A Cellular Automaton-Based Optimization Method for Scheduling Multiple Examinations in a Single Location for Outpatients

Abstract

This invention belongs to the field of medical service scheduling and relates to an optimization method for scheduling multiple examinations in a single location for outpatients based on cellular automata. The method includes: S1: acquiring patient information and data from each service station; S2: based on the patient information and service station data, using a cellular automata model to simulate the patient's behavior in choosing a service station, generating multiple initial scheduling schemes; S3: using an adaptive large neighborhood search algorithm to iteratively optimize the initial scheduling schemes and construct a Pareto front; S4: using an improved ideal point decision method to balance multiple optimization objectives and select the optimal scheduling scheme from the Pareto front. Through a simulation and optimization integrated framework, this method overcomes the limitations of traditional methods that rely on the passive assumption of patients and fixed examination sequences, effectively shortening patient waiting time, alleviating service station congestion, and improving overall medical scheduling efficiency.

Description

Technical Field

[0001] This invention relates to the field of medical service scheduling technology, and specifically discloses a method for optimizing the scheduling of multiple examinations for outpatients in a single location based on cellular automata. Background Technology

[0002] With the continuous increase in outpatient visits nationwide, large tertiary hospitals face enormous resource allocation pressure during peak outpatient periods. Outpatients typically need to complete multiple examinations, such as blood tests, electrocardiograms, and CT scans, requiring them to visit multiple service counters in succession. This constitutes a typical scheduling problem of "multiple patients, multiple examinations, and multiple service counters." Furthermore, when choosing the order of examinations, patients weigh multiple objectives such as minimizing travel distance, shortening waiting time, and avoiding crowded service counters, further increasing the complexity of the problem and evolving it into a "four-multiple" scheduling problem.

[0003] Current research on scheduling multiple outpatient examinations suffers from three main shortcomings: First, most studies treat patients as passive service recipients, rarely analyzing individual patient decisions based on preferences such as distance, waiting time, and queue length. Furthermore, fixed-weight methods are commonly used when solving multi-objective problems, leading to strong subjectivity and failing to reflect patients' real and dynamically changing preferences. Second, most existing studies assume a fixed or pre-set examination order, failing to fully consider the independence and adjustability of the examinations, thus missing a significant opportunity to optimize scheduling efficiency by adjusting the examination order. Third, these studies typically rely on single simulation or optimization methods, lacking an integrated framework that coordinates simulation and optimization algorithms, making it difficult to fully capture the dynamics and complexity of the multiple examination scheduling process.

[0004] In view of this, the present invention provides an optimization method for scheduling multiple examinations in a single location for outpatients based on cellular automata. Through a framework that integrates simulation and optimization, it breaks through the limitations of the passive assumption of patients and the fixed order of examinations in traditional methods, effectively shortens the waiting time of patients, alleviates congestion at the service desk, and improves the overall efficiency of medical scheduling. Summary of the Invention

[0005] The purpose of this invention is to provide a method for optimizing the scheduling of multiple examinations for outpatients in a single location based on cellular automata, addressing the technical problem of simulating dynamic patient behavior and performing multi-objective optimization of the scheduling scheme. The specific solution is as follows: A method for optimizing the scheduling of multiple outpatient examinations in a single location based on cellular automata includes: S1: acquiring patient information and service station data; the patient information includes patient number, examination item combination, and arrival time; the service station data includes service station number, examination function type, location, service rate, and maximum queue size; S2: based on the patient information and service station data, using a cellular automata model to simulate the patient's behavior in service station selection, generating multiple initial scheduling schemes; S3: using an adaptive large neighborhood search algorithm to iteratively optimize the initial scheduling schemes, constructing a Pareto front; S4: using an improved ideal point decision method to balance multiple optimization objectives, selecting the optimal scheduling scheme from the Pareto front; the optimal scheduling scheme includes the order of examination items for each patient and the corresponding service station number.

[0006] Further, S2 includes: treating a single patient as the central cell and the service desk composite cell group as neighboring cells; the service desk composite cell group includes a service desk cell and multiple patient cells currently in the queue; defining the types and states of patient cells and service desk cells; the types of patient cells are classified according to the patient's examination needs, and the states include not yet arriving at the service desk, waiting in the queue, undergoing examination at the service desk, and leaving the service desk after examination; the types of service desk cells are classified according to the service desk's examination functions, and the states include working state and idle state; and calculating the transition probability formula. Calculate the transition probability from the patient cell to each service station cell; the transition probability formula includes a static field part, a dynamic field part, and a local density field part; the patient randomly selects a service station from the candidate service stations and enters the queue of the selected service station to wait for examination; the candidate service stations are selected from the preset proportion of service stations after sorting the transition probabilities from high to low; update the number of people in the queue and the expected waiting time of each service station, and repeat the process of the patient selecting a service station until all patients complete all examination items to obtain an initial scheduling scheme; repeat the process of generating the initial scheduling scheme to obtain multiple initial scheduling schemes.

[0007] Furthermore, the transition probability formula is as follows: ; in, Let N be the probability of patient cell i being transferred to service desk cell j; N is the coefficient to ensure probability normalization; exp is the exponential function. , and These are respectively the static field, the dynamic field, and the local density field; , and These are the static field coefficients, dynamic field coefficients, and local density field coefficients, respectively. This indicates whether patient cell i can enter the queue of service desk cell j. The value is 0 if it can enter and 1 if it cannot enter. This indicates whether the examination request of patient cell i matches that of service desk cell j. The value is 1 when they match and 0 when they do not match.

