A multi-objective path optimization method based on fear of tiredness dominance relation

Abstract

The application discloses a multi-objective path optimization method based on a Pareto dominance relationship, and comprises the following steps: S1, before each path exploration, candidate paths are selected according to the Pareto dominance relationship between the explored paths; S2, breadth-first traversal is performed on the candidate paths in sequence, and single-step exploration of the paths is realized; S3, after each round of path exploration, the current path is compared with the paths in the known optimal solution set, and the paths that cannot become the optimal solution are removed; and S4, steps S1-S3 are repeatedly executed until no new optimal solution appears. The application realizes the Pareto optimal solution through multiple rounds of path exploration, and solves the problems of how to improve the efficiency of the multi-objective path optimization problem and how to improve the quality of the multi-objective path optimization solution set.

Description

Technical Field

[0001] This invention relates to the field of network communication technology, and in particular to a multi-objective path optimization method based on the fear of being overridden. Background Technology

[0002] The continuous evolution of network technology and the increasing ease of network access are leading to an exponential growth in network data. With the development of Artificial Intelligence (AI), the Internet of Things (IoT), and Automation, providing differentiated network services and improving Quality of Service (QoS) based on user needs have become essential requirements for next-generation communication networks.

[0003] The Third Generation Partnership Project (3GPP) has identified three key 5G application scenarios: enhanced mobile broadband (eMBB), ultra-reliable low-latency communication (uRLLC), and massive machine-type communication (mMTC). Each scenario has specific quality of service requirements. For example, eMBB's commercial applications mainly include AR and HD online video transmission, which have high demands on network bandwidth and coverage; while uRLLC's main application scenarios include vehicle-to-everything (V2X) and smart grids, which have high requirements for network latency and transmission reliability. Clearly, with the emergence of new communication technologies such as 5G / 6G, future demands for network services will become more diversified and granular, and this area will receive more attention from academia and industry.

[0004] Traditional IP networks, which rely heavily on packet forwarding technology, mostly employ a best-effort transmission service model. This architecture cannot meet the diverse service delivery needs. To address this issue, researchers have proposed a series of network architectures and data forwarding technologies.

[0005] Among these technologies, Software-Defined Networking (SDN) is considered a promising architecture. Routing devices typically consist of a control plane and a data plane. The control plane is responsible for generating routing policies, while the data plane handles packet forwarding. SDN separates these two planes of the routing device and centralizes the control plane into a single management platform, thus achieving unified management. Based on this centralized management platform, service providers can monitor network traffic in real time, formulate specific routing policies, and thereby provide differentiated services.

[0006] Furthermore, Multi-Protocol Label Switching (MPLS), as a packet forwarding technology with a different concept, is also widely used in existing network architectures. Proposed by the Internet Engineering Task Force (IETF), this technology is a protocol that uses labels to guide the high-speed forwarding of data packets over IP backbones. When a data packet enters a network supporting MPLS, multiple labels identifying different routing devices within the network are appended to the packet header. Routing devices then forward packets based on these labels, forming a specific forwarding path. Therefore, MPLS can also be seen as a tunneling technology. Combined with technologies such as SDN, MPLS can be effectively applied to scenarios such as traffic engineering, QoS optimization, and virtual private networks.

[0007] While the aforementioned network technologies and architectures enable differentiated service delivery, research on the core issue behind these technologies—the multi-objective path optimization problem—remains limited. The multi-objective path optimization problem addresses how to determine the optimal path when considering multiple conflicting objectives such as link states, congestion levels, and bandwidth. To solve this problem, many scholars have transformed it into a multi-constraint shortest path problem and employed heuristics or improved versions of Dijkstra's method for solving it. However, these methods often suffer from inefficient path planning and flawed model construction.

[0008] From a mathematical perspective, current solutions for multi-objective path optimization problems include the following:

[0009] 1. Linear Weighted Method. This method is widely used in multi-objective optimization problems. Its core idea is to assign a weight to each objective function and then simply linearly weight and sum all the objective functions, thus transforming the multi-objective optimization problem into a single-objective optimization problem. The linear weighted method is simple, intuitive, and easy to deploy in engineering. However, the effectiveness of the linear weighted method heavily depends on the selection of the weights; if the weights are not set appropriately, the solution quality may be degraded.

