CN-121981488-A - Cascade time uncertainty-oriented infrastructure emergency repair collaborative scheduling method

CN121981488ACN 121981488 ACN121981488 ACN 121981488ACN-121981488-A

Abstract

The invention discloses a cascade time uncertainty oriented infrastructure emergency repair collaborative scheduling method, which relates to the technical field of emergency management and intelligent scheduling optimization and comprises the following steps of. The method comprises the steps of firstly, carrying out structural modeling on a disaster-affected infrastructure system, a failure unit, technicians and road network topology, secondly, constructing a task allocation and cooperative path integrated optimization model aiming at planning recovery timeliness maximization, thirdly, establishing probability constraint that repair time length and arrival time uncertainty are transmitted and accumulated step by step along a path based on mean variance and normal quantile, fourthly, adopting segmentation cut lines to realize error controllable linearization of square root relation, and fifthly, combining variable neighborhood search and integer planning local optimization to quickly solve and output an executable scheme. The method can effectively improve the timeliness of post-disaster emergency repair and the steady executable of the scheme, and provides scientific decision support for emergency repair of key infrastructure such as electric power, water supply, traffic, communication and the like.

Inventors

CUI XINHAO
XIAO YIYONG
Qi Penghao
LI BO
XIAO FANGCHENG
JI ZIGUANG
REN YI

Assignees

北京航空航天大学

Dates

Publication Date: 20260505
Application Date: 20260209

Claims (10)

