Three key entities are selected as the research objects to analyze the problem of location optimization accurately, namely “cargo”, “cargo location” and “handling equipment”, the mathematical model is established to analyze the equilibrium relationship among cargo, cargo location and handling equipment, and finally we realize the goal of optimization assigned on location selection.

To make the mathematical model standardized, on the basis of objective reality, to the best solution oriented, the model assumptions are as follows:

(1) The storage unit is a pallet or container, goods stored in a single pallet or container is the same kind;

(2) All the size of the pallet or container are the same, and match with the cargo box, (the box size is the same), each cargo box, just can accommodate a pallet (or container).

(3) Shelves display are rectangular, the cargo box is a cube shape;

(4) In-out warehouse’s frequency of all types of cargo in the system will not change too much in a short time;

(5) The initial position of a stacker is located on the position which shelves closed to the entrance and exit;

(6) In the horizontal and vertical operations, the stacker speed value is a constant;

(7) The stacker can only save or take a cargo unit at a time;

(8) The goods can be directly complete stock pick without putting into warehouse;

Automated stereoscopic warehouse has a total of A row of the shelf, each row has B column and C layer, one of the closest to the ground as the first layer, the nearest to entrance and exit as the first column, there is a stacker machine in each roadway, and a row of shelves on both sides of the roadway, a container (or pallet) on the shelf sides can be made accessing operation by a stacker.

In the process of optimization assigned on location selection , this article selects two optimizing principles that are “nearest picking” principle based on in-out warehouse frequency and “first in first out” principle based on turnover rate, this paper establishes the specific optimization objectives which are “minimizing the total operation time” and “the total storage time of chosen goods is maximum”, combining with the constraint: warehouse space limitation, the “multi-objective mathematical model of optimization assigned on location selection” is built.

The multi-objective optimization model is shown.

Coding problem, which is how to code the solution of problem becomes chromosome [1]. This article encodes the chromosome by adopting the binary coding method. Specifically, the chromosome gene site refers to the selected outbound goods, if a certain location was selected out of the warehouse, the corresponding gene value is 1, otherwise, the value is 0. The binary coding is a conclusive presentation, lacking specific description of the cargo information; therefore, it needs to use auxiliary string to describe the cargo information.

(1) Selection operator design

It is selected the operator selection in this paper by using “the roulette wheel selection method”, Assuming the population number is N, and the fitness function value of individual i is Fi, the corresponding selection probability is P_i:

Each round will produce a uniform random number between [0, 1] as a pointer to determine selected individual. The individual can be made the crossover operation after being selected.

(2) Crossover operator design

This paper chooses the way of “single point crossover”, namely selecting two individuals from the group to make interlace operation after selection operation and randomly generate a crossing point which the two individuals interchange parts genetic code, thus forming two new individuals.

(3) Mutation operator design

Mutation operation is to change the chromosome genevalue of each individual in the current group according to initial setting of the mutation probability [3] [4]. Based on the binary coding, this paper makes the gene value of chromosome code string to inverse operation and achieves the effect of variation, thus forming a new individual.

In advance, some parameters are set in the algorithm run, “the control parameters”. In this article, the control parameters of the model are: population size M, termination evolution algebra T, crossover probability Pc, and mutation probability P_m. Among them, the population size refers to the individuals number contained in the group, the range is from 20 to 100; the termination evolution algebra of genetic algorithm, the range is 100 - 500; crossover probability P_C, the range is from 0.4 to 0.99; mutation probability P_M, the range is from 0.0001 to 0.1.

The storage area of an automated warehouse of a pharmaceutical company in Daxing Beijing Economic and Technological Development Zone including normal temperature area, easy odor area, cold storage area, special medicine area and so on.

Two rows shelves area of the 1th roadway in normal temperature zone is selected as the analysis area, the region has 2*10*8 cargo locations.

The basic constant parameters of the handling equipment and shelves in the automated warehouse are as follow:

v₁ = 2 m/s, v₂ = 1 m/s, v₃ = 1 m/s.

A = 2, B = 10, C = 8, w = 1 m, l = 1.2 m.

The time how long it takes on putting in storage and other information about ten locations of drug 4 is seen in Table 1.

This article, firstly, solves assignment location model of one class cargo, gets the drugs chosen location assignment scheme and solves the rest class drugs waiting for out-warehouse by category, ultimately, acquiring picking operation list.

After running in the MATLAB software, the change curve of the objective function S can be derived, see Figure 1.

The curve change trend in the figure is showed that the objective function value is decreasing in the iteration process; the total operating time tends to be minimized, while the total storage time tends to be maximized. After 160 iterations, the fluctuation in the objective function value decreases and tends to be stable, and its value is S = 20.39. Therefore, the model is feasible.

After the end of the iteration, assignment result of the location selection is shown in Table 2.

It can be seen from the results of the table above, the selected operation location is located on the six cargo locations of column 6, 7, 8 in the first row and the second row.

From the above analysis, the assignment model of location selection can be solved by MATLAB software and obtain ideal location assignment strategy, meanwhile the model meets the requirements which the operation efficiency and turnover rate, so it has the feasibility.