[0008] Furthermore, the static field is: ; in, The maximum distance patient i can travel to all available service counters; The distance traveled; ; in, The distance traveled; The horizontal distance from patient i to the elevator; The horizontal distance from the elevator to the service desk is j. Let θ be the floor height difference between patient i and service desk j; θ is the conversion factor for converting the time cost of waiting for the elevator into an equivalent distance.

[0009] Furthermore, the dynamic field is: ; in, Select the estimated wait time for service desk j for patient i; The longest wait time for patient i across all available service desks; Furthermore, the local density field is: ; in, The number of people currently waiting in line at the service desk; This represents the maximum number of people in the queue among all the service counters available to patient i.

[0010] Furthermore, S3 includes: using multiple initial scheduling schemes generated by the cellular automata model as an initial solution set; selecting destruction and repair operators using roulette wheel selection to perform destruction and repair operations on the current solution to generate a new solution; comparing the multi-objective performance of the new solution with that of the current solution using an improved ideal point decision method; if the new solution is better than the current solution, accepting the new solution and updating it; otherwise, determining whether to accept the new solution based on a threshold acceptance criterion; and constructing a Pareto front based on the updated solution.

[0011] Furthermore, the destruction operators include a random destruction operator and a maximum contribution destruction operator; the repair operators include a random repair operator and a greedy repair operator; after each iteration, the weights of each operator are recalculated and their selection probabilities are updated.

[0012] Furthermore, the formula for updating the weights is: ; in, and , respectively, are the weights of operator r in the k-th and k+1-th iterations; β is the update coefficient of the operator weights; Let r be the score of operator r in the kth iteration; Let r be the number of times the operator r is used in the k-th iteration.

[0013] Further, step S4 includes: normalizing the objective function values ​​of the Pareto solutions in the Pareto front according to the optimization objectives; the optimization objectives include minimizing the average patient movement distance, minimizing the average patient waiting time, and achieving workload balancing between service stations; calculating the weighted Euclidean distance squared from each Pareto solution to the ideal point; constructing an optimal weight model based on the objective distribution characteristics of the Pareto solution set, and solving for the optimal weight coefficients of each objective; selecting the Pareto solution with the smallest weighted Euclidean distance as the optimal solution, and using the scheduling scheme corresponding to the optimal solution as the optimal scheduling scheme.

[0014] The present invention has the following advantages and beneficial effects: This invention introduces the cellular automata model into the patient scheduling scenario. By analyzing patients' movement characteristics, path selection preferences, and queuing behavior within the hospital, it demonstrates the adaptability of the cellular automata model in characterizing patients' autonomous decision-making behavior, providing a theoretical basis and implementation method for realistically recreating outpatient scheduling scenarios and constructing behavior-driven scheduling models.

[0015] This invention, based on a cellular automata model, breaks through the traditional assumption of "patients passively receiving services" in scheduling research, and constructs a dynamic scheduling model that considers multiple dimensions of patient preferences, such as travel distance, waiting time, and queue size. This model no longer treats patients as passive service recipients, but instead simulates their autonomous choice behavior among different examination items through the evolutionary rules of cellular automata. This makes the scheduling scheme closer to real outpatient scenarios, effectively improving the feasibility and patient acceptance of the scheme.

[0016] This invention proposes an integrated framework combining simulation and optimization. It utilizes a cellular automata model to simulate patients' dynamic selection behavior, recreating a realistic outpatient scheduling scenario. Simultaneously, it employs an Adaptive Large Neighborhood Search (ALNS) algorithm to solve for the optimal scheduling scheme, achieving multi-objective optimization of patient waiting time, travel distance, and service desk load balancing. This framework overcomes the shortcomings of single simulation methods (lacking optimization capabilities) and single optimization methods (difficult to simulate real patient behavior), significantly improving the overall performance of the scheduling scheme. Attached Figure Description

[0017] Figure 1A schematic diagram illustrating the transformation of the patient selection service desk process into a cellular automata simulation provided by the present invention; Figure 2 A schematic diagram illustrating the coding scheme for a single patient scheduling method provided by the present invention; Figure 3 An exemplary flowchart for obtaining the initial scheduling scheme through simulation; Figure 4 An exemplary flowchart for obtaining the optimal scheduling scheme through algorithmic solution; Figure 5 The Pareto solution when the number of reservations is 100; Figure 6 The Pareto solution when the number of reservations is 140; Figure 7 The Pareto solution is for a reservation with 180 people. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0019] This invention constructs a single-site multi-examination scheduling optimization method for outpatients based on cellular automata, for scheduling multiple examination items: First, the behavior of patients in choosing a service desk is simulated using a cellular automata (CA) model to generate multiple initial scheduling schemes; then, the above schemes are iteratively optimized using an adaptive large neighborhood search (ALNS) algorithm; finally, an improved ideal point decision method is used to balance multiple optimization objectives to obtain the scheduling scheme with the best overall performance.

[0020] This invention focuses on outpatients who have already made appointments and have clearly defined examination items. These patients have typically completed a preliminary diagnosis and health assessment by a doctor and can proceed directly to a multi-stage examination process. Patients need to complete several examinations, such as blood tests and electrocardiograms. The required combination of examination items varies among patients, and each type of examination usually has multiple service counters available. Furthermore, the order in which these examinations are selected is relatively flexible, allowing patients to choose the most suitable order based on the queue status at the service counters.

[0021] Patient behavior in choosing the service desk can be simulated using a cellular automata model, such as... Figure 1As shown. Patients can obtain real-time information such as the location of service counters, queue length, and estimated waiting time through the hospital information system. In the absence of strict examination order constraints, patients can dynamically determine the order in which their examinations will be completed based on the current queue status of each service counter, such as... Figure 1 As shown. For ease of demonstration, this invention places all inspection items on the same floor, but in reality, these inspection items are usually distributed across different floors.

