WO2022252268A1 - 一种智能立体仓库优化调度方法 - Google Patents

一种智能立体仓库优化调度方法 Download PDF

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WO2022252268A1
WO2022252268A1 PCT/CN2021/099119 CN2021099119W WO2022252268A1 WO 2022252268 A1 WO2022252268 A1 WO 2022252268A1 CN 2021099119 W CN2021099119 W CN 2021099119W WO 2022252268 A1 WO2022252268 A1 WO 2022252268A1
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stacker
model
intelligent
goods
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彭力
张鑫和
彭岩
谢林柏
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江南大学
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    • G06N3/00—Computing arrangements based on biological models
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    • G06N3/006—Artificial life, i.e. computing arrangements simulating life based on simulated virtual individual or collective life forms, e.g. social simulations or particle swarm optimisation [PSO]
    • G—PHYSICS
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    • G—PHYSICS
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Definitions

  • the invention relates to the technical field of warehousing and logistics scheduling, in particular to an optimal scheduling method for an intelligent three-dimensional warehouse.
  • Automated warehouse AS/RS Automated Storage and Retrieval System
  • the functions of the three-dimensional warehouse include storage, management, freight, scheduling, etc., which can significantly improve the utilization rate of the warehouse area and space and reduce management costs.
  • the three-dimensional warehouse helps to realize large-scale cargo storage and efficient logistics transportation, so as to meet modern production daily needs.
  • the research on the dispatching system is the key point of the three-dimensional warehouse design.
  • the core of the dispatching algorithm is to reduce the time of entering and exiting the warehouse, speed up the turnover rate and maintain the stability of the shelf.
  • the existing scheduling mode is: packing after unloading, and each box has multiple pieces of goods.
  • the forklifts are manually controlled to store the boxes into the shelves in order.
  • the goods will be out of the warehouse in the order of first-in-first-out. If there are surplus goods, the remaining goods will be packed and stored in the warehouse again.
  • the design of the business process is directly related to how to model and conduct simulation experiments.
  • the existing model has shortcomings such as low degree of automation and poor scheduling efficiency. For the optimization of the three-dimensional warehouse scheduling system, it is necessary to optimize the inbound and outbound business process on the existing basis. Make improvements.
  • Warehousing plan After the goods arrive at the warehouse, they first need quality inspection, warehousing, sorting and packing, and sticking barcodes. Put the boxes on the pallet and place them in the conveyor. When the goods pass through the radio frequency scanning system, the goods information will be recorded in the background system, the scheduling system algorithm is activated at this time. If the working conditions are not met, the stacker waits. If the working conditions are met, the background system distributes the goods and sends a running command to the stacker in sequence. The stacker receives the signal and executes the command to deliver the goods to the designated position on the shelf.
  • Outbound plan In order to ensure that all goods can enter and exit the warehouse, the first-in-first-out principle is adopted for outbound. In the original plan, when there are surplus goods, the goods will be stored again. This scheme makes the whole process less efficient. Therefore, a buffer zone is set in the new outbound operation plan. When there are surplus goods, the remaining The goods are stored in the outbound buffer zone. If there is a new order, the goods in the outbound buffer zone will be given priority. If the outbound buffer is full, the excess containers will be re-stored to the shelf according to a certain algorithm.
  • COI unit order volume index principle Cube-per-Order Index
  • COI is the ratio of the inventory capacity required to store the total amount of a certain product to the frequency of delivery of the product
  • COI is closely related to the turnover rate
  • the turnover rate reflects the inventory speed of the warehouse.
  • Wang Jie considered the factor of the center of gravity when modeling. Lowering the center of gravity can improve safety and reduce energy loss when the stacker operates in the vertical direction.
  • the location allocation problem of the three-dimensional warehouse is a typical NP-hard problem, and the scale that can be solved by the precise algorithm is very small, so the intelligent algorithm is studied to solve this kind of problem.
  • Intelligent algorithms include simulated annealing algorithm (SA), genetic algorithm (GA), particle swarm optimization algorithm (PSO), ant colony algorithm (ACO) and so on.
  • Xue Yali and others combined the genetic algorithm and the simulated annealing algorithm, and compared the results with the traditional genetic algorithm by solving the model to prove the effectiveness of the new algorithm.
  • Jia Yuliang adopted the FCFS principle for batch operations, and used the simulated annealing algorithm for location allocation, with the goal of minimizing the total time to solve the problem.
  • the technical problem to be solved by the present invention is to overcome the problems of slow convergence speed, local optimization, deadlock, low turnover rate and the like in the neutral library scheduling algorithm in the prior art.
  • the present invention provides an intelligent three-dimensional warehouse optimization scheduling method, comprising the following steps:
  • Step S1 Establishing the XYZ three-axis coordinate model of the three-dimensional warehouse, the arrangement of the three-dimensional warehouse is a two-way mode, and the three-dimensional warehouse is provided with a roadway for multiple stackers to shuttle and transport in the Y-axis direction;
  • Step S2 Considering the turnover rate of goods, establish the minimum evaluation function of the total running time of the stacker for the model with the goal of the minimum running time of the stacker to complete the transportation task, and establish the minimum evaluation function of the center of gravity of the model according to the principle of the lowest overall cargo center of gravity, Considering the load-bearing threshold of the shelf to establish a constraint function;
  • Step S3 Combine the minimum evaluation function of the total running time of the stacker and the minimum evaluation function of the center of gravity with the square weighted ideal point method combined with normalization to obtain a weighted minimum model;
  • Step S4 using a simulated annealing algorithm to optimize the weighted minimum model to obtain an optimal scheduling scheme.
