Method for multi-objective optimization of a list of time slots for stakeholders
The method optimizes flight slot assignments using evolutionary algorithms with privacy-preserving computation to balance stakeholder preferences, addressing inefficiencies in ATFM and ensuring confidentiality, achieving faster and better results than traditional methods.
Patent Information
- Authority / Receiving Office
- WO · WO
- Patent Type
- Applications
- Current Assignee / Owner
- FREQUENTIS
- Filing Date
- 2025-11-17
- Publication Date
- 2026-05-21
AI Technical Summary
Existing flight rescheduling methods in Air Traffic Flow Management (ATFM) are inefficient due to varying delay costs among flights, leading to suboptimal adjustments during disruptions, and lack privacy-preserving optimization for stakeholder preferences.
A method combining evolutionary algorithms with privacy-preserving computation, using multi-party computation and homomorphic encryption to optimize flight slot assignments while maintaining stakeholder confidentiality, balancing multiple objectives through a mutation mechanism and imbalance ratio.
Achieves fair and efficient flight slot assignments that minimize overall delay costs, ensuring confidentiality and meeting stakeholder constraints within time constraints, outperforming traditional methods in solution quality and speed.
Smart Images
Figure AT2025060424_21052026_PF_FP_ABST
Abstract
Description
[0001] Method for multi-objective optimization of a list of time slots for stakeholders
[0002] The invention relates to a method for multi-objective optimization of a list of time slots for stakeholders.
[0003] In Air Traffic Flow Management (ATFM), flights are assigned to specific departure and arrival times at airports. When unexpected events such as disruptive weather conditions reduce airport capacities, these assignments must be adjusted, leading to potential delays and additional costs for airspace users. Traditionally, flights are rescheduled on a first-come, first-served basis, which is not always cost-effective due to varying delay costs between individual flights.
[0004] The known Computer-Assisted Slot Allocation (CASA) algorithm calculates target times of arrival (TTAs) - or slots - on a first-planned, first-served basis. This means that when regulating a flight sequence, the order of the flights is generally retained, but the flights are shifted back in time. For some of those flights, however, the delay is more problematic than for others due to varying delay costs. The delay costs of a flight can be described by a non-linear function with one or more delay targets. A delay target is an interval of arrival times that, for example, allows passengers to reach a connecting flight despite the delay.
[0005] The objective of the invention is to provide a method to achieve a fair result in a shorter time.
[0006] The result should comprise an optimal assignment for airspace users to minimize the overall delay costs based on the individual cost functions. The method of the invention should also process the provided information reliably and confidentially. Other tasks include suppressing possible misconduct of the stakeholders and being able to give special consideration to the constraints of at least one selected stakeholder. The system should also be cost-effective, secure and maintenance-free.
[0007] The invention solves this objective by the features of claim 1 with the steps:
[0008] (a) wherein an initial list is provided, whereas the initial list comprises at least a plurality of time slots and a parameter for each time slot, which can be occupied by an item-ID, preferably a flight-ID, (b) wherein each stakeholder provides preferences in the format of a weight map comprising at least a time preference value assigned to each combination of time slot and item-ID for the respective stakeholder, whereas the weight maps are compiled in the format of a first matrix, the dimensions of which are the time slots to be allocated and the number of item-IDs,
[0009] (c) wherein a value of satisfaction is defined that corresponds to the fulfilment of the preferences by distributing either the time slots or item-IDs in a specific list, and wherein a first objective is provided that consists of generating an improved list in which the value of satisfaction is the highest,
[0010] (d) wherein repeatedly for a predefined number of times two items are permutatively swapped or candidate lists are generated by random assignment of item-IDs to slots, in the initial list of time slots to generate a first generation of candidate lists, each list having a specific value of satisfaction,
[0011] (e) generate a next generation of candidate lists comprising a predefined number of lists (Lc2i) by
[0012] (e.l) taking a predefined number of candidate lists with best specific values of satisfaction (vi) of the given generation and for each of the chosen lists doing a predefined number of swaps according to a constraint, which can be chosen, for example a swap mutation that randomly swaps a subset of the flights, and / or
[0013] (e .2) taking a predefined number of candidate lists and combine two or more of the chosen lists according to a constraint, which can be chosen, for example a partially matched crossover that takes a sequence from one solution and swaps it with the sequence of another solution, each list having a specific value of satisfaction,
[0014] (f) repeat step (e) either for a predefined number of times or when a predefined time available for optimization concludes or until the specific value of satisfaction of the best list or lists of a generation deviates from the specific value of satisfaction of the best list or lists of the previous generation within a specified difference range,
[0015] (g) wherein the group of candidate lists with the highest value of satisfaction is selected as the improved lists of time slots, wherein the group comprises one or more lists. In order to embed the method in a reliable work flow with all stakeholders, it is advantageous to further implement:
[0016] in step (a) the initial list is provided to one or more stakeholders,
[0017] in step (b) the weight maps are collected from one or more stakeholders and
[0018] after step (g) the improved lists of time slots is provided to one or more stakeholders for confirmation or rejection.