[0022] Unlike traditional cellular automata models that focus on the transition probability design of spatial movement, the core of the transition probability proposed in this invention lies in abstractly simulating the process of a patient choosing a service station, rather than simulating the patient's spatial location movement. This invention treats a single patient as the central cell and the server composite cell group (SCCG) as neighboring cells. The SCCG consists of a main service station cell and multiple sub-patient cells currently in the queue, with different colors representing different examination items. This invention allows multiple patient cells to enter the SCCG, but the number cannot exceed the queue limit. The SCCG is arranged around the patient cells to more clearly demonstrate the patient's selection process, rather than their actual spatial distribution. Based on the neighborhood interaction characteristics of the cellular automata model, the patient cell perceives the real-time status of the surrounding SCCG, selects a relatively free service station, and enters its queue to wait for examination; after the examination, the patient cell leaves the SCCG.

[0023] Patient cells are categorized based on their examination needs, specifically the type and number of examinations each patient requires. Patient cell states are divided into four categories: not yet at the service counter, waiting in the queue, undergoing examination at the service counter, and leaving the service counter after examination. Service counter cells are categorized based on their examination functions, such as blood collection, electrocardiogram, and CT scan. Service counter cell states are divided into two categories: active and idle. Interactions between patient and service counter cells are subject to type-matching constraints; interaction only occurs when the service counter's examination function matches the patient's examination needs. This type-matching constraint ensures the feasibility of the simulation and realistically simulates the patient's decision-making process when choosing a service counter. To avoid violating the unified transition rules of cellular automata, the above type-matching constraint will be incorporated into the subsequent transition probability formula design to ensure that interactions between patient and service counter cells still follow the unified transition rules.

[0024] The patient's arrival process was independent and smooth, following a Poisson distribution. ; in, Let λ be the probability of n patients arriving within time t; e is an exponential function; λ is the average arrival rate, i.e., the number of patients arriving at the service desk per unit time; t is a time variable; and n is the number of patients.

[0025] Each service desk can only serve one patient at a time and cannot serve multiple patients simultaneously; once the examination begins, the patient must complete the entire examination process without interruption. The service duration s of each service desk follows an exponential distribution: ; Where μ is the service rate, i.e. the number of patients that can be served per minute, 1 / μ is the average service duration, and s is the service duration.

[0026] The transition probability formula of this invention comprises three key parts: a static floor field (SFF), a dynamic floor field (DFF), and a local density floor field (LFF). The static floor field represents the influence of the distance between service counters on patient selection behavior; the dynamic floor field represents the influence of real-time changes in the expected waiting time at each service counter on patient selection behavior; and the local density field represents the congestion level of the service counter queues. The transition probability formula is as follows: ; Where N is the coefficient that ensures probability normalization. ; , and These represent the static field, the dynamic field, and the local density field, respectively. , and These are the scaling factors for the aforementioned fields; This indicates whether patient cell i can enter the queue of service desk cell j. The value is 0 if it can enter and 1 if it cannot enter. This indicates whether the examination request of patient cell i matches that of service desk cell j. The value is 1 when they match and 0 when they do not match.

[0027] This indicates the attractiveness of the service desk to patients based on distance, with a value ranging from 0 to 1: ; in, The distance from patient i to service desk j, in meters; This represents the maximum distance, in meters, from patient i to all available service counters. The farther the service counter is, the less likely the patient is to choose that counter.

[0028] When service counters are located on different floors, patients need to use elevators to move between floors. The distance between service counters on different floors cannot be simply measured by horizontal distance; the waiting time cost incurred by patients taking the elevator must also be considered. Therefore, this invention uses the equivalent distance method to characterize the cost of cross-floor movement. When patient i and service counter j are on the same floor, the movement distance is measured by horizontal distance. This means that when the two floors are not on the same floor, the patient must first walk to elevator e, then take the elevator to the target floor, and finally walk to the service desk j. The total distance consists of three parts: the horizontal distance from the patient to the elevator. Horizontal distance from elevator to service desk and equivalent distance The unit is meters. The distance from patient i to service desk j is: ; in, Let θ be the floor height difference between patient i and service desk j; θ is the conversion factor for converting the waiting time cost of the elevator into an equivalent distance based on the floor height difference.

[0029] This indicates the attractiveness of the service desk to patients based on the estimated wait time, with a value ranging from 0 to 1: ; in, This indicates the estimated wait time for patient i at service desk j, in minutes. This represents the longest expected wait time for patient i across all available service counters, in minutes. The longer the expected wait time at a service counter, the less likely the patient is to choose that service counter.

[0030] Reflects the congestion level of the service counter queue, with a value ranging from 0 to 1: ; in, This indicates the number of people currently waiting in line at service desk j. This represents the maximum number of people in the queue among all the service counters available to patient i. The longer the queue at a service counter, the lower the probability that the patient will choose that service counter.

[0031] This indicates whether a patient cell can enter the service desk cell queue: ; in, This is the maximum number of people that the service counter queue can accommodate.

[0032] This indicates whether the examination needs of patient cell i match those of service desk cell j: .

