding behaviors:
Ei＝X-+Xi (13)
wherein, XiIndicating the current individual position of dragonfly, Xj、VjRespectively representing the position and velocity, X, of the j-th adjacent individual+、X-Respectively representing the positions of the food source and the natural enemies, and N representing the number of adjacent mosquito hawk individuals.
2a) Collision avoidance weight:
Figure GDA0003368887990000094
2b) association weight:
Figure GDA0003368887990000095
2c) aggregation weight:
Figure GDA0003368887990000096
2d) foraging weight:
f＝2·rand (17)
2e) avoidance of weight:
Figure GDA0003368887990000097
2f) inertial weight:
Figure GDA0003368887990000098
wherein rand is a random number between [0, 1], t is the current evolution algebra, and G _ max is the maximum evolution algebra.
(3-4-2) updating the neighborhood radius r by adopting a Gaussian operator, wherein the specific implementation process is as follows:
in the standard dragonfly algorithm, the neighborhood radius r is updated linearly, and considering that the group intelligent algorithm has certain randomness and nonlinear characteristics in the evolution process, the neighborhood radius r updated in a linear mode can cause the algorithm to miss the optimal solution or suboptimal solution in the evolution process, so that the solving quality and convergence speed of the algorithm are reduced. Therefore, the method adopts the Gaussian operator to disturb the neighborhood radius r in the standard dragonfly algorithm, so that the neighborhood radius r generates certain oscillation while being updated linearly, the chance of finding the optimal solution or suboptimal solution in the neighborhood is increased, and the solving efficiency of the algorithm is accelerated. The improved neighborhood radius r update formula is:
Figure GDA0003368887990000101
UB and LB are the upper and lower limits of each dimension variable respectively, N (mu, sigma) is a random number obeying Gaussian distribution [0, 1], mu and sigma are 0.5 and 0.2 respectively, t is the current evolution algebra, and G _ max is the maximum evolution algebra.
(3-4-3) if an individual dragonfly exists in the current dragonfly neighborhood radius, updating the step length delta X and executing a multi-marriage strategy; otherwise, executing the Levy flight strategy. The step updating and the Levy flight strategy are the prior art and are not described again, and the multi-marriage strategy is described as follows:
currently, the individual dragonflies is: xm＝[x1m，x2m，…，xqm]Q is the dimension of the problem to be solved, and a dragonfly is randomly selected as a mating individual X in the neighborhood radius rg＝[x1g，x2g，…，xqg]Then, the multi-match strategy is described as follows:
first neighborhood marriage operator
Figure GDA0003368887990000102
Second operator marriage operator
Figure GDA0003368887990000103
③ average marriage operator
Figure GDA0003368887990000104
Fourthly, extreme value marriage operator
Figure GDA0003368887990000105
Fifth edge marriage operator
Figure GDA0003368887990000106
Wherein rand is a random number between [0, 1], i is an arbitrary integer between [1, q ], and UB and LB are respectively the upper limit and the lower limit of each dimension variable.
(3-4-4) updating the food and the natural enemy position;
this step is prior art and will not be described further.
(3-4-5) if N is less than N, returning to the step (3-4); otherwise, turning to the step (3-5);
(3-5) if t < G _ max, returning to the step (3); otherwise, outputting the optimal solution.
The embodiment relates to a scheduling optimization problem of a storage yard crane considering customer satisfaction degree in storage of a certain storage yard, and the optimal solution or the suboptimal solution meeting constraint conditions is solved by using the method.