[0019] In order to achieve at least one improved result as quickly as possible, it is advantageous further implement step (d) by a constraint that is:
[0020] (d.l) providing a parameter p representing the probability of a swap of items that leads to an increase of the value of satisfaction, wherein distance d of two items in the list is dependent of the parameter p,
[0021] (d.2) generating a new generation of candidate lists by
[0022] randomly selecting a first flight for each candidate list in, then calculating a distance d, which determines the second flight that is to be swapped with the first flight, where the second flight is the flight that is d slots after the first flight, by first generating a random variable with an expectancy value that equals p which is multiplied by the length of the flight list, which is repeated a predefined number of times, preferably about ten times,
[0023] calculating the value of satisfaction for each candidate list.
[0024] In order to balance constraints and requirements between regular stakeholders, such as airlines, and one selected stakeholder, such as an airport, it is advantageous to further implement the steps:
[0025] (h) a ratio of satisfaction for each improved list is defined as the sum of the achieved preferences divided by the sum of the highest possible achievement according to the matrix of stakeholder, (i) providing a second matrix of a further, selected stakeholder, preferably the airport, (j) a ratio of satisfaction for each improved list is defined as the sum of the achieved preferences divided by the sum of the highest possible achievement according to the matrix of the selected stakeholder,
[0026] (k) producing an imbalance ratio for each pair of ratios of satisfaction defined as the amount of their difference,
[0027] (I) selecting the improved list with the lowest imbalance ratio as the balanced improved list.
[0028] In order to process information confidentially, it is advantageous to encrypt the weight maps by the stakeholders in step (b) and sent to a privacy engine, preferably using multi-party computation.
[0029] In order to both process information confidentially and to evaluate results quickly, it is advantageous to further introduce an Orchestrator component and wherein before step (d) - the Orchestrator component initializes the Privacy Engine component with secret shares of the weight maps, and the Privacy Engine component distributes the secret shares to MPC nodes hosted by different parties,
[0030] whereas for optimization steps (d) and (e), a Heuristic Optimizer component is used, whereas the Heuristic Optimizer component provides generations of candidate lists to the Privacy Engine component for evaluation,
[0031] the Privacy Engine component uses the MPC nodes to evaluate a generation of candidate lists and obtains an obfuscated evaluation result that is used by the evolutionary algorithm to create the next generation of candidate lists, and
[0032] in step (g) the best solutions found are returned to the Orchestrator component.
[0033] One preferred, albeit not restricting, embodiment of the invention is presented with regard to the figures: Figure 1 schematically shows a system of servers implementing the method,
[0034] Figure 2 schematically shows a flow chart of the method,
[0035] Figure 3 schematically shows two flight lists,
[0036] Figures 4 to 7 each show the probability function f(p),
[0037] Figure 8a and 8b each show a matrix of flight lists,
[0038] Figure 9 schematically shows six flight lists with different fitness values,
[0039] Figure 10 schematically shows two flight lists,
[0040] Figure 11 schematically shows a flight list,
[0041] Figure 12 shows two flight lists in which two segments are exchanged step by step,
[0042] Figure 13 schematically shows a detailed block diagram implementing the method,
[0043] Figure 14 shows an UML sequence diagram of optimization in a Target Time Management System for an honest-but-curious platform provider.
[0044] The invention extends the single-objective problem of flight prioritization in Air Traffic Flow Management (ATFM) to a multi-objective problem that includes airport operations. It addresses the need for long-term equity for a Target-Time Management System (TTMS) and presented the architecture of a TTMS for a trusted platform provider and extended this architecture for an honest-but-curious platform provider for privacy-preserving optimization. Results from tests indicate that good results can be achieved, both under the assumption of a trusted platform provider as well as an honest-but-curious platform provider. The invention is a method for combining evolutionary optimization algorithms, in particular genetic algorithms, with a Privacy Engine P, which may employ (secure) multi-party computation or homomorphic encryption as the basis for building a platform for optimizing the assignment of arrival or departure times to different flights under the assumption of an honest-but-curious platform provider.
[0045] The core comprises three aspects: Mutation mechanism for an evolutionary algorithm: The method comprises a mutation mechanism or mutation operator for the evolutionary algorithm that works by applying mutation between two points based on a mutation probability p. The mechanism uses a linear function to generate a random variable that defines the distance between the two points, and adjusts the function parameters depending on the value of p. The mechanism ensures that the expectancy value of the random variable is equal to p.