[0010] 2. Principal Objective Method. This method, also known as the ε-constraint method, selects a principal objective from multiple optimization objectives as the function to be optimized, and uses the other sub-objective functions as constraints, through a set of upper bounds ε. k Constraints need to be imposed. During the optimization process towards the objective, the value of the sub-objective function needs to be limited to ε. kWithin this range, if any sub-objective function exceeds the limit, the solution will be discarded without further optimization. Although the primary objective method has good solution efficiency and high solution quality, its feasibility depends heavily on the constraint ε. k The choice of constraints is crucial; if the constraints are not chosen appropriately, the final valid solution may be empty, which is unacceptable in some network scenarios.

[0011] 3. Artificial Intelligence-Based Optimization Schemes. In recent years, the rapid development of artificial intelligence has greatly expanded its application scenarios and provided new ideas for solving multi-objective optimization problems. In the field of path optimization, reinforcement learning is becoming a key research focus. Reinforcement learning, based on Markov decision chains, uses environmental reward feedback to correct the current policy network parameters, thereby forming a better path selection scheme. Although schemes combined with artificial intelligence can greatly simplify the problem-solving process, most of these schemes suffer from low model interpretability and difficulty in guaranteeing solution quality. Summary of the Invention

[0012] This invention addresses the problems of low efficiency, poor solution quality, and unreasonable model construction in existing technologies by proposing a multi-objective path optimization method (NDRA) based on the Pareto dominance relationship, which is highly efficient and has high solution set quality.

[0013] To achieve the above objectives, the present invention provides the following technical solution:

[0014] This invention provides a multi-objective path optimization method based on the fear of burden dominance relationship, comprising the following steps:

[0015] S1. Before each path exploration, candidate paths are selected based on the Pareto dominance relationship between explored paths. All feasible path information is stored in the list structure AP_list, and candidate path information is stored in the list structure CP_list, which is a subset of AP_list.

[0016] S2. Perform a breadth-first traversal on the candidate paths to achieve single-step exploration of the paths; insert all paths that have been explored step by step and are considered feasible back into AP_list;

[0017] S3. After each round of path exploration, compare the current path with the paths in the known optimal solution set and remove paths that cannot become the optimal solution.

[0018] S4. Repeat steps S1-S3 until no new optimal solution appears.

[0019] Furthermore, the candidate path selection process in step S1 includes:

[0020] For any network topology G(N, E), N is the set of network nodes, and E is the set of network links; any network link e i，j The attributes of ∈E are represented by a fixed-length vector v. i，j ∈R 1×k The identifier is defined as k, where k represents the number of objectives to be optimized; the path planning task is defined as T(N). s N d ), where N s N d These represent the source node and the destination node, respectively; the goal of the multi-objective path optimization problem is to find a series of intermediate nodes. This forms a forwarding path. Make:

[0021] max p f(p)=[f1(p), f2(p),...,f k (p)]

[0022] Define any objective function as the sum of the attribute values ​​of all links within path p, and we get:

[0023]

[0024] Define Pareto dominance:

[0025] For two paths p1 and p2 with the same source node, the following condition is met:

[0026]

[0027] and

[0028] If p1 is Pareto-dominated by p2, then p1 is not Pareto-dominated by p2; otherwise, p1 is not Pareto-dominated by p2.

[0029] If p1 is Pareto dominant to p2, then p1 is a candidate path; if p1 is not Pareto dominant to p2, then both paths are candidate paths.

[0030] Furthermore, the specific process of step S3 includes:

[0031] A function PD_relation is used to determine the Pareto dominance relationship between the current path and the paths in the known optimal path set OP_list. If the current path is Pareto dominated by any path in OP_list, the path will be removed; otherwise, the path will be retained and further path exploration will be carried out.

[0032] Furthermore, the optimal path collection process in step S3 includes:

[0033] After each path exploration is completed, check whether the explored path reaches the destination node. If so, compare the path with the paths in OP_list. If the path has a Pareto dominance relationship with a path in OP_list, choose to keep the better path and remove the other path; otherwise, insert the path directly into OP_list.

[0034] Furthermore, the termination condition for step S4 is: once the number of elements in AP_list becomes 0, no further path exploration is performed, and at this time OP_list contains all the optimal path solutions.

[0035] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0036] The multi-objective path optimization method (NDRA) proposed in this invention, based on Pareto dominance, obtains the Pareto optimal solution through multiple rounds of path exploration. It addresses two technical problems: how to improve the efficiency of multi-objective path optimization and how to improve the quality of the solution set of multi-objective path optimization.