[0033] During simulation, if the patient consistently chooses the service station with the highest transfer probability, the inherent randomness of the patient's actual choice behavior cannot be reflected. Furthermore, multiple simulations tend to generate highly similar scheduling schemes, which is detrimental to subsequent optimization. Therefore, this invention sets the scenario where the patient randomly selects one of the top a% of candidate service stations ranked by transfer probability. This strategy preserves the patient's preference for high-probability service stations while introducing necessary random perturbations, thereby generating differentiated scheduling schemes that not only reflect the patient's actual choice behavior but also provide diverse initial solutions for subsequent optimization. This invention uses a cellular automata model for generation. Scheduling schemes for multiple patients and multiple examination items, the coding method for a single patient scheduling scheme is as follows: Figure 2 As shown, M represents the total number of examination items. For example, if a patient's examination item number sequence is (1, 3, 2, 4) and the corresponding service desk number is (2, 6, 4, 8), then the patient's scheduling scheme can be encoded as (1, 2, 3, 6, 2, 4, 4, 8). If the number of examination items required by the patient is less than the total number M, the remaining positions in the patient's code are padded with 0s.

[0034] The constraints for simulation modeling are constructed to ensure the feasibility of scheduling multiple examinations, including constraints on examination time relationships, service time, examination items, patient arrival, examination service desk, number of people in queue, movement distance, and waiting time.

[0035] The examination time relationship describes the time relationship between patient i's arrival at and departure from service desk j: ; in, and These represent the time when patient i enters the queue at service counter j and the time when patient i leaves the service counter. Let I be the duration of the examination of patient i at service desk j, in minutes. Let I and J be the patient set and the service desk set, respectively.

[0036] The service time constraint means that the actual start time of service at desk j must not be earlier than the actual arrival time of patient i. ; in, The actual start time of service from service desk j to patient i.

[0037] The examination item constraint is the number of examination items for patient i: ; in, Let M be the number of examinations for patient i, and M be the total number of examinations.

[0038] Patient arrival constraint means that each patient must arrive at the service desk in turn: ; in, and These represent the times when patient i and patient i+1 entered the service desk queue, respectively.

[0039] The check-in desk restrictions ensure that patients can only select one check-in desk for each examination: ; Where K is the set of inspection items. To check the service desk set corresponding to item k.

[0040] Queue size constraint for service counter j: , ; in, The number of people currently queuing at the service desk. Let j be the maximum number of people queuing at service counter j.

[0041] The movement distance constraint indicates that the total movement distance of patient i consists of three parts: ; The three parts include the distance from the entrance to the first selected service desk. The sum of the distances between adjacent service counters And the distance from the last selected service counter to the exit. .

[0042] Suppose patient i needs to complete The corresponding service desk access sequence for each inspection item is recorded as follows: ; in, Select the first option for patient i The service desk number corresponding to each inspection item.

[0043] The waiting time constraint represents the total waiting time for patient i: ; The total waiting time is the sum of the waiting times of the patient at all service counters. The total waiting time for patient i.

[0044] Simulation process as follows Figure 3As shown, this invention models the patient's service station selection process as an asynchronous update system that integrates time-driven and step-driven update methods. The patient's arrival time follows an independent and random Poisson distribution, reflecting the time-driven update characteristics; during the queuing process, whether a patient can receive an examination depends on whether the patient ahead of them has already completed their examination, conforming to the step-driven update characteristics; the examination duration at each service station follows an exponential distribution, conforming to the time-driven update characteristics; finally, the patient completes the examination and leaves the queue, transitioning from the "accepting examination state" to the "examination completed state," conforming to the step-driven update characteristics. Therefore, the patient selection behavior process model constructed in this invention based on a cellular automata model is an asynchronous update system that integrates time-driven and step-driven update methods.

[0045] This invention constructs a multi-objective optimization model aimed at improving patient examination experience and medical system operational efficiency. The optimization objectives include: minimizing the average patient movement distance, minimizing the average patient waiting time, and achieving workload balancing between service counters. ; ; ; The workload balancing of the service desk is measured by the maximum difference in the number of people queuing for different inspection items at the same time. Here, min represents the minimum value. The average distance the patient traveled. denoted as the total distance traveled by patient i, in meters; Num represents the total number of patients. The average waiting time for patients. The total waiting time for patient i, in minutes; This represents the maximum difference in the number of people queuing for different inspection items at the same time. , Let be the number of people queuing for examination items k1 and k2 at time t, where t and k are the time index and examination item index, respectively; T is the total time step during the simulation, and M is the total number of examination items. The three optimization objectives mentioned above collectively represent the operational state of the medical system from the dimensions of spatial efficiency, time efficiency, and resource utilization efficiency. Furthermore, these objectives are inherently consistent with the patient behavior mechanism described in the cellular automata model: minimizing the average patient movement distance, minimizing the average patient waiting time, and achieving service desk load balancing correspond to the static field, dynamic field, and local density field in the transition probability formula, respectively, reflecting the patient's preferences during the service desk selection process. By introducing an objective function that matches the simulated behavior mechanism, the optimization model proposed in this invention improves system performance while ensuring that the optimization results are consistent with the patient's actual decision-making logic, thus constructing a collaborative simulation-driven optimization framework. The constraints in the optimization model are consistent with those in the cellular automata model, and no additional constraints are introduced during the optimization process.

[0046] The solution process of the ALNS algorithm is as follows: Figure 4 As shown, this invention uses a cellular automata model to generate... An initial scheduling scheme is used as the initial solution set, with relevant parameters including the algorithm iteration count (Iter), the decay coefficient η of the TA criterion, and the update coefficient β of the operator weights. This invention generates new solutions by disrupting and repairing operators, and determines whether the new solution is superior to the current solution. If superior, the new solution is accepted and the corresponding scheduling scheme is updated; otherwise, the TA criterion is used to determine whether to accept it. If the criterion is not met, the new solution is rejected. After processing all scheduling schemes in the current population, a Pareto front is constructed based on the updated solutions. Subsequently, an improved ideal point decision method is used to assign reasonable weights to multiple objectives, and the optimal compromise solution is selected from the Pareto front. The above steps are repeated until the preset number of iterations is reached, outputting the optimal solution and its corresponding scheduling scheme.