[0046] Imbalance ratio for search process: The method further comprises the use of an imbalance ratio to measure how balanced the optimization is between the two objectives of satisfying the airspace users' preferences and the airport's preferences. The imbalance ratio is calculated by comparing the value of each objective to the maximum possible value and taking the absolute difference between the two ratios. The imbalance ratio ranges from zero to one, where zero means equal optimization and one means complete skewness.
[0047] Invention of privacy-preserving evolutionary optimization for air traffic flow management: The method further comprises optimizing the assignment of arrival or departure times to different flights without revealing the preferences of the stakeholders, such as airspace users and the airport, to each other or to a platform provider. The method uses evolutionary algorithms, such as genetic algorithms, combined with a Privacy Engine P that can encrypt and evaluate the inputs using secure multi-party computation or homomorphic encryption.
[0048] The result of the method does not have to lead to the best possible list or in a single list. The goal is achieved if it is a significantly better list in a given time than is possible in the prior art. In addition, it is useful for particular embodiments if the method consists of a group of lists that can subsequently be processed according to further aspects.
[0049] A system implementing the proposed method comprises, e.g., airspace users and at least one airport as contributing stakeholders and a network manager providing an optimization platform according to Fig. 1. The optimization platform comprises an evolutionary algorithm and a privacy engine. The components are provided either as servers or as software modules or the like. In the beginning the initial flight list Lo as shown in Fig. 3 is, according to Fig. 2, requested (1) from the Flight Network Manager. The Flight Network Manager is a with respect to the stakeholders neutral superordinate authority that is integrated into the network. Any flight list shows a distribution of item-IDs, such as flight-IDs or airli nes-l Ds over time slots 1, 2 ... 6. In the examples given the airli nes-l Ds equal the stakeholder-IDs A, B, ... F.
[0050] The collection process is than announce (2) to the involved stakeholders like airlines, airports, and Air Navigation Service Providers (ANSPs). During the collection process (3) airspace users can submit their preferences (3a) and at the same time airports users can submit their preferences (3b). Both airspace users, preferably airlines, and the (for example one single) airport together form the group of participating stakeholders in this example.
[0051] The airlines may submit the preferences as a weight map wi. a weight map wiis a list of time slots (e.g., time slot position 1 to 6 in the figures), wherein one of the airspace users A to F discloses for each time slot position a utility value. In this example, the utility value is in the range from 0 to 5. Other ranges such as 1 to 100 are also possible. The higher the weight the more useful a slot would be for a particular flight. Multiple answers and omissions are possible when completing the weight map wi. In other words, a weight map is a list of key-value pairs with the available arrival times as the keys and the weights as the values indicating the importance of a particular arrival time for a particular flight. The higher the numerical value, the more important the arrival time for this flight. Weight maps wi allow a much more fine-granular representation of preferences than the time triplets but at the same time are more difficult to derive and compare between airspace users.
[0052] The collected weight maps wi are combined according to Fig. 8a to a matrix Ml that defines for each combination of flight and slot the utility value.
[0053] When allowing airspace users to provide their preferences as weight maps wi, a TTMS shall ensure that airspace users do not cheat, that the weight maps wi are comparable to the preferences encoded as time triples and that the weight maps of an airspace user are comparable to the weight maps wi of other airspace users. For example, if an airspace user specifies very high weights for only a few target times in a weight map, they are more likely to receive one of those target times, giving them an unfair advantage over others who specify more optimization-friendly preferences. To prevent such unfavourable behaviour, a TTMS needs to establish rules for constructing weight maps, such as a minimum and maximum value for the weights together with limiting the amount of weights an airspace user can spend on one weight map or all of its weight maps wi.
[0054] In the proposed invention, according to Fig. 2, an algorithm (4) then iteratively generates a population or generation of candidate solutions elt (4.1) to a flight prioritization problem while a further component evaluates the generation of candidate solutions (4.2) in each iteration step. After the termination condition is fulfilled the best flight lists Lfi are submitted to stakeholders for confirmation or rejection (5). Then the best acceptable list (6) is sent to the Network Manager to pick one flight list for adoption.
[0055] More specifically, an evolutionary algorithm in (4) iteratively generates a population or generation of candidate solutions Lcli (4.1) to a flight prioritization problem while furthermore a Privacy Engine P component evaluates the generation of candidate solutions Lcli (4.2) in each iteration step. The stakeholders' private inputs are kept from others and not even the platform provider - who is not one of the stakeholders but a third party service provider - knows those inputs, receiving only encrypted inputs, which are processed by the Privacy Engine P in a way that preserves the secrecy of the inputs.