  • the minimum evaluation function of the total running time of the stacker is:
  • V x , V y , and V z are the operating speeds of the stacker in the directions of X, Y, and Z axes respectively, num indicates the laneway position where the current cargo location is located, V r is the steering speed of the forklift, and r is the racking speed Width dimension, P xyz is the turnover rate of the goods, t xyz is the running time of the stacker, C xyz is the operating efficiency of the stacker, and the coordinates of the goods in the warehouse are the row number x, column number y, layer on the shelf
  • the number z, a, b, and c are the maximum value of the number of rack rows, columns, and layers.
  • the lowest evaluation function of the center of gravity is:
  • z i is the ordinate of the goods
  • m i is the weight of the goods
  • M is the total weight of all goods.
  • the constraint function is:
  • the weighted minimum model is:
  • F 1min is the global minimum of F 1 (x, y, z)
  • F 2min is the global minimum of F 2 (x, y, z)
  • F 1max and F 2max are F 1 (x, y ,z) and the global maximum of F 2 (x,y,z)
  • ⁇ and ⁇ are weights.
  • the ⁇ and ⁇ are taken as 0.7 and 0.3 respectively.
  • step S4 using the simulated annealing algorithm to optimize the weighted minimum model to obtain the optimal scheduling plan includes: initializing the population, randomly updating the position for each cargo, and calculating a new solution ; If the new solution is better than the old solution, update the position and enter the next iteration, otherwise, accept the new solution according to the Metropolis criterion; iterate through the inner loop and outer cooling and satisfy the particle when the temperature drops to the minimum.
  • the Metropolis criterion is expressed as:
  • E is the internal energy at temperature T
  • dE is the change number of E
  • E new is the update value
  • E old is the value before update
  • k is Boltzmann's constant.
  • step S4 using the simulated annealing algorithm to optimize the weighted minimum model to obtain the optimal scheduling scheme includes: first optimizing the parameters of the simulation algorithm, including: optimizing the parameters of the annealing algorithm To update the numerical value, compare the random steps of the simulated annealing algorithm to obtain the optimal number of moving steps, take the average value of the annealing tolerance value solved multiple times as the annealing tolerance value, and then optimize the weighted minimum value model to obtain Optimal scheduling scheme.
  • the numerical update of the annealing algorithm is as follows:
  • (X i+1 , Y i+1 , Z i+1 ) is the position update value of the i-th container, and the random value is recorded as the number of steps.
  • the present invention introduces the system turnover rate, establishes a mathematical model through the storage rules, integrates multiple target formulas into an evaluation function, and then combines the simulated annealing algorithm and optimizes the algorithm parameters to obtain the fastest convergence speed and the moving distance of the stacker.
  • the least three-dimensional warehouse scheduling solution is provided.
  • Figure 1 is a schematic diagram of a three-dimensional warehouse.
  • Fig. 2 is an effect diagram of solving the formula F 1 (x, y, z), wherein (a) the iteration diagram of the formula F 1 (x, y, z), and (b) a scatter diagram of the distribution of cargo locations.
  • Fig. 3 is an effect diagram of solving the formula F 2 (x, y, z), wherein (a) the iteration diagram of the formula F 2 (x, y, z), and (b) the scatter diagram of the distribution of cargo locations.
  • Figure 4 is a comparison diagram of algorithms, in which (a) solution diagram of annealing algorithm, (b) solution diagram of particle swarm optimization algorithm.
  • Figure 5 is a comparison chart of steps.
  • Figure 6 is a comparison chart of q values.
  • Figure 7 is a comparison chart before and after optimization.
  • Figure 8 is a comparison chart of multiple simulation parameters.
  • This embodiment provides an optimal scheduling method for an intelligent three-dimensional warehouse. Include the following steps:
  • Step S1 Establish a library model
  • the present invention will consider factors such as turnover rate, center of gravity and stacker moving speed, because the turnover rate and stacker moving speed have a strong correlation, they can be combined into one evaluation formula, so a mathematical model needs to be established including two main evaluations Formulas and related constraints.
  • the schematic diagram of the three-dimensional warehouse is shown in Figure 1.
  • the squares of various colors represent different types of goods.
  • the coordinates of the goods in the warehouse are represented by the number of rows x, the number of columns y, and the number of layers z on the shelf.
  • the arrangement of goods in the warehouse is a two-way mode.
  • the 2nd, 5th, and 8th rows are set as roadways. Relatively independent and non-interfering with each other.
  • V x , V y , and V z are the operating speeds of the stacker in the directions of X, Y, and Z respectively, num indicates the location of the roadway where the current cargo location (the location of the storage unit of the warehoused goods) is located, and V r is the steering speed of the forklift , r is the width of the unit shelf, P xyz is the turnover rate of goods, t xyz is the running time of the stacker, C xyz is the operating efficiency of the stacker, a, b, c are the number of rack rows, columns, and layers the maximum value.
  • the energy consumption of the three-dimensional warehouse mainly comes from the energy consumed by the operation of the stacker.
  • the stacker consumes energy in both horizontal and vertical directions.
  • the energy consumption in the horizontal direction is mainly friction
  • the energy consumption in the vertical direction is the energy consumption during the lifting process.
  • the center of gravity of the shelf should be as low as possible.
  • the risk of collapse caused by excessive local load-bearing of the shelf should be considered. Therefore, under the premise of the low center of gravity of the shelf, the overall shelf should be light at the top and heavy at the bottom.
  • the evaluation formula of the principle of the lowest center of gravity of the model is shown in formula (2):
  • z i is the vertical coordinate of the container
  • m i is the weight of the container
  • M is the total weight of all the containers.
  • the allocated storage space must be stored within the fixed range of the shelf.