(1) Overview of the problem
According to the above technical solution, a certain yard storage is taken as an application background for illustration, and fig. 3 is a layout diagram of the yard storage. 30 customer orders are randomly generated for testing, specific customer order information is shown in table 1, and satisfaction factors related to 6 customer grades are illustrated in table 2. Average speed v of trolley of yard cranexAverage speed v of cartyAnd the average lifting speed v of the hookzRespectively as follows: 20m/min, 30m/min and 12m/min, the maximum height H30m of the storage yard takes the buffer area of the storage yard as the coordinate origin P0(0, 0, 0), the storage yard has Ka, Kb, Kc, Kd, Ke and Kf 6 kinds of articles, only the same kind of articles can be stacked, and the same kind of articles individually occupy one row of goods positions, and the Ka, Kb, Kc, Kd, Ke and Kf 6 kinds of articles sequentially occupy one row of goods positions from the buffer area. In the same row of cargo space, the spacing distance between two adjacent rows of cargo space and the height of each article are shown in table 3, the spacing distance between any two adjacent rows in the yard is 4m, and the distances between the first row of cargo space and the origin of coordinates in the horizontal direction and the vertical direction are 3m and 2.5m respectively. The experiment is carried out in a Win10 system platform, an Intel processor with 3.7GHz main frequency, a 4GB memory and a Matlab R2014b development environment. The population scale N and the maximum evolution algebra G _ max of the IDA are respectively 50 and 600; for comparative fairness, the standard dragonfly algorithm uses the same population size and maximum evolutionary algebra as IDA, and the parameters s, a, c, f, e, ω of IDA also remain the same as DA. The algorithms in this embodiment are run for 30 times, and the optimal solution, the worst solution, the average value, and the standard deviation are counted to increase the discrimination, and the optimal value is displayed in a bold manner.
(2) Comparison analysis of optimized results
With respect to the embodiment of crane scheduling optimization for customer satisfaction, fig. 4, 5 and table 4 intuitively demonstrate the superior solution performance of the IDA algorithm. In the aspect of solving efficiency, the IDA can be converged to the optimal solution or the suboptimal solution at a higher speed; in terms of solving quality, the optimal solution, the worst solution and the average value of the 30 experiments in table 4 are superior to those of the standard DA algorithm, and meanwhile, fig. 5 reveals that the 30 solving results of the IDA are relatively small in fluctuation compared with the DA, which fully proves that the IDA has strong robustness. Furthermore, from the optimal scheduling scheme found by the IDA algorithm in table 5, all orders of the same customer with a higher rank are not picked up continuously, mainly because the picking positions of some orders of the customer are not located at the top position of the cargo space, so that the customer can pick the orders after picking the orders of the upper layer is finished. IDA performs well, and benefits from the following two points: firstly, the multi-match strategy greatly improves the probability that excellent genes are inherited to filial generations, and improves the solving quality; secondly, the neighborhood radius nonlinear adjustment mechanism based on the Gaussian operator can further avoid the problem of optimal solution or suboptimal solution error caused by neighborhood radius linear adjustment of the standard dragonfly algorithm, and is beneficial to improving the optimization efficiency and precision.
The invention is not described in detail in the prior art, and it is apparent to a person skilled in the art that the invention is not limited to details of the above-described exemplary embodiments, but that the invention can be embodied in other specific forms without departing from the spirit or essential characteristics thereof; the present embodiments are therefore to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein, and any reference signs in the claims are not intended to be construed as limiting the claim concerned.
TABLE 1 customer order information
Figure GDA0003368887990000121
Figure GDA0003368887990000131
TABLE 2 customer satisfaction factor
Figure GDA0003368887990000132
TABLE 3 article information
Figure GDA0003368887990000133
Table 430 solving result comparisons
Figure GDA0003368887990000134
TABLE 5 scheduling scheme derived by IDA
Figure GDA0003368887990000141

Claims (3)

1. A method for optimizing the dispatching of a storage yard crane considering customer satisfaction is characterized by comprising the following specific steps:
(1) under the condition of considering customer satisfaction, analyzing constraints existing in a yard and a target to be optimized, and establishing a yard crane scheduling optimization mathematical model considering the customer satisfaction with constraints, wherein the target to be optimized is the selected customer satisfaction for completing all customer orders, the constraints are that the quantity of hooks of the yard crane is limited and the goods selection order on a goods position is limited, and meanwhile, a customer satisfaction factor is associated with a customer grade, namely the customer satisfaction factor is in a direct proportion relation with the customer grade, and the mathematical model is defined as follows:
Figure DEST_PATH_IMAGE001
(1)
s.t.
Figure DEST_PATH_IMAGE002
(2)
Figure DEST_PATH_IMAGE003
(3)
Figure DEST_PATH_IMAGE004
(4)
Figure DEST_PATH_IMAGE005
(5)
Figure DEST_PATH_IMAGE006
(6)
Figure DEST_PATH_IMAGE007
(7)
wherein, the formula (1) is an objective function, namely a disappointment level; the expressions (2) to (6) are various constraints, and specifically: formula (2) represents
Figure DEST_PATH_IMAGE008
The goods can be picked only by one crane; the formula (3) limits that the number of cargos hoisted by the crane cannot exceed the number of hooks per se; the formula (4) requires the crane to complete all picking tasks; the formula (5) limits the goods picked by the crane to be positioned at the topmost layer of the goods position; equations (6) and (7) are binary value domain constraints for the decision variables;
Figure DEST_PATH_IMAGE009
representing a set of customer orders to be picked;
Figure DEST_PATH_IMAGE010
a set of paths representing the crane completing all customer order picking tasks;
Figure DEST_PATH_IMAGE011
representing a sub-path;
Figure DEST_PATH_IMAGE012
indicating the picking of the crane
Figure 461056DEST_PATH_IMAGE008
The time taken for each cargo is represented by equation (8);
Figure DEST_PATH_IMAGE013
representing goods
Figure 461021DEST_PATH_IMAGE008
Whether it belongs to a sub-path
Figure 506337DEST_PATH_IMAGE011
Herein, the
Figure DEST_PATH_IMAGE014
，
Figure DEST_PATH_IMAGE015
If it is at first
Figure 963864DEST_PATH_IMAGE008
The goods are at the first
Figure 309394DEST_PATH_IMAGE011
When the secondary sorting is completed, then
Figure 663015DEST_PATH_IMAGE013
=1, otherwise
Figure 195628DEST_PATH_IMAGE013
=0；
Figure DEST_PATH_IMAGE016
Representing sub-paths
Figure 456845DEST_PATH_IMAGE011
Goods in (1)
Figure 656882DEST_PATH_IMAGE008
Whether or not it is on the top level of the cargo space, where
Figure 915825DEST_PATH_IMAGE014
，
Figure 201313DEST_PATH_IMAGE015
；
Figure DEST_PATH_IMAGE017
Representing goods
Figure 735062DEST_PATH_IMAGE008
Customer satisfaction factor corresponding to the level of the affiliated customer order
Figure DEST_PATH_IMAGE018
(8)
In the formula
Figure DEST_PATH_IMAGE019
、
Figure DEST_PATH_IMAGE020
And
Figure DEST_PATH_IMAGE021
individual watchThe average speed of the crane trolley, the average speed of the crane trolley and the average lifting speed of the lifting hook are shown,
Figure DEST_PATH_IMAGE022
、
Figure DEST_PATH_IMAGE023
and
Figure DEST_PATH_IMAGE024
is as follows
Figure 713907DEST_PATH_IMAGE008
The spatial coordinates of the individual cargo in the yard,
Figure DEST_PATH_IMAGE025
is the maximum height of the storage yard;
(2) initializing parameters: dragonfly population scale
Figure DEST_PATH_IMAGE026
Maximum evolution algebra
Figure DEST_PATH_IMAGE027
Evolution algebra counter
Figure DEST_PATH_IMAGE028
Dragonfly number counter
Figure DEST_PATH_IMAGE029
Step length
Figure DEST_PATH_IMAGE030
Initializing dragonfly population individuals;
(3) order to
Figure DEST_PATH_IMAGE031
Carrying out global search;
(3-1) decoding the individual dragonflies into a feasible yard goods picking order;
(3-2) calculating the individual fitness of each dragonfly based on the mathematical model established in the step (1);
(3-3) updating the food and the natural enemy position;
(3-4) order
Figure DEST_PATH_IMAGE032
Local search is carried out;
(3-4-1) updating 5 behavior factors of collision avoidance, accompaniment, aggregation, foraging and enemy avoidance
Figure DEST_PATH_IMAGE033
,
Figure DEST_PATH_IMAGE034
,
Figure DEST_PATH_IMAGE035
,
Figure DEST_PATH_IMAGE036
,
Figure DEST_PATH_IMAGE037
And its corresponding weight and inertial weight
Figure DEST_PATH_IMAGE038
,
Figure DEST_PATH_IMAGE039
,
Figure DEST_PATH_IMAGE040
,
Figure DEST_PATH_IMAGE041
,
Figure DEST_PATH_IMAGE042
,
Figure DEST_PATH_IMAGE043
；
(3-4-2) updating neighborhood radius by adopting Gaussian operator
Figure 373778DEST_PATH_IMAGE011
；
(3-4-3) if the dragonfly individual exists in the current dragonfly neighborhood radius, updating the step length
Figure 880982DEST_PATH_IMAGE030
And executing a multi-marriage strategy; otherwise executeLevyA flight strategy;
(3-4-4) updating the food and the natural enemy position;
(3-4-5) if
Figure DEST_PATH_IMAGE044
And returning to the step (3-4); otherwise, turning to the step (3-5);
(3-5) if
Figure DEST_PATH_IMAGE045
And then returning to the step (3); otherwise, outputting the optimal solution.
2. The method for optimizing the dispatching of the yard cranes, considering the customer satisfaction, as claimed in claim 1, wherein: the step (3-4-2) adopts a Gaussian operator to update the neighborhood radius
Figure 484002DEST_PATH_IMAGE011
Radius of neighborhood
Figure 658632DEST_PATH_IMAGE011
The update formula is:
Figure DEST_PATH_IMAGE046
wherein the content of the first and second substances,UB、LBare respectively asThe upper and lower limits of each dimension variable,
Figure DEST_PATH_IMAGE047
to obey Gaussian distribution [0, 1]The random number in the middle of the random number,
Figure DEST_PATH_IMAGE048
、
Figure DEST_PATH_IMAGE049
respectively 0.5 and 0.2,
Figure 852852DEST_PATH_IMAGE028
for the current evolution algebra, the method is that,
Figure 847353DEST_PATH_IMAGE027
is the maximum evolution algebra.
3. The method for optimizing the dispatching of the yard cranes, considering the customer satisfaction, as claimed in claim 1, wherein: the step (3-4-3) implements a multi-match strategy, which is described as follows:
currently, the individual dragonfly is recorded as:
Figure DEST_PATH_IMAGE050
，
Figure DEST_PATH_IMAGE051
for the dimension of the problem to be solved, in the neighborhood radius
Figure 254064DEST_PATH_IMAGE011
Randomly selecting a dragonfly as a mating individual
Figure DEST_PATH_IMAGE052
，
Figure DEST_PATH_IMAGE053
Neighborhood zoneMarriage operator
Figure DEST_PATH_IMAGE054
Figure DEST_PATH_IMAGE055
Arithmetic marriage operator
Figure DEST_PATH_IMAGE056
Figure DEST_PATH_IMAGE057
Average marriage operator
Figure DEST_PATH_IMAGE059
Figure DEST_PATH_IMAGE060
Extreme value marriage operator
Figure DEST_PATH_IMAGE061
Figure DEST_PATH_IMAGE062
Edge marriage operator
Figure DEST_PATH_IMAGE063
Wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE064
is [0, 1]]A random number in between, and a random number,
Figure 535397DEST_PATH_IMAGE008
is [1, q ]]Any integer between (a) and (b),UB、LBrespectively, the upper limit and the lower limit of each dimension variable.
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