[0056] The proposed evolutionary algorithm comprises the use of a mutation operator. It starts with a mutation step in (4.1) on the basis of a probability function f(p). The proposed mutation operator works, as shown in Fig. 3, as follows. Mutation is applied between two flights with a distance d from each other in the flight list Li. The distance d depends on the on the mutation probability p. The parameter p represents the probability of a swap of items that leads to an increase of the value of satisfaction Vi.
[0057] To compute the distance d, a random variable rpwith an expectancy value that equals p is required. This random variable rpmultiplied by the length of the flight list defines the distance d between the two flights that are to be swapped. To obtain a specific random value rp, an equally distributed random variable r is first generated. So, it is randomly selected a first flight fi for each candidate list in Lcli, then calculating a distance d, which determines the second flight fz that is to be swapped with the first flight fi, where the second flight fz is the flight that is d slots after the first flight fi, by first generating a random variable rpwith an expectancy value that equals p which is multiplied by the length of the flight list.
[0058] To this end, a linear function
[0059] f(p) = m x p + b
[0060] is required, indicating the distribution of the created random value rp. The random value rpis then equal to the position on the x-axis where the integral of the linear function f(p) between zero and rpis equal to the generated random value r.
[0061] Based on the value of p, the distribution function f(p) must be calculated in different ways. If p is equal to 0.5, each distance is equally likely, and thus rpis evenly distributed. In this case, the distribution function f(p) is a constant equal to 1. In this case, the probability is not shifted, and the generated random value r can be used to determine the distance between the positions d. For the two extreme cases, where p equals one or p equals zero, the generated random value r does not influence the result. If p is equal to 1, each flight's position must be mutated, leading to d being equal to the length of the flight sequence and rpbeing equal to 1. Then, no function f(p) is specified. The process when p is equal to 0 is similar. In this case, no flight positions are mutated at all. Therefore, rpis set to zero without setting a function f(p).
[0062] For other cases, m and b of the linear function / p^ = m x p + b must be calculated. If p is smaller than 0.5, the gradient is negative. If p is greater than 0.5, the gradient is positive. Furthermore, it must be distinguished if the intersection with the x-axis is before or after x = 1 for negative gradients. For positive gradients, it must be distinguished if the intersection of f(p) with the x- axis is before or after x = 0. The area under f(p) with positive values must be equal to 1 since rpmust be in the interval [0, 1], The area under the function is divided in half at position f(p) because the expectancy value of rpis p. With these assumptions, two equations can be defined, which include m and b. The system of equations is solved to calculate the function parameters. With the function f(p), rpis calculated based on ras the integral between 0 and rforp < 0.5, or as 1 minus the integral between r and 1 for p > 0.5. The distance d between the flights to be swapped is then rpmultiplied by the length of the flight list.
[0063] Four cases have to be considered:
[0064] (1.) For p values less than 0.292893, as shown in Fig. 4, the linear function f(p) has
[0065] b = (2 - sqrt(2)) 4- p and m = -b24- 2.
[0066] The distance d is then [-b 4- sqrt(b2 + 2 x r x m)] 4- m.
[0067] (2.) For p values greater than or equal to 0.292893 and less than 0.5 (see Fig. 5), the linear function f(p) has
[0068] b = (p2- 0.5) 4- (p2- p) and
[0069] m = 2 - 2b.
[0070] The distance d is then [-b + sqrt(b2 + 2 x r x m)] 4- m.
[0071] (3.) For p values greater than 0.5 and less than 0.707107, the linear function f(p) has
[0072] b = (p2- 0.5) 4- (p2- p) and
[0073] m = 2 - 2b. This case is shown in Fig. 6.
[0074] The distance d is then [b - sqrt(b2+ 2 x m x (r- l + b + 0.5m))] 4- m.
[0075] (4.) For p values greater than or equal to 0.707107 and less than 1, see Fig.7, the linear function f(p) has
[0076] b = 0.5 x [1 - (([2 - sq rt(2)] 4- (1 - p)) - l)2] and
[0077] m = -b + sq rt( 1 - 2b) + 1.
[0078] The distance d is then [b - sqrt(b2+ 2 x m x (r- l + b + 0.5m))] 4- m.
[0079] Finally, a predefined number of random swaps for each candidate list Li is implemented. In testing the system a number of about 100 random swaps showed reliable results. Then the value of satisfaction (vt) for each candidate list is calculated. In a simple embodiment the flight list Li with the highest value may be chosen as the final flight list Lf.