  • the shelf has a total of c rows, r columns, and f floors; the weight of the box cannot exceed the load-bearing threshold of the shelf, and the total weight of the local goods cannot be too heavy.
  • the model constraint formula is as follows: 3) As shown:
  • Axyz represents the storage capacity, expressed as a percentage.
  • the application scene of the present invention can pick up the goods according to the number of pieces according to the demand, and the stacker can run along the horizontal and vertical directions at the same time, which makes the logic and mathematical modeling of entering and leaving the warehouse slightly different from the traditional three-dimensional warehouse; because the stored goods have no shelf life, Inflammable, explosive and perishable problems, so the cargo boxes can be stored randomly.
  • Step S2 Establish evaluation function
  • F 1min is the global minimum value of F 1 (x, y, z)
  • F 2min is the global minimum value of F 2 (x, y, z)
  • the parameters need to use the corresponding target formula separately.
  • F 1max and F 2max are global maximum values respectively
  • ⁇ and ⁇ are weights, and the weights are set to 0.7 and 0.3 respectively according to the importance of parameters.
  • Step S3 Propose an intelligent algorithm for system optimization scheduling
  • Step S31 annealing algorithm
  • the simulated annealing algorithm is similar to the hill-climbing algorithm. Because the simulated annealing strategy can jump out of the local optimum, it is widely used in the research of non-neural network intelligent algorithms.
  • the annealing algorithm is to simulate the annealing process of a solid. When the temperature in the solid is high, the particles are active and unstable, and are in a random hash state. When the temperature is low, the internal energy of the particles inside the object is small, and the particles are relatively ordered and gradually tend to at a fixed position. When the temperature drops to a certain value, the internal energy reaches the minimum, and the particles are the most stable at this time.
  • the annealing algorithm has been proven to have asymptotic convergence, can converge to the global optimal solution with a high probability, and is fast.
  • the annealing algorithm first initializes the population, randomly updates the position for each container, and calculates the new solution through the formula. If the new solution is better than the old solution, the updated position enters the next iteration. Otherwise, the new solution is accepted according to the Metropolis criterion, and the inner loop and The algorithm ends after the external cooling iterations meet the exit conditions. According to the Metropolis criterion, the particle tends to be stable when the temperature drops to the minimum value, that is, the particle reaches a relatively optimal position.
  • the Metropolis criterion is often expressed as a probability formula as shown in formula (5):
  • E is the internal energy at temperature T
  • dE is the change number of E
  • E new is the update value
  • E old is the value before update
  • k is the Boltzmann constant.
  • Step S32 particle swarm optimization algorithm
  • Particle swarm optimization is also a commonly used heuristic algorithm. Particle swarm optimization randomly initializes multiple particles, assuming that particles propagate in space at an initial velocity, particles pass through space, and evaluate according to appropriate criteria after each time step . As time goes by, the particles will accelerate towards the best particle position and the current particle optimal position, and generate greater inertia to affect other particles. Compared with the genetic algorithm, the particle swarm algorithm has simpler coding and fewer parameters, and is suitable for rapid development. At the same time, the particle swarm algorithm has a better convergence speed.
  • the particle swarm optimization algorithm first randomly initializes the population, determines the formula parameters and calculates the particle fitness for each particle. If the exit condition is met, the algorithm ends. If not, the particle fitness is re-evaluated until all particles meet the exit condition.
  • the core formula of the particle swarm optimization algorithm is shown in formula (6):
  • w is the speed inertia
  • c1 and c2 are the learning rate of moving distance
  • rand() is a random number between 0 and 1
  • pb i is the historical optimal value of the current particle
  • gb is the historical optimal value of the entire particle cluster value
  • p i is the current evaluation value of the i-th particle
  • V i is the running speed of the i-th particle.
  • Step S33 Combining (5) and (6) to realize the intelligent optimal scheduling of the vertical warehouse, and perform a global optimization solution to the vertical warehouse model formula (3).
  • Step S4 Verify the effect
  • Verification environment The experiment assumes that the turnover rate of goods will not change suddenly, the stacker runs at a constant speed and is not affected by interference factors, and the stacker can only carry one box of items at a time, and each box has the same size and volume.
  • Experimental parameters include warehouse parameters, stacker parameters and cargo parameters.
  • the unit shelf size of the warehouse is 1 ⁇ 1 ⁇ 1
  • the overall shelf size is 12 ⁇ 12 ⁇ 6, and the load capacity of the cargo space is 1 ton.
  • the horizontal movement speed of the stacker is 3m/s
  • the vertical movement speed is 1.5m/s
  • the time required for turning is 1.5s.
  • Cargo parameters include category, turnover rate, quantity per box, single piece weight, etc., where the categories of goods are A, B, C, D, and E, and the corresponding turnover rates are 0.4, 0.2, 0.1, 0.2, and 0.1 for the initial allocation of goods location, the maximum number of goods scanned each time is 40 pieces, and the background data is recorded after scanning and the initial goods are randomly assigned.
  • Table 1 Some of the goods information is shown in Table 1:
  • the evaluation formula parameters F 1min and F 2min of the annealing algorithm need to be calculated.
  • Calculation of F 1min only needs to consider the formula F 1 (x, y, z), and scan 40 boxes of goods in a single time.
  • the calculated value of F 1min is 87.6.
  • the minimum value is obtained after multiple left and right iterations.
  • the goods are closely stacked at the entrance.
  • the frequency of using the lifting device of the stacker should be reduced as much as possible, and the goods should be arranged as close to the ground as possible.
  • Such current permutation schemes are less secure and therefore not optimal.
  • the annealing algorithm and the particle swarm optimization algorithm are solved respectively, and the results are shown in Figure 4.