[0047] Based on practical considerations, this invention designs two destruction operators: the RandomDestruction Operator (RaD) and the Best Wasted Distance Destruction Operator (BWD). The RandomDestruction Operator randomly removes a specified number of service stations from the scheduling options for several patients and temporarily stores them in the deletion set. The Best Wasted Distance Destruction Operator removes the service station with the longest distance or the longest waiting time from the scheduling options for several patients and temporarily stores them in the deletion set. This invention also designs two repair operators: the Random Repair Operator (RaR) and the Greedy Repair Operator (GrR). The Random Repair Operator randomly assigns a service station to the patients whose service stations were removed; the Greedy Repair Operator assigns the service station with the shortest distance or the shortest waiting time to these patients. This optimization algorithm only adjusts the service station selection corresponding to each examination item and does not directly change the order of the patients' examination items. However, due to the dynamic coupling of patients' choices of multiple service counters, changes in the service counter selection of some patients will affect the queue length and waiting time of the service counter, and thus affect the order of subsequent patients' examinations. In fact, the algorithm adjusts the order of patients' examinations and the corresponding service counter selection.

[0048] Operator selection strategy: After each iteration, the weights of each operator need to be recalculated, and their selection probabilities updated accordingly. During each iteration, a roulette wheel selection method is used to choose between the destructive and repair operators. Let the weight of operator r in the k-th iteration be... Then the probability of selecting operator r in the k-th iteration for: ; Where R is the set of all operators r.

[0049] The operator weights are affected by their usage in the previous iteration. Let the score and usage count of operator r in the k-th iteration be respectively... and Then the weight of operator r in the (k+1)th iteration is: ; Where β is the update coefficient for the operator weights. In the first iteration, each operator has an equal probability of being selected, and the initial score is... Set to 0. If a new global optimal solution is obtained after a certain destruction-repair operation, both operators used will be awarded 40 points; if the obtained solution is better than the current solution but is not the global optimal solution, 20 points will be awarded; otherwise, no points will be awarded.

[0050] Acceptance criterion for solutions: The present invention adopts a threshold acceptance criterion. The multi-objective performance of the new solution and the current solution is compared by an improved ideal point decision-making method. After normalizing the objective values, the adaptive weights are determined according to the objective distribution of the current Pareto solution set, and the weighted Euclidean distances f(new) and f(old) from the new solution and the current solution to the ideal point are calculated respectively. If f(new) < f(old), the new solution is accepted; otherwise, f(new) - f(old) is compared with the preset threshold T. If f(new) - f(old) < T, the new solution is accepted; otherwise, it is rejected. The initial threshold is the absolute value difference between the new solution and the current solution in the first iteration: = 0.2|f(new) - f(old)|. Subsequently, the threshold T gradually decreases according to the attenuation coefficient η, that is , where k is the number of iterations.

[0051] When solving multi-objective problems, the traditional ideal point decision-making method often requires artificial setting of weights, which is easily affected by subjective preferences, resulting in the compromise solution tending to a specific objective. To address this problem, the present invention adopts an improved ideal point decision-making method. This method obtains the optimal weights according to the objective distribution characteristics of the Pareto solution set, calculates the weighted distances between each Pareto solution after normalization and the ideal point, so as to obtain the optimal compromise solution that takes into account multiple objectives. This method believes that the weight value should be determined by the objective distribution characteristics of the Pareto solution set: specifically, the more dispersed the normalized value of a certain objective is, the more difficult it is to optimize this objective, but its optimization effect in multi-objective optimization is also more significant, so a higher weight should be given.

[0052] Normalize the objective function values of the Pareto solutions: ; where is the normalized value of the h-th objective function, is the m-th Pareto solution, and are the maximum and minimum values of the h-th objective function among all Pareto solutions respectively.

[0053] The ideal point of the normalized Pareto front is (0, 0, 0), and the square of the Euclidean distance from each Pareto solution to the ideal point can be calculated: ; where is the square of the Euclidean distance from the m-th Pareto solution to the ideal point, is the weight coefficient of the h-th objective, and H is the set of all optimization objectives.

[0054] To assign more reasonable weight coefficients to each objective, an optimal weight model can be constructed. By constructing a Lagrangian function, the optimal combination of weight coefficients can be obtained: ; ; Where Z is the objective function value, representing the sum of the squared weighted Euclidean distances from all non-dominated solutions to the ideal point; Let be the number of nondominated solutions on the Pareto front.

[0055] Therefore, the optimal solution is determined as follows: ; in, This is the optimal compromise solution.

[0056] Example 1 This invention selects four commonly used examination items in hospitals: blood sampling (BC), electrocardiogram (ECG), computed tomography (CT), and ultrasound (US). The study subjects are outpatients who have already made appointments and whose examinations are clearly defined. These patients do not need to undergo further diagnostic procedures and can directly proceed to multiple examination stages. Relevant parameters for each examination item (including the number of available service counters and average examination time) are shown in Table 1. Blood sampling, ECG, CT, and ultrasound are all located within the outpatient building, with CT on the 1st floor and the other three examinations on the 3rd floor. The outpatient building has a floor height of 4.2m, and its structure is similar to that of existing literature cases; therefore, a conversion factor θ=4 is used to convert the height difference between floors into equivalent travel distances. The distance matrix between each examination item and the entrance / exit is calculated using the formula for travel distance, and the results are shown in Table 2.