1. The utility model provides a cascade time uncertainty oriented infrastructure emergency repair collaborative scheduling method, which is characterized in that an integrated process of 'structural modeling-collaborative optimization-uncertainty quantization-linearization conversion-hybrid solution' is adopted, and failure unit repair task allocation, technician collaborative path planning, cascade time uncertainty reliability constraint and system recovery aging evaluation are planned in the same framework in order to realize the maximization of accumulated weighted service recovery in planning time domain H and ensure that a scheduling scheme is steady and executable, and the method comprises the following steps: Step one, carrying out structural modeling on a disaster-stricken infrastructure system, a failure unit, schedulable technicians and a network topology, and setting a planning time domain H, a reliability requirement alpha and a recovery logic relation set U and W; Step two, defining decision variables and intermediate variables, constructing an objective function taking timeliness as a guide, and constructing a basic constraint system which covers path topology, task allocation, time recursion, time domain limitation, system recovery logic, timeliness evaluation and logic dependence, so as to form a basic scheduling optimization model; Step three, describing random fluctuation characteristics of repair duration and arrival time based on mean variance, introducing an accumulated variance variable g i and an accumulated standard deviation variable s i , establishing a cascade relation of gradual transmission and accumulated amplification of multi-source time uncertainty along a rush-repair path, and correcting time domain constraint and system recovery logic constraint into a probability form by utilizing a standard normal quantile z α so as to control scheduling reliability; Step four, setting a maximum allowable approximate error epsilon and a value range upper and lower boundary G min 、G max aiming at a square root nonlinear relation between an accumulated standard deviation and an accumulated variance, constructing a segmentation cut line parameter, introducing a segmentation selection variable, and realizing error-controllable segmentation linearization conversion to keep a mixed integer linear programming structure; Generating and iterating an improved scheduling scheme by adopting a mixed solution strategy integrating variable neighborhood search and integer programming, selecting a set to be optimized by an aging greedy construction initial solution and a self-adaptive neighborhood operator, calling a commercial solver in a limited time to accurately optimize and dynamically adjust parameters, and outputting a technician task allocation result, a collaborative path sequence, unit completion time and accumulated uncertainty thereof, a system recovery time and time-efficiency contribution quantity and an overall aging index value.
2. The method of claim 1, wherein the first step includes determining a disaster recovery infrastructure system set C, the service capacity of the system C e C is o c , the importance weight is w c , determining a failure unit set N contained in the system C, the coordinates of the unit i e N are (x i , y i ), the required repair time period expected value is τ i , the repair time period variance is σ i 2 , the required skill class is e iq , the skill threshold value is h iq , determining a schedulable technician set R, the initial position coordinates of the technician R e R, the basic travelling speed is V r , the arrival time expected value is τ ' r , the arrival time variance is σ' r 2 , the skill class degrees are ω rq , and establishing a unit-to-system attribution relation N ci , and abstracting the failure unit and the technician initial position as a node set V, the inter-node passable path forms an arc set a, the arc (i, j) e a corresponds to a distance d ij , and the distance of the technician R from the initial position to the unit ir .
3. The method of claim 1, wherein the decision variables and intermediate variables defined in step two include at least a system recovery variable a c , a unit completion recovery variable β i , a unit allocation variable λ ir , a path head variable y ir , a path tail variable y' ir , a path sequence variable l ij , a unit repair completion time variable t i , a system recovery time variable δ c , and a system aging contribution variable θ c .
4. The method according to claim 1, wherein the objective function constructed in the second step is an objective function guided by maximizing the total weighted timeliness, and comprehensively considering the system importance weight w c , the service capacity o c , and the success recovery probability or the trusted recovery coefficient fc, wherein the timeliness is defined as the accumulation of the capability of the system to continuously provide service in the remaining time of the planning time domain H after recovery, and the earlier the system recovers, the greater the timeliness contribution, and the formula of the objective function is expressed as: 。
5. The method according to claim 1, wherein the basic constraint system in the second step at least includes a path topology constraint and a traffic conservation constraint, a task allocation constraint and a skill feasibility constraint, a time recurrence constraint and a time domain restriction constraint, and a logic dependency constraint, wherein the path topology constraint and the traffic conservation constraint are used to ensure that each technician participating in the rush-repair has a unique starting point and an endpoint, the in-out traffic conservation of each unit, and the path sequence variable is activated only between units allocated by the same technician, and the formula is as follows: , , , , , , ; Task allocation constraints and skill feasibility constraints are used to ensure that each unit to be repaired is allocated to only one technician and that the assigned technician's skill proficiency ω rq meets the unit proficiency threshold h iq , expressed as: , ; the time recursion constraint is used for establishing a completion time recursion relation of the first station and the subsequent stations and covering the arrival time, the inter-station travel time and the repair time length, and the formula is expressed as follows: , ; The time domain restriction constraint is used for restricting the unit repair completion time not to exceed the planning time domain H, and the formula is as follows: , ; The logic dependency constraint is used for establishing inter-unit repair sequence constraint based on the set U and establishing inter-system function dependency constraint based on the set W, and the formula is as follows: , , , 。
6. the method according to claim 1, wherein the second step further includes a system restoration logic constraint and an aging evaluation constraint, wherein the system restoration logic constraint requires that the system be restored only after all the constituent units thereof complete repair and the system restoration time is the maximum value of the completion time of the constituent units thereof, and the formula is: , ; The aging evaluation constraint enables the aging contribution of the system to be equal to the product of the service capacity and the residual operation time after the system is recovered and enables the aging contribution of the unrecovered system to be zero, and the formula is as follows: , 。
7. The method of claim 1, wherein step three comprises introducing a cumulative time variance variable g i and a cumulative time standard deviation variable s i for the unit repair completion time and making the cumulative variance equal to the sum of the technician arrival time variance σ' r 2 and the head repair duration variance σ i 2 at the head station of the path, expressed as: , let the cumulative variance equal to the sum of the cumulative variance of the predecessor unit and the current unit repair duration variance at the subsequent site of the path, expressed as: , therefore, the multi-source time uncertainty is transmitted step by step along the repair path and the accumulated amplification is described.
8. The method according to claim 1, wherein the third step further comprises performing probabilistic form correction on the time constraint and the system recovery logic constraint using a standard normal quantile z α , so that the unit repair completion time and the system recovery time satisfy the planned time domain constraint at the reliability level α, thereby controlling the on-time completion probability of the scheduling scheme and reducing the risk of timeout violations, including the following constraints: , , 。
9. The method of claim 1, wherein the piecewise tangent linearization conversion in step four comprises setting a maximum allowable approximation error ε and determining a lower bound G min and an upper bound G max of the cumulative variance range, determining the number of segments based on the error accuracy and calculating a tangent slope k p and an intercept b p for each segment P ε P, constructing η approximation secants, expressed as: , ; The 0/1 variable m p of the segment selection is introduced to ensure that each unit selects only a unique segment and causes the cumulative variance to fall within the selected segment interval, thereby representing the cumulative standard deviation in a linear relationship and maintaining the model as a mixed integer linear program. Including segment selection uniqueness constraints, ensure that each cell can only select a unique secant segment to approximate: , Interval activation constraints to indicate and activate the approximate cut line selected within a particular segment: , , The linear approximation constraint, the standard deviation and variance variable corresponding to a specific unit are expressed by S i and G i respectively, so that the substitution relation between piecewise linearization and the original constraint can be directly shown: , Each segment endpoint and coefficient k p ,b p may be generated offline according to error control rules and solidified into a parameter table for multiplexing in different instances.
10. The method of claim 1, wherein the hybrid solution strategy in the fifth step includes calculating the age importance of the failure units and arranging the failure units in descending order to construct an initial feasible solution, alternately adopting a nearest neighbor selection operator and a path priority selection operator to construct a to-be-optimized set, wherein the nearest neighbor selection operator brings the units in the space neighborhood radius D into the to-be-optimized set, the path priority selection operator brings K units before the current rush-repair path of a technician into the to-be-optimized set, the total number of the to-be-optimized units does not exceed a set upper limit, fixing the distribution variable and the path sequence variable of the units outside the to-be-optimized set to be a current solution value, only releasing the fixed state of the variables in the to-be-optimized set, calling a commercial solver for local accurate optimization within a limited time, updating the current solution if a better solution is obtained, otherwise expanding the to-be-optimized set or switching the neighborhood operator, and dynamically adjusting the space neighborhood radius D and the number selected by monitoring each round of local optimization calculation to achieve balance of solution quality and calculation efficiency.