  • the goods are divided into five categories: A, B, C, D, and E, which are marked in different colors in the figure.
  • the entrance and exit coordinates of the warehouse are (1, 1, 1), and the optimal goods are located in the lower left corner.
  • the simulated annealing algorithm can jump out of the local optimum through a certain tolerance, each particle has a certain randomness, and is subject to the least local interference, so continue to optimize the parameters of the annealing algorithm.
  • Step S5 Parameter optimization of the simulated annealing algorithm
  • step1 represents the range of steps from -1 to 1
  • step2 represents the range of steps from -2 to 2.
  • Figure 5 The comparison of different synchronization numbers is shown in Figure 5.
  • the number of steps 1 and 3 have better fast convergence, and the convergence of step 1 may be faster, but the final optimization value of step 1 falls into a local Optimal, probably because the number of steps is too small, when a single item is not in the optimal position, and there are a lot of items around, it cannot jump out, and the effect of the number of steps is 3 is the most obvious. Therefore, the number of steps 3 is selected as the formula for loop iterative movement.
  • the annealing tolerance value (set as q value) is also an important parameter that needs to be adjusted.
  • the value range of q is generally between 0.7-1.0, with 0.05 as a step, solve each q value 10 times and take the average number, as shown in Figure 6 As shown, it can be observed that when q is 0.85, it is the best. When q is greater than 0.85, the solution value does not decrease but increases. The reason is that it falls into a local optimum, so it can be used as the optimal q value in this paper.
  • the optimized annealing algorithm was used to carry out the simulation experiment.
  • the coordinates of the single-allocation cargo are shown in Table 2.
  • the cargo is allocated to a position closer to the entrance and exit, and the overall center of gravity is lower.
  • the embodiments of the present application may be provided as methods, systems, or computer program products. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) having computer-usable program code embodied therein.
  • computer-usable storage media including but not limited to disk storage, CD-ROM, optical storage, etc.
  • These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing apparatus to operate in a specific manner, such that the instructions stored in the computer-readable memory produce an article of manufacture comprising instruction means, the instructions