[0080] In a further embodiment of the method, candidate lists Li can also be further developed by exchanging groups rather than individual positions. This is implemented with a combination operator. As shown in the Fig. 12, two new lists Ls, Le can be recombined from two given ones. First, sections of the same length are cut out of both given lists Li, L2 - in the case shown, positions No. 3 to No. 5, comprising 3 flights - and swapped. The resulting interim lists L3, L4 need to be checked and corrected for any flights that may have been duplicated or lost as a result of the swap. In one list this is flight B, in the other list it is flight F. In the example shown, the correction is achieved by transferring the duplicate flights in the section of a list Li, L2 that was not exchanged. This is implemented in a second step of the swap using the combination operator. This finally produces the completed new lists Ls, Le shown in Fig. 12 below. These new lists L5, Le can now be evaluated as shown above and used further if required.
[0081] In an embodiment the use of an imbalance ratio irin the search process is proposed in order to not excessively favor airspace users' preferences over the airport's preferences, and vice versa. For the imbalance ratio ir, the found solution is compared to the maximum value for each objective. For the calculation of the imbalance ratio, the ratio of the satisfaction of the airspace user preferences is divided by the theoretical best or highest possible value. The approach is also applied to the satisfaction of airport preferences. The imbalance ratio iris then set to the absolute value of the difference between these two ratios. The ratio is between zero and 1: an imbalance ratio of zero would mean that the two objectives are equally optimized; an imbalance ration of 1 would mean that the result is completely skewed toward one objective.
[0082] The airlines may submit the preferences as a weight map wi as described above. Additionally to matrix Ml, also the airport provides a matrix M2 according to the airport's preferences concerning other issues such as an even utilization of airport operating hours, noise regulations or flight safety aspects that come from outside. Fig. 8a and fig. 8b show examples of a matrix Ml and a contrasting matrix M2. In the example of Fig. 9, three flight lists Li, L2, L3 are found by swapping flights A and B, B and E as well as C and D, respectively, compared to the original flight list announced by the Network Manager.
[0083] The overall fitness Fi of a flight list Liforthe airlines is introduced and can then be determined by summing up the weights associated by the airlines with the respective 1...6 slot for the flight allocated to the respective slot 1...6. For example, the first flight list Li, where A and B are swapped compared to the original flight list, has a fitness relative Fairlines, 1 to the airlines' objective of 4 + 5 + 3 + 4 + 4 + 4 = 24. The second flight list L2, where B and E are swapped compared to the original flight list, has a fitness relative Fairlines, 2 to the airlines' objective of 5 + 0 + 3 + 4 + 0 + 4 = 16. The third flight list L3, where C and D are swapped compared to the original flight list, has a fitness relative Fairlines, 3 to the airlines' objective of 5 + 3 + 5 + 3 + 4 + 4 = 24. The overall fitness Fairport, i of a flight list for the airport can be determined analogously by summing up the weights associated by the airport with the respective slot 1...6 for the flight allocated to the respective slot.
[0084] Both fitness values (Fairlines, i and Fairport, i) can be combined in different ways to determine the overall fitness of a flight list relative to both the airlines' and the airport's objective.
[0085] The finally returned flight lists Li can also be evaluated according to Fig. 10 using the imbalance ratio ir. Mathematically speaking, the imbalance ratio iris the amount of the difference between two ratios. The best fitness Fairlines, max of any possible flight lists Li relative to the airlines' objective would be 25. The best fitness Fairport, max of any possible flight lists relative to the airport's objective would be 29. For the first flight list Li returned to the stakeholders, where the order is B, A, C, D, E, and F, the imbalance ratio ii is
[0086] | (24 + 25) - (29 + 29) | = 0.04.
[0087] For the second flight list returned to the stakeholders - which is the third flight list L3 of the example in Fig. 9 -, where the order is A, B, D, C, E, and F, the imbalance ratio is is
[0088] | (24 + 25) - (24 + 29) | = 0.13. The second flight list is more imbalanced, being better optimized for airlines than for the airport. Therefore, this flight list L3 is discarded while the first list Li is preferred and chosen to be the final balanced flight list LFB according to Fig. 11.
[0089] Collaborative optimization based on sensitive information requires either trust between the participants or methods for privacy-preserving computation that protect the sensitiveinformation from unauthorized access. Various methods for privacy-preserving computation have been proposed, such as secure multi-party computation (MPC) and homomorphic encryption. In time-critical settings, solutions must be found within the time constraints of the problem context. Optimizing the slot assignment during ATFM regulation, for example, must be finished within minutes. In addition, the solution of the optimization should be better than the solutions known in the art. However, methods for privacy-preserving computation cause considerable additional runtime overhead, which makes it difficult for privacy-preserving optimization to find solutions in the time available for optimization.
[0090] Deterministic algorithmsalwaysfind an optimal solution for an optimization problem. Considering flight prioritization asan assignment problem, the Hungarian method, for example, always finds an optimal solution. Even with multiple objectives, the optimization problem can be converted into a single-objective optimization problem by weighting and combining the objectives. The run-time of privacy-preserving implementations of deterministic algorithms based on MPC to solve singleobjective assignment problems has been investigated. However, the runtime may not be sufficient for flight prioritization, i.e., using these implementations may lead to situations where a solution is not found in time.