[0057] Table 1: Number of available service counters and average inspection time

[0058] Table 2: Distance matrix (meters) between each inspection item and the entrance / exit

[0059] This invention collected appointment data for the aforementioned examination items at the hospital from August 2021 to May 2022. Daily patient appointments ranged from 70 to 180, with peak appointments concentrated between 130 and 150. Therefore, this invention selected three typical appointment volumes of 100, 140, and 180, representing low, medium, and high workload scenarios, respectively. The number of appointments for different examination items is shown in Table 3. Each patient needs to complete at least one examination, with over 40% of patients requiring four. Since blood tests require fasting, the vast majority of patients are scheduled for examinations in the morning, with only a small number scheduled for the afternoon. Therefore, this invention only considers the morning examination scenario. The service desk's morning operating hours are from 7:00 AM to 12:00 PM. To avoid overtime work due to patient lateness, all patients must arrive at the hospital before 11:00 AM. When outpatient demand is high, the service desk may extend its operating hours as needed to complete examinations for patients already in the queue. This invention does not consider emergency cases or patient no-shows, assumes all patients have the same priority, and completes examinations according to the first-come, first-served (FCFS) principle. Furthermore, it assumes there are no strict sequential constraints between the aforementioned examination items.

[0060] Table 3: Number of appointments for each inspection item

[0061] The parameter settings are shown in Table 4. To ensure that all patients arrive at the hospital before 11:00 AM under different appointment numbers, the average arrival rate λ is set to 0.42, 0.58, and 0.75, respectively. Since the average examination times for the four tests are 2, 5, 5, and 10 minutes, the corresponding service rates μ are set to 0.5, 0.2, 0.2, and 0.1, respectively. Maximum queue size. Set to 30. To avoid manually setting patient preferences for travel distance, waiting time, and queue length, the scaling factors for the static field, dynamic field, and local density field are all set to 0.33. The number of initial scheduling schemes generated by the cellular automata model. The threshold α% for candidate service stations is set to 50%. The number of algorithm iterations (Iter) is 500, the decay coefficient η of the TA criterion is 0.9, and the operator weight update coefficient β is 0.4.

[0062] Table 4: Parameter Settings

[0063] Common patient selection strategies during service counter selection include random selection, selection of the service counter with the shortest average examination time, selection of the nearest service counter, selection of the service counter with the fewest queues, and selection of the service counter with the shortest expected waiting time. Among these strategies, the strategy based on selecting the service counter with the shortest expected waiting time is a relatively efficient and representative decision-making method, especially suitable for scenarios where the average examination time varies greatly for different examination items. Therefore, it is used as the benchmark strategy in this invention. To evaluate the optimization performance of the proposed CA-ALNS method in multi-examination scheduling, two representative patient selection strategies are selected as comparison benchmarks. The first strategy is to prioritize selecting the service counter with the shortest expected waiting time (ST), representing a decision-making method based on a single evaluation criterion. The second strategy is a simulation strategy (CA) based on a cellular automata model. This strategy comprehensively considers travel distance, waiting time, and queue length, and can characterize the dynamic selection behavior of patients in multi-examination scenarios. To ensure fairness in the comparison, the arrival time and examination time of patients are kept consistent under all three strategies, with differences only in the order of the patient's examination items and the selection of the corresponding service counter.

[0064] The performance of the ST, CA, and CA-ALNS strategies was compared when the number of appointments was 100, 140, and 180, and the results under different appointment numbers and selection strategies are shown in Table 5. Under different appointment numbers, the ST strategy performed the worst in terms of average patient movement distance, average waiting time, and the difference in maximum queue size between different examination items. Compared with the ST strategy, the CA strategy effectively reduced the average patient movement distance by approximately 26.32 to 54.84 meters, and the difference in average patient waiting time and maximum queue size also decreased. This is because the CA strategy comprehensively considers factors such as movement distance and queue length when patients choose a service station, which reduces ineffective patient movement within the hospital and promotes load balancing among service stations, thereby improving overall resource utilization efficiency and indirectly shortening patient waiting time. The results show that a single-criteria-driven service station selection strategy (such as considering only the estimated waiting time) cannot simultaneously address both patient experience (increased movement distance) and service station load balancing, while a multi-factor collaborative selection strategy is more conducive to improving the overall performance of the healthcare system.

[0065] The experiment examined the distribution of patient movement distance and waiting time under different appointment numbers and chosen strategies. The ST strategy resulted in longer movement distances and greater fluctuations. Both the CA and CA-ALNS strategies significantly shortened patient movement distances, with similar effects. Regarding patient waiting time distribution, compared to the ST and CA strategies, the CA-ALNS strategy effectively reduced patient waiting time and decreased the fluctuations in waiting time distribution, indicating stronger stability.

[0066] Table 5: Comparison of Results under Different Number of Reservations and Selection Strategies

[0067] Table 6 compares the peak queue size and waiting time for each examination under different appointment numbers and selection strategies. Ultrasound examination, with the longest average examination time (10 minutes), is the main factor affecting the peak queue size and waiting time. Compared to the ST and CA strategies, the CA-ALNS strategy effectively reduces the peak queue size and speeds up the queuing process under different appointment numbers, reducing the peak queue size by approximately 3-7 people and shortening the queuing time by 25.40-39.19 minutes. This is because the CA-ALNS strategy can adjust the order of patient examinations, allocating some patients originally scheduled for ultrasound examinations to other examinations, thereby avoiding congestion for those examinations and improving queuing efficiency.

