CN-122022103-A - School site selection optimization method based on robustness self-adaptive differential evolution algorithm

CN122022103ACN 122022103 ACN122022103 ACN 122022103ACN-122022103-A

Abstract

The invention discloses a school address selection optimization method based on a robustness self-adaptive differential evolution algorithm, which comprises the following steps of constructing a school address selection optimization model, providing a dynamic parameter self-adaptive strategy, calculating a selection probability weight by recording the speed of updating an optimal solution by combining various groups of parameters, realizing cooperative self-adaptive adjustment of a variation factor and a cross probability, designing an acceptance strategy based on the average distance of a history successful individual, and obtaining the most robust school address selection scheme with the shortest total commute distance. The invention breaks through the limitation that the existing school site selection model can only be planned in a deterministic environment, and the self-adaptive parameter mechanism and the stagnation processing strategy considering the historical information effectively reduce the dependence of the algorithm on manual parameter adjustment, improve the automation degree and reliability of solving the complex reality problem, and provide a quantifiable site selection scheme for coping with the actual uncertainty such as population fluctuation.

Inventors

ZHANG QIONGBING
FANG JIAXIN
LIN YATING

Assignees

湖南科技大学

Dates

Publication Date: 20260512
Application Date: 20260413

Claims (10)

1. The school site selection optimization method based on the robustness self-adaptive differential evolution algorithm is characterized by comprising the following steps of: step 1, constructing a school site selection optimization model, and then adopting a budget uncertainty set to characterize the fluctuation of the number of students and the commute distance, and constructing a linearized robust model; Step 2, providing a dynamic parameter self-adaptive strategy, calculating a selection probability weight by recording the speed of updating the optimal solution of each group of parameter combinations, and realizing cooperative self-adaptive adjustment of a variation factor and a crossover probability; Step 3, designing an acceptance strategy based on the average distance of the individuals with history success, and in the selection stage, taking the average distance between the individuals with history success in updating the optimal solution as a reference to set probability to accept the suboptimal solution so as to overcome the premature convergence of the population; And 4, obtaining the most robust school address scheme with the shortest total commute distance.
2. The method for optimizing school address selection based on the robust adaptive differential evolution algorithm according to claim 1, wherein the specific process of step 1 is as follows: step 11, acquiring student position, student number, candidate school position and school capacity data, and establishing a school address optimization model with the aim of minimizing the total commute distance of all students under the condition that the school capacity and student allocation constraint are met; step 12, taking actual uncertainty of the number of students and the commute distance into consideration, introducing budget uncertainty set description parameter fluctuation, and establishing a robust optimization model on the basis; and step 13, converting the robust optimization model into a solvable linear programming model through a linear dual theory.
3. The method for optimizing school address based on robust adaptive differential evolution algorithm according to claim 2, wherein in step 11, the school address optimization model is: ; In the formula, Representing slave student positions Assigned to schools Is the number of students; representing a student location index; The number of the positions of students; Is the number of schools; Representing a school index; Representing slave student positions To school Is a commute distance of (2); For student position Reading school If the student positions School with student reading Then 1, Otherwise Is 0; To minimize the function.
4. A method of optimizing school addressing based on a robust adaptive differential evolution algorithm according to claim 3, wherein in step 12, the budget uncertainty set comprises a student number uncertainty set And a commute distance uncertainty set , , ; Deviation between the actual value and the nominal value of the number of students from the position of the students to the school; For student position To school Deviation between the actual value and the nominal value of the number of students; deviation between actual value and nominal value of distance from student position to school; For student position To school Deviation of the actual value from the nominal value; the upper limit of the total deviation of the number of students in the school reflects the conservation degree of uncertainty of the number of students in the school; The upper limit of the total deviation of the distance from the student position to the school reflects the conservation degree of the uncertainty of the distance from the student position to the school; on the basis, a robust optimization model is established: ; In the formula, Representing student position To school Fluctuation range of the number of students; representing the position of the student To school Is a fluctuation range of the distance of (2); To maximize the function.
5. The method for optimizing school address selection based on robust adaptive differential evolution algorithm according to claim 4, wherein in step 13, the linear programming model is: ; In the formula, Representation for precautions Marginal cost to pay for adverse fluctuations; representation for precautions Marginal cost to pay for adverse fluctuations; A dual variable representing uncertainty of a corresponding population; A dual variable representing the corresponding distance uncertainty.
6. The method for optimizing school address selection based on the robust adaptive differential evolution algorithm according to claim 5, wherein the specific process of step 2 is as follows: Step 21, constructing candidate parameter matrix ; Step 22, recording the performance of the parameter combination, and introducing the update speed as an evaluation index, ; Is the first Update speed of the individual parameter combinations; is the first The total iteration times required by the current optimal solution are updated by the individual parameter combinations; is the first The number of times the combination of parameters is selected; index for parameter combinations; step 23, converting the update speed into a selection probability, wherein the expression is: ; Wherein, the Is the first The selection probability of the individual parameter combinations; normalizing the weights of all the parameter combinations to obtain the first Actual probability of individual parameter combinations being selected The expression is: ; Wherein, the Index for parameter combinations; Is the total number of parameter combinations; step 24, when a certain parameter combination is not selected in the set time, judging that the parameter combination is a slowly updated parameter combination, and actively and randomly perturbing the slowly updated parameter combination; Step 25, combining the parameter fine adjustment of the algorithm execution stage, and selecting the first time when the fitness evaluation number NFE is half of the total number Variation factors in individual parameter combinations Temporarily shrink to 0.8 Performing fine local search, selecting when the fitness evaluation number NFE exceeds half of the total number, to avoid trapping in local optimum Temporary amplification of 1.1 。
7. The method for optimizing school address based on robust adaptive differential evolution algorithm according to claim 6, wherein in step 21, the candidate parameter matrix is The mathematical expression of (2) is: ; In the formula, Representing the total number of parameter combinations; represents the first Variation factors in the individual parameter combinations; represents the first Variation factors in the individual parameter combinations; represents the first Cross probabilities in the individual parameter combinations; represents the first Cross probabilities in the parameter combinations.
8. The method for optimizing school address based on robust adaptive differential evolution algorithm according to claim 7, wherein in step 22, the performance of the parameter combination is performed by And To be embodied in a method of manufacturing a semiconductor device, The set of times selected for each parameter combination, The set of total iterations required for the current optimal solution is updated for each parameter combination, , , Represent the first The number of times the combination of parameters is selected; Represent the first The number of times the combination of parameters is selected; Represent the first The total iteration times required by the current optimal solution are updated by the individual parameter combinations; Represent the first And the total iteration times required by the current optimal solution are updated by the parameter combinations.
9. The method for optimizing school address selection based on robust adaptive differential evolution algorithm according to claim 8, wherein in step 24, the formula of random perturbation is: ; In the formula, Represents the first Variation factors in the individual parameter combinations; represents the first Variation factors in the individual parameter combinations; represents the first Cross probabilities in the individual parameter combinations; representing the total number of parameter combinations; To pair(s) Results after active random disturbance are carried out; represents the first Cross probabilities in the individual parameter combinations; To pair(s) Results after active random disturbance are carried out; Is a random perturbation term.
10. The method for optimizing school address based on robust adaptive differential evolution algorithm according to claim 9, wherein in step 3, after each generation of iteration, it is checked whether the current global optimal solution is updated, if the objective function value of the continuous N generations of global optimal solutions is not improved, the algorithm is determined to enter a stagnated state, and then an acceptance probability is dynamically calculated according to the average value of the distances between the historic successfully updated individuals and the population center, so as to determine whether to accept a sub-optimal solution, and the accepted sub-optimal solution is substituted for the worse individuals in the current population, thereby increasing population diversity.