[0091] In contrast to deterministic algorithms, evolutionary algorithms can be terminated at any point in time and still provide solutions. Various works of the art address privacy-preserving optimization using evolutionary algorithms. A privacy-preserving implementation of the genetic algorithm following the concept of evolutionary computation as a service has been proposed in this regard. Privacy-preserving implementations of evolutionary algorithms always find solutions in the time available. Nevertheless, the solutions may be of insufficient quality because the privacy- preserving computation of the entire algorithm slows down the runtime behaviour and thus reduces the number of possible generations.
[0092] It proposed here to separate the search for solutions from the evaluation of the solutions for privacy-preserving optimization in time-critical settings. Therefore, methods for privacypreserving computation are only required to evaluate the solutions, which reduces the impact on runtime performance. Moreover, this approach is extended for the multi- objective flight prioritization problem to design a Heuristic Optimizer for a TTMS.
[0093] To this end, the weight maps wi are encrypted by the stakeholders in step (b) and sent to a privacy engine P. The encryption is performed with tools known in the art. The use of multi-party computation, MPC, is advantageous for the following reasons.
[0094] The TTMS will enable airspace users and the airport to collaboratively optimize arrival flight lists even under the assumption of an honest-but-curious platform provider. Fig. 13 shows the architecture of a TTMS for an honest-but-curious platform provider. In contrast to the architecture for a trusted platform provider, this architecture includes a Privacy Engine component for privacy-preserving computations. Fig. 14 illustrates the optimization involving a Privacy Engine component.
[0095] In the case of an honest-but-curious platform provider, the preferences of airspace users are only available in secret shares of the weight maps wi. In contrast to optimization in the TTMS for a trusted platform provider, an Orchestrator component is introduced. It needs to first initialize the Privacy Engine component with secret shares of the weight maps wi. The Privacy Engine component distributes the secret shares to MPC nodes hosted by different parties. For optimization, a Heuristic Optimizer component uses an evolutionary algorithm as described above to search for solutions and provides populations of solutions to the Privacy Engine component for the evaluation. The Privacy Engine component uses the MPC nodes to evaluate a population of solutions and obtains an obfuscated evaluation result that is used by the evolutionary algorithm to create the next population of solutions. The optimization terminates when the time available for optimization concludes, and the best solutions found so far are returned to the Orchestrator component. As to the setup, the metrics, and the results of preliminary experiments using a Heuristic Optimizer for privacy-preserving optimization: We generated 20 datasets, each with 100 flights and target times, and each flight was assigned a weight map for the preferences of the airspace userand a weight map for the preferences of the airport. The preferences of airspace users were generated based on the statistical distribution of an airline's preferences. For the preferences of the airport, we assumed that the airport prioritizes 20% of flights with a high priority, 40% of flights with a medium priority and 40% are not prioritized at all.
[0096] For conducting experiments, we developed a prototype, which is a Java library for genetic algorithms. For the sake of simplicity, the prototype only simulates the Privacy Engine. More precisely, the evaluation results are obfuscated but the evaluation does not use an MPC protocol. While the results are the same as if a Privacy Engine had been used, it allows us to carry out the experiments faster and without dealing with the technological complexity of MPC for the performance experiments.
[0097] We assumed an honest-but-curious platform provider and assumed that only the preferences of airspace users are sensitive information and need to be obfuscated before the evaluation results are revealed to the Privacy Engine. We used the obfuscation methods order, order quantiles, and fitness range quantiles because they performed well in previous work.
[0098] The TTMS uses a weight matrix Ml, M2 for optimization, since the evaluation of solutions with MPC for privacy-preserving optimization works well if only the values of the weight matrix Ml, M2 have to be summed up. Therefore, the TTMS must be able to map the preferences provided as time triplets into weight maps wi that are comparable to the preferences provided as weight maps Wj. Various mapping approaches are possible for this purpose. For example, the target time that corresponds to the TimeWished receives the highest value, while the weights decrease linearly to the target times that correspond to the TimeNotBefore and TimeNotAfter. The optimal assignment for airport operations improves several key performance indicators (KPIs), such as minimizing the average passenger delay. The optimization therefore requires the KPIs and the information necessary for calculating the KPIs as input from the airport. In contrast to the airspace user preferences, the KPIs and the information required for calculation may not be sensitive. The KPIs may however conflict with the airspace user preferences.
