Optimization models for shared bicycle parking lot layouts that take multiple constraints into account suffer from dimensionality problems because the number of equations (1) increases rapidly. (1) to (11). Therefore, in solving more nodes and larger models, a widely used heuristic algorithm, namely Genetic Algorithm (GA), is used to obtain a satisfactory solution faster.
Genetic algorithm is a randomized search method that imitates Darwin's idea of ”survival of the fittest” and is developed from the laws of evolution such as survival of the fittest and survival of the fittest in the biological world. This algorithm borrows several concepts from biological genetics (chromosomes, genes, populations, replication, hybridization, mutation, parents, offspring, adaptation, etc.) and simulates natural selection and biological inheritance processes. It is often used to solve largescale combinatorial optimization problems.
There is a contradictory relationship between the two objective functions of Model I. Equation (1) considers that the more parking points, the better, whereas Equation (1) believes that the more parking points, the better. (2) We believe that the less we have, the better. Solving this multiobjective optimization problem using a basic genetic algorithm raises the following problem:

1.
Multiobjective genetic algorithms have low local search ability, and when genetic inheritance continues for a certain number of generations, individuals are highly similar and no new individuals are created.

2.
The optimal solution may converge slowly, or even be difficult to reach the optimal solution region.

3.
Complex parameters slow down operation.
Therefore, this paper introduces a fused symmetric individual precision control mechanism to improve the design of encoding method, selection method and other operators of basic genetic algorithm.
solution space structure
When using genetic algorithms to solve optimization problems, the solution code for the problem is first defined as a natural array with specific design rules. In this paper, vectors from 0 to 1 are used to represent the parking lot layout scheme and initial chromosomes. \(chromium\) Designed.
$$ chrome = [x_{1} ,x_{2} , \cdots ,x_{i} , \cdots x_{n} ] $$
Where is each gene locus located? \(x_{i}\) In chromosomes, values are taken \(\{ 0,1\}\), indicates whether a stopping region is set at that alternate point. 1 is yes, 0 is no. In order to solve the problem that although it is possible to obtain similarities between individuals through repeated genetic algorithms, it is not possible to generate new individuals. Designed to randomly place special individuals. In this paper, we will refer to it as a “symmetrical individual.”Individuals between symmetrical individuals \(C\) and \(C^{ * }\) I'm satisfied \(x_{i} = 1 – x_{i}^{ * }\). The advantage of randomly generating “symmetrical individuals” is that it helps generate richer population diversity while continuously opening up space if genetic segments do not interbreed or mutate. A symmetric individual is defined when the variation between the mean and maximum fitness values of a modern population is controlled to within a certain precision, or when the variation between the maximum fitness values of two adjacent generations is controlled within a certain precision. Placed if within precision. Control accuracy can be either relative control accuracy or absolute control accuracy.
fitness features
For two objective functions in the model, this paper combines weighting methods to redetermine the value of the objective function.^{20}. On the other hand, the reality of roads in urban areas is that some roads are often cut off. A fitness function, that is, a penalty function, is introduced to represent such road conditions. The fitness of an individual is mainly determined by the value of the objective function. In this paper, when calculating chromosome fitness, we apply a penalty coefficient to some gene values that exceed the limit or cannot be realized. \(+ \infty\) and step function \(J(x)\) has been introduced and is defined as:
$$J(x) = \left\{ {\begin{array}{*{20}c} {1,\,} & {L_{{ij}} = + \infty \,i \ne j} \ \ {0,\,} & {else} \\ \end{array} } \right. {\text{ }}$$
(12)
Incorporating the penalty function into the objective function gives us
$$ F = M \cdot J(x) + \omega_{1} \cdot Z_{1} + \omega_{2} \cdot Z_{2} $$
(13)
genetic operator
option
In this paper, we adopt an “elite retention” selection strategy that requires optimal settings of parking points according to different initial schemes, directly inputting relatively superior individuals into offspring, and then randomly traversing the current population. Perform sampling. The number of offspring is the same as the number of parents.
Control accuracy \(\varepsilon_{1} ,\varepsilon_{2}\) and symmetry coefficient \(\lambda\) A symmetric individual of the input symmetric individual is introduced, and the symmetric individual is introduced after the amount of change between the average fitness value and the best fitness value of the individual in a certain generation, or the amount of change in the best fitness value of two adjacent generations reaches a certain value. Deploy. Constant control accuracy and \(2\left\lfloor {\lambda \times M} \right\rfloor\) Symmetrical individuals are randomly generated and placed. The symmetrically arranged individuals are considered to be seed individuals, and the individuals directly generated by roulette are considered to be nonseed individuals. When performing a crossover operation, the seed individual randomly selects an individual in the nonseed group to perform the operation, and the remaining nonseed individuals perform the pairwise operation.
crossover and mutation
The crossover operation in the genetic algorithm has been improved to enable area crossover operations as shown in Figure 2.At the same time, mutation operations have been improved to randomly select genetic loci within an individual to perform mutations, and the mutation method has been improved to change its value, i.e. \(x_{i} \leftarrow 1 – x_{i}\).
GA algorithm
The steps for the improved genetic algorithm to solve the model are:
step 1 Algorithm initialization: Set algebra counter and initial algebra. \(n \leftarrow 1\)set the maximum evolutionary algebra \(T\)when randomly generating a population, the symmetry coefficient is \(\lambda\)individual control accuracy of cast symmetry \(\varepsilon_{1} ,\varepsilon_{2}\)form the parent group.
Step 2 Individual evaluation: Calculate the objective function, or fitness, of the individual in the initial parent population.
Step 3 Selection operations: Apply selection operators to parent groups. The purpose of selection is to directly inherit optimized individuals to the next generation, or to generate new individuals by pair crossing and inherit them to the next generation. Selection operations are based on fitness assessments of individuals within the population.
Step 4 Symmetrical individual input: if the variation between the average and best fitness values of individuals in a generation is within accuracy \(\Valepsilon_{1}\)or the variation of the best fitness values of two adjacent generations is within the precision \(\Valepsilon_{2}\)generated using the roulette method. \(M – 2\left\lfloor {\lambda \times M} \right\rfloor – 1\) the number of new generation individuals in the group, and \(2\left\lfloor {\lambda \times M} \right\rfloor\) A symmetric number of individuals is randomly generated and expressed as: \(C_{1} ,C_{2} , \cdots ,C_{{2\left\lfloor {\lambda \times M} \right\rfloor }}\), added to next generation. At this time, the population consisting of symmetric individuals is called the seed subgroup, and the population consisting of other new generation individuals directly generated by roulette is called the nonseed population.
Step 5 Intersection Operator: Applies an intersection operator to a population. A central role in genetic algorithms is played by the crossover operator, which is used to generate offspring individuals. In step 4, a crossover operator is applied to the seeded individuals, one of the unseeded individuals is randomly selected to perform the operation, and the remaining unseeded individuals are paired.
Step 6 Mutation Operator: Applies a mutation operator to a population. It involves changing the genetic values of some loci of individual strings in a population to generate new offspring.population algebra \(P
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