Description

School site selection optimization method based on robustness self-adaptive differential evolution algorithm Technical Field The invention relates to the technical field of urban planning, in particular to a school site selection optimization method based on a robust self-adaptive differential evolution algorithm. Background With the acceleration of the urban process, the school position determined by the traditional site selection problem often has static characteristics, and is only suitable for the existing environment because uncertainty factors in a real scene are not fully considered. For example, fluctuations in student entrance numbers due to population migration, and changes in commute distance due to road network modification, can significantly impact the efficiency of school layout. The traditional addressing problem is mainly aimed at determining the optimal school position and student allocation scheme under the given environment, and aims at shortening the commute distance of students to the maximum extent and balancing the school capacity. Therefore, developing an addressing model that can comprehensively consider environmental uncertainty has a vital practical significance. In recent years, research on uncertainty problems in different application scenes is increasing. For example, the layout planning of emergency facilities in the background of natural disasters such as earthquakes, floods, landslides and the like is focused on the influence of environmental changes on the site selection layout of medical facilities in the next years. Unfortunately, there is still a clear gap in current site selection studies that deal with practical uncertainty conditions. In particular, birth rate transitions and population migration pattern adjustments induced by the urbanization process make the number of students exhibit fluctuations over time that are difficult to predict accurately. Meanwhile, road transformation and traffic network updating in city planning can also cause the change of the actual learning distance of students. Therefore, in the school address and layout decisions, two uncertainty factors, namely the source number and the distance between the universities, must be considered simultaneously. However, the prior study is still lack of deep discussion on the aspect of school layout optimization under the double uncertainties of student quantity fluctuation and general school distance change, and the academic study in the field is still obviously blank. Disclosure of Invention In order to solve the technical problems, the invention provides the school address selection optimization method with simple algorithm and good robustness based on the robust self-adaptive differential evolution algorithm. The technical scheme for solving the technical problems is that the school address selection optimization method based on the robustness self-adaptive differential evolution algorithm comprises the following steps: step 1, constructing a school site selection optimization model, and then adopting a budget uncertainty set to characterize the fluctuation of the number of students and the commute distance, and constructing a linearized robust model; Step 2, providing a dynamic parameter self-adaptive strategy, calculating a selection probability weight by recording the speed of updating the optimal solution of each group of parameter combinations, and realizing cooperative self-adaptive adjustment of a variation factor and a crossover probability; Step 3, designing an acceptance strategy based on the average distance of the individuals with history success, and in the selection stage, taking the average distance between the individuals with history success in updating the optimal solution as a reference to set probability to accept the suboptimal solution so as to overcome the premature convergence of the population; And 4, obtaining the most robust school address scheme with the shortest total commute distance. The school site selection optimization method based on the robustness self-adaptive differential evolution algorithm, the specific process of the step 1 is as follows: step 11, acquiring student position, student number, candidate school position and school capacity data, and establishing a school address optimization model with the aim of minimizing the total commute distance of all students under the condition that the school capacity and student allocation constraint are met; step 12, taking actual uncertainty of the number of students and the commute distance into consideration, introducing budget uncertainty set description parameter fluctuation, and establishing a robust optimization model on the basis; and step 13, converting the robust optimization model into a solvable linear programming model through a linear dual theory. In the above method for optimizing school address selection based on robust adaptive differential evolution algorithm, in step 11, the school address selection op