[0099] Optimization becomes increasingly difficult as the number of objectives increases. The following approaches to multi-objective flight prioritization are therefore conceivable. The invention's approach to multi-objective flight prioritization is to consider the preferences of the airspace users as one objective, and a combination of the KPIs of the airport as an additional objective (summed up in matrix M2). The airport objective can, for example, be computed from a situation-dependent weighted sum of the KPIs, and translated either into time triplets or weight maps. The prioritization of flights is therefore a bi-objective optimization problem of the preferences of airspace users and the airport.
[0100] This enables the use of efficient evolutionary algorithms that can approximate near-optimal solutions that reconcile both objectives.
[0101] The TTMS will enable airspace users and the airport to collaboratively optimize flight lists in the case of ATFM regulations. Fig. 13 shows the proposed architecture of a TTMS considering a trusted platform provider. During continuous operations, the Orchestrator component of a TTMS continuously receives the current preferences of the airport and airspace users, and stores the preferences in a database of the TTMS (see Fig. 13). The Orchestrator component also continuously requests active regulations from the EUROCONTROL Network Manager and the Network Manager responds with an Air Traffic Flow and Capacity Management (ATFCM) measures list. In case the measures list is relevant fora particular airport, it startsan optimization of slot assignments. For the optimization, the Orchestrator component requests all necessary information related to the regulation from the EUROCONTROL Network Manager, such as the list of regulated flights and the flight list proposed by a CASA algorithm. The Orchestrator component selects the preferences of the regulated flights from the database, converts the preferences into weight maps wi if necessary, and requests equity information from an Equity Manager component. The Equity Manager component computes, for example, inequity weights, based on historical data from previous regulations stored in the database. The Orchestrator component uses the received equity information to modify the weight maps, e.g., by adding the inequity weights to the weight maps wi. Once all the information for the optimization has been collected, the Orchestrator component calls the Heuristic Optimizer component to perform an optimization. The Heuristic Optimizer component performs an optimization using the weight maps received from the Orchestrator component and returns optimized flight lists. The Orchestrator component stores the optimization result in the database of the TTMS, selects one of the optimized flight lists by, e.g., using an approach for selecting the best compromise solution known in the art, evaluates the selected solution against internal KPIs, and sends a request with the optimized TTA assignments to the EUROCONTROL Network Manager in case the optimized solution surpasses the predefined KPIs. The Orchestrator component then stores the implemented TTA updates in the database in order to enable the Equity Manager component to take the implemented arrival flight list into account for future optimizations.
[0102] The Heuristic Optimizer component uses either a deterministic or an evolutionary algorithm for optimization. In the case of a trusted platform provider, the TTMS receives the preferences of airspace users as plain text, eliminating the need for privacy-preserving computation. Thus, a deterministic algorithm may be efficient enough to provide solutions in time.
[0103] If a deterministic algorithm is sufficient for the time constraints, the Heuristic Optimizer component normalizes and combines the weight maps wi of the airspace users and the airport to obtain a single weight map for each flight. The weight maps together form a weight matrix Ml, M2 for which a deterministic algorithm such as the Hungarian method known in the art finds an optimal solution. The Heuristic Optimizer may use different weightings between the objective of the airspace users and the objective of the airport to obtain different weight maps and thus a set of Pareto-optimal solutions.
[0104] In contrast to deterministic algorithms, evolutionary algorithms cannot guarantee optimal solutions, but they can remove the above-mentioned difficulty of choosing the correct weights and provide the flexibility to adjust the weights based on the solutions obtained. In an iterative process, an evolutionary algorithm such as a genetic algorithm searches for solutions, and the solutions found are evaluated based on the weight maps wi, assigning each solution with two fitness values.