Description

Cascade time uncertainty-oriented infrastructure emergency repair collaborative scheduling method Technical Field The invention belongs to the technical field of emergency management and intelligent scheduling, and particularly relates to a cascade time uncertainty oriented infrastructure emergency repair collaborative scheduling method. Aiming at the rush-repair tasks of scattered failure units in a key infrastructure network after natural disasters, the characteristics of random fluctuation of repair time length, uncertainty of arrival time of technicians, gradual accumulation and amplification of multi-source uncertainty along a rush-repair path and the like are comprehensively considered, the integrated decision of repair task allocation optimization and collaborative path planning is utilized, the computational modeling and solving of uncertainty are realized by means of mean variance characterization and accurate linearization technology, and finally, timeliness maximization of the rush-repair operation and steady executable of a scheduling scheme are realized. Background The key infrastructure network is an important support for operation in the modern society, and covers a plurality of fields such as power supply, water supply and drainage, transportation, communication guarantee and the like. However, as climate change exacerbates and the urbanization process accelerates, such interrelated, interdependent systems face increasingly severe disaster threats. Natural disasters such as earthquake, typhoon, flood and the like can cause a large range of facility failure in a short time, cause cascading failure and regional service interruption, and bring great loss to society and economy. The post-disaster recovery speed is highly related to community toughness and public safety, so that the fast coordinated emergency repair capability is important. The time urgency of post-disaster repair operations makes it a substantial distinction from conventional repairs. The conventional maintenance takes efficiency indexes as a main factor, and the emergency maintenance needs to maximize the accumulated service recovery amount within a limited time window, namely pursuing the timeliness of recovery. This time dimension requirement is particularly critical in the presence of golden repair windows, where damaged parts may lose repairability due to secondary failure or environmental deterioration if not repaired in time. In addition, the system capacity recovered in the early stage can support the subsequent repair operation and can also effectively inhibit further spreading and spreading of faults. Current emergency repair scenarios face the challenge of multi-source time uncertainty. Uncertainty of repair duration is caused by incomplete damage assessment, changeable field conditions and fluctuation of resource constraint, and randomness of technician arrival time is influenced by factors such as traffic delay, road damage and the like. More importantly, these independent uncertainties do not exist in isolation, but are passed and accumulated step-by-step along the repair path, with the deviation being conducted to all subsequent task nodes in cascade as the technician encounters a delay at some repair point, resulting in a gradual amplification of the scheduling uncertainty and a continuous increase in the risk of timeout violations. The cascade accumulation characteristics are overlapped with complex logic dependency relationships inside and among infrastructure systems to form a highly dynamic and difficult-to-predict decision-making environment, so that a deterministic method is difficult to effectively cope with. In the prior art, the emergency repair scheduling mainly adopts methods such as mathematical planning and heuristic algorithm, and the like, and has high calculation efficiency but lacks of optimal guarantee and sensitive parameters. For the treatment of time uncertainty, the existing methods mostly adopt strategies such as random expected optimization, but the methods have the limitation in practical application that the risk situation of rapid evolution is difficult to capture. Therefore, an emergency repair collaborative scheduling method capable of effectively describing the uncertainty of cascading time and simultaneously considering the timeliness target and the calculation feasibility in a unified frame is urgently needed, and the problems that scheduling decision and path planning are split, uncertainty modeling and optimization solving are disjointed, and large-scale instance calculation efficiency is insufficient in the prior art are solved. Disclosure of Invention (1) The purpose of the invention is that: The invention aims to provide a cascade time uncertainty oriented infrastructure emergency repair collaborative scheduling method. The method is used for solving the problems that in the prior art, task allocation and path planning are mutually split, repairing duration fluctuation and arr