  • the device realizes the function specified in one or more procedures of the flowchart and/or one or more blocks of the block diagram.

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Abstract

本发明涉及一种智能立体仓库优化调度方法。本发明包括建立立体仓库XYZ三轴坐标模型；考虑货物周转率，以堆垛机完成输送任务完成的最少运行时间为目标对模型建立堆垛机总运行时间最小评价函数，根据整体货物重心最低原则并建立模型的重心最低评价函数，考虑货架承重阈值建立约束函数，得到加权最小值模型；利用模拟退火算法对所述加权最小值模型进行优化得到最优调度方案。本发明结合模拟退火算法并对算法参数进行优化，得到收敛速度最快、堆垛机移动距离最少的立体仓库调度解决方案。

Description

一种智能立体仓库优化调度方法 技术领域
本发明涉及仓储物流调度技术领域，尤其是指一种智能立体仓库优化调度方法。
背景技术
自动化立体仓库AS/RS(Automated Storage and Retrieval System)是现代化仓储管理系统的重要组成部分。立体仓库的功能包括存储、管理、货运、调度等，可显著提高仓库面积的利用率以及空间利用率并降低管理费用，立体仓库有助于实现大规模货物仓储和高效物流运输，从而满足现代生产生活需要。调度系统的研究是立体仓库设计的重点，调度算法的核心是减少出入库时间、加快周转率以及维持货架稳定性。
现有调度模式为：卸货后装箱，每箱有多件货物。由人工控制叉车将货箱按顺序存入货架，当有出库订单时，按照先入先出的顺序将货物出库，若货物有剩余，则将剩余货物装箱再次存入仓库。业务流程的设计直接关系到如何建模并进行仿真实验，现有模式存在自动化程度低、调度方式效率差等不足，对立体仓库调度系统的优化需求，需在现有基础上对出入库业务流程进行改进。
入库方案：货物到达仓库后首先需质检、入库、分类装箱、贴条形码，将货箱放入托盘并置于传送装置中，当货物通过射频扫描系统时，货物信息被记录在后台系统，此时调度系统算法被激活。若不满足工作条件则堆垛机等待，若满足工作条件，则后台系统分配货物并向堆垛机按顺序发送一条运行命令，堆垛机收到信号执行命令将货物运送至货架的指定位置。
出库方案：为保障所有货物可以进库出库，因此采用先入先出的原则进行出库。在原方案中，当取货有剩余时会将货物再次入库，该方案使得整个过程效率较低，因此在新的出库作业方案中设置一个出库缓冲区，当货物有剩余时，将剩余货物存入出库缓冲区，若有新订单时，优先考虑出库缓冲区中的货物。若出库缓冲区满，则将多余货箱按照一定的算法重新存储至货架。
Heskett提出的COI的概念(单位订单体积索引原则Cube-per-Order Index，COI为某种货品存储总量所需的库存容量与该种货品的出库频率的比值)，COI与周转率密切相关，周转率反映了仓库的存货速度。王杰在建模时考虑了重心的因素，降低重心可提高安全性，同时降低堆垛机在竖直方向作业时的能量损耗。
立体仓库的货位分配问题属于典型的NP-hard的问题，其精确算法能求解的规模很小，因此研究智能算法来对该类问题进行求解。智能算法包括模拟退火算法(SA)、遗传算法(GA)、粒子群算法(PSO)、蚁群算法(ACO)等。
国内外学者已经对调度系统进行了大量研究。Boysen等设计了一种简便的元组表示法，从仓库布局、作业模式、入库任务货位分配策略、调度目标等4个维度对立体仓库单堆垛机调度问题进行描述。Miguel Horta在立体仓库的基础上提出了基于最小二乘的路径规划方法，该方法设计了一个交叉对接的仓库布局，可以进行实时配送。Ene等考虑堆垛机的电量消耗因素,建立以堆垛机耗电量最少为目标的数学模型，并采用智能算法对其求解。薛亚莉等人将遗传算法和模拟退火算法相结合，通过对模型的求解，将结果与传统遗传算法作比较，证明新算法的有效性。贾煜亮采用了FCFS原则进行批量作业，用模拟退火算法进行货位分配，以总时长最小为目标进行求解。
上述文献对立体仓库做了较为深入的研究，但一些文献中对评价公式使用直接加权的方法，但因量纲不同使得效果未达到最佳；在智能算法选择上，遗传算法编程实现很复杂，运行速度慢，并且找到最优解后还需要解码，对初始种群选择有一定的依赖性；蚁群算法如果参数选择不当，蚂蚁选择的路 径会有很大的偏差；粒子群算法也容易陷入局部最优。
发明内容
为此，本发明所要解决的技术问题在于克服现有技术中立库调度算法存在收敛速度慢、局部优化、死锁、周转率低等问题。
为解决上述技术问题，本发明提供了一种智能立体仓库优化调度方法，包括以下步骤：
步骤S1：建立立体仓库XYZ三轴坐标模型，所述立体仓库排布方式为双向模式，所述立体仓库设有供多台堆垛机在Y轴方向穿梭运输的巷道；
步骤S2：考虑货物周转率，以堆垛机完成输送任务完成的最少运行时间为目标对模型建立堆垛机总运行时间最小评价函数，根据整体货物重心最低原则并建立模型的重心最低评价函数，考虑货架承重阈值建立约束函数；
步骤S3：将堆垛机总运行时间最小评价函数与重心最低评价函数利用归一化结合的平方加权理想点法得到加权最小值模型；
步骤S4：利用模拟退火算法对所述加权最小值模型进行优化得到最优调度方案。
在本发明的一个实施例中，所述堆垛机总运行时间最小评价函数为：
Figure PCTCN2021099119-appb-000001
式中，V x，V y，V z为堆垛机分别在X、Y、Z三轴方向的运行速度，num表明当前货位所在的巷道位置，V r为叉车转向速度，r为货架的宽度尺寸，P xyz是货物的周转率，t xyz为堆垛机运行时间，C xyz为堆垛机运行效率，货物在仓库中的坐标为其位于货架上的排数x、列数y、层数z，a、b、c为货架排数、列数、层数的最大值。
在本发明的一个实施例中，所述重心最低评价函数为：
Figure PCTCN2021099119-appb-000002
式中，z i是货物的纵坐标，m i是货物的重量，M为所有货物的总重量。
在本发明的一个实施例中，所述约束函数为：
Figure PCTCN2021099119-appb-000003
其中，M max(A xyz＝1)表示库容量达到100％。
在本发明的一个实施例中，所述加权最小值模型为：