[0105] The choice of optimization algorithm ultimately depends on various factors, such as the time available for optimization and the relationship between airspace user and airport preferences. List of references
[0106] A, B, C, D, E, F stakeholder
[0107] d constraint
[0108] cmconstraint
[0109] fi first flight
[0110] fz second flight
[0111] Fi fitness value
[0112] F airlines, i fitness value
[0113] F airport, i fitness value
[0114] in, iri, ... imbalance ratio
[0115] Lo initial list (of flights in time slots)
[0116] Lei generations of candidate lists
[0117] Lcli first generation of candidate lists (of flights in time slots) Li, Li, L2... a list or a specific list (of flights in time slots)
[0118] Lf improved list (of flights in time slots)
[0119] LFB balanced improved list
[0120] Lfi improved lists (of flights in time slots)
[0121] Ml first Matrix
[0122] M2 second Matrix
[0123] MPC multi party computation
[0124] ti time preference value
[0125] v value of satisfaction
[0126] Vi specific value of satisfaction Wi weight map for each stakeholder
Claims
Claims1. Method for multi-objective optimization of a list of time slots for stakeholders (A, B, ...), (a) wherein an initial list (Lo) is provided, whereas the initial list (Lo) comprises at least a plurality of time slots and a parameter for each time slot, which can be occupied by an item-ID, preferably a flight-ID,(b) wherein each stakeholder (A, B, ...) provides preferences in the format of a weight map (wi) comprising at least a time preference value (ti) assigned to each combination of time slot and item-ID for the respective stakeholder, whereas the weight maps (wt) are compiled in the format of a first matrix (Ml), the dimensions of which are the time slots to be allocated and the number of item-IDs,(c) wherein a value of satisfaction (v) is defined that corresponds to the fulfilment of the preferences by distributing either the time slots or item-IDs in a specific list (Li), and wherein a first objective is provided that consists of generating an improved list (Lf) in which the value of satisfaction (v) is the highest,(d) wherein repeatedly for a predefined number of times two items are permutatively swapped or candidate lists are generated by random assignment of item-IDs to slots, in the initial list of time slots (Lo) to generate a first generation of candidate lists (Lcli), each list having a specific value of satisfaction (vt),(e) generate a next generation of candidate lists comprising a predefined number of lists (Lc2i) by(e.l) taking a predefined number of candidate lists with best specific values of satisfaction (vi) of the given generation and for each of the chosen lists doing a predefined number of swaps according to a constraint (cm), which can be chosen, for example a swap mutation that randomly swaps a subset of the flights, and / or(e.2) taking a predefined number of candidate lists and combine two or more of the chosen lists according to a constraint (cc), which can be chosen, for example a partially matched crossover that takes a sequence from one solution and swaps it with the sequence of another solution, each list having a specific value of satisfaction (vt),(f) repeat step (e) either for a predefined number of times or when a predefined time available for optimization concludes or until the specific value of satisfaction (vt) of the best list or lists of a generation deviates from the specific value of satisfaction (vt) of the best list or lists of the previous generation within a specified difference range,(g) wherein the group of candidate lists (Li) with the highest value of satisfaction (vt) is selected as the improved lists of time slots ( Lft), wherein the group comprises one or more lists.
2. Method according claim 1, whereinin step (a) the initial list (Lo) is provided to one or more stakeholders (A, B ...),in step (b) the weight maps (wi) are collected from one or more stakeholders (A, B, ...) and after step (g) the improved lists of time slots (Lft) is provided to one or more stakeholders (A, B, ...) for confirmation or rejection.
3. Method according to claim 1 or 2, wherein step (d) is implemented by a constraint that is:(d.l) providing a parameter p representing the probability of a swap of items that leads to an increase of the value of satisfaction (vt), wherein distance d of two items in the list is dependent of the parameter p,(d.2) generating a new generation of candidate lists (Lcli) byo randomly selecting a first flight (fi) for each candidate list (Lcli), then calculating a distance d, which determines the second flight (fz) that is to be swapped with the first flight (fi), where the second flight (fz) is the flight that is d slots after the first flight (fi), by first generating a random variable (rp) with an expectancy value that equals p which is multiplied by the length of the flight list, which is repeated a predefined number of times, preferably about ten times,o calculating the value of satisfaction (vt) for each candidate list.
4. Method according to one of the preceding claims, wherein(h) a ratio of satisfaction for each improved list (Lft) is defined as the sum of the achieved 5 preferences (Fairlines, i) divided by the sum of the highest possible achievement (Fairlines, max) according to the matrix of stakeholder (Ml),(i) providing a second matrix (M2) of a further, selected stakeholder, preferably the airport, (j) a ratio of satisfaction for each improved list (Lfi) is defined as the sum of the achieved preferences (Fairport, i) divided by the sum of the highest possible achievement (Fairport, max) 10 according to the matrix (M2) of the selected stakeholder,(k) producing an imbalance ratio (in) for each pair of ratios of satisfaction defined as the amount of their difference,(l) selecting the improved list (Lfi) with the lowest imbalance ratio (in) as the balanced improved list (LFB).
155. Method according to one of the preceding claims, wherein the weight maps (wi) are encrypted by the stakeholders in step (b) and sent to a privacy engine, preferably using multi-party computation (MPC).20 6. Method according to claim 5, wherein an Orchestrator component is introduced and wherein before step (d)the Orchestrator component initializes the Privacy Engine component (P) with secret shares of the weight maps (wi), and the Privacy Engine component (P) distributes the secret shares to MPC nodes hosted by different parties,25- whereas for optimization steps (d) and (e), a Heuristic Optimizer component is used, whereas the Heuristic Optimizer component provides generations of candidate lists (Let) to the Privacy Engine component (P) for evaluation,the Privacy Engine component uses the MPC nodes to evaluate a generation of candidate lists (Lei) and obtains an obfuscated evaluation result that is used by the evolutionary algorithm to create the next generation of candidate lists (Lei), andin step (g) the best solutions found are returned to the Orchestrator component.