[0068] Table 6: Comparison of peak queue size and queuing duration under different reservation numbers and selection strategies

[0069] Table 7 shows the usage frequency of the destruction and repair operators. The frequency of operator usage reflects their performance in the neighborhood search process. The high usage rate of the destruction operator BWD indicates that the CA-ALNS method tends to rely more on strategic local search during optimization and less on random strategies to explore new solution spaces. The usage frequency of the repair operators RaR and GrR is not significantly different, which shows that the CA-ALNS method effectively avoids the risk of getting trapped in local optima by combining greedy strategies (to improve solution quality) and random strategies (to enrich search diversity), thereby achieving a more comprehensive search. This helps the algorithm better adapt to the optimization needs at different stages and ultimately improve the quality of solutions.

[0070] Table 7: Comparison of usage frequency of destruction and repair operators under different number of reservations

[0071] like Figure 5 , Figure 6 and Figure 7The distribution of Pareto solutions under different number of reservations is shown. In scenarios with 100, 140, and 180 reservations, 11, 14, and 14 Pareto solutions were obtained, respectively, with corresponding multi-objective weights of (0.35, 0.41, 0.24), (0.31, 0.35, 0.34), and (0.27, 0.39, 0.34). As the number of reservations increases, the Pareto solutions become more dispersed in the objective space, indicating that the conflict between different optimization objectives becomes more pronounced under medium-to-high load scenarios, further expanding the feasible space of scheduling schemes. Simultaneously, the multi-objective weights also change with the number of reservations; as the number of reservations increases, the weight of objectives related to server load balancing gradually increases, demonstrating the increasing importance of addressing server load imbalance in scheduling decisions.

[0072] The selection of the compromise solution has a significant impact on the final scheduling scheme. Traditional ideal point decision-making methods typically determine the compromise solution by manually assigning fixed weights to each optimization objective. In this invention, the traditional compromise solution is obtained by assigning equal weights (0.33, 0.33, 0.33) to the three objectives. In contrast, the improved ideal point decision-making method adaptively determines the objective weights by analyzing the distribution characteristics of the Pareto solution set. Table 8 compares the performance of the traditional and improved compromise solutions on the three objectives, where Scheme 1 represents the traditional compromise solution and Scheme 2 represents the improved compromise solution. When the number of reservations is 100, compared to the traditional compromise solution, the improved compromise solution increases the average movement distance by only 2.66%, while reducing the average waiting time by 14.88%. When the number of reservations increases to 140 and 180, the improved compromise solution increases the average movement distance by only 1.00% and 1.93%, respectively, while reducing the maximum queue size difference by 7.14% and 10.42%, respectively. In conclusion, the improved ideal point decision method can effectively reduce patient waiting time and alleviate the uneven load on the service desk at the cost of a slight increase in travel distance, and this advantage becomes more pronounced as the number of appointments increases.

[0073] Table 8: Comparison between traditional compromise solutions and improved compromise solutions

[0074] Existing research often treats patients as passive service recipients, employing fixed weights to handle multi-objective problems. This approach is highly subjective and fails to reflect patients' true preferences. This invention first uses a cellular automata model to incorporate patient preferences such as travel distance, waiting time, and queue length into dynamic selection rules, realistically portraying patients' autonomous decision-making behavior in multiple examination scenarios. Building on this, the invention further proposes an improved ideal point decision-making method. By analyzing the distribution characteristics of the Pareto solution set, it adaptively determines multi-objective weights, avoiding the subjectivity of traditional manual weighting. Experimental results show that, compared to the traditional compromise solution using fixed weights, this invention, in medium-to-high load scenarios with 140 and 180 appointments, significantly reduces the average patient waiting time (by 14.88%) at the cost of only a slight increase in average patient travel distance (1.00%–1.93%), while simultaneously reducing the maximum queue length difference at the service counter by 7.14%–10.42%, achieving a simultaneous improvement in patient experience and system load.

[0075] Most existing studies assume that the order of patient examinations is fixed or pre-set, failing to fully utilize the independence and adjustable order of examination items, thus limiting the space for scheduling optimization. This invention employs the ALNS algorithm, which, through a combination of destruction and repair operators, can dynamically adjust the order of patient examination items and the choice of service station. Experimental results show that this method can effectively alleviate congestion in bottleneck examination items (such as ultrasound examinations with an average examination time of 10 minutes), reducing the peak queue length by approximately 3-7 people and shortening the queue completion time by approximately 25.40-39.19 minutes. Through dynamic optimization of the order, this invention breaks through the scheduling bottleneck caused by a fixed order, significantly improving the overall operating efficiency of the system.

[0076] Existing research typically relies on single simulation or optimization methods, lacking an integrated framework that can coordinate both, making it difficult to fully capture the complexity of scheduling multiple examinations. This invention constructs an integrated framework combining simulation and optimization, where a cellular automata model simulates the dynamic selection behavior of patients, and the ALNS algorithm solves for high-quality scheduling schemes under complex constraints; the two work synergistically. Compared to schemes using only a single optimization algorithm, the CA-ALNS method of this invention can effectively reduce patient waiting time and significantly reduce waiting time fluctuations while ensuring the stability of the scheduling scheme, thus improving the stability of system performance. Furthermore, by combining greedy and stochastic strategies, this method avoids the risk of getting trapped in local optima, demonstrating good adaptability under different appointment numbers and system loads, and effectively addressing the dynamics and complexity of scheduling multiple examinations.