Figure PCTCN2021099119-appb-000004
式中，F 1min是F 1(x,y,z)的全局最小值，F 2min是F 2(x,y,z)的全局最小值，F 1max和F 2max分别为F 1(x,y,z)和F 2(x,y,z)的全局最大值，α和β是权重。
在本发明的一个实施例中，所述α和β分别取为0.7和0.3。
在本发明的一个实施例中，所述步骤S4中，利用模拟退火算法对所述加权最小值模型进行优化得到最优调度方案包括：初始化种群，为每个货物随机更新位置，计算出新解；若新解优于旧解，则更新位置并进入下一次迭代，反之按Metropolis准则接受新解；经过内循环和外部降温迭代并满足粒子在温度降低到最小值时结束。
在本发明的一个实施例中，所述Metropolis准则表示为：
Figure PCTCN2021099119-appb-000005
式中，E为温度T时的内能，dE为E的改变数,E new为更新值，E old为 更新前的值，k为波茲曼常数。
在本发明的一个实施例中，所述步骤S4中，利用模拟退火算法对所述加权最小值模型进行优化得到最优调度方案包括：首先对模拟算法的参数进行优化，包括：对退火算法的数值更新，通过模拟退火算法的随机步数大小进行对比，得到最佳的移动步数，将多次求解的退火容忍值取平均值作为退火容忍值，再对所述加权最小值模型进行优化得到最优调度方案。
在本发明的一个实施例中，所述退火算法的数值更新如下所示：
Figure PCTCN2021099119-appb-000006
其中，(X i+1,Y i+1,Z i+1)为第i个货箱的位置更新值，随机值记为步数。
本发明的上述技术方案相比现有技术具有以下优点：
本发明通过引入系统周转率，通过入库规则建立数学模型，将多个目标公式整合为一个评价函数，随后结合模拟退火算法并对算法参数进行优化，得到收敛速度最快、堆垛机移动距离最少的立体仓库调度解决方案。
附图说明
为了使本发明的内容更容易被清楚的理解，下面根据本发明的具体实施例并结合附图，对本发明作进一步详细的说明，其中
图1是立体仓库示意图。
图2是公式F 1(x,y,z)求解效果图，其中(a)公式F 1(x,y,z)迭代图，(b)货位分布散点图。
图3是公式F 2(x,y,z)求解效果图，其中(a)公式F 2(x,y,z)迭代图，(b)货位分布散点图。
图4是算法对比图，其中(a)退火算法求解图，(b)粒子群算法求解图。
图5是步数对比图。
图6是q值对比图。
图7是优化前后对比图。
图8是多次模拟参数对比图。
具体实施方式
下面结合附图和具体实施例对本发明作进一步说明，以使本领域的技术人员可以更好地理解本发明并能予以实施，但所举实施例不作为对本发明的限定。
实施例
本实施例提供一种智能立体仓库优化调度方法。包括以下步骤：
步骤S1：建立立库模型
本发明将考虑周转率、重心和堆垛机移动速度等因素，因周转率与堆垛机移动速度有较强相关性，可合并为1个评价公式，因此要建立数学模型包括两个主要评价公式及相关约束条件。
立体仓库示意图如图1所示，各色的方块代表不同种类的货物，货物在仓库中的坐标由其位于货架上的排数x、列数y、层数z表示。仓库的货物排布方式为双向模式，本实施例中，设置第2、5、8排为巷道，巷道总数为货架排数的一半，供堆垛机在仓库中穿梭运输，各个堆垛机运行相对独立互不干涉。
对于周转率高的货物，应将其放至靠近出入口的货位上，同时应当使堆垛机总运行时间最小，由此得到评价公式如式(1)所示：
Figure PCTCN2021099119-appb-000007
式中V x，V y，V z为堆垛机分别在X、Y、Z三轴方向的运行速度，num表明当前货位(仓储货物存储单元位置)所在巷道位置，V r为叉车转向速度， r为单元货架的宽度尺寸，P xyz是货物的周转率，t xyz为堆垛机运行时间，C xyz为堆垛机运行效率，a、b、c为货架排数、列数、层数的最大值。
立体仓库能耗主要来源于堆垛机运行所消耗的能量，堆垛机在水平和竖直方向都会消耗能量，水平方向的能耗主要为摩擦力，竖直方向的能耗为提升过程中的克服重力做功，显然堆垛机在垂直方向移动同样距离比水平方向能耗大，因此货架的重心应尽可能低。同时应当考虑货架局部承重过大造成的倒塌风险，因此在货架重心低的前提下还要使货架整体呈现上轻下重，得到模型的重心最低原则的评价公式如式(2)所示：
Figure PCTCN2021099119-appb-000008
式中z i是货箱的纵坐标，m i是货箱的重量，M为所有货箱的总重量。
分配的货位必须存储在货架固定的范围内，货架共c排、r列、f层；货箱的重量不能超过货架的承重阈值，不能使局部货物总重量过重，模型约束公式如式(3)所示：
Figure PCTCN2021099119-appb-000009
其中，M max(A xyz＝1)表示库容量达到100％， Axyz代表仓储的容量，用百分比表示。
本发明的应用场景可根据需求按照件数取货，堆垛机可以同时沿水平和竖直方向运行，这使得进出库逻辑、数学建模和传统立体仓库略有不同；因存储货物无保质期、易燃易爆易腐等问题，因此货箱之间可以随机存放。
步骤S2：建立评价函数
因多目标优化模型各个参数的量纲不同，不能对多个目标函数进行简单求和，因此将多个目标公式构造一个评价函数，以它作为目标函数，求解单 目标规划问题，常用的评价方法有线性加权和法、极大极小法和理想点法。
利用与归一化结合的平方加权理想点法将两约束条件合并求出加权最小值，方法如式(4)所示。
Figure PCTCN2021099119-appb-000010
式中F 1min是F 1(x,y,z)的全局最小值，F 2min是F 2(x,y,z)的全局最小值，参数需要单独使用对应的目标公式。F 1max和F 2max分别为全局最大值，α和β是权重，根据参数重要程度将权重分别取为0.7和0.3。
从上述模型评价公式可以看出立体仓库的货位分配问题属于典型的NP-hard问题，其精确算法能求解的规模很小，因此由于公式的复杂性，通过智能算法快速迭代来求解模型，寻求最优解。
上述通过入库规则建立数学模型，将多个目标公式整合为一个评价函数，随后将结合应用选取多种智能算法求解并进行分析比较，得到适用于实际工况的最优算法，最后对算法参数进行优化，得到收敛速度最快、堆垛机移动距离最少的立体仓库调度解决方案。
步骤S3：提出系统优化调度智能算法