[0037] 1. Regarding path planning efficiency, before each round of path exploration, this invention determines candidate paths based on the Pareto dominance relationship among explored paths and performs a breadth-first traversal on these candidate paths, achieving single-step path exploration. The process of selecting candidate paths effectively reduces the number of path explorations and avoids the computational overhead of a full traversal. Furthermore, to further improve path planning efficiency, this invention innovatively introduces a pruning process. After each round of path exploration, the current path is compared with paths in the known optimal solution set, and paths that are unlikely to become optimal solutions are promptly removed, thereby avoiding unnecessary exploration overhead. Research results show that the method of this invention exhibits high path planning efficiency in different network scenarios.

[0038] 2. Regarding the quality of the solution set, since NDRA strictly selects candidate paths and explores paths based on Pareto dominance in each round of path exploration, it can be proven that all solutions generated by NDRA are Pareto optimal. Compared with existing heuristic-based multi-objective path optimization schemes, NDRA can significantly improve the quality of the solutions.

[0039] Compared to existing solutions, NDRA offers several advantages. Compared to multi-objective path optimization schemes based on linear weighting, NDRA introduces Pareto dominance, ensuring all objectives are treated equally. This guarantees the quality of the final optimization result, preventing the excessive sacrifice of one objective for another. Compared to multi-path optimization schemes based on primary objective methods, NDRA guarantees a non-empty final result, making it more widely applicable in real-world network scenarios. Compared to AI-based multi-objective path optimization schemes, NDRA offers stronger interpretability and better guarantees the quality of the solution.

[0040] In summary, the NDRA of this invention is an efficient, lightweight, and solution-quality-guaranteed multi-objective path optimization method. Compared with existing solutions, NDRA achieves improvements in both path planning efficiency and solution quality. Attached Figure Description

[0041] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this invention. For those skilled in the art, other drawings can be obtained based on these drawings.

[0042] Figure 1 The flowchart illustrates the multi-objective path optimization method based on the Pareto dominance relationship provided in this embodiment of the invention. Detailed Implementation

[0043] This invention, based on the traditional Dijkstra method, introduces the concept of Pareto dominance to transform it into a path planning scheme applicable to multi-objective path optimization scenarios.

[0044] Specifically, in the candidate path selection process, the traditional Dijkstra method uses a single optimization objective to compare path costs, while this invention considers multiple link state attributes and selects candidate paths by comparing the Pareto dominance relationships among multiple links. Since candidate paths require comparing the Pareto relationships among multiple paths, this introduces additional computational overhead. However, compared to an unrestricted full traversal approach, this invention's candidate path selection strategy effectively reduces the space size of the path exploration problem, thereby improving the overall efficiency of the solution.

[0045] Furthermore, after each round of path exploration, this invention employs a pruning process to remove paths that are unlikely to be optimal, thereby reducing additional path overhead. This process is achieved by comparing the Pareto dominance of the current path with that of paths in the known optimal solution set. Once a path is found to be dominated by any path in the optimal solution set, it is directly removed because it is unlikely to be optimal. The pruning process significantly reduces the exploration space in the later stages of path exploration, helping the algorithm converge quickly and reducing unnecessary computational overhead.

[0046] Finally, during the optimal path collection process, any path reaching the destination node needs to be compared with paths in the known optimal solution set, and the Pareto-dominated path is removed. This process strictly guarantees that the final solution is always Pareto optimal, thereby optimizing the solution quality.

[0047] To better understand this technical solution, the technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described examples are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art based on this application are within the scope of protection of the present invention.

[0048] In this invention, any network structure can be abstracted as a graph G(N, E), where N is the set of network nodes and E is the set of network links. Any network link e... i，j The attributes of ∈E can all be represented by a fixed-length vector v. j，j ∈R 1 ×k The identifier, where k represents the number of objectives to be optimized. All the above parameters are positive by default. We define the path planning task as T(N) s N d ), where N s N d These represent the source node and the destination node, respectively. The goal of the multi-objective path optimization problem is to find a set of intermediate nodes. This forms a forwarding path. Make:

[0049] max p f(p)=[f1(p), f2(p),...,f k (p)]

[0050] To simplify the problem, we define any objective function as the sum of the attribute values ​​of all links within path p. Therefore, we can obtain:

[0051]

[0052] The problem described above can be viewed as a discrete multi-objective optimization problem. Compared to single-objective optimization problems, finding an absolutely optimal solution—one that simultaneously achieves optimal values ​​for all objective functions—is often impossible. Instead, the final result of a multi-objective optimization problem is often a solution set D, also known as the Pareto optimal solution set. All solutions in solution set D are considered optimal because further optimization of the objective function of a particular solution in one dimension will inevitably lead to a decrease in the value of at least one other objective function. Therefore, our goal is to find this Pareto optimal solution set D.