[0077] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for optimizing the scheduling of multiple outpatient examinations in a single location based on cellular automata, characterized in that, include: S1: Obtain patient information and data from each service desk; the patient information includes patient number, combination of examination items, and arrival time; The service desk data includes service desk number, inspection function type, location, service rate, and maximum queue size; S2: Based on patient information and data from each service desk, a cellular automata model is used to simulate the patient's behavior in choosing a service desk and generate multiple initial scheduling schemes. S3: The initial scheduling scheme is iteratively optimized using an adaptive large neighborhood search algorithm to construct the Pareto front; S4: The improved ideal point decision method is used to balance multiple optimization objectives, and the optimal scheduling scheme is selected from the Pareto front; The optimal scheduling scheme includes the order of examinations for each patient and the corresponding service desk number.

2. The method for optimizing the scheduling of multiple outpatient examinations in a single location based on cellular automata according to claim 1, characterized in that, S2 includes: A single patient is considered as the central cell, and a service desk composite cell group is considered as a neighboring cell; the service desk composite cell group includes a service desk cell and multiple patient cells currently in the queue. Define the types and states of patient cells and service desk cells; the types of patient cells are classified according to the patient's examination needs, and the states include not yet arriving at the service desk, waiting in the queue, undergoing examination at the service desk, and leaving the service desk after examination; the types of service desk cells are classified according to the examination functions of the service desk, and the states include working state and idle state. The transfer probability from the patient cell to each service station cell is calculated using a constructed transfer probability formula; the transfer probability formula includes a static field part, a dynamic field part, and a local density field part. The patient randomly selects a service station from the candidate service stations and enters the queue of the selected service station to wait for examination; the candidate service stations are a set of service stations selected from the top of the preset proportion after sorting the transfer probabilities from high to low. Update the queue size and estimated waiting time for each service station, and repeat the process of patients selecting a service station until all patients have completed all examinations, thus obtaining the initial scheduling plan; The process of generating the initial scheduling scheme is repeated to obtain multiple initial scheduling schemes.

3. The method for optimizing the scheduling of multiple outpatient examinations in a single location based on cellular automata according to claim 2, characterized in that, The transition probability formula is: ； in, Let N be the probability of patient cell i being transferred to service desk cell j; N is the coefficient to ensure probability normalization; exp is the exponential function. , and These are respectively the static field, the dynamic field, and the local density field; , and These are the static field coefficients, dynamic field coefficients, and local density field coefficients, respectively. This indicates whether patient cell i can enter the queue of service desk cell j. The value is 0 if it can enter and 1 if it cannot enter. This indicates whether the examination request of patient cell i matches that of service desk cell j. The value is 1 when they match and 0 when they do not match.

4. The method for optimizing the scheduling of multiple outpatient examinations in a single location based on cellular automata according to claim 3, characterized in that, The static field is: ； in, The maximum distance patient i can travel to all available service counters; The distance traveled; ； in, The distance traveled; The horizontal distance from patient i to the elevator; The horizontal distance from the elevator to the service desk is j. Let θ be the floor height difference between patient i and service desk j; θ is the conversion factor for converting the time cost of waiting for the elevator into an equivalent distance.

5. The method for optimizing the scheduling of multiple outpatient examinations in a single location based on cellular automata according to claim 3, characterized in that, The dynamic field is: ； in, Select the estimated wait time for service desk j for patient i; This represents the longest wait time for patient i across all available service counters.

6. The method for optimizing the scheduling of multiple outpatient examinations in a single location based on cellular automata according to claim 3, characterized in that, The local density field is: ； in, The number of people currently waiting in line at the service desk; This represents the maximum number of people in the queue among all the service counters available to patient i.

7. The method for optimizing the scheduling of multiple outpatient examinations in a single location based on cellular automata according to claim 1, characterized in that, The S3 includes: The various initial scheduling schemes generated by the cellular automata model are used as the initial solution set; The roulette wheel method is used to select destruction and repair operators, and the current solution is destroyed and repaired to generate a new solution. An improved ideal point decision method is used to compare the multi-objective performance of the new solution with that of the current solution. If the new solution is better than the current solution, the new solution is accepted and the current solution is updated; otherwise, a threshold acceptance criterion is used to determine whether to accept the new solution. The Pareto frontier is constructed based on the updated solution.

8. The method for optimizing the scheduling of multiple outpatient examinations in a single location based on cellular automata according to claim 7, characterized in that, The destruction operators include a random destruction operator and a maximum contribution destruction operator; the repair operators include a random repair operator and a greedy repair operator; after each iteration, the weights of each operator are recalculated and their selection probabilities are updated.

9. The method for optimizing the scheduling of multiple outpatient examinations in a single location based on cellular automata according to claim 8, characterized in that, The formula for updating the weights is: ； in, and , respectively, are the weights of operator r in the k-th and k+1-th iterations; β is the update coefficient of the operator weights; Let r be the score of operator r in the kth iteration; Let r be the number of times the operator r is used in the k-th iteration.

10. The method for optimizing the scheduling of multiple outpatient examinations in a single location based on cellular automata according to claim 1, characterized in that, Step S4 includes: Based on the optimization objectives, the objective function values ​​of the Pareto solutions in the Pareto front are normalized; the optimization objectives include minimizing the average patient travel distance, minimizing the average patient waiting time, and achieving workload balancing between service counters. Calculate the squared weighted Euclidean distance from each Pareto solution to the ideal point; The optimal weight model is constructed based on the target distribution characteristics of the Pareto solution set, and the optimal weight coefficients of each target are obtained by solving the model. The Pareto solution with the smallest weighted Euclidean distance is selected as the optimal solution, and the scheduling scheme corresponding to the optimal solution is selected as the optimal scheduling scheme.

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