步骤S31退火算法
模拟退火算法类似于爬山算法，由于模拟退火策略可以跳出局部最优的特性，因此被广泛的应用在非神经网络的智能算法研究中。退火算法是在模拟固体退火的过程，固体内温度较高时，粒子活跃不稳定，处于随机散列状态，当温度较低时，物体内部的粒子内能较小，粒子相对有序并逐渐趋于某一固定位置。当温度降低到一定值时，内能达到最小，此时粒子最稳定。退火算法已经被证明了具有渐进收敛性，可以大概率收敛于全局最优解，并且速度较快。
退火算法首先初始化种群，为每个货箱随机更新位置，通过公式计算出新解，若新解优于旧解，则更新位置进入下一次迭代，反之按Metropolis准 则接受新解，经过内循环和外部降温迭代并满足退出条件后结束算法。根据Metropolis准则，粒子在温度降低到最小值时趋于稳定，也就是粒子到达了相对最优的位置上。Metropolis准则常表示为概率公式如式(5)所示：
Figure PCTCN2021099119-appb-000011
式中，E为温度T时的内能，dE为E的改变数,E new为更新值，E old为更新前的值，k为Boltzmann常数。
步骤S32：粒子群算法
粒子群算法也是一种常用的启发式算法，粒子群算法随机初始化多个粒子，假设粒子在空间中以初速度传播，粒子穿过空间，并在每个时间步长后根据合适的标准进行评估。随着时间的推移，粒子将加速朝着最好的粒子位置和当前粒子最优位置方向移动，并产生较大惯性影响其他粒子。粒子群算法比遗传算法编码简单、参数少，适合快速开发，同时粒子群算法有较好的收敛速度。
粒子群算法首先随机初始化种群，确定公式参数并对每一个粒子计算粒子适应度，若满足退出条件则结束算法，若不满足则重新评价粒子适应度，直至所有粒子满足退出条件。粒子群算法的核心公式如式(6)所示：
Figure PCTCN2021099119-appb-000012
式中w为速度惯性，c1和c2为移动距离的学习率，rand()为0～1之间的随机数，pb i为当前粒子的历史最优值,gb为整个粒子集群的历史最优值，p i为第i个粒子的当前评价值，V i为第i个粒子运行速度。
步骤S33：将(5)与(6)结合实现立库智能优化调度，对立库模型公式(3)进行全局优化求解。
步骤S4：验证效果
验证环境：实验假设货物周转率不会发生突变，堆垛机匀速运行不受干 扰因素影响，堆垛机每次只能搬运一箱物品，每个货箱大小容积相同。
实验参数包括仓库参数，堆垛机参数和货物参数。其中，仓库的单元货架尺寸为1×1×1，整体货架尺寸为12×12×6，货位承重1吨。堆垛机水平移动速度为3m/s，垂直移动速度为1.5m/s，转向所需时间1.5s。
货物参数包括类别、周转率、每箱数量、单件重量等，其中货物类别为A、B、C、D、E，分别对应的周转率为0.4、0.2、0.1、0.2、0.1为货物初始化分配位置，每次扫描货物最大数量为40件，扫描后记录后台数据并随机分配初始货物，其中部分货物信息如表1所示：
表1部分货物参数
Figure PCTCN2021099119-appb-000013
步骤S41评价函数参数计算
首先需要计算退火算法的评价公式参数F 1min和F 2min。计算F 1min只需考虑公式F 1(x,y,z)，单次扫描40箱货物，此时F 1min计算值为87.6，如图2所示，经过多次左右迭代得到最小值。货物紧密堆积在入口的位置，为防止损坏和减少做功，应当尽量减小堆垛机使用升高装置的频率，尽量将货物排布贴近地面。如此当前的排列方案安全性较低，因此并非最优的选择。
单独针对F 2(x,y,z)求解如图3所示，此时F 2min为0.995。经过约200次迭代，公式F 2(x,y,z)得到最小值，仅考虑重心时，所有物品会优先排列在最下层，但显然货物距离出入口较远，入口处货架没有充分利用，调度效率未达到预期标准。
最终得到F 1min为87.6，F 2min为0.995。
分别对退火算法和粒子群算法进行求解，得到结果如图4所示，货物按种类分为A、B、C、D、E五大类，在图中分别以不同颜色标出。仓库的出入口坐标为(1，1，1)，最优货物位于左下角。
由图4中对比可得，粒子群算法优化结果明显比退火算法差，粒子收敛于中间靠下位置，而并未向最优货位收敛，此时算法陷入局部最优。
而模拟退火算法可通过一定的容忍度跳出局部最优，每个粒子具有一定的随机性，受到局部干扰最小，因此继续对退火算法的参数进行优化。
步骤S5：模拟退火算法的参数优化
上述实验中验证了模拟退火算法的有效性，进一步通过模拟退火算法随机循环迭代的步数大小进行对比，对算法进一步优化。退火算法的数值更新如式(7)所示：
Figure PCTCN2021099119-appb-000014
(X i+1,Y i+1,Z i+1)为第i个货箱的位置更新值，随机值可记为步数。步数1～7的范围进行模拟，例如step1代表步数范围为-1～1，step2代表步数范围为-2～2。对不同步数进行对比如图5所示，可以看到步数1和步数3具有较好的快速收敛性，步数1的收敛性可能更快，但是步数1最终优化值陷入了局部最优，可能是由于步数过小，当单个货物不是在最优位置，且周围存在大量货物时无法跳出，步数3的效果最明显。因此选用步数3作为循环迭代移动的公式。
退火容忍值(设为q值)也是需要调节的重要参数，q的取值范围一般在0.7-1.0之间，以0.05为一步，对每次q值求解10次并取平均数，如图6所示，可以观察到当q取0.85时最佳，当q大于0.85时，求解值不降反增，原因是陷入局部最优，因此可作为本文最优的q值。
步骤S6：优化结果
使用优化后的退火算法进行模拟实验，单次分配货物坐标如表2所示，货物被分配到距离出入口较近位置，且整体重心较低。
表2优化后货物坐标分配
Figure PCTCN2021099119-appb-000015
使用优化后的模型模拟10次入库出库，多次模拟以验证系统在一定时间内的稳定性，每次随机出入库多件货物，将优化前和优化后的步数进行对比，优化前的货物按顺序摆放，第一列满则分配至第二列，第一层满则分配到第二层，以此类推；优化后的方案是首先随机初始化货物，再通过优化后的退火算法进行货位分配。对比结果如图7所示，在完成10次入出库后，每次步数优化幅度达到52％左右，随着时间推移优化效果更加明显。