[0053] To address the aforementioned issues, this invention proposes a highly efficient, high-quality solution set-based multi-objective path optimization method—NDRA—based on Pareto dominance. In simple terms, starting from the source node, NDRA employs a breadth-first traversal similar to Dijkstra's method. Before each path exploration, NDRA selects a series of candidate paths from the currently explored path set, thus avoiding the computational overhead of a full traversal. Subsequently, NDRA expands the candidate paths step-by-step and compares the new paths with those in the existing optimal solutions, thereby reducing unnecessary exploration overhead. This process is repeated until we confirm that no new optimal solutions will emerge.

[0054] Specifically, the multi-objective path optimization method based on the fear of being overridden dominance relationship proposed in this invention, such as... Figure 1 As shown, it includes the following steps:

[0055] S1. Before each path exploration, candidate paths are selected based on the Pareto dominance relationship between the explored paths.

[0056] Path exploration process:

[0057] All currently feasible path information is stored in a list structure AP_list, which is initialized to contain only one element, namely p(N s N s Candidate path information is stored in a list structure CP_list. It's important to note that CP_list is a subset of AP_list. Before each path exploration, CP_list is generated through a candidate path selection process, which will be discussed in detail later.

[0058] Candidate path selection process:

[0059] Before path exploration, NDRA invokes candidate path selection to avoid the computational overhead of a full traversal. The candidate path selection process typically involves comparing the overall cost of each path. Traditional Dijkstra's methods often consider only one optimization objective, making cost comparison relatively easy. However, in multi-objective path optimization, multiple link states such as bandwidth and latency need to be considered simultaneously. In this scenario, comparing the merits of multiple links becomes much more difficult. To address this issue, NDRA references the Pareto dominance concept from game theory and proposes the following definition:

[0060] For two paths p1 and p2 with the same source node, the following condition is met:

[0061]

[0062] and

[0063] If p1 is Pareto-dominated by p2, then p1 is not Pareto-dominated by p2; otherwise, p1 is not Pareto-dominated by p2.

[0064] If a Pareto dominance exists between two paths, comparing their total costs becomes simpler. If p1 Pareto dominates p2, then p1 is more likely to be the optimal solution, and therefore p1 is a candidate path. If p1 is not Pareto dominant over p2, then we cannot determine which path is better, and both paths are considered candidate paths. Based on this concept, NDRA can quickly select candidate paths from AP_list and generate CP_list.

[0065] S2. Perform a breadth-first traversal on the candidate paths in sequence to achieve single-step exploration of the paths; all paths that have been explored in single steps and are considered feasible will be inserted back into AP_list.

[0066] During path exploration, paths in CP_list are selected sequentially and traversed step-by-step in a breadth-first manner. All paths that have been explored step-by-step and deemed feasible are then inserted back into AP_list.

[0067] S3. After each round of path exploration, compare the current path with the paths in the known optimal solution set and remove paths that cannot become the optimal solution.

[0068] To improve the overall performance of the solution, after each round of exploration, paths that cannot be the optimal solution will be removed, thereby reducing unnecessary path exploration overhead. This process is figuratively called the "pruning" process.

[0069] In its implementation, NDRA uses a function PD_relation to determine the Pareto dominance relationship between the current path and the paths in the known optimal path set OP_list. If the current path is Pareto dominated by any path in OP_list, the path will be removed because it cannot be the optimal solution; otherwise, the path will be retained and further path exploration will be carried out.

[0070] The process of collecting the optimal path includes:

[0071] After each path exploration is completed, check whether the explored path reaches the destination node. If so, compare the path with the paths in OP_list. If the path has a Pareto dominance relationship with a path in OP_list, choose to keep the better path and remove the other path; otherwise, insert the path directly into OP_list, because the path is equivalent to other paths and is the optimal solution.

[0072] S4. Repeat steps S1-S3 until no new optimal solution appears.

[0073] The termination condition for step S4 is: once the number of elements in AP_list becomes 0, NDRA will terminate, that is, no further path exploration will be performed, and at this time OP_list contains all the optimal path solutions.

[0074] In the initial stages of path exploration, since no path to the destination node has been found, NDRA will explore as many paths as possible and continuously insert feasible paths into AP_list. During this process, since OP_list is empty, the infeasible path pruning process will not take effect. Once a complete path is found, OP_list will no longer be empty, and the infeasible path pruning process will take effect, continuously removing paths from AP_list that are not optimal solutions. Eventually, the elements in AP_list and CP_list will decrease until they reach 0. At this point, no further path exploration is needed, OP_list contains all optimal path solutions, and NDRA terminates.

[0075] This invention proposes a multi-objective path optimization method, NDRA, based on Pareto dominance. Compared with existing schemes, NDRA achieves improvements in both path planning efficiency and solution quality.

[0076] Regarding path planning efficiency, NDRA avoids the excessive exploration space caused by full traversal by exploring only candidate paths at a time, thereby reducing the overall computational cost of the solution. Furthermore, NDRA introduces a pruning process: after each path exploration, the newly generated path is compared with paths in the known optimal solution set. If a path is dominated by any path in the known optimal solution set, then that path cannot be the optimal solution, and NDRA removes it, thus reducing unnecessary exploration. Combining candidate path selection and pruning, NDRA can significantly improve path planning efficiency and reduce the time overhead associated with path planning.

[0077] Regarding the quality of the solutions, since NDRA rigorously compares the Pareto dominance relationships between each candidate path during each selection process and retains only the better solutions during the optimal path collection process, it can be rigorously proven that the solutions ultimately generated by NDRA are all Pareto optimal solutions.

[0078] In summary, the multi-objective path optimization method based on Pareto dominance relationships proposed in this invention, compared to the traditional Dijkstra method, although incurring additional time overhead in calculating the Pareto dominance relationships between multiple paths, has achieved significant improvements. Experiments have shown that when the number of network nodes is around 500, the number of optimization objectives is 5, and the connectivity rate between network nodes is 40%, the NDRA calculation time is only 200ms. This time overhead is perfectly acceptable in practical network applications. Furthermore, compared to existing solutions, NDRA achieves significant improvements in both path planning efficiency and solution quality.

[0079] The above description is merely a detailed explanation of preferred embodiments and principles of the present invention and is not intended to limit the scope of protection of the present invention. For those skilled in the art, any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention, based on the ideas provided by the present invention, should be considered within the scope of protection of the present invention.

Claims

1. A multi-objective path optimization method based on the fear of burden dominance relationship, characterized in that: Includes the following steps: S1. Before each path exploration, candidate paths are selected based on the Pareto dominance relationships among the explored paths; all currently feasible path information is stored in a list structure. In this context, candidate path information is stored in a list structure. middle, yes A subset of; The candidate path selection process in step S1 includes: For any network topology , For a set of network nodes, A set of network links; any network link The attributes are represented by a fixed-length vector. The logo, among which Indicates the number of objectives to be optimized; defines the path planning task as... ,in These represent the source node and the destination node, respectively; the goal of the multi-objective path optimization problem is to find a series of intermediate nodes. This forms a forwarding path. , so that: ， Define any objective function as a path The sum of the attribute values ​​of all links within the chain is obtained as follows: ， Define Pareto dominance: For two paths with the same source node and If and only if the following conditions are met: ， ， say Pareto Domination Otherwise, it is called Non-Pareto Domination ; if Pareto Domination ,but As a candidate path; if Non-Pareto Domination If both paths are considered as candidate paths; S2. Perform a breadth-first traversal on the candidate paths, exploring each path step by step; then insert all paths that have been explored step by step and are considered feasible back into the list. middle; S3. After each round of path exploration, compare the current path with the paths in the known optimal solution set, and remove paths that cannot become the optimal solution; step S3 uses a function. To compare the current path with the known set of optimal paths Pareto dominance among paths within a given path, if the current path is... If any path is Pareto dominant, the current path will be removed; otherwise, the current path will be retained, and further path exploration will proceed. S4. Repeat steps S1-S3 until no new optimal solution appears.

2. The multi-objective path optimization method based on the dominance relationship according to claim 1, characterized in that, The optimal path collection process in step S3 includes: After each path exploration is completed, check whether the explored path reaches the destination node. If so, compare the path with the current path. The paths are compared, and if the path matches... If a path exhibits Pareto dominance, the better path is retained, and the other path is removed; otherwise, the path is directly inserted into the... among.

3. The multi-objective path optimization method based on the dominance relationship according to claim 1, characterized in that, The termination condition for step S4 is: once When the number of elements in the path becomes 0, meaning no further path exploration is performed, at this point... It contains all the optimal path solutions.

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