为了再次验证稳定性，多次重复对整体10次入库出库流程的实验，如图8所示，优化前算法固定，因此每次计算步数相同，优化后的数值小幅波动，但整体保持在一定范围内且相对于优化前的堆垛机移动步数有了大幅度的下降，系统稳定性较强，达到了预期的效果。结构表明，本发明的退火算法的容忍度和随机性可以防止陷入局部最优。
本领域内的技术人员应明白，本申请的实施例可提供为方法、系统、或 计算机程序产品。因此，本申请可采用完全硬件实施例、完全软件实施例、或结合软件和硬件方面的实施例的形式。而且，本申请可采用在一个或多个其中包含有计算机可用程序代码的计算机可用存储介质(包括但不限于磁盘存储器、CD-ROM、光学存储器等)上实施的计算机程序产品的形式。
本申请是参照根据本申请实施例的方法、设备(系统)、和计算机程序产品的流程图和/或方框图来描述的。应理解可由计算机程序指令实现流程图和/或方框图中的每一流程和/或方框、以及流程图和/或方框图中的流程和/或方框的结合。可提供这些计算机程序指令到通用计算机、专用计算机、嵌入式处理机或其他可编程数据处理设备的处理器以产生一个机器，使得通过计算机或其他可编程数据处理设备的处理器执行的指令产生用于实现在流程图一个流程或多个流程和/或方框图一个方框或多个方框中指定的功能的装置。
这些计算机程序指令也可存储在能引导计算机或其他可编程数据处理设备以特定方式工作的计算机可读存储器中，使得存储在该计算机可读存储器中的指令产生包括指令装置的制造品，该指令装置实现在流程图一个流程或多个流程和/或方框图一个方框或多个方框中指定的功能。
这些计算机程序指令也可装载到计算机或其他可编程数据处理设备上，使得在计算机或其他可编程设备上执行一系列操作步骤以产生计算机实现的处理，从而在计算机或其他可编程设备上执行的指令提供用于实现在流程图一个流程或多个流程和/或方框图一个方框或多个方框中指定的功能的步骤。
显然，上述实施例仅仅是为清楚地说明所作的举例，并非对实施方式的限定。对于所属领域的普通技术人员来说，在上述说明的基础上还可以做出其它不同形式变化或变动。这里无需也无法对所有的实施方式予以穷举。而由此所引申出的显而易见的变化或变动仍处于本发明创造的保护范围之中。

Claims (10)

  1. 一种智能立体仓库优化调度方法，其特征在于，包括以下步骤：
    步骤S1：建立立体仓库XYZ三轴坐标模型，所述立体仓库排布方式为双向模式，所述立体仓库设有供多台堆垛机在Y轴方向穿梭运输的巷道；
    步骤S2：考虑货物周转率，以堆垛机完成输送任务完成的最少运行时间为目标对模型建立堆垛机总运行时间最小评价函数，考虑货架承重阈值的约束函数并根据整体货物重心最低原则并建立模型的重心最低评价函数；
    步骤S3：将堆垛机总运行时间最小评价函数与重心最低评价函数利用归一化结合的平方加权理想点法得到加权最小值模型；
    步骤S4：利用模拟退火算法对所述加权最小值模型进行优化得到最优调度方案。
  2. 根据权利要求1所述的一种智能立体仓库优化调度方法，其特征在于，所述堆垛机总运行时间最小评价函数为：
    Figure PCTCN2021099119-appb-100001
    式中，V x，V y，V z为堆垛机分别在X、Y、Z三轴方向的运行速度，num表明当前货位所在的巷道位置，V r为叉车转向速度，r为单元货架的宽度尺寸，P xyz是货物的周转率，t xyz为堆垛机运行时间，C xyz为堆垛机运行效率，货物在仓库中的坐标为其位于货架上的排数x、列数y、层数z，a、b、c分别为货架排数、列数、层数的最大值。
  3. 根据权利要求1所述的一种智能立体仓库优化调度方法，其特征在于，所述重心最低评价函数为：
    Figure PCTCN2021099119-appb-100002
    式中，z i是货物的纵坐标，m i是货物的重量，M为所有货物的总重量。
  4. 根据权利要求1所述的一种智能立体仓库优化调度方法，其特征在于，所述约束函数为：
    Figure PCTCN2021099119-appb-100003
    其中，M max(A xyz＝1)表示库容量达到100％。
  5. 根据权利要求1所述的一种智能立体仓库优化调度方法，其特征在于，所述加权最小值模型为：
    Figure PCTCN2021099119-appb-100004
    式中，F 1min是F 1(x,y,z)的全局最小值，F 2min是F 2(x,y,z)的全局最小值，F 1max和F 2max分别为F 1(x,y,z)和F 2(x,y,z)的全局最大值，α和β是权重。
  6. 根据权利要求5所述的一种智能立体仓库优化调度方法，其特征在于，所述α和β分别取为0.7和0.3。
  7. 根据权利要求1所述的一种智能立体仓库优化调度方法，其特征在于，所述步骤S4中，利用模拟退火算法对所述加权最小值模型进行优化得到最优调度方案包括：初始化种群，为每个货物随机更新位置，计算出新解；若新解优于旧解，则更新位置并进入下一次迭代，反之按Metropolis准则接受新解；经过内循环和外部降温迭代并满足粒子在温度降低到最小值时结束。
  8. 根据权利要求7所述的一种智能立体仓库优化调度方法，其特征在于，所述Metropolis准则表示为：
    Figure PCTCN2021099119-appb-100005
    式中，E为温度T时的内能，dE为E的改变数,E new为更新值，E old为更新前的值，k为波茲曼常数。
  9. 根据权利要求1所述的一种智能立体仓库优化调度方法，其特征在于，所述步骤S4中，利用模拟退火算法对所述加权最小值模型进行优化得到最优调度方案包括：对模拟算法的参数进行优化，包括：对退火算法的数值进行更新，通过模拟退火算法的先后随机步数大小进行对比，得到最佳的移动步数，将多次求解的退火容忍值取平均值作为退火容忍值，再对所述加权最小值模型进行优化得到最优调度方案。
  10. 根据权利要求9所述的一种智能立体仓库优化调度方法，其特征在于，所述退火算法的数值进行更新如下所示：
    Figure PCTCN2021099119-appb-100006
    式中，(X i+1,Y i+1,Z i+1)为第i个货箱的位置更新值，随机